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Age and the critical period hypothesis

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Christian Abello-Contesse, Age and the critical period hypothesis, ELT Journal , Volume 63, Issue 2, April 2009, Pages 170–172, https://doi.org/10.1093/elt/ccn072

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In the field of second language acquisition (SLA), how specific aspects of learning a non-native language (L2) may be affected by when the process begins is referred to as the ‘age factor’. Because of the way age intersects with a range of social, affective, educational, and experiential variables, clarifying its relationship with learning rate and/or success is a major challenge.

There is a popular belief that children as L2 learners are ‘superior’ to adults ( Scovel 2000 ), that is, the younger the learner, the quicker the learning process and the better the outcomes. Nevertheless, a closer examination of the ways in which age combines with other variables reveals a more complex picture, with both favourable and unfavourable age-related differences being associated with early- and late-starting L2 learners ( Johnstone 2002 ).

The ‘critical period hypothesis’ (CPH) is a particularly relevant case in point. This is the claim that there is, indeed, an optimal period for language acquisition, ending at puberty. However, in its original formulation ( Lenneberg 1967 ), evidence for its existence was based on the relearning of impaired L1 skills, rather than the learning of a second language under normal circumstances.

Furthermore, although the age factor is an uncontroversial research variable extending from birth to death ( Cook 1995 ), and the CPH is a narrowly focused proposal subject to recurrent debate, ironically, it is the latter that tends to dominate SLA discussions ( García Lecumberri and Gallardo 2003 ), resulting in a number of competing conceptualizations. Thus, in the current literature on the subject ( Bialystok 1997 ; Richards and Schmidt 2002 ; Abello-Contesse et al. 2006), references can be found to (i) multiple critical periods (each based on a specific language component, such as age six for L2 phonology), (ii) the non-existence of one or more critical periods for L2 versus L1 acquisition, (iii) a ‘sensitive’ yet not ‘critical’ period, and (iv) a gradual and continual decline from childhood to adulthood.

It therefore needs to be recognized that there is a marked contrast between the CPH as an issue of continuing dispute in SLA, on the one hand, and, on the other, the popular view that it is an invariable ‘law’, equally applicable to any L2 acquisition context or situation. In fact, research indicates that age effects of all kinds depend largely on the actual opportunities for learning which are available within overall contexts of L2 acquisition and particular learning situations, notably the extent to which initial exposure is substantial and sustained ( Lightbown 2000 ).

Thus, most classroom-based studies have shown not only a lack of direct correlation between an earlier start and more successful/rapid L2 development but also a strong tendency for older children and teenagers to be more efficient learners. For example, in research conducted in the context of conventional school programmes, Cenoz (2003) and Muñoz (2006) have shown that learners whose exposure to the L2 began at age 11 consistently displayed higher levels of proficiency than those for whom it began at 4 or 8. Furthermore, comparable limitations have been reported for young learners in school settings involving innovative, immersion-type programmes, where exposure to the target language is significantly increased through subject-matter teaching in the L2 ( Genesee 1992 ; Abello-Contesse 2006 ). In sum, as Harley and Wang (1997) have argued, more mature learners are usually capable of making faster initial progress in acquiring the grammatical and lexical components of an L2 due to their higher level of cognitive development and greater analytical abilities.

In terms of language pedagogy, it can therefore be concluded that (i) there is no single ‘magic’ age for L2 learning, (ii) both older and younger learners are able to achieve advanced levels of proficiency in an L2, and (iii) the general and specific characteristics of the learning environment are also likely to be variables of equal or greater importance.

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Critical Period In Brain Development and Childhood Learning

Charlotte Nickerson

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Charlotte Nickerson is a student at Harvard University obsessed with the intersection of mental health, productivity, and design.

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Key Takeaways

• Critical period is an ethological term that refers to a fixed and crucial time during the early development of an organism when it can learn things that are essential to survival. These influences impact the development of processes such as hearing and vision, social bonding, and language learning.
• The term is most often experienced in the study of imprinting, where it is thought that young birds could only develop an attachment to the mother during a fixed time soon after hatching.
• Neurologically, critical periods are marked by high levels of plasticity in the brain before neural connections become more solidified and stable. In particular, critical periods tend to end when synapses that inhibit the neurotransmitter GABA mature.
• In contrast to critical periods, sensitive periods, otherwise known as “weak critical periods,” happen when an organism is more sensitive than usual to outside factors influencing behavior, but this influence is not necessarily restricted to the sensitive period.
• Scholars have debated the extent to which older organisms can develop certain skills, such as natively-accented foreign languages, after the critical period.

The critical period is a biologically determined stage of development where an organism is optimally ready to acquire some pattern of behavior that is part of typical development. This period, by definition, will not recur at a later stage.

If an organism does not receive exposure to the appropriate stimulus needed to learn a skill during a critical period, it may be difficult or even impossible for that organism to develop certain functions associated with that skill later in life.

This happens because a range of functional and structural elements prevent passive experiences from eliciting significant changes in the brain (Cisneros-Franco et al., 2020).

The first strong proponent of the theory of critical periods was Charles Stockhard (1921), a biologist who attempted to experiment with the effects of various chemicals on the development of fish embryos, though he gave credit to Dareste for originating the idea 30 years earlier (Scott, 1962).

Stockhard’s experiments showed that applying almost any chemical to fish embryos at a certain stage of development would result in one-eyed fish.

These experiments established that the most rapidly growing tissues in an embryo are the most sensitive to any change in conditions, leading to effects later in development (Scott, 1962).

Meanwhile, psychologist Sigmund Freud attempted to explain the origins of neurosis in human patients as the result of early experiences, implying that infants are particularly sensitive to influences at certain points in their lives.

Lorenz (1935) later emphasized the importance of critical periods in the formation of primary social bonds (otherwise known as imprinting) in birds, remarking that this psychological imprinting was similar to critical periods in the development of the embryo.

Soon thereafter, McGraw (1946) pointed out the existence of critical periods for the optimal learning of motor skills in human infants (Scott, 1962).

Example: Infant-Parent Attachment

The concept of critical or sensitive periods can also be found in the domain of social development, for example, in the formation of the infant-parent attachment relationship (Salkind, 2005).

Attachment describes the strong emotional ties between the infant and caregiver, a reciprocal relationship developing over the first year of the child’s life and particularly during the second six months of the first year.

During this attachment period , the infant’s social behavior becomes increasingly focused on the principal caregivers (Salkind, 2005).

The 20th-century English psychiatrist John Bowlby formulated and presented a comprehensive theory of attachment influenced by evolutionary theory.

Bowlby argued that the infant-parent attachment relationship develops because it is important to the survival of the infant and that the period from six to twenty-four months of age is a critical period of attachment.

This coincides with an infant’s increasing tendency to approach familiar caregivers and to be wary of unfamiliar adults. After this critical period, it is still possible for a first attachment relationship to develop, albeit with greater difficulty (Salkind, 2005).

This has brought into question, in a similar vein to language development, whether there is actually a critical development period for infant-caregiver attachment.

Sources debating this issue typically include cases of infants who did not experience consistent caregiving due to being raised in institutions prior to adoption (Salkind, 2005).

Early research into the critical period of attachment, published in the 1940s, reports consistently that children raised in orphanages subsequently showed unusual and maladaptive patterns of social behavior, difficulty in forming close relationships, and being indiscriminately friendly toward unfamiliar adults (Salkind, 2005).

Later, research from the 1990s indicated that adoptees were actually still able to form attachment relationships after the first year of life and also made developmental progress following adoption.

Nonetheless, these children had an overall increased risk of insecure or maladaptive attachment relationships with their adoptive parents. This evidence supports the notion of a sensitive period, but not a critical period, in the development of first attachment relationships (Salkind, 2005).

Mechanisms for Critical Periods

Both genetics and sensory experiences from outside the body shape the brain as it develops (Knudsen, 2004). However, the developmental stage that an organism is in significantly impacts how much the brain can change based on these experiences.

In scientific terms, the brain’s plasticity changes over the course of a lifespan. The brain is very plastic in the early stages of life before many key connections take root, but less so later.

This is why researchers have shown that early experience is crucial for the development of, say, language and musical abilities, and these skills are more challenging to take up in adulthood (Skoe and Kraus, 2013; White et al., 2013; Hartshorne et al., 2018).

As brains mature, the connections in them become more fixed. The brain’s transitions from a more plastic to a more fixed state advantageously allow it to retain new and complex processes, such as perceptual, motor, and cognitive functions (Piaget, 1962).

Children’s gestures, for example, pride and predict how they will acquire oral language skills (Colonnesi et al., 2010), which in turn are important for developing executive functions (Marcovitch and Zelazo, 2009).

However, this formation of stable connections in the brain can limit how the brain’s neural circuitry can be revised in the future. For example, if a young organism has abnormal sensory experiences during the critical period – such as auditory or visual deprivation – the brain may not wire itself in a way that processes future sensory inputs properly (Gallagher et al., 2020).

One illustration of this is the timing of cochlear implants – a prosthesis that restores hearing in some deaf people. Children who receive cochlear implants before two years of age are more likely to benefit from them than those who are implanted later in life (Kral and Eggermont, 2007; Gallagher et al., 2020).

Similarly, the visual deprivation caused by cataracts in infants can cause similar consequences. When cataracts are removed during early infancy, individuals can develop relatively normal vision; however, when the cataracts are not removed until adulthood, this results in substantially poorer vision (Martins Rosa et al., 2013).

After the critical period closes, abnormal sensory experiences have a less drastic effect on the brain and lead to – barring direct damage to the central nervous system – reversible changes (Gallagher et al., 2020). Much of what scientists know about critical periods derives from animal studies , as these allow researchers greater control over the variables that they are testing.

This research has found that different sensory systems, such as vision, auditory processing, and spatial hearing, have different critical periods (Gallagher et al., 2020).

The brain regulates when critical periods open and close by regulating how much the brain’s synapses take up neurotransmitters , which are chemical substances that affect the transmission of electrical signals between neurons.

In particular, over time, synapses decrease their uptake of gamma-aminobutyric acid, better known as GABA. At the beginning of the critical period, outside sources become more effective at influencing changes and growth in the brain.

Meanwhile, as the inhibitory circuits of the brain mature, the mature brain becomes less sensitive to sensory experiences (Gallagher et al., 2020).

Critical Periods vs Sensitive Periods

Critical periods are similar to sensitive periods, and scholars have, at times, used them interchangeably. However, they describe distinct but overlapping developmental processes.

A sensitive period is a developmental stage where sensory experiences have a greater impact on behavioral and brain development than usual; however, this influence is not exclusive to this time period (Knudsen, 2004; Gallagher, 2020). These sensitive periods are important for skills such as learning a language or instrument.

In contrast, A critical period is a special type of sensitive period – a window where sensory experience is necessary to shape the neural circuits involved in basic sensory processing, and when this window opens and closes is well-defined (Gallagher, 2020).

Researchers also refer to sensitive periods as weak critical periods. Some examples of strong critical periods include the development of vision and hearing, while weak critical periods include phenome tuning – how children learn how to organize sounds in a language, grammar processing, vocabulary acquisition, musical training, and sports training (Gallagher et al., 2020).

Critical Period Hypothesis

One of the most notable applications of the concept of a critical period is in linguistics. Scholars usually trace the origins of the debate around age in language acquisition to Penfield and Robert’s (2014) book Speech and Brain Mechanisms.

In the 1950s and 1960s, Penfield was a staunch advocate of early immersion education (Kroll and De Groot, 2009). Nonetheless, it was Lenneberg, in his book Biological Foundations of Language, who coined the term critical period (1967) in describing the language period.

Lennenberg (1967) described a critical period as a period of automatic acquisition from mere exposure” that “seems to disappear after this age.” Scovel (1969) later summarized and narrowed Penfield’s and Lenneberg’s view on the critical period hypothesis into three main claims:

• Adult native speakers can identify non-natives by their accents immediately and accurately.
• The loss of brain plasticity at about the age of puberty accounts for the emergence of foreign accents./li>
• The critical period hypothesis only holds for speech (whether or not someone has a native accent) and does not affect other areas of linguistic competence.

Linguists have since attempted to find evidence for whether or not scientific evidence actually supports the critical period hypothesis, if there is a critical period for acquiring accentless speech, for “morphosyntactic” competence, and if these are true, how age-related differences can be explained on the neurological level (Scovel, 2000).

The critical period hypothesis applies to both first and second-language learning. Until recently, research around the critical period’s role in first language acquisition revolved around findings about so-called “feral” children who had failed to acquire language at an older age after having been deprived of normal input during the critical period.

However, these case studies did not account for the extent to which social deprivation, and possibly food deprivation or sensory deprivation, may have confounded with language input deprivation (Kroll and De Groot, 2009).

More recently, researchers have focused more systematically on deaf children born to hearing parents who are therefore deprived of language input until at least elementary school.

These studies have found the effects of lack of language input without extreme social deprivation: the older the age of exposure to sign language is, the worse its ultimate attainment (Emmorey, Bellugi, Friederici, and Horn, 1995; Kroll and De Groot, 2009).

However, Kroll and De Groot argue that the critical period hypothesis does not apply to the rate of acquisition of language. Adults and adolescents can learn languages at the same rate or even faster than children in their initial stage of acquisition (Slavoff and Johnson, 1995).

However, adults tend to have a more limited ultimate attainment of language ability (Kroll and De Groot, 2009).

There has been a long lineage of empirical findings around the age of acquisition. The most fundamental of this research comes from a series of studies since the late 1970s documenting a negative correlation between age of acquisition and ultimate language mastery (Kroll and De Grott, 2009).

Nonetheless, different periods correspond to sensitivity to different aspects of language. For example, shortly after birth, infants can perceive and discriminate speech sounds from any language, including ones they have not been exposed to (Eimas et al., 1971; Gallagher et al., 2020).

Around six months of age, exposure to the primary language in the infant’s environment guides phonetic representations of language and, subsequently, the neural representations of speech sounds of the native language while weakening those of unused sounds (McClelland et al., 1999; Gallagher et al., 2020).

Vocabulary learning experiences rapid growth at about 18 months of age (Kuhl, 2010).

Critical Evaluation

More than any other area of applied linguistics, the critical period hypothesis has impacted how teachers teach languages. Consequently, researchers have critiqued how important the critical period is to language learning.

For example, several studies in early language acquisition research showed that children were not necessarily superior to older learners in acquiring a second language, even in the area of pronunciation (Olson and Samuels, 1973; Snow and Hoefnagel-Hohle, 1978; Scovel, 2000).

In fact, the majority of researchers at the time appeared to be skeptical about the existence of a critical period, with some explicitly denying its existence.

Counter to one of the primary tenets of Scovel’s (1969) critical period hypothesis, there have been several cases of people who have acquired a second language in adulthood speaking with native accents.

For example, Moyer’s study of highly proficient English-speaking learners of German suggested that at least one of the participants was judged to have native-like pronunciation in his second language (1999), and several participants in Bongaerts (1999) study of highly proficient Dutch speakers of French spoke with accents judged to be native (Scovel, 2000).

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Critical period hypothesis

The critical period hypothesis says that there is a period of growth in which full native competence is possible when acquiring a language. This period is from early childhood to adolescence.

The critical period hypothesis has implications for teachers and learning programmes, but it is not universally accepted. Acquisition theories say that adults do not acquire languages as well as children because of external and internal factors, not because of a lack of ability.

Example Older learners rarely achieve a near-native accent. Many people suggest this is due to them being beyond the critical period.

In the classroom A problem arising from the differences between younger learners and adults is that adults believe that they cannot learn languages well. Teachers can help learners with this belief in various ways, for example, by talking about the learning process and learning styles, helping set realistic goals, choosing suitable methodologies, and addressing the emotional needs of the adult learner.

Further links:

https://www.teachingenglish.org.uk/article/how-maximise-language-learning-senior-learners

https://www.teachingenglish.org.uk/article/how-much-do-your-learners-use-english-outside-classroom

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Critical Period

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• First Online: 01 January 2021
• pp 1588–1590
• Cite this reference work entry

• Yan Wang 3 &
• Jing Guo 3  

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Crucial time ; Sensitive period

A maturational stage during the lifespan of an organism in which the organism’s nervous system is especially sensitive to certain environmental stimuli. The organism is more sensitive to environmental stimulation during a critical period than at other times during its life.

Introduction

The phenomenon of critical period was first described by William James ( 1899 ) as “the transitoriness of instincts.” The term “critical period” was proposed by the Austrian ecologist based on his observations that newly hatched poultries, such as chicks and geese, would follow the object, usually their mother, if exposed to within a certain short time after birth.

According to Lorenz, if the young animal was not exposed to the particular stimulus during the “critical period” to learn a given skill or trait, it would become extremely struggling to develop particular behavioral pattern in the later life.

A vast of existing literature has identified the...

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Wang, Y., Guo, J. (2021). Critical Period. In: Shackelford, T.K., Weekes-Shackelford, V.A. (eds) Encyclopedia of Evolutionary Psychological Science. Springer, Cham. https://doi.org/10.1007/978-3-319-19650-3_1060

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The Critical Period Hypothesis states that we would not be able to develop language to a fluent level if we are not exposed to it in the first few years of our lives. Let's have a look at this concept in more detail!

Critical period hypothesis

The Critical Period Hypothesis (CPH) holds that there is a critical time period for a person to learn a new language to a native proficiency. This critical period typically starts at around age two and ends before puberty¹. The hypothesis implies that acquiring a new language after this critical window will be more difficult and less successful.

Critical period in Psychology

The critical period is a key concept within the subject of Psychology. Psychology often has close links with English Language and Linguistics with a key area of study being Language Acquisition .

Critical period Psychology definition

In developmental psychology, the critical period is the maturing stage of a person, where their nervous system is primed and sensitive to environmental experiences. If a person doesn't get the right environmental stimuli during this period, their ability to learn new skills will weaken, affecting many social functions in adult life. If a child passes through a critical period without learning a language, it will be very unlikely for them to gain native fluency in their first language².

During the critical period, a person is primed to acquire new skills because of the brains' neuroplasticity. The connections in the brain, called synapses, are highly receptive to new experiences since they can form new pathways. The developing brain has a high degree of plasticity and gradually becomes less 'plastic' in adulthood.

Critical and sensitive periods

Similar to the critical period, researchers use another term called the 'sensitive period' or 'weak critical period'. The sensitive period is similar to the critical period since it's characterized as a time in which the brain has a high level of neuroplasticity and is quick to form new synapses. The main difference is that the sensitive period is considered to last for a longer time beyond puberty, but the boundaries are not strictly set.

First language acquisition in the critical period

It was Eric Lenneberg in his book Biological Foundations of Language (1967), who first introduced the Critical Period Hypothesis concerning language acquisition. He proposed that learning a language with high-level proficiency can only happen within this period. L anguage acquisition outside of this period is more challenging, making it less likely to achieve native proficiency.

He proposed this hypothesis based on evidence from children with certain childhood experiences that affected their first language ability. More specifically, the evidence was based on these cases:

Deaf children that didn't develop native proficiency in verbal language after puberty .

Children that experienced brain injury had better recovery prospects than adults. It is more likely for children with aphasia to learn a language than it is for adults with aphasia.

Children who were victims of child abuse during early childhood had more difficulties learning the language since they were not exposed to it during the critical period.

Critical period example

An example of the critical period is Genie. Genie, the so-called 'feral child', is a key case study in regard to the critical period and language acquisition.

As a child, Genie was a victim of domestic abuse and social isolation. T his took place from the age of 20 months until 13 years old. During this period, she didn't speak to anyone and rarely had any interaction with other people. This meant that she wasn't able to develop adequate language skills.

When authorities discovered her, she could not speak. Over a few months, she acquired some language skills with direct teaching but the process was quite slow. Although her vocabulary grew over time, she had difficulty learning basic grammar and maintaining conversations.

The scientists that worked with her concluded that because she wasn't able to learn a language during the critical period, she wouldn't be able to achieve full competency in language for the rest of her life. Although she made clear improvements in her ability to speak, her speech still had a lot of abnormalities, and she had difficulty with social interaction .

The case of Genie supports Lenneberg 's theory to an extent. However, academics and researchers still argue about this topic. Some scientists claim that Genie's development was disrupted because of the inhumane and traumatic treatment she suffered as a child, which caused her inability to learn a language.

Second language acquisition in the critical period

The Critical Period Hypothesis can be applied in the context of second language acquisition. It applies to adults or children who have fluency in their first language and try to learn a second language.

The main point of evidence given for the CPH for second language acquisition is assessing older learners' ability to grasp a second language compared to children and adolescents. A general trend that can be observed is that younger learners grasp a complete command over the language compared to their older counterparts³.

Although there may be examples where adults achieve very good proficiency in a new language, they usually retain a foreign accent which isn't common with younger learners. Retaining a foreign accent is usually because of the function that the neuromuscular system plays in the pronunciation of speech.

Adults are unlikely to attain a native accent since they are beyond the critical period to learn new neuromuscular functions. With all this being said, there are special cases of adults who achieve near-native proficiency in all aspects of a second language. For this reason, researchers have found it tricky to distinguish between correlation and causation.

Some have argued that the critical period doesn't apply to second language acquisition. Instead of age being the main factor, other elements such as the effort put in, the learning environment, and time spent learning have a more significant influence on the learner's success.

Critical Period - Key takeaways

• The critical period is said to take place in adolescence, typically from 2 years old until puberty.
• The brain has a higher level of neuroplasticity during the critical period, which allows new synaptic connections to form.
• Eric Lenneberg introduced the hypothesis in 1967.
• The case of Genie, the feral child, offered direct evidence in support of the CPH.
• The difficulty adult learners have in learning a second language is used to support the CPH.

1. Kenji Hakuta et al, Critical Evidence: A Test of the Critical-Period Hypothesis for Second-Language Acquisition, 2003 .

2. Angela D. Friederici et al, Brain signatures of artificial language processing: Evidence challenging the critical period hypothesis, 2002 .

3. Birdsong D. , Second Language Acquisition and the Critical Period Hypothesis. Routledge, 1999 .

Flashcards inCritical Period 52

Eric Lenneberg was born in ________ in 1921.

How are adolescents more capable of learning a new language than adults?

The brain of adolescents has a higher level of neuroplasticity since they are still in the critical period.

What field of linguistics did Lenneberg play a major role in?

Biolinguistics

At university, Lenneberg studied:

Why was Genie unable to develop native proficiency in her first language?

She didn’t have the opportunity to develop basic language skills during the critical period.

True or False? Adults are unable to develop native proficiency in a second language.

False. It is more difficult, but adults can still develop full proficiency in a second language.

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Frequently Asked Questions about Critical Period

What a critical periods?

The critical time for a person to learn a new language with native proficiency.

What happens during the critical period?

The brain is more neuroplastic during this period, making it easier for a person to learn a new skill.

How long is the critical period?

The common period for the critical period is from 2 years old until puberty. Although academics differ slightly on the age range for the critical period.

What is the critical period hypothesis?

The Critical Period Hypothesis (CPH) holds that there is a critical time period for a person to learn a new language to a native proficiency.

What is critical period example

An example of the critical period is Genie the 'feral child'. Genie was isolated from birth and was not exposed to language in her first 13 years of life. Once she was rescued, she was able to grow her vocabulary, however, she did not acquire a native level of fluency in terms of grammar. Her case supports the critical period hypothesis but it is also important to remember the effect of her inhumane treatment on her ability to learn language. 

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The Critical Period Hypothesis in Second Language Acquisition: A Statistical Critique and a Reanalysis

Jan vanhove.

Department of Multilingualism, University of Fribourg, Fribourg, Switzerland

Analyzed the data: JV. Wrote the paper: JV.

Associated Data

In second language acquisition research, the critical period hypothesis ( cph ) holds that the function between learners' age and their susceptibility to second language input is non-linear. This paper revisits the indistinctness found in the literature with regard to this hypothesis's scope and predictions. Even when its scope is clearly delineated and its predictions are spelt out, however, empirical studies–with few exceptions–use analytical (statistical) tools that are irrelevant with respect to the predictions made. This paper discusses statistical fallacies common in cph research and illustrates an alternative analytical method (piecewise regression) by means of a reanalysis of two datasets from a 2010 paper purporting to have found cross-linguistic evidence in favour of the cph . This reanalysis reveals that the specific age patterns predicted by the cph are not cross-linguistically robust. Applying the principle of parsimony, it is concluded that age patterns in second language acquisition are not governed by a critical period. To conclude, this paper highlights the role of confirmation bias in the scientific enterprise and appeals to second language acquisition researchers to reanalyse their old datasets using the methods discussed in this paper. The data and R commands that were used for the reanalysis are provided as supplementary materials.

Introduction

In the long term and in immersion contexts, second-language (L2) learners starting acquisition early in life – and staying exposed to input and thus learning over several years or decades – undisputedly tend to outperform later learners. Apart from being misinterpreted as an argument in favour of early foreign language instruction, which takes place in wholly different circumstances, this general age effect is also sometimes taken as evidence for a so-called ‘critical period’ ( cp ) for second-language acquisition ( sla ). Derived from biology, the cp concept was famously introduced into the field of language acquisition by Penfield and Roberts in 1959 [1] and was refined by Lenneberg eight years later [2] . Lenneberg argued that language acquisition needed to take place between age two and puberty – a period which he believed to coincide with the lateralisation process of the brain. (More recent neurological research suggests that different time frames exist for the lateralisation process of different language functions. Most, however, close before puberty [3] .) However, Lenneberg mostly drew on findings pertaining to first language development in deaf children, feral children or children with serious cognitive impairments in order to back up his claims. For him, the critical period concept was concerned with the implicit “automatic acquisition” [2, p. 176] in immersion contexts and does not preclude the possibility of learning a foreign language after puberty, albeit with much conscious effort and typically less success.

sla research adopted the critical period hypothesis ( cph ) and applied it to second and foreign language learning, resulting in a host of studies. In its most general version, the cph for sla states that the ‘susceptibility’ or ‘sensitivity’ to language input varies as a function of age, with adult L2 learners being less susceptible to input than child L2 learners. Importantly, the age–susceptibility function is hypothesised to be non-linear. Moving beyond this general version, we find that the cph is conceptualised in a multitude of ways [4] . This state of affairs requires scholars to make explicit their theoretical stance and assumptions [5] , but has the obvious downside that critical findings risk being mitigated as posing a problem to only one aspect of one particular conceptualisation of the cph , whereas other conceptualisations remain unscathed. This overall vagueness concerns two areas in particular, viz. the delineation of the cph 's scope and the formulation of testable predictions. Delineating the scope and formulating falsifiable predictions are, needless to say, fundamental stages in the scientific evaluation of any hypothesis or theory, but the lack of scholarly consensus on these points seems to be particularly pronounced in the case of the cph . This article therefore first presents a brief overview of differing views on these two stages. Then, once the scope of their cph version has been duly identified and empirical data have been collected using solid methods, it is essential that researchers analyse the data patterns soundly in order to assess the predictions made and that they draw justifiable conclusions from the results. As I will argue in great detail, however, the statistical analysis of data patterns as well as their interpretation in cph research – and this includes both critical and supportive studies and overviews – leaves a great deal to be desired. Reanalysing data from a recent cph -supportive study, I illustrate some common statistical fallacies in cph research and demonstrate how one particular cph prediction can be evaluated.

Delineating the scope of the critical period hypothesis

First, the age span for a putative critical period for language acquisition has been delimited in different ways in the literature [4] . Lenneberg's critical period stretched from two years of age to puberty (which he posits at about 14 years of age) [2] , whereas other scholars have drawn the cutoff point at 12, 15, 16 or 18 years of age [6] . Unlike Lenneberg, most researchers today do not define a starting age for the critical period for language learning. Some, however, consider the possibility of the critical period (or a critical period for a specific language area, e.g. phonology) ending much earlier than puberty (e.g. age 9 years [1] , or as early as 12 months in the case of phonology [7] ).

Second, some vagueness remains as to the setting that is relevant to the cph . Does the critical period constrain implicit learning processes only, i.e. only the untutored language acquisition in immersion contexts or does it also apply to (at least partly) instructed learning? Most researchers agree on the former [8] , but much research has included subjects who have had at least some instruction in the L2.

Third, there is no consensus on what the scope of the cp is as far as the areas of language that are concerned. Most researchers agree that a cp is most likely to constrain the acquisition of pronunciation and grammar and, consequently, these are the areas primarily looked into in studies on the cph [9] . Some researchers have also tried to define distinguishable cp s for the different language areas of phonetics, morphology and syntax and even for lexis (see [10] for an overview).

Fourth and last, research into the cph has focused on ‘ultimate attainment’ ( ua ) or the ‘final’ state of L2 proficiency rather than on the rate of learning. From research into the rate of acquisition (e.g. [11] – [13] ), it has become clear that the cph cannot hold for the rate variable. In fact, it has been observed that adult learners proceed faster than child learners at the beginning stages of L2 acquisition. Though theoretical reasons for excluding the rate can be posited (the initial faster rate of learning in adults may be the result of more conscious cognitive strategies rather than to less conscious implicit learning, for instance), rate of learning might from a different perspective also be considered an indicator of ‘susceptibility’ or ‘sensitivity’ to language input. Nevertheless, contemporary sla scholars generally seem to concur that ua and not rate of learning is the dependent variable of primary interest in cph research. These and further scope delineation problems relevant to cph research are discussed in more detail by, among others, Birdsong [9] , DeKeyser and Larson-Hall [14] , Long [10] and Muñoz and Singleton [6] .

Formulating testable hypotheses

Once the relevant cph 's scope has satisfactorily been identified, clear and testable predictions need to be drawn from it. At this stage, the lack of consensus on what the consequences or the actual observable outcome of a cp would have to look like becomes evident. As touched upon earlier, cph research is interested in the end state or ‘ultimate attainment’ ( ua ) in L2 acquisition because this “determines the upper limits of L2 attainment” [9, p. 10]. The range of possible ultimate attainment states thus helps researchers to explore the potential maximum outcome of L2 proficiency before and after the putative critical period.

One strong prediction made by some cph exponents holds that post- cp learners cannot reach native-like L2 competences. Identifying a single native-like post- cp L2 learner would then suffice to falsify all cph s making this prediction. Assessing this prediction is difficult, however, since it is not clear what exactly constitutes sufficient nativelikeness, as illustrated by the discussion on the actual nativelikeness of highly accomplished L2 speakers [15] , [16] . Indeed, there exists a real danger that, in a quest to vindicate the cph , scholars set the bar for L2 learners to match monolinguals increasingly higher – up to Swiftian extremes. Furthermore, the usefulness of comparing the linguistic performance in mono- and bilinguals has been called into question [6] , [17] , [18] . Put simply, the linguistic repertoires of mono- and bilinguals differ by definition and differences in the behavioural outcome will necessarily be found, if only one digs deep enough.

A second strong prediction made by cph proponents is that the function linking age of acquisition and ultimate attainment will not be linear throughout the whole lifespan. Before discussing how this function would have to look like in order for it to constitute cph -consistent evidence, I point out that the ultimate attainment variable can essentially be considered a cumulative measure dependent on the actual variable of interest in cph research, i.e. susceptibility to language input, as well as on such other factors like duration and intensity of learning (within and outside a putative cp ) and possibly a number of other influencing factors. To elaborate, the behavioural outcome, i.e. ultimate attainment, can be assumed to be integrative to the susceptibility function, as Newport [19] correctly points out. Other things being equal, ultimate attainment will therefore decrease as susceptibility decreases. However, decreasing ultimate attainment levels in and by themselves represent no compelling evidence in favour of a cph . The form of the integrative curve must therefore be predicted clearly from the susceptibility function. Additionally, the age of acquisition–ultimate attainment function can take just about any form when other things are not equal, e.g. duration of learning (Does learning last up until time of testing or only for a more or less constant number of years or is it dependent on age itself?) or intensity of learning (Do learners always learn at their maximum susceptibility level or does this intensity vary as a function of age, duration, present attainment and motivation?). The integral of the susceptibility function could therefore be of virtually unlimited complexity and its parameters could be adjusted to fit any age of acquisition–ultimate attainment pattern. It seems therefore astonishing that the distinction between level of sensitivity to language input and level of ultimate attainment is rarely made in the literature. Implicitly or explicitly [20] , the two are more or less equated and the same mathematical functions are expected to describe the two variables if observed across a range of starting ages of acquisition.

But even when the susceptibility and ultimate attainment variables are equated, there remains controversy as to what function linking age of onset of acquisition and ultimate attainment would actually constitute evidence for a critical period. Most scholars agree that not any kind of age effect constitutes such evidence. More specifically, the age of acquisition–ultimate attainment function would need to be different before and after the end of the cp [9] . According to Birdsong [9] , three basic possible patterns proposed in the literature meet this condition. These patterns are presented in Figure 1 . The first pattern describes a steep decline of the age of onset of acquisition ( aoa )–ultimate attainment ( ua ) function up to the end of the cp and a practically non-existent age effect thereafter. Pattern 2 is an “unconventional, although often implicitly invoked” [9, p. 17] notion of the cp function which contains a period of peak attainment (or performance at ceiling), i.e. performance does not vary as a function of age, which is often referred to as a ‘window of opportunity’. This time span is followed by an unbounded decline in ua depending on aoa . Pattern 3 includes characteristics of patterns 1 and 2. At the beginning of the aoa range, performance is at ceiling. The next segment is a downward slope in the age function which ends when performance reaches its floor. Birdsong points out that all of these patterns have been reported in the literature. On closer inspection, however, he concludes that the most convincing function describing these age effects is a simple linear one. Hakuta et al. [21] sketch further theoretically possible predictions of the cph in which the mean performance drops drastically and/or the slope of the aoa – ua proficiency function changes at a certain point.

The graphs are based on based on Figure 2 in [9] .

Although several patterns have been proposed in the literature, it bears pointing out that the most common explicit prediction corresponds to Birdsong's first pattern, as exemplified by the following crystal-clear statement by DeKeyser, one of the foremost cph proponents:

[A] strong negative correlation between age of acquisition and ultimate attainment throughout the lifespan (or even from birth through middle age), the only age effect documented in many earlier studies, is not evidence for a critical period…[T]he critical period concept implies a break in the AoA–proficiency function, i.e., an age (somewhat variable from individual to individual, of course, and therefore an age range in the aggregate) after which the decline of success rate in one or more areas of language is much less pronounced and/or clearly due to different reasons. [22, p. 445].

DeKeyser and before him among others Johnson and Newport [23] thus conceptualise only one possible pattern which would speak in favour of a critical period: a clear negative age effect before the end of the critical period and a much weaker (if any) negative correlation between age and ultimate attainment after it. This ‘flattened slope’ prediction has the virtue of being much more tangible than the ‘potential nativelikeness’ prediction: Testing it does not necessarily require comparing the L2-learners to a native control group and thus effectively comparing apples and oranges. Rather, L2-learners with different aoa s can be compared amongst themselves without the need to categorise them by means of a native-speaker yardstick, the validity of which is inevitably going to be controversial [15] . In what follows, I will concern myself solely with the ‘flattened slope’ prediction, arguing that, despite its clarity of formulation, cph research has generally used analytical methods that are irrelevant for the purposes of actually testing it.

Inferring non-linearities in critical period research: An overview

Group mean or proportion comparisons

[T]he main differences can be found between the native group and all other groups – including the earliest learner group – and between the adolescence group and all other groups. However, neither the difference between the two childhood groups nor the one between the two adulthood groups reached significance, which indicates that the major changes in eventual perceived nativelikeness of L2 learners can be associated with adolescence. [15, p. 270].

Similar group comparisons aimed at investigating the effect of aoa on ua have been carried out by both cph advocates and sceptics (among whom Bialystok and Miller [25, pp. 136–139], Birdsong and Molis [26, p. 240], Flege [27, pp. 120–121], Flege et al. [28, pp. 85–86], Johnson [29, p. 229], Johnson and Newport [23, p. 78], McDonald [30, pp. 408–410] and Patowski [31, pp. 456–458]). To be clear, not all of these authors drew direct conclusions about the aoa – ua function on the basis of these groups comparisons, but their group comparisons have been cited as indicative of a cph -consistent non-continuous age effect, as exemplified by the following quote by DeKeyser [22] :

Where group comparisons are made, younger learners always do significantly better than the older learners. The behavioral evidence, then, suggests a non-continuous age effect with a “bend” in the AoA–proficiency function somewhere between ages 12 and 16. [22, p. 448].

The first problem with group comparisons like these and drawing inferences on the basis thereof is that they require that a continuous variable, aoa , be split up into discrete bins. More often than not, the boundaries between these bins are drawn in an arbitrary fashion, but what is more troublesome is the loss of information and statistical power that such discretisation entails (see [32] for the extreme case of dichotomisation). If we want to find out more about the relationship between aoa and ua , why throw away most of the aoa information and effectively reduce the ua data to group means and the variance in those groups?

Comparison of correlation coefficients

Correlation-based inferences about slope discontinuities have similarly explicitly been made by cph advocates and skeptics alike, e.g. Bialystok and Miller [25, pp. 136 and 140], DeKeyser and colleagues [22] , [44] and Flege et al. [45, pp. 166 and 169]. Others did not explicitly infer the presence or absence of slope differences from the subset correlations they computed (among others Birdsong and Molis [26] , DeKeyser [8] , Flege et al. [28] and Johnson [29] ), but their studies nevertheless featured in overviews discussing discontinuities [14] , [22] . Indeed, the most recent overview draws a strong conclusion about the validity of the cph 's ‘flattened slope’ prediction on the basis of these subset correlations:

In those studies where the two groups are described separately, the correlation is much higher for the younger than for the older group, except in Birdsong and Molis (2001) [ =  [26] , JV], where there was a ceiling effect for the younger group. This global picture from more than a dozen studies provides support for the non-continuity of the decline in the AoA–proficiency function, which all researchers agree is a hallmark of a critical period phenomenon. [22, p. 448].

In Johnson and Newport's specific case [23] , their correlation-based inference that ua levels off after puberty happened to be largely correct: the gjt scores are more or less randomly distributed around a near-horizontal trend line [26] . Ultimately, however, it rests on the fallacy of confusing correlation coefficients with slopes, which seriously calls into question conclusions such as DeKeyser's (cf. the quote above).

It can then straightforwardly be deduced that, other things equal, the aoa – ua correlation in the older group decreases as the ua variance in the older group increases relative to the ua variance in the younger group (Eq. 3).

Lower correlation coefficients in older aoa groups may therefore be largely due to differences in ua variance, which have been reported in several studies [23] , [26] , [28] , [29] (see [46] for additional references). Greater variability in ua with increasing age is likely due to factors other than age proper [47] , such as the concomitant greater variability in exposure to literacy, degree of education, motivation and opportunity for language use, and by itself represents evidence neither in favour of nor against the cph .

Regression approaches

Having demonstrated that neither group mean or proportion comparisons nor correlation coefficient comparisons can directly address the ‘flattened slope’ prediction, I now turn to the studies in which regression models were computed with aoa as a predictor variable and ua as the outcome variable. Once again, this category of studies is not mutually exclusive with the two categories discussed above.

In a large-scale study using self-reports and approximate aoa s derived from a sample of the 1990 U.S. Census, Stevens found that the probability with which immigrants from various countries stated that they spoke English ‘very well’ decreased curvilinearly as a function of aoa [48] . She noted that this development is similar to the pattern found by Johnson and Newport [23] but that it contains no indication of an “abruptly defined ‘critical’ or sensitive period in L2 learning” [48, p. 569]. However, she modelled the self-ratings using an ordinal logistic regression model in which the aoa variable was logarithmically transformed. Technically, this is perfectly fine, but one should be careful not to read too much into the non-linear curves found. In logistic models, the outcome variable itself is modelled linearly as a function of the predictor variables and is expressed in log-odds. In order to compute the corresponding probabilities, these log-odds are transformed using the logistic function. Consequently, even if the model is specified linearly, the predicted probabilities will not lie on a perfectly straight line when plotted as a function of any one continuous predictor variable. Similarly, when the predictor variable is first logarithmically transformed and then used to linearly predict an outcome variable, the function linking the predicted outcome variables and the untransformed predictor variable is necessarily non-linear. Thus, non-linearities follow naturally from Stevens's model specifications. Moreover, cph -consistent discontinuities in the aoa – ua function cannot be found using her model specifications as they did not contain any parameters allowing for this.

Using data similar to Stevens's, Bialystok and Hakuta found that the link between the self-rated English competences of Chinese- and Spanish-speaking immigrants and their aoa could be described by a straight line [49] . In contrast to Stevens, Bialystok and Hakuta used a regression-based method allowing for changes in the function's slope, viz. locally weighted scatterplot smoothing ( lowess ). Informally, lowess is a non-parametrical method that relies on an algorithm that fits the dependent variable for small parts of the range of the independent variable whilst guaranteeing that the overall curve does not contain sudden jumps (for technical details, see [50] ). Hakuta et al. used an even larger sample from the same 1990 U.S. Census data on Chinese- and Spanish-speaking immigrants (2.3 million observations) [21] . Fitting lowess curves, no discontinuities in the aoa – ua slope could be detected. Moreover, the authors found that piecewise linear regression models, i.e. regression models containing a parameter that allows a sudden drop in the curve or a change of its slope, did not provide a better fit to the data than did an ordinary regression model without such a parameter.

To sum up, I have argued at length that regression approaches are superior to group mean and correlation coefficient comparisons for the purposes of testing the ‘flattened slope’ prediction. Acknowledging the reservations vis-à-vis self-estimated ua s, we still find that while the relationship between aoa and ua is not necessarily perfectly linear in the studies discussed, the data do not lend unequivocal support to this prediction. In the following section, I will reanalyse data from a recent empirical paper on the cph by DeKeyser et al. [44] . The first goal of this reanalysis is to further illustrate some of the statistical fallacies encountered in cph studies. Second, by making the computer code available I hope to demonstrate how the relevant regression models, viz. piecewise regression models, can be fitted and how the aoa representing the optimal breakpoint can be identified. Lastly, the findings of this reanalysis will contribute to our understanding of how aoa affects ua as measured using a gjt .

Summary of DeKeyser et al. (2010)

I chose to reanalyse a recent empirical paper on the cph by DeKeyser et al. [44] (henceforth DK et al.). This paper lends itself well to a reanalysis since it exhibits two highly commendable qualities: the authors spell out their hypotheses lucidly and provide detailed numerical and graphical data descriptions. Moreover, the paper's lead author is very clear on what constitutes a necessary condition for accepting the cph : a non-linearity in the age of onset of acquisition ( aoa )–ultimate attainment ( ua ) function, with ua declining less strongly as a function of aoa in older, post- cp arrivals compared to younger arrivals [14] , [22] . Lastly, it claims to have found cross-linguistic evidence from two parallel studies backing the cph and should therefore be an unsuspected source to cph proponents.

The authors set out to test the following hypotheses:

• Hypothesis 1: For both the L2 English and the L2 Hebrew group, the slope of the age of arrival–ultimate attainment function will not be linear throughout the lifespan, but will instead show a marked flattening between adolescence and adulthood.
• Hypothesis 2: The relationship between aptitude and ultimate attainment will differ markedly for the young and older arrivals, with significance only for the latter. (DK et al., p. 417)

Both hypotheses were purportedly confirmed, which in the authors' view provides evidence in favour of cph . The problem with this conclusion, however, is that it is based on a comparison of correlation coefficients. As I have argued above, correlation coefficients are not to be confused with regression coefficients and cannot be used to directly address research hypotheses concerning slopes, such as Hypothesis 1. In what follows, I will reanalyse the relationship between DK et al.'s aoa and gjt data in order to address Hypothesis 1. Additionally, I will lay bare a problem with the way in which Hypothesis 2 was addressed. The extracted data and the computer code used for the reanalysis are provided as supplementary materials, allowing anyone interested to scrutinise and easily reproduce my whole analysis and carry out their own computations (see ‘supporting information’).

Data extraction

In order to verify whether we did in fact extract the data points to a satisfactory degree of accuracy, I computed summary statistics for the extracted aoa and gjt data and checked these against the descriptive statistics provided by DK et al. (pp. 421 and 427). These summary statistics for the extracted data are presented in Table 1 . In addition, I computed the correlation coefficients for the aoa – gjt relationship for the whole aoa range and for aoa -defined subgroups and checked these coefficients against those reported by DK et al. (pp. 423 and 428). The correlation coefficients computed using the extracted data are presented in Table 2 . Both checks strongly suggest the extracted data to be virtually identical to the original data, and Dr DeKeyser confirmed this to be the case in response to an earlier draft of the present paper (personal communication, 6 May 2013).

Results and Discussion

Modelling the link between age of onset of acquisition and ultimate attainment.

I first replotted the aoa and gjt data we extracted from DK et al.'s scatterplots and added non-parametric scatterplot smoothers in order to investigate whether any changes in slope in the aoa – gjt function could be revealed, as per Hypothesis 1. Figures 3 and ​ and4 4 show this not to be the case. Indeed, simple linear regression models that model gjt as a function of aoa provide decent fits for both the North America and the Israel data, explaining 65% and 63% of the variance in gjt scores, respectively. The parameters of these models are given in Table 3 .

The trend line is a non-parametric scatterplot smoother. The scatterplot itself is a near-perfect replication of DK et al.'s Fig. 1.

The trend line is a non-parametric scatterplot smoother. The scatterplot itself is a near-perfect replication of DK et al.'s Fig. 5.

To ensure that both segments are joined at the breakpoint, the predictor variable is first centred at the breakpoint value, i.e. the breakpoint value is subtracted from the original predictor variable values. For a blow-by-blow account of how such models can be fitted in r , I refer to an example analysis by Baayen [55, pp. 214–222].

Solid: regression with breakpoint at aoa 18 (dashed lines represent its 95% confidence interval); dot-dash: regression without breakpoint.

Solid: regression with breakpoint at aoa 18 (dashed lines represent its 95% confidence interval); dot-dash (hardly visible due to near-complete overlap): regression without breakpoint.

Solid: regression with breakpoint at aoa 16 (dashed lines represent its 95% confidence interval); dot-dash: regression without breakpoint.

Solid: regression with breakpoint at aoa 6 (dashed lines represent its 95% confidence interval); dot-dash (hardly visible due to near-complete overlap): regression without breakpoint.

In sum, a regression model that allows for changes in the slope of the the aoa – gjt function to account for putative critical period effects provides a somewhat better fit to the North American data than does an everyday simple regression model. The improvement in model fit is marginal, however, and including a breakpoint does not result in any detectable improvement of model fit to the Israel data whatsoever. Breakpoint models therefore fail to provide solid cross-linguistic support in favour of critical period effects: across both data sets, gjt can satisfactorily be modelled as a linear function of aoa .

On partialling out ‘age at testing’

As I have argued above, correlation coefficients cannot be used to test hypotheses about slopes. When the correct procedure is carried out on DK et al.'s data, no cross-linguistically robust evidence for changes in the aoa – gjt function was found. In addition to comparing the zero-order correlations between aoa and gjt , however, DK et al. computed partial correlations in which the variance in aoa associated with the participants' age at testing ( aat ; a potentially confounding variable) was filtered out. They found that these partial correlations between aoa and gjt , which are given in Table 9 , differed between age groups in that they are stronger for younger than for older participants. This, DK et al. argue, constitutes additional evidence in favour of the cph . At this point, I can no longer provide my own analysis of DK et al.'s data seeing as the pertinent data points were not plotted. Nevertheless, the detailed descriptions by DK et al. strongly suggest that the use of these partial correlations is highly problematic. Most importantly, and to reiterate, correlations (whether zero-order or partial ones) are actually of no use when testing hypotheses concerning slopes. Still, one may wonder why the partial correlations differ across age groups. My surmise is that these differences are at least partly the by-product of an imbalance in the sampling procedure.

The upshot of this brief discussion is that the partial correlation differences reported by DK et al. are at least partly the result of an imbalance in the sampling procedure: aoa and aat were simply less intimately tied for the young arrivals in the North America study than for the older arrivals with L2 English or for all of the L2 Hebrew participants. In an ideal world, we would like to fix aat or ascertain that it at most only weakly correlates with aoa . This, however, would result in a strong correlation between aoa and another potential confound variable, length of residence in the L2 environment, bringing us back to square one. Allowing for only moderate correlations between aoa and aat might improve our predicament somewhat, but even in that case, we should tread lightly when making inferences on the basis of statistical control procedures [61] .

On estimating the role of aptitude

Having shown that Hypothesis 1 could not be confirmed, I now turn to Hypothesis 2, which predicts a differential role of aptitude for ua in sla in different aoa groups. More specifically, it states that the correlation between aptitude and gjt performance will be significant only for older arrivals. The correlation coefficients of the relationship between aptitude and gjt are presented in Table 10 .

The problem with both the wording of Hypothesis 2 and the way in which it is addressed is the following: it is assumed that a variable has a reliably different effect in different groups when the effect reaches significance in one group but not in the other. This logic is fairly widespread within several scientific disciplines (see e.g. [62] for a discussion). Nonetheless, it is demonstrably fallacious [63] . Here we will illustrate the fallacy for the specific case of comparing two correlation coefficients.

Apart from not being replicated in the North America study, does this difference actually show anything? I contend that it does not: what is of interest are not so much the correlation coefficients, but rather the interactions between aoa and aptitude in models predicting gjt . These interactions could be investigated by fitting a multiple regression model in which the postulated cp breakpoint governs the slope of both aoa and aptitude. If such a model provided a substantially better fit to the data than a model without a breakpoint for the aptitude slope and if the aptitude slope changes in the expected direction (i.e. a steeper slope for post- cp than for younger arrivals) for different L1–L2 pairings, only then would this particular prediction of the cph be borne out.

Using data extracted from a paper reporting on two recent studies that purport to provide evidence in favour of the cph and that, according to its authors, represent a major improvement over earlier studies (DK et al., p. 417), it was found that neither of its two hypotheses were actually confirmed when using the proper statistical tools. As a matter of fact, the gjt scores continue to decline at essentially the same rate even beyond the end of the putative critical period. According to the paper's lead author, such a finding represents a serious problem to his conceptualisation of the cph [14] ). Moreover, although modelling a breakpoint representing the end of a cp at aoa 16 may improve the statistical model slightly in study on learners of English in North America, the study on learners of Hebrew in Israel fails to confirm this finding. In fact, even if we were to accept the optimal breakpoint computed for the Israel study, it lies at aoa 6 and is associated with a different geometrical pattern.

Diverging age trends in parallel studies with participants with different L2s have similarly been reported by Birdsong and Molis [26] and are at odds with an L2-independent cph . One parsimonious explanation of such conflicting age trends may be that the overall, cross-linguistic age trend is in fact linear, but that fluctuations in the data (due to factors unaccounted for or randomness) may sometimes give rise to a ‘stretched L’-shaped pattern ( Figure 1, left panel ) and sometimes to a ‘stretched 7’-shaped pattern ( Figure 1 , middle panel; see also [66] for a similar comment).

Importantly, the criticism that DeKeyser and Larsson-Hall levy against two studies reporting findings similar to the present [48] , [49] , viz. that the data consisted of self-ratings of questionable validity [14] , does not apply to the present data set. In addition, DK et al. did not exclude any outliers from their analyses, so I assume that DeKeyser and Larsson-Hall's criticism [14] of Birdsong and Molis's study [26] , i.e. that the findings were due to the influence of outliers, is not applicable to the present data either. For good measure, however, I refitted the regression models with and without breakpoints after excluding one potentially problematic data point per model. The following data points had absolute standardised residuals larger than 2.5 in the original models without breakpoints as well as in those with breakpoints: the participant with aoa 17 and a gjt score of 125 in the North America study and the participant with aoa 12 and a gjt score of 117 in the Israel study. The resultant models were virtually identical to the original models (see Script S1 ). Furthermore, the aoa variable was sufficiently fine-grained and the aoa – gjt curve was not ‘presmoothed’ by the prior aggregation of gjt across parts of the aoa range (see [51] for such a criticism of another study). Lastly, seven of the nine “problems with supposed counter-evidence” to the cph discussed by Long [5] do not apply either, viz. (1) “[c]onfusion of rate and ultimate attainment”, (2) “[i]nappropriate choice of subjects”, (3) “[m]easurement of AO”, (4) “[l]eading instructions to raters”, (6) “[u]se of markedly non-native samples making near-native samples more likely to sound native to raters”, (7) “[u]nreliable or invalid measures”, and (8) “[i]nappropriate L1–L2 pairings”. Problem No. 5 (“Assessments based on limited samples and/or “language-like” behavior”) may be apropos given that only gjt data were used, leaving open the theoretical possibility that other measures might have yielded a different outcome. Finally, problem No. 9 (“Faulty interpretation of statistical patterns”) is, of course, precisely what I have turned the spotlights on.

Conclusions

The critical period hypothesis remains a hotly contested issue in the psycholinguistics of second-language acquisition. Discussions about the impact of empirical findings on the tenability of the cph generally revolve around the reliability of the data gathered (e.g. [5] , [14] , [22] , [52] , [67] , [68] ) and such methodological critiques are of course highly desirable. Furthermore, the debate often centres on the question of exactly what version of the cph is being vindicated or debunked. These versions differ mainly in terms of its scope, specifically with regard to the relevant age span, setting and language area, and the testable predictions they make. But even when the cph 's scope is clearly demarcated and its main prediction is spelt out lucidly, the issue remains to what extent the empirical findings can actually be marshalled in support of the relevant cph version. As I have shown in this paper, empirical data have often been taken to support cph versions predicting that the relationship between age of acquisition and ultimate attainment is not strictly linear, even though the statistical tools most commonly used (notably group mean and correlation coefficient comparisons) were, crudely put, irrelevant to this prediction. Methods that are arguably valid, e.g. piecewise regression and scatterplot smoothing, have been used in some studies [21] , [26] , [49] , but these studies have been criticised on other grounds. To my knowledge, such methods have never been used by scholars who explicitly subscribe to the cph .

I suspect that what may be going on is a form of ‘confirmation bias’ [69] , a cognitive bias at play in diverse branches of human knowledge seeking: Findings judged to be consistent with one's own hypothesis are hardly questioned, whereas findings inconsistent with one's own hypothesis are scrutinised much more strongly and criticised on all sorts of points [70] – [73] . My reanalysis of DK et al.'s recent paper may be a case in point. cph exponents used correlation coefficients to address their prediction about the slope of a function, as had been done in a host of earlier studies. Finding a result that squared with their expectations, they did not question the technical validity of their results, or at least they did not report this. (In fact, my reanalysis is actually a case in point in two respects: for an earlier draft of this paper, I had computed the optimal position of the breakpoints incorrectly, resulting in an insignificant improvement of model fit for the North American data rather than a borderline significant one. Finding a result that squared with my expectations, I did not question the technical validity of my results – until this error was kindly pointed out to me by Martijn Wieling (University of Tübingen).) That said, I am keen to point out that the statistical analyses in this particular paper, though suboptimal, are, as far as I could gather, reported correctly, i.e. the confirmation bias does not seem to have resulted in the blatant misreportings found elsewhere (see [74] for empirical evidence and discussion). An additional point to these authors' credit is that, apart from explicitly identifying their cph version's scope and making crystal-clear predictions, they present data descriptions that actually permit quantitative reassessments and have a history of doing so (e.g. the appendix in [8] ). This leads me to believe that they analysed their data all in good conscience and to hope that they, too, will conclude that their own data do not, in fact, support their hypothesis.

I end this paper on an upbeat note. Even though I have argued that the analytical tools employed in cph research generally leave much to be desired, the original data are, so I hope, still available. This provides researchers, cph supporters and sceptics alike, with an exciting opportunity to reanalyse their data sets using the tools outlined in the present paper and publish their findings at minimal cost of time and resources (for instance, as a comment to this paper). I would therefore encourage scholars to engage their old data sets and to communicate their analyses openly, e.g. by voluntarily publishing their data and computer code alongside their articles or comments. Ideally, cph supporters and sceptics would join forces to agree on a protocol for a high-powered study in order to provide a truly convincing answer to a core issue in sla .

Supporting Information

aoa and gjt data extracted from DeKeyser et al.'s North America study.

aoa and gjt data extracted from DeKeyser et al.'s Israel study.

Script with annotated R code used for the reanalysis. All add-on packages used can be installed from within R.

Acknowledgments

I would like to thank Irmtraud Kaiser (University of Fribourg) for helping me to get an overview of the literature on the critical period hypothesis in second language acquisition. Thanks are also due to Martijn Wieling (currently University of Tübingen) for pointing out an error in the R code accompanying an earlier draft of this paper.

Funding Statement

No current external funding sources for this study.

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Critical Period in Brain Development: Definition, Importance

Toketemu has been multimedia storyteller for the last four years. Her expertise focuses primarily on mental wellness and women’s health topics. 

Catherine Falls Commercial / Getty Images

• When Does the Critical Period Begin and End?
• The Critical Period Hypothesis—What It States
• What Happens to the Brain in the Critical Period?
• What Kind of Events Impact the Brain During the Critical Period?
• How Do Adverse Events Impact the Brain?
• What's the Difference Between a Critical Period and a Sensitive Period?
• What Happens to the Brain When the Critical Period Ends?

The critical period in brain development is an immensely significant and specific time frame during which the brain is especially receptive to environmental stimuli and undergoes a series of rapid changes. 

These changes have lifelong effects as essential neural connections and pathways are established, playing a vital role in cognitive, emotional, and social development. 

This article will explore the timeline, impacting events, and subsequent consequences of the critical period on brain development. It also explores the distinction between critical periods and sensitive periods and what happens to the brain once the critical period ends.

When Does the Critical Period Begin and End? 

The starting point of the critical period is at conception. The brain starts to form and develop from the moment you are conceived. During pregnancy, a baby's brain is already beginning to shape itself for the world outside. The brain is gearing up and getting ready to absorb a massive amount of information.

The Early Years of a Child's Life

Once the baby is born, the brain kicks into high gear. The early years of a child's life, from birth to around the age of five, are generally considered the core of the critical period. The brain is incredibly absorbent during these years, taking in information rapidly. Everything from language to motor skills to social cues is being learned and processed extensively.

Different aspects of learning and development have different critical periods. For instance, the critical period for language acquisition extends into early adolescence. This means that while the brain is still very good at learning languages during early childhood, it continues to be relatively efficient at it until the teenage years.

The brain is incredibly absorbent during these years, taking in information rapidly. Everything from language to motor skills to social cues is being learned and processed extensively.

Vision Develops During This Period

On the other hand, for certain sensory abilities like vision, the critical period might end much earlier. This means that the brain is most receptive to developing visual abilities in the first few years of life, and after that, it becomes significantly harder to change or improve these abilities.

The Critical Period Hypothesis—What It States 

The brain has a certain time window when it's exceptionally good at learning new things, especially languages. This window of time is what is referred to as the "critical period."

Younger People Learn Languages Faster Than Older People

Eric Lenneberg, a neuropsychologist, introduced the Critical Period Hypothesis. He was very interested in how people learn languages . Through his observations and research, Lenneberg noticed that younger people were much more adept at learning languages than older people. This observation led him to the idea that there is a specific period during which the brain is highly efficient and capable of absorbing languages.

As You Age, It Becomes More Difficult to Absorb New Information

If the critical period is a wide open window in the early years of life, allowing the brain to take in an abundance of information quickly and efficiently, as time progresses, this window begins to close gradually. As it closes, the brain becomes less capable of easily absorbing languages.

This doesn't mean that learning becomes impossible as you age; it merely indicates that the ease and efficiency with which the brain learns start to decline.

What Happens to the Brain in the Critical Period? 

During the critical period, the brain experiences explosive growth. Let's take a look at some of the changes that happen in the brain during the critical period.

Neurons Form Connections

In the early stages, neurons in the brain start to form connections. These connections are called synapses.

Synapses are bridges that help different parts of the brain communicate with each other. In the critical period, the brain is building these bridges at an incredible pace.

Neuroplasticity Strengthens Brain Connections

As a baby interacts with the world, certain connections strengthen while others weaken. For instance, if a baby hears a lot of music, the parts of the brain associated with sounds and music will become stronger. This process of strengthening certain connections is known as brain plasticity because the brain molds itself like plastic.

Attachment to Primary Caregivers

An essential aspect of the critical period is the development of attachment to caregivers. During the early months and years, babies and toddlers form strong bonds with the people caring for them .

These attachments are critical for emotional development. When a caregiver responds to a baby's needs with warmth and care, the baby learns to form secure attachments . This lays the foundation for healthy relationships later in life.

What Happens When Children Are Not Given Attention?

What if a child is not given the attention and care they need during the critical period? This is a significant concern. Without proper attention and stimulation, the brain doesn't develop as effectively. The bridges or connections that should be built might not form properly. This can lead to various issues, including difficulty forming relationships, emotional problems, and learning difficulties.

When a child is given proper attention, stimulation, and care during the critical period, their brain thrives. The connections form rapidly and robustly. This sets the stage for better learning, emotional regulation, and relationship-building throughout life.

What Kind of Events Impact the Brain During the Critical Period? 

When a child is exposed to a rich, stimulating environment where they can play, explore, and learn, it tremendously impacts the brain. Engaging in interactive learning, being read to, and having supportive relationships with caregivers can significantly contribute to a well-developed brain.

Events such as abuse, neglect, head trauma , or extreme stress—collectively known as adverse childhood experiences (ACEs)—can be detrimental to brain development. These adverse events can impede the formation of neural connections and lead to behavioral, emotional, and cognitive difficulties later in life. "Unfortunately, disruptions to normal brain development due to environmental influences such as poverty, neglect, or exposure to toxins can cause lasting damage. This is why it is so important for children to receive adequate nutrition, stimulation, and parental care during these first few years of life; without it, they may suffer developmental delays and other issues that could potentially be avoided with proper attention,"  Harold Hong, MD , a board-certified psychiatrist says.

How Do Adverse Events Impact the Brain? 

When a child is neglected or abused, stress can impact how their brain develops. The parts of the brain involved in emotions and handling stress might not develop properly. This can make it hard for the person to manage their emotions later in life.

The hippocampus, involved in learning and memory, and the amygdala, which plays a role in emotion processing, are especially vulnerable. 

Similarly, if a child does not have enough food to eat or a safe place to live, the chronic stress of these conditions can impact brain development. The brain might focus on survival instead of other important areas of development, like learning and building relationships.

Even accidents that cause head injuries can impact the brain during the critical period. If a child experiences head trauma, it can affect the brain's development depending on the injury's severity and location.

What's the Difference Between a Critical Period and a Sensitive Period?

It is imperative to distinguish between critical periods and sensitive periods.

• Critical periods are specific windows of time during development when the brain is exceptionally receptive to certain types of learning and experiences. Once this period is over, acquiring those skills or attributes becomes significantly more challenging.
• Sensitive periods are phases in which the brain is more responsive to certain experiences. It's easier to learn or be influenced by specific experiences during sensitive periods, but unlike critical periods, missing this timeframe doesn't make it impossible to acquire those skills or traits later.

For example, while there is a critical period for acquiring native-like pronunciation and grammar, there is also a sensitive period for language learning. Children are more adept at learning new languages when they are young, but even if someone misses this window, they can still learn languages later in life.

One way to visualize the difference is to think of critical periods as a tightly defined window of time with a clear beginning and end, during which certain development must occur. In contrast, sensitive periods are more like a gradual slope, where learning at the beginning is optimal, but the ability doesn't disappear entirely over time.

What Happens to the Brain When the Critical Period Ends? 

It's essential to recognize that the end of the critical period does not mean the end of learning or brain development. Instead, it signifies a shift in how the brain learns and adapts. 

During the critical period, the brain is highly plastic, meaning it can change and form new connections rapidly. As this period ends, the brain doesn't lose this plasticity entirely, but the rate at which it can make new connections slows down. 

According to Hong, although some of these connections can still be altered by experiences later in life, such as learning a new language or practicing a skill, it is much harder to make significant changes after the critical period has ended. This highlights just how important it is for parents to provide proper care and nurture during those first few years.

The Brain Becomes More Specialized Via Adult Plasticity

The brain also becomes more specialized in the skills and information it has acquired as this period ends. During the critical period, the brain forms numerous connections, and as it ends, it starts to use these connections more efficiently for specialized tasks.

Even though the critical period ends, the brain still possesses a degree of plasticity and continues to learn throughout life. This is called adult plasticity.

Adult plasticity is not as robust during the critical period, but it allows for the continuous adaptation and learning necessary for us to navigate the ever-changing demands of life.

The conventional view is that critical periods close relatively tightly. However, research has started to challenge this rigid view. It's more accurate to say that the doors of critical periods close but do not necessarily lock.

While the brain's plasticity decreases after these periods, learning and adaptation can still take place, albeit with more effort and over a longer time. This phenomenon of 'metaplasticity'—the brain's ability to change its plasticity levels—remains an exciting area of ongoing research,  Dr. Ryan Sultan , a neuroscientist, child psychiatrist, and professor of psychiatry at Columbia University, says. 

What This Means For You

The critical period represents an invaluable window during which the foundations for cognitive, emotional, and social abilities are established. The environment, experiences, and attachments formed during this period have far-reaching consequences on a person's life.  Understanding the nuances of the critical period is essential for educators, parents, and policymakers to create nurturing environments that support healthy brain development. Providing support and early interventions for children exposed to adverse experiences is vital for ensuring their potential is not hindered by the circumstances of their early life.

Siahaan F. The critical period hypothesis of sla eric lenneberg’s . Journal of Applied Linguistics . 2022;2(1):40-45.

Nelson CA, Gabard-Durnam LJ. Early adversity and critical periods: neurodevelopmental consequences of violating the expectable environment. Trends in Neurosciences. 2020;43(3):133-143.

Colombo J, Gustafson KM, Carlson SE. Critical and sensitive periods in development and nutrition. Ann Nutr Metab . 2019;75(Suppl. 1):34-42.

Patton MH, Blundon JA, Zakharenko SS. Rejuvenation of plasticity in the brain: opening the critical period. Current Opinion in Neurobiology . 2019;54:83-89.

By Toketemu Ohwovoriole Toketemu has been multimedia storyteller for the last four years. Her expertise focuses primarily on mental wellness and women’s health topics.

Critical Period Hypothesis

The critical period hypothesis is the subject of a long-standing debate in linguistics and language acquisition over the extent to which the ability to acquire language is biologically linked to age. The hypothesis claims that there is an ideal ‘window’ of time to acquire language in a linguistically rich environment, after which further language acquisition becomes much more difficult and effortful.

The critical period hypothesis states that the first few years of life is the crucial time in which an individual can acquire a first language if presented with adequate stimuli. If language input doesn’t occur until after this time, the individual will never achieve a full command of language—especially grammatical systems.

The evidence for such a period is limited, and support stems largely from theoretical arguments and analogies to other critical periods in biology such as visual development, but nonetheless is widely accepted. The nature of this phenomenon, however, has been one of the most fiercely debated issues in psycholinguistics and cognitive science in general for decades. Some writers have suggested a “sensitive” or “optimal” period rather than a critical one; others dispute the causes (physical maturation, cognitive factors). The duration of the period also varies greatly in different accounts. In second language acquisition, the strongest evidence for the critical period hypothesis is in the study of accent, where most older learners do not reach a native-like level. However, under certain conditions, native-like accent has been observed, suggesting that accent is affected by multiple factors, such as identity and motivation, rather than a critical period biological constraint (Moyer, 1999; Bongaerts et al., 1995; Young-Scholten, 2002).

The critical period hypothesis was first proposed by Montreal neurologist Wilder Penfield and co-author Lamar Roberts in a 1959 paper Speech and Brain Mechanisms, and was popularised by Eric Lenneberg in 1967 with Biological Foundations of Language.

Lenneberg states that there are maturational constraints on the time a first language can be acquired. First language acquisition relies on neuroplasticity. If language acquisition does not occur by puberty, some aspects of language can be learnt but full mastery cannot be achieved. This was called the “critical period hypothesis.”

An interesting example of this is the case of Genie. A thirteen-year-old victim of lifelong child abuse, Genie was discovered in her home on November 4, 1970, strapped to a potty chair and wearing diapers. She appeared to be entirely without language. Her father had judged her retarded at birth and had chosen to isolate her, and so she had remained until her discovery.

It was an ideal opportunity to test the theory that a nurturing environment could somehow make up for a total lack of language past the age of 12. She was unable to acquire language completely, although the degree to which she acquired language is disputed.

Detractors of the “Critical Period Hypothesis” point out that in this example and others like it (see Feral children), the child is hardly growing up in a nurturing environment, and that the lack of language acquisition in later life may be due to the results of a generally abusive environment rather than being specifically due to a lack of exposure to language.

Recently, it has been suggested that if a critical period does exist, it may be due at least partially to the delayed development of the prefrontal cortex in human children. Researchers have suggested that delayed development of the prefrontal cortex and a concomitant delay in the development of cognitive control may facilitate convention learning, allowing young children to learn language far more easily than cognitively mature adults and older children. This pattern of prefrontal development is unique to humans among similar mammalian (and primate) species, and may explain why humans—and not chimpanzees—are so adept at learning language.

Second language acquisition

The theory has often been extended to a critical period for second language acquisition (SLA), although this is much less widely accepted. Certainly, older learners of a second language rarely achieve the native-like fluency that younger learners display, despite often progressing faster than children in the initial stages. David Singleton states that in learning a second language, “younger = better in the long run,” but points out that there are many exceptions, noting that five percent of adult bilinguals master a second language even though they begin learning it when they are well into adulthood—long after any critical period has presumably come to a close.

While the window for learning a second language never completely closes, certain linguistic aspects appear to be more affected by the age of the learner than others. For example, adult second-language learners nearly always retain an immediately identifiable foreign accent, including some who display perfect grammar (Oyama 1976). Some writers have suggested a younger critical age for learning phonology than for syntax. Singleton (1995) reports that there is no critical period for learning vocabulary in a second language. Robertson (2002)] observed that factors other than age may be even more significant in successful second language learning, such as personal motivation, anxiety, input and output skills, settings and time commitment.

On reviewing the published material, Bialystok and Hakuta (1994) conclude that second-language learning is not necessarily subject to biological critical periods, but “on average, there is a continuous decline in ability [to learn] with age.”

Experimental and observational studies

How children acquire native language (L1) and the relevance of this to foreign language (L2) learning has long been debated. Although evidence for L2 learning ability declining with age is controversial, a common notion is that children learn L2s easily, whilst older learners rarely achieve fluency. This assumption stems from ‘critical period’ (CP) ideas. A CP was popularised by Eric Lenneberg in 1967 for L1 acquisition, but considerable interest now surrounds age effects on second language acquisition (SLA). SLA theories explain learning processes and suggest causal factors for a possible CP for SLA, mainly attempting to explain apparent differences in language aptitudes of children and adults by distinct learning routes, and clarifying them through psychological mechanisms. Research explores these ideas and hypotheses, but results are varied: some demonstrate pre-pubescent children acquire language easily, and some that older learners have the advantage, whilst others focus on existence of a CP for SLA. Recent studies (e.g. Mayberry and Lock, 2003) have recognised certain aspects of SLA may be affected by age, whilst others remain intact. The objective of this study is to investigate whether capacity for vocabulary acquisition decreases with age.

Other work has challenged the biological approach; Krashen (1975) re-analysed clinical data used as evidence and concluded cerebral specialisation occurs much earlier than Lenneberg calculated. Therefore, if a CP exists, it does not coincide with lateralisation. Despite concerns with Lenneberg’s original evidence and the dissociation of lateralisation from the language CP idea, however, the concept of a CP remains a viable hypothesis, which later work has better explained and substantiated.

Effects of aging

A review of SLA theories and their explanations for age-related differences is necessary before considering empirical studies. The most reductionist theories are those of Penfield and Roberts (1959) and Lenneberg (1967), which stem from L1 and brain damage studies; children who suffer impairment before puberty typically recover and (re-)develop normal language, whereas adults rarely recover fully, and often do not regain verbal abilities beyond the point reached five months after impairment. Both theories agree that children have a neurological advantage in learning languages, and that puberty correlates with a turning point in ability. They assert that language acquisition occurs primarily, possibly exclusively, during childhood as the brain loses plasticity after a certain age. It then becomes rigid and fixed, and loses the ability for adaptation and reorganisation, rendering language (re-)learning difficult. Penfield and Roberts (1959) claim children under nine can learn up to three languages: early exposure to different languages activates a reflex in the brain allowing them to switch between languages without confusion or translation into L1 (Penfield, 1964). Lenneberg (1967) asserts that if no language is learned by puberty, it cannot be learned in a normal, functional sense. He also supports Penfield and Roberts’ (1959) proposal of neurological mechanisms responsible for maturational change in language learning abilities. This, Lenneberg maintains, coincides with brain lateralisation and left-hemispherical specialisation for language around age thirteen: infants’ motor and linguistic skills develop simultaneously, but by age thirteen the cerebral hemispheres’ functions separate and become set, making language acquisition extremely difficult (Lenneberg, 1967).

Deaf and feral children

Cases of deaf and feral children provide evidence for a biologically determined CP for L1. Feral children are those not exposed to language in infancy/childhood due to being brought up in the wild, in isolation and/or confinement. A classic example is ‘Genie’, who was deprived of social interaction from birth until discovered aged thirteen (post-pubescent). She was completely without language, and after seven years of rehabilitation still lacked linguistic competence. Another case is ‘Isabelle’, who was incarcerated with her deaf-mute mother until the age of six and a half (pre-pubescent). She also had no language skills, but, unlike Genie, quickly acquired normal language abilities through systematic specialist training.

Such studies are however problematic; isolation can result in general retardation and emotional disturbances, which may confound conclusions drawn about language abilities. Studies of deaf children learning American Sign Language (ASL) have fewer methodological weaknesses. Newport and Supalla (1987) studied ASL acquisition in deaf children differing in age of exposure; few were exposed to ASL from birth, most of them first learned it at school.

Results showed a linear decline in performance with increasing age of exposure; those exposed to ASL from birth performed best, and ‘late learners’ worst, on all production and comprehension tests. Their study thus provides direct evidence for language learning ability decreasing with age, but it does not add to Lennerberg’s CP hypothesis as even the oldest children, the ‘late learners’, were exposed to ASL by age four, and had therefore not reached puberty, the proposed end of the CP. In addition, the declines were shown to be linear, with no sudden ‘drop off’ of ability at a certain age, as would be predicted by a strong CP hypothesis. That the children performed significantly worse, however, suggests the CP may end earlier than originally postulated.

Behavioural approaches

Contrary to biological views, behavioural approaches assert that languages are learned as any other behaviour, through conditioning. Skinner (1957) details how operant conditioning forms connections with the environment through interaction and, alongside O. Hobart Mowrer (1960), applies the ideas to language acquisition. Mowrer hypothesises that languages are acquired through rewarded imitation of ‘language models’; the model must have an emotional link to the learner (e.g. parent, spouse), as imitation then brings pleasant feelings which function as positive reinforcement. Because new connections between behaviour and the environment are formed and reformed throughout life, it is possible to gain new skills, including language(s), at any age.

To accommodate observed language learning differences between children and adults, Felix (1985) describes that children, whose brains create countless new connections daily, may handle the language learning process more effectively than do adults. This assumption, however, remains untested and is not a reliable explanation for children’s aptitude for L2 learning. Problematic of the behaviourist approach is its assumption that all learning, verbal and non-verbal, occurs through the same processes. A more general problem is that, as Pinker (1995) notes, almost every sentence anybody voices is an original combination of words, never previously uttered, therefore a language cannot consist only of word combinations learned through repetition and conditioning; the brain must contain innate means of creating endless amounts of grammatical sentences from a limited vocabulary. This is precisely what Chomsky (1965) argues with his proposition of a Universal Grammar (UG).

Universal Grammar

Chomsky (1965) asserts that environmental factors must be relatively unimportant for language emergence, as so many different factors surround children acquiring L1. Instead, Chomsky claims language learners possess innate principles building a ‘language acquisition device’ (LAD) in the brain. These principles denote restricted possibilities for variation within the language, and enable learners to construct a grammar out of ‘raw input’ collected from the environment. Input alone cannot explain language acquisition because it is degenerated by characteristic features such as stutters, and lacks corrections from which learners discover incorrect variations.

Singleton and Newport (2004) demonstrate the function of UG in their study of ‘Simon’. Simon learned ASL as his L1 from parents who had learned it as an L2 after puberty and provided him with imperfect models. Results showed Simon learned normal and logical rules and was able to construct an organised linguistic system, despite being exposed to inconsistent input. Chomsky developed UG to explain L1 acquisition data, but maintains it also applies to L2 learners who achieve near-native fluency not attributable solely to input and interaction (Chomsky, 1965).

Although it does not describe an optimal age for SLA, the theory implies that younger children can learn languages more easily than older learners, as adults must reactivate principles developed during L1 learning and forge an SLA path: children can learn several languages simultaneously as long as the principles are still active and they are exposed to sufficient language samples (Pinker, 1995). The parents of Singleton and Newport’s (2004) patient also had linguistic abilities in line with these age-related predictions; they learned ASL after puberty and never reached complete fluency.

Problems within UG Theory for L2 acquisition

There are, however, problems with the extrapolation of the UG theory to SLA: L2 learners go through several phases of types of utterance that are not similar to their L1 or the L2 they hear. Other factors include the cognitive maturity of most L2 learners, that they have different motivation for learning the language, and already speak one language fluently. Other studies also highlight these problems: Dehaene (1999) investigates how cerebral circuits used to handling one language adapt for the efficient storage of two or more. He reports observations of cerebral activation when reading and translating two languages. They found the most activated brain areas during the tasks were not those generally associated with language, but rather those related to mapping orthography to phonology. They conclude that the left temporal lobe is the physical base of L1, but the L2 is ‘stored’ elsewhere, thus explaining cases of bilingual aphasia where one language remains intact. They maintain that only languages learned simultaneously from birth are represented, and cause activity, in the left hemisphere: any L2 learned later is stored separately (possibly in the right hemisphere), and rarely activates the left temporal lobe.

This suggests that L2 may be qualitatively different from L1 due to its dissociation from the ‘normal’ language brain regions, thus the extrapolation of L1 studies and theories to SLA is placed in question. A further disadvantage of UG is that supporting empirical data are taken from a limited sample of syntactic phenomena: a general theory of language acquisition should cover a larger range of phenomena. Despite these problems, several other theorists have based their own models of language learning on it; amongst others Felix’ (1985) ‘competing cognitive systems’ idea. These ideas are supported by empirical evidence, which consequently supports Chomsky’s ideas. Due to this support and its descriptive and explanatory strength, many theorists regard UG as the best explanation of language, and particularly grammar, acquisition.

UG and the critical period hypothesis

A key question about the relationship of UG and SLA is: is the language acquisition device posited by Chomsky and his followers still accessible to learners of a second language? Research suggests that it becomes inaccessible at a certain age (see Critical Period Hypothesis), and learners increasingly depended on explicit teaching (see pedagogical effects above, and age below). In other words, although all of language may be governed by UG, older learners might have great difficulty in gaining access to the target language’s underlying rules from positive input alone.

Piaget (1926) is one psychologist reluctant to ascribe specific innate linguistic abilities to children: he considers the brain a homogeneous computational system, with language acquisition being one part of general learning. He agrees this development may be innate, but claims there is no specific language acquisition module in the brain. Instead, he suggests external influences and social interaction trigger language acquisition: information collected from these sources constructs symbolic and functional schemata (thought or behaviour patterns). According to Piaget, cognitive development and language acquisition are life-long active processes that constantly update and re-organise schemata. He proposes children develop L1 as they build a sense of identity in reference to the environment, and describes phases of general cognitive development, with processes and patterns changing systematically with age. Piaget assumes language acquisition is part of this complex cognitive development, and that these developmental phases are the basis for an optimal period for language acquisition in childhood. Interactionist approaches derived from Piaget’s ideas supports his theory. Some studies (e.g. Newport and Supalla, 1987) show that, rather than abrupt changes in SLA ability after puberty, language ability declines with age, coinciding with declines in other cognitive abilities, thus supporting Piaget.

Several researchers, however, remain unconvinced that language acquisition is part of general development: Felix (1985) claims cognitive abilities alone are useless for language learning, as only vocabulary and meaning are connected to cognition; lexicology and related meanings have conceptual bases. Felix’ criticism of the assumption that L2 fluency simply requires skilful applications of the correct rules is supported by the lack of psychological empirical evidence for Piaget’s idea.

Although Krashen (1975) also criticises this theory, neither he nor Felix discredit the importance of age for second language acquisition. Krashen (1975), and later Felix (1985), proposed theories for the close of the CP for L2 at puberty, based on Piaget’s cognitive stage of formal operations beginning at puberty, as the ‘ability of the formal operational thinker to construct abstract hypotheses to explain phenomena’ inhibits the individual’s natural ability for language learning.

The term “language acquisition” became commonly used after Stephen Krashen contrasted it with formal and non-constructive “learning.” Today, most scholars use “language learning” and “language acquisition” interchangeably, unless they are directly addressing Krashen’s work. However, “second language acquisition” or “SLA” has become established as the preferred term for this academic discipline.

Though SLA is often viewed as part of applied linguistics, it is typically concerned with the language system and learning processes themselves, whereas applied linguistics may focus more on the experiences of the learner, particularly in the classroom. Additionally, SLA has mostly examined naturalistic acquisition, where learners acquire a language with little formal training or teaching.

Other directions of research

Impact of illiteracy

Virtually all research findings on SLA to date build on data from literate learners. Tarone, Bigelow and Hansen (2009) find significantly different results when replicating standard SLA studies with low literate L2 learners. Specifically, learners with lower alphabetic literacy levels are significantly less likely to notice corrective feedback on form or to perform elicited imitation tasks accurately. These findings are consistent with research in cognitive psychology showing significant differences in phonological awareness between literate and illiterate adults (Reis and Castro-Caldas 1997; Castro-Caldas et al. 1998). An important direction for SLA research must therefore involve the exploration of the impact of alphabetic literacy on cognitive processing in second language acquisition.

Empirical research has attempted to account for variables detailed by SLA theories and provide an insight into L2 learning processes, which can be applied in educational environments. Recent SLA investigations have followed two main directions: one focuses on pairings of L1 and L2 that render L2 acquisition particularly difficult, and the other investigates certain aspects of language that may be maturationally constrained. Flege, Mackay and Piske (2002) looked at bilingual dominance to evaluate two explanations of L2 performance differences between bilinguals and monolingual-L2 speakers, i.e. a maturationally defined CP or interlingual interference.

Bilingual dominance

Flege, Mackay and Piske investigated whether the age at which participants learned English affected dominance in Italian-English bilinguals, and found the early bilinguals were English (L2) dominant and the late bilinguals Italian (L1) dominant. Further analysis showed that dominant Italian bilinguals had detectable foreign accents when speaking English, but early bilinguals (English dominant) had no accents in either language. This suggests that, though interlingual interference effects are not inevitable, their emergence, and bilingual dominance, may be related to a CP.

Sebastián-Gallés, Echeverría and Bosch (2005) also studied bilinguals and highlight the importance of early language exposure. They looked at vocabulary processing and representation in Spanish-Catalan bilinguals exposed to both languages simultaneously from birth in comparison to those who had learned L2 later and were either Spanish- or Catalan-dominant. Findings showed ‘from birth bilinguals’ had significantly more difficulty distinguishing Catalan words from non-words differing in specific vowels than Catalan-dominants did (measured by reaction time).

These difficulties are attributed to a phase around age eight months where bilingual infants are insensitive to vowel contrasts, despite the language they hear most. This affects how words are later represented in their lexicons, highlighting this as a decisive period in language acquisition and showing that initial language exposure shapes linguistic processing for life. Sebastián-Gallés et al. (2005) also indicate the significance of phonology for L2 learning; they believe learning an L2 once the L1 phonology is already internalised can reduce individuals’ abilities to distinguish new sounds that appear in the L2.

Age effects on grammar learning

Most studies into age effects on specific aspects of SLA have focused on grammar, with the common conclusion that it is highly constrained by age, more so than semantic functioning. B. Harley (1986) compared attainment of French learners in early and late immersion programs. She reports that after 1000 exposure hours, late learners had better control of French verb systems and syntax. However, comparing early immersion students (average age 6.917 years) with age-matched native speakers identified common problem areas, including third person plurals and polite ‘vous’ forms. This suggests grammar (in L1 or L2) is generally acquired later, possibly because it requires abstract cognition and reasoning (B. Harley, 1986).

B. Harley also measured eventual attainment and found the two age groups made similar mistakes in syntax and lexical selection, often confusing French with the L1. The general conclusion from these investigations is that different aged learners acquire the various aspects of language with varying difficulty. Some variation in grammatical performance is attributed to maturation (discussed in B. Harley, 1986), however, all participants began immersion programs before puberty and so were too young for a strong critical period hypothesis to be directly tested.

This corresponds to Noam Chomsky’s UG theory, which states that while language acquisition principles are still active, it is easy to learn a language, and the principles developed through L1 acquisition are vital for learning an L2.

Scherag, Demuth, Rösler, Neville and Röder (2004) also suggest learning some syntactic processing functions and lexical access may be limited by maturation, whereas semantic functions are relatively unaffected by age. They studied the effect of late SLA on speech comprehension by German immigrants to the U.S.A. and American immigrants to Germany. They found that native-English speakers who learned German as adults were disadvantaged on certain grammatical tasks but performed at near-native levels on lexical tasks. These findings are consistent with work by Hahne (2001, cited in Scherag et al., 2004).

Semantic functions acquisition

One study that specifically mentions semantic functions acquisition is that of Weber-Fox and Neville (1996). Their results showed that Chinese-English bilinguals who had been exposed to English after puberty, learned vocabulary to a higher competence level than syntactic aspects of language. They do, however, report that the judgment accuracies in detecting semantic anomalies were altered in subjects who were exposed to English after sixteen years of age, but were affected to a lesser degree than were grammatical aspects of language. It has been speculated (Neville and Bavelier, 2001, and Scherag et al., 2004) that semantic aspects of language are founded on associative learning mechanisms, which allow life-long learning, whereas syntactical aspects are based on computational mechanisms, which can only be constructed during certain age periods. Consequently, it is reasoned, semantic functions are easier to access during comprehension of an L2 and therefore dominate the process: if these are ambiguous, understanding of syntactic information is not facilitated. These suppositions would help explain the results of Scherag et al.’s (2004) study.

Advantages of bilingual education for children

It is commonly believed that children are better suited to learn a second language than are adults. However, general second language research has failed to support the critical period hypothesis in its strong form (i.e., the claim that full language acquisition is impossible beyond a certain age). According to Linda M. Espinosa, especially in the United States the number of children growing up with a home language that is not English but Spanish is constantly increasing. Therefore these children have to learn the English language before kindergarten as a second language. It is better to dispose young children to maintain both, their home language and their second language. Cultivating his home language, the child creates his own cultural identity and becomes aware of his roots. This fact leads to the question whether having the ability to speak two languages helps or harms young children. Research shows that the acquisition of a second language in early childhood confers several advantages, especially a greater awareness of linguistic structures. Furthermore it is advantageous for young children to grow up bilingually because they do not need to be taught systematically but learn languages intuitively. How fast a child can learn a language depends on several personal factors, such as interest and motivation, and its learning environment. Communication should be facilitated rather than a child should be forced to learn a language with strict rules. Education in early childhood can lead to an effective educational achievement for children from various cultural environments.

Another aspect that is worth considering is that bilingual children are often doing code switching which does not mean that the child is not able to separate the languages. The reason for code switching is the child’s lack of vocabulary in a certain situation. The acquisition of a second language in early childhood broadens the children’s minds and enriches them more than it harms them. Thus they are not only able to speak two languages in spite of being very young but they also acquire knowledge about the different cultures and environments. It is possible that one language can dominate. This depends on how much time is spent on learning each language.

Evolutionary Explanations for the Critical Period in First and Second Language Acquisition

Hurford’s Model

In order to provide evidence for the evolutionary functionality of the critical period in language acquisition, Hurford (1991) generated a computer simulation of plausible conditions of evolving generations, based on three central assumptions:

• Language is an evolutionary adaptation that is naturally selected for.
• Any given individual’s language can be quantified or measured.
• Various aspects of maturation and development are under genetic control, which would extend to determine the timing for critical periods for certain capacities (i.e. polygenic inheritance).

According to Hurford’s evolutionary model, language acquisition is an adaptation that has survival value for humans, and that knowing a language correlated positively with an individual’s reproductive advantage. This finding is in line with views of other researchers such as Chomsky (1982) and Pinker & Bloom (1990). For example, Steven Pinker and Paul Bloom argue that due to the fact that language is a complex design that serves a specific function that cannot be replaced by any other existing capacity, the trait of language acquisition can be attributed to natural selection.

However, while arguing that language itself is adaptive and “did not ‘just happen’” (p.172), Hurford suggests that the critical period is not an adaptation, but rather a constraint on language that emerged due to a lack of selection pressures that reinforce acquiring more than one language. In other words, Hurford explains the existence of a critical period with genetic drift, the idea that when there are no selection pressures on multiple alleles acting on the same trait, one of the alleles will gradually diminish through evolution. Because the simulation reveals no evolutionary advantage of acquiring more than one language, Hurford suggests that the critical period evolved simply as a result of a lack of selection pressure.

Komarova and Nowak’s Dynamical System

Komarova and Nowak (2001) supported Hurford’s model, yet pointed out that it was limited in the sense that it did not take into account the costs of learning a language. Therefore, they created their own algorithmic model, with the following assumptions:

• Language ability correlates with an individual’s reproductive fitness
• The ability to learn language is inherited
• There are costs to learning a language

Their model consists of a population with constant size, where language ability is a predictor of reproductive fitness. The learning mechanism in their model is based on Chomsky’s (1980, 1993) language acquisition device (LAD) and the notion of universal grammar. The results of their model show that the critical period for language acquisition is an “evolutionarily stable strategy (ESS)” (Komarova & Nowak, 2001, p. 1190). They suggest that this ESS is due to two competing selection pressures. First, if the period for learning is short, language does not develop as well, and thus decreases the evolutionary fitness of the individual. Alternatively, if the period for learning language is long, it becomes too costly to the extent that it reduces reproductive opportunity for the individual, and therefore limits reproductive fitness. Therefore, the critical period is an adaptive mechanism that keeps these pressures at equilibrium, and aims at optimal reproductive success for the individual.

What Is the Critical Period Hypothesis?

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The critical period hypothesis is a theory in the study of language acquisition which posits that there is a critical period of time in which the human mind can most easily acquire language. This idea is often considered with regard to primary language acquisition, and those who agree with this hypothesis argue that language must be learned in the first few years of life or else the ability to acquire language is greatly hindered. The critical period hypothesis is also used in secondary language acquisition, regarding the idea of a time period in which a secondary language can be most easily acquired.

With regard to primary language acquisition, which refers to the process by which a person learns his or her first language , the critical period hypothesis is quite dramatic. This idea indicates that a person has only a set period of time in which he or she can learn a first language, usually the first three to ten years of development. During this time, language can be learned and acquired through exposure to language; simply hearing others talking on an ongoing and regular basis is sufficient. Once this time period is over, however, those who agree with the critical period hypothesis argue that primary language acquisition may be impossible or greatly impaired.

There is a great deal of research into human brain development that supports this hypothesis, but it is still difficult to prove. One of the only conclusive ways to prove this hypothesis would be to have a person isolated from infancy until about the age of ten, without exposure to human speech. Such upbringing would be unthinkable, however, so this type of experiment cannot be conducted and the hypothesis remains largely unproven.

Unfortunate situations in which a child has been abused and isolated by his or her caregivers have provided opportunities to support the critical period hypothesis. In at least one instance, medical care and study of the child did demonstrate that full language acquisition was nearly impossible. Though this occurrence did support the hypothesis, secondary factors such as possible brain damage make the evidence flawed.

The critical period hypothesis is also frequently applied to secondary language acquisition, though in a somewhat less dramatic way. With regard to secondary language, many linguists and speech therapists agree that a second language can be acquired more easily when someone is young. Studies of the brain indicate that in youth the brain is still developing more quickly and new linguistic information can be processed and incorporated into the brain more easily. Once this period is over, however, secondary language acquisition is still certainly possible, though it can be more difficult.

• https://www.pbs.org/wgbh/nova/transcripts/2112gchild.html

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Research Article

The Critical Period Hypothesis in Second Language Acquisition: A Statistical Critique and a Reanalysis

* E-mail: [email protected]

Affiliation Department of Multilingualism, University of Fribourg, Fribourg, Switzerland

• Jan Vanhove

• Published: July 25, 2013
• https://doi.org/10.1371/journal.pone.0069172
• Reader Comments

17 Jul 2014: The PLOS ONE Staff (2014) Correction: The Critical Period Hypothesis in Second Language Acquisition: A Statistical Critique and a Reanalysis. PLOS ONE 9(7): e102922. https://doi.org/10.1371/journal.pone.0102922 View correction

In second language acquisition research, the critical period hypothesis ( cph ) holds that the function between learners' age and their susceptibility to second language input is non-linear. This paper revisits the indistinctness found in the literature with regard to this hypothesis's scope and predictions. Even when its scope is clearly delineated and its predictions are spelt out, however, empirical studies–with few exceptions–use analytical (statistical) tools that are irrelevant with respect to the predictions made. This paper discusses statistical fallacies common in cph research and illustrates an alternative analytical method (piecewise regression) by means of a reanalysis of two datasets from a 2010 paper purporting to have found cross-linguistic evidence in favour of the cph . This reanalysis reveals that the specific age patterns predicted by the cph are not cross-linguistically robust. Applying the principle of parsimony, it is concluded that age patterns in second language acquisition are not governed by a critical period. To conclude, this paper highlights the role of confirmation bias in the scientific enterprise and appeals to second language acquisition researchers to reanalyse their old datasets using the methods discussed in this paper. The data and R commands that were used for the reanalysis are provided as supplementary materials.

Citation: Vanhove J (2013) The Critical Period Hypothesis in Second Language Acquisition: A Statistical Critique and a Reanalysis. PLoS ONE 8(7): e69172. https://doi.org/10.1371/journal.pone.0069172

Editor: Stephanie Ann White, UCLA, United States of America

Received: May 7, 2013; Accepted: June 7, 2013; Published: July 25, 2013

Copyright: © 2013 Jan Vanhove. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Funding: No current external funding sources for this study.

Competing interests: The author has declared that no competing interests exist.

Introduction

In the long term and in immersion contexts, second-language (L2) learners starting acquisition early in life – and staying exposed to input and thus learning over several years or decades – undisputedly tend to outperform later learners. Apart from being misinterpreted as an argument in favour of early foreign language instruction, which takes place in wholly different circumstances, this general age effect is also sometimes taken as evidence for a so-called ‘critical period’ ( cp ) for second-language acquisition ( sla ). Derived from biology, the cp concept was famously introduced into the field of language acquisition by Penfield and Roberts in 1959 [1] and was refined by Lenneberg eight years later [2] . Lenneberg argued that language acquisition needed to take place between age two and puberty – a period which he believed to coincide with the lateralisation process of the brain. (More recent neurological research suggests that different time frames exist for the lateralisation process of different language functions. Most, however, close before puberty [3] .) However, Lenneberg mostly drew on findings pertaining to first language development in deaf children, feral children or children with serious cognitive impairments in order to back up his claims. For him, the critical period concept was concerned with the implicit “automatic acquisition” [2, p. 176] in immersion contexts and does not preclude the possibility of learning a foreign language after puberty, albeit with much conscious effort and typically less success.

sla research adopted the critical period hypothesis ( cph ) and applied it to second and foreign language learning, resulting in a host of studies. In its most general version, the cph for sla states that the ‘susceptibility’ or ‘sensitivity’ to language input varies as a function of age, with adult L2 learners being less susceptible to input than child L2 learners. Importantly, the age–susceptibility function is hypothesised to be non-linear. Moving beyond this general version, we find that the cph is conceptualised in a multitude of ways [4] . This state of affairs requires scholars to make explicit their theoretical stance and assumptions [5] , but has the obvious downside that critical findings risk being mitigated as posing a problem to only one aspect of one particular conceptualisation of the cph , whereas other conceptualisations remain unscathed. This overall vagueness concerns two areas in particular, viz. the delineation of the cph 's scope and the formulation of testable predictions. Delineating the scope and formulating falsifiable predictions are, needless to say, fundamental stages in the scientific evaluation of any hypothesis or theory, but the lack of scholarly consensus on these points seems to be particularly pronounced in the case of the cph . This article therefore first presents a brief overview of differing views on these two stages. Then, once the scope of their cph version has been duly identified and empirical data have been collected using solid methods, it is essential that researchers analyse the data patterns soundly in order to assess the predictions made and that they draw justifiable conclusions from the results. As I will argue in great detail, however, the statistical analysis of data patterns as well as their interpretation in cph research – and this includes both critical and supportive studies and overviews – leaves a great deal to be desired. Reanalysing data from a recent cph -supportive study, I illustrate some common statistical fallacies in cph research and demonstrate how one particular cph prediction can be evaluated.

Delineating the scope of the critical period hypothesis

First, the age span for a putative critical period for language acquisition has been delimited in different ways in the literature [4] . Lenneberg's critical period stretched from two years of age to puberty (which he posits at about 14 years of age) [2] , whereas other scholars have drawn the cutoff point at 12, 15, 16 or 18 years of age [6] . Unlike Lenneberg, most researchers today do not define a starting age for the critical period for language learning. Some, however, consider the possibility of the critical period (or a critical period for a specific language area, e.g. phonology) ending much earlier than puberty (e.g. age 9 years [1] , or as early as 12 months in the case of phonology [7] ).

Second, some vagueness remains as to the setting that is relevant to the cph . Does the critical period constrain implicit learning processes only, i.e. only the untutored language acquisition in immersion contexts or does it also apply to (at least partly) instructed learning? Most researchers agree on the former [8] , but much research has included subjects who have had at least some instruction in the L2.

Third, there is no consensus on what the scope of the cp is as far as the areas of language that are concerned. Most researchers agree that a cp is most likely to constrain the acquisition of pronunciation and grammar and, consequently, these are the areas primarily looked into in studies on the cph [9] . Some researchers have also tried to define distinguishable cp s for the different language areas of phonetics, morphology and syntax and even for lexis (see [10] for an overview).

Fourth and last, research into the cph has focused on ‘ultimate attainment’ ( ua ) or the ‘final’ state of L2 proficiency rather than on the rate of learning. From research into the rate of acquisition (e.g. [11] – [13] ), it has become clear that the cph cannot hold for the rate variable. In fact, it has been observed that adult learners proceed faster than child learners at the beginning stages of L2 acquisition. Though theoretical reasons for excluding the rate can be posited (the initial faster rate of learning in adults may be the result of more conscious cognitive strategies rather than to less conscious implicit learning, for instance), rate of learning might from a different perspective also be considered an indicator of ‘susceptibility’ or ‘sensitivity’ to language input. Nevertheless, contemporary sla scholars generally seem to concur that ua and not rate of learning is the dependent variable of primary interest in cph research. These and further scope delineation problems relevant to cph research are discussed in more detail by, among others, Birdsong [9] , DeKeyser and Larson-Hall [14] , Long [10] and Muñoz and Singleton [6] .

Formulating testable hypotheses

Once the relevant cph 's scope has satisfactorily been identified, clear and testable predictions need to be drawn from it. At this stage, the lack of consensus on what the consequences or the actual observable outcome of a cp would have to look like becomes evident. As touched upon earlier, cph research is interested in the end state or ‘ultimate attainment’ ( ua ) in L2 acquisition because this “determines the upper limits of L2 attainment” [9, p. 10]. The range of possible ultimate attainment states thus helps researchers to explore the potential maximum outcome of L2 proficiency before and after the putative critical period.

One strong prediction made by some cph exponents holds that post- cp learners cannot reach native-like L2 competences. Identifying a single native-like post- cp L2 learner would then suffice to falsify all cph s making this prediction. Assessing this prediction is difficult, however, since it is not clear what exactly constitutes sufficient nativelikeness, as illustrated by the discussion on the actual nativelikeness of highly accomplished L2 speakers [15] , [16] . Indeed, there exists a real danger that, in a quest to vindicate the cph , scholars set the bar for L2 learners to match monolinguals increasingly higher – up to Swiftian extremes. Furthermore, the usefulness of comparing the linguistic performance in mono- and bilinguals has been called into question [6] , [17] , [18] . Put simply, the linguistic repertoires of mono- and bilinguals differ by definition and differences in the behavioural outcome will necessarily be found, if only one digs deep enough.

A second strong prediction made by cph proponents is that the function linking age of acquisition and ultimate attainment will not be linear throughout the whole lifespan. Before discussing how this function would have to look like in order for it to constitute cph -consistent evidence, I point out that the ultimate attainment variable can essentially be considered a cumulative measure dependent on the actual variable of interest in cph research, i.e. susceptibility to language input, as well as on such other factors like duration and intensity of learning (within and outside a putative cp ) and possibly a number of other influencing factors. To elaborate, the behavioural outcome, i.e. ultimate attainment, can be assumed to be integrative to the susceptibility function, as Newport [19] correctly points out. Other things being equal, ultimate attainment will therefore decrease as susceptibility decreases. However, decreasing ultimate attainment levels in and by themselves represent no compelling evidence in favour of a cph . The form of the integrative curve must therefore be predicted clearly from the susceptibility function. Additionally, the age of acquisition–ultimate attainment function can take just about any form when other things are not equal, e.g. duration of learning (Does learning last up until time of testing or only for a more or less constant number of years or is it dependent on age itself?) or intensity of learning (Do learners always learn at their maximum susceptibility level or does this intensity vary as a function of age, duration, present attainment and motivation?). The integral of the susceptibility function could therefore be of virtually unlimited complexity and its parameters could be adjusted to fit any age of acquisition–ultimate attainment pattern. It seems therefore astonishing that the distinction between level of sensitivity to language input and level of ultimate attainment is rarely made in the literature. Implicitly or explicitly [20] , the two are more or less equated and the same mathematical functions are expected to describe the two variables if observed across a range of starting ages of acquisition.

But even when the susceptibility and ultimate attainment variables are equated, there remains controversy as to what function linking age of onset of acquisition and ultimate attainment would actually constitute evidence for a critical period. Most scholars agree that not any kind of age effect constitutes such evidence. More specifically, the age of acquisition–ultimate attainment function would need to be different before and after the end of the cp [9] . According to Birdsong [9] , three basic possible patterns proposed in the literature meet this condition. These patterns are presented in Figure 1 . The first pattern describes a steep decline of the age of onset of acquisition ( aoa )–ultimate attainment ( ua ) function up to the end of the cp and a practically non-existent age effect thereafter. Pattern 2 is an “unconventional, although often implicitly invoked” [9, p. 17] notion of the cp function which contains a period of peak attainment (or performance at ceiling), i.e. performance does not vary as a function of age, which is often referred to as a ‘window of opportunity’. This time span is followed by an unbounded decline in ua depending on aoa . Pattern 3 includes characteristics of patterns 1 and 2. At the beginning of the aoa range, performance is at ceiling. The next segment is a downward slope in the age function which ends when performance reaches its floor. Birdsong points out that all of these patterns have been reported in the literature. On closer inspection, however, he concludes that the most convincing function describing these age effects is a simple linear one. Hakuta et al. [21] sketch further theoretically possible predictions of the cph in which the mean performance drops drastically and/or the slope of the aoa – ua proficiency function changes at a certain point.

• PPT PowerPoint slide
• PNG larger image
• TIFF original image

The graphs are based on based on Figure 2 in [9] .

https://doi.org/10.1371/journal.pone.0069172.g001

Although several patterns have been proposed in the literature, it bears pointing out that the most common explicit prediction corresponds to Birdsong's first pattern, as exemplified by the following crystal-clear statement by DeKeyser, one of the foremost cph proponents:

[A] strong negative correlation between age of acquisition and ultimate attainment throughout the lifespan (or even from birth through middle age), the only age effect documented in many earlier studies, is not evidence for a critical period…[T]he critical period concept implies a break in the AoA–proficiency function, i.e., an age (somewhat variable from individual to individual, of course, and therefore an age range in the aggregate) after which the decline of success rate in one or more areas of language is much less pronounced and/or clearly due to different reasons. [22, p. 445].

DeKeyser and before him among others Johnson and Newport [23] thus conceptualise only one possible pattern which would speak in favour of a critical period: a clear negative age effect before the end of the critical period and a much weaker (if any) negative correlation between age and ultimate attainment after it. This ‘flattened slope’ prediction has the virtue of being much more tangible than the ‘potential nativelikeness’ prediction: Testing it does not necessarily require comparing the L2-learners to a native control group and thus effectively comparing apples and oranges. Rather, L2-learners with different aoa s can be compared amongst themselves without the need to categorise them by means of a native-speaker yardstick, the validity of which is inevitably going to be controversial [15] . In what follows, I will concern myself solely with the ‘flattened slope’ prediction, arguing that, despite its clarity of formulation, cph research has generally used analytical methods that are irrelevant for the purposes of actually testing it.

Inferring non-linearities in critical period research: An overview

Group mean or proportion comparisons.

[T]he main differences can be found between the native group and all other groups – including the earliest learner group – and between the adolescence group and all other groups. However, neither the difference between the two childhood groups nor the one between the two adulthood groups reached significance, which indicates that the major changes in eventual perceived nativelikeness of L2 learners can be associated with adolescence. [15, p. 270].

Similar group comparisons aimed at investigating the effect of aoa on ua have been carried out by both cph advocates and sceptics (among whom Bialystok and Miller [25, pp. 136–139], Birdsong and Molis [26, p. 240], Flege [27, pp. 120–121], Flege et al. [28, pp. 85–86], Johnson [29, p. 229], Johnson and Newport [23, p. 78], McDonald [30, pp. 408–410] and Patowski [31, pp. 456–458]). To be clear, not all of these authors drew direct conclusions about the aoa – ua function on the basis of these groups comparisons, but their group comparisons have been cited as indicative of a cph -consistent non-continuous age effect, as exemplified by the following quote by DeKeyser [22] :

Where group comparisons are made, younger learners always do significantly better than the older learners. The behavioral evidence, then, suggests a non-continuous age effect with a “bend” in the AoA–proficiency function somewhere between ages 12 and 16. [22, p. 448].

The first problem with group comparisons like these and drawing inferences on the basis thereof is that they require that a continuous variable, aoa , be split up into discrete bins. More often than not, the boundaries between these bins are drawn in an arbitrary fashion, but what is more troublesome is the loss of information and statistical power that such discretisation entails (see [32] for the extreme case of dichotomisation). If we want to find out more about the relationship between aoa and ua , why throw away most of the aoa information and effectively reduce the ua data to group means and the variance in those groups?

Comparison of correlation coefficients.

Correlation-based inferences about slope discontinuities have similarly explicitly been made by cph advocates and skeptics alike, e.g. Bialystok and Miller [25, pp. 136 and 140], DeKeyser and colleagues [22] , [44] and Flege et al. [45, pp. 166 and 169]. Others did not explicitly infer the presence or absence of slope differences from the subset correlations they computed (among others Birdsong and Molis [26] , DeKeyser [8] , Flege et al. [28] and Johnson [29] ), but their studies nevertheless featured in overviews discussing discontinuities [14] , [22] . Indeed, the most recent overview draws a strong conclusion about the validity of the cph 's ‘flattened slope’ prediction on the basis of these subset correlations:

In those studies where the two groups are described separately, the correlation is much higher for the younger than for the older group, except in Birdsong and Molis (2001) [ =  [26] , JV], where there was a ceiling effect for the younger group. This global picture from more than a dozen studies provides support for the non-continuity of the decline in the AoA–proficiency function, which all researchers agree is a hallmark of a critical period phenomenon. [22, p. 448].

In Johnson and Newport's specific case [23] , their correlation-based inference that ua levels off after puberty happened to be largely correct: the gjt scores are more or less randomly distributed around a near-horizontal trend line [26] . Ultimately, however, it rests on the fallacy of confusing correlation coefficients with slopes, which seriously calls into question conclusions such as DeKeyser's (cf. the quote above).

https://doi.org/10.1371/journal.pone.0069172.g002

Lower correlation coefficients in older aoa groups may therefore be largely due to differences in ua variance, which have been reported in several studies [23] , [26] , [28] , [29] (see [46] for additional references). Greater variability in ua with increasing age is likely due to factors other than age proper [47] , such as the concomitant greater variability in exposure to literacy, degree of education, motivation and opportunity for language use, and by itself represents evidence neither in favour of nor against the cph .

Regression approaches.

Having demonstrated that neither group mean or proportion comparisons nor correlation coefficient comparisons can directly address the ‘flattened slope’ prediction, I now turn to the studies in which regression models were computed with aoa as a predictor variable and ua as the outcome variable. Once again, this category of studies is not mutually exclusive with the two categories discussed above.

In a large-scale study using self-reports and approximate aoa s derived from a sample of the 1990 U.S. Census, Stevens found that the probability with which immigrants from various countries stated that they spoke English ‘very well’ decreased curvilinearly as a function of aoa [48] . She noted that this development is similar to the pattern found by Johnson and Newport [23] but that it contains no indication of an “abruptly defined ‘critical’ or sensitive period in L2 learning” [48, p. 569]. However, she modelled the self-ratings using an ordinal logistic regression model in which the aoa variable was logarithmically transformed. Technically, this is perfectly fine, but one should be careful not to read too much into the non-linear curves found. In logistic models, the outcome variable itself is modelled linearly as a function of the predictor variables and is expressed in log-odds. In order to compute the corresponding probabilities, these log-odds are transformed using the logistic function. Consequently, even if the model is specified linearly, the predicted probabilities will not lie on a perfectly straight line when plotted as a function of any one continuous predictor variable. Similarly, when the predictor variable is first logarithmically transformed and then used to linearly predict an outcome variable, the function linking the predicted outcome variables and the untransformed predictor variable is necessarily non-linear. Thus, non-linearities follow naturally from Stevens's model specifications. Moreover, cph -consistent discontinuities in the aoa – ua function cannot be found using her model specifications as they did not contain any parameters allowing for this.

Using data similar to Stevens's, Bialystok and Hakuta found that the link between the self-rated English competences of Chinese- and Spanish-speaking immigrants and their aoa could be described by a straight line [49] . In contrast to Stevens, Bialystok and Hakuta used a regression-based method allowing for changes in the function's slope, viz. locally weighted scatterplot smoothing ( lowess ). Informally, lowess is a non-parametrical method that relies on an algorithm that fits the dependent variable for small parts of the range of the independent variable whilst guaranteeing that the overall curve does not contain sudden jumps (for technical details, see [50] ). Hakuta et al. used an even larger sample from the same 1990 U.S. Census data on Chinese- and Spanish-speaking immigrants (2.3 million observations) [21] . Fitting lowess curves, no discontinuities in the aoa – ua slope could be detected. Moreover, the authors found that piecewise linear regression models, i.e. regression models containing a parameter that allows a sudden drop in the curve or a change of its slope, did not provide a better fit to the data than did an ordinary regression model without such a parameter.

To sum up, I have argued at length that regression approaches are superior to group mean and correlation coefficient comparisons for the purposes of testing the ‘flattened slope’ prediction. Acknowledging the reservations vis-à-vis self-estimated ua s, we still find that while the relationship between aoa and ua is not necessarily perfectly linear in the studies discussed, the data do not lend unequivocal support to this prediction. In the following section, I will reanalyse data from a recent empirical paper on the cph by DeKeyser et al. [44] . The first goal of this reanalysis is to further illustrate some of the statistical fallacies encountered in cph studies. Second, by making the computer code available I hope to demonstrate how the relevant regression models, viz. piecewise regression models, can be fitted and how the aoa representing the optimal breakpoint can be identified. Lastly, the findings of this reanalysis will contribute to our understanding of how aoa affects ua as measured using a gjt .

Summary of DeKeyser et al. (2010)

I chose to reanalyse a recent empirical paper on the cph by DeKeyser et al. [44] (henceforth DK et al.). This paper lends itself well to a reanalysis since it exhibits two highly commendable qualities: the authors spell out their hypotheses lucidly and provide detailed numerical and graphical data descriptions. Moreover, the paper's lead author is very clear on what constitutes a necessary condition for accepting the cph : a non-linearity in the age of onset of acquisition ( aoa )–ultimate attainment ( ua ) function, with ua declining less strongly as a function of aoa in older, post- cp arrivals compared to younger arrivals [14] , [22] . Lastly, it claims to have found cross-linguistic evidence from two parallel studies backing the cph and should therefore be an unsuspected source to cph proponents.

The authors set out to test the following hypotheses:

• Hypothesis 1: For both the L2 English and the L2 Hebrew group, the slope of the age of arrival–ultimate attainment function will not be linear throughout the lifespan, but will instead show a marked flattening between adolescence and adulthood.
• Hypothesis 2: The relationship between aptitude and ultimate attainment will differ markedly for the young and older arrivals, with significance only for the latter. (DK et al., p. 417)

Both hypotheses were purportedly confirmed, which in the authors' view provides evidence in favour of cph . The problem with this conclusion, however, is that it is based on a comparison of correlation coefficients. As I have argued above, correlation coefficients are not to be confused with regression coefficients and cannot be used to directly address research hypotheses concerning slopes, such as Hypothesis 1. In what follows, I will reanalyse the relationship between DK et al.'s aoa and gjt data in order to address Hypothesis 1. Additionally, I will lay bare a problem with the way in which Hypothesis 2 was addressed. The extracted data and the computer code used for the reanalysis are provided as supplementary materials, allowing anyone interested to scrutinise and easily reproduce my whole analysis and carry out their own computations (see ‘supporting information’).

Data extraction

In order to verify whether we did in fact extract the data points to a satisfactory degree of accuracy, I computed summary statistics for the extracted aoa and gjt data and checked these against the descriptive statistics provided by DK et al. (pp. 421 and 427). These summary statistics for the extracted data are presented in Table 1 . In addition, I computed the correlation coefficients for the aoa – gjt relationship for the whole aoa range and for aoa -defined subgroups and checked these coefficients against those reported by DK et al. (pp. 423 and 428). The correlation coefficients computed using the extracted data are presented in Table 2 . Both checks strongly suggest the extracted data to be virtually identical to the original data, and Dr DeKeyser confirmed this to be the case in response to an earlier draft of the present paper (personal communication, 6 May 2013).

https://doi.org/10.1371/journal.pone.0069172.t001

https://doi.org/10.1371/journal.pone.0069172.t002

Results and Discussion

Modelling the link between age of onset of acquisition and ultimate attainment.

I first replotted the aoa and gjt data we extracted from DK et al.'s scatterplots and added non-parametric scatterplot smoothers in order to investigate whether any changes in slope in the aoa – gjt function could be revealed, as per Hypothesis 1. Figures 3 and 4 show this not to be the case. Indeed, simple linear regression models that model gjt as a function of aoa provide decent fits for both the North America and the Israel data, explaining 65% and 63% of the variance in gjt scores, respectively. The parameters of these models are given in Table 3 .

The trend line is a non-parametric scatterplot smoother. The scatterplot itself is a near-perfect replication of DK et al.'s Fig. 1.

https://doi.org/10.1371/journal.pone.0069172.g003

The trend line is a non-parametric scatterplot smoother. The scatterplot itself is a near-perfect replication of DK et al.'s Fig. 5.

https://doi.org/10.1371/journal.pone.0069172.g004

https://doi.org/10.1371/journal.pone.0069172.t003

To ensure that both segments are joined at the breakpoint, the predictor variable is first centred at the breakpoint value, i.e. the breakpoint value is subtracted from the original predictor variable values. For a blow-by-blow account of how such models can be fitted in r , I refer to an example analysis by Baayen [55, pp. 214–222].

Solid: regression with breakpoint at aoa 18 (dashed lines represent its 95% confidence interval); dot-dash: regression without breakpoint.

https://doi.org/10.1371/journal.pone.0069172.g005

Solid: regression with breakpoint at aoa 18 (dashed lines represent its 95% confidence interval); dot-dash (hardly visible due to near-complete overlap): regression without breakpoint.

https://doi.org/10.1371/journal.pone.0069172.g006

https://doi.org/10.1371/journal.pone.0069172.t004

https://doi.org/10.1371/journal.pone.0069172.g007

Solid: regression with breakpoint at aoa 16 (dashed lines represent its 95% confidence interval); dot-dash: regression without breakpoint.

https://doi.org/10.1371/journal.pone.0069172.g008

Solid: regression with breakpoint at aoa 6 (dashed lines represent its 95% confidence interval); dot-dash (hardly visible due to near-complete overlap): regression without breakpoint.

https://doi.org/10.1371/journal.pone.0069172.g009

https://doi.org/10.1371/journal.pone.0069172.t005

https://doi.org/10.1371/journal.pone.0069172.t006

https://doi.org/10.1371/journal.pone.0069172.t007

https://doi.org/10.1371/journal.pone.0069172.t008

In sum, a regression model that allows for changes in the slope of the the aoa – gjt function to account for putative critical period effects provides a somewhat better fit to the North American data than does an everyday simple regression model. The improvement in model fit is marginal, however, and including a breakpoint does not result in any detectable improvement of model fit to the Israel data whatsoever. Breakpoint models therefore fail to provide solid cross-linguistic support in favour of critical period effects: across both data sets, gjt can satisfactorily be modelled as a linear function of aoa .

On partialling out ‘age at testing’

As I have argued above, correlation coefficients cannot be used to test hypotheses about slopes. When the correct procedure is carried out on DK et al.'s data, no cross-linguistically robust evidence for changes in the aoa – gjt function was found. In addition to comparing the zero-order correlations between aoa and gjt , however, DK et al. computed partial correlations in which the variance in aoa associated with the participants' age at testing ( aat ; a potentially confounding variable) was filtered out. They found that these partial correlations between aoa and gjt , which are given in Table 9 , differed between age groups in that they are stronger for younger than for older participants. This, DK et al. argue, constitutes additional evidence in favour of the cph . At this point, I can no longer provide my own analysis of DK et al.'s data seeing as the pertinent data points were not plotted. Nevertheless, the detailed descriptions by DK et al. strongly suggest that the use of these partial correlations is highly problematic. Most importantly, and to reiterate, correlations (whether zero-order or partial ones) are actually of no use when testing hypotheses concerning slopes. Still, one may wonder why the partial correlations differ across age groups. My surmise is that these differences are at least partly the by-product of an imbalance in the sampling procedure.

https://doi.org/10.1371/journal.pone.0069172.t009

The upshot of this brief discussion is that the partial correlation differences reported by DK et al. are at least partly the result of an imbalance in the sampling procedure: aoa and aat were simply less intimately tied for the young arrivals in the North America study than for the older arrivals with L2 English or for all of the L2 Hebrew participants. In an ideal world, we would like to fix aat or ascertain that it at most only weakly correlates with aoa . This, however, would result in a strong correlation between aoa and another potential confound variable, length of residence in the L2 environment, bringing us back to square one. Allowing for only moderate correlations between aoa and aat might improve our predicament somewhat, but even in that case, we should tread lightly when making inferences on the basis of statistical control procedures [61] .

On estimating the role of aptitude

Having shown that Hypothesis 1 could not be confirmed, I now turn to Hypothesis 2, which predicts a differential role of aptitude for ua in sla in different aoa groups. More specifically, it states that the correlation between aptitude and gjt performance will be significant only for older arrivals. The correlation coefficients of the relationship between aptitude and gjt are presented in Table 10 .

https://doi.org/10.1371/journal.pone.0069172.t010

The problem with both the wording of Hypothesis 2 and the way in which it is addressed is the following: it is assumed that a variable has a reliably different effect in different groups when the effect reaches significance in one group but not in the other. This logic is fairly widespread within several scientific disciplines (see e.g. [62] for a discussion). Nonetheless, it is demonstrably fallacious [63] . Here we will illustrate the fallacy for the specific case of comparing two correlation coefficients.

Apart from not being replicated in the North America study, does this difference actually show anything? I contend that it does not: what is of interest are not so much the correlation coefficients, but rather the interactions between aoa and aptitude in models predicting gjt . These interactions could be investigated by fitting a multiple regression model in which the postulated cp breakpoint governs the slope of both aoa and aptitude. If such a model provided a substantially better fit to the data than a model without a breakpoint for the aptitude slope and if the aptitude slope changes in the expected direction (i.e. a steeper slope for post- cp than for younger arrivals) for different L1–L2 pairings, only then would this particular prediction of the cph be borne out.

Using data extracted from a paper reporting on two recent studies that purport to provide evidence in favour of the cph and that, according to its authors, represent a major improvement over earlier studies (DK et al., p. 417), it was found that neither of its two hypotheses were actually confirmed when using the proper statistical tools. As a matter of fact, the gjt scores continue to decline at essentially the same rate even beyond the end of the putative critical period. According to the paper's lead author, such a finding represents a serious problem to his conceptualisation of the cph [14] ). Moreover, although modelling a breakpoint representing the end of a cp at aoa 16 may improve the statistical model slightly in study on learners of English in North America, the study on learners of Hebrew in Israel fails to confirm this finding. In fact, even if we were to accept the optimal breakpoint computed for the Israel study, it lies at aoa 6 and is associated with a different geometrical pattern.

Diverging age trends in parallel studies with participants with different L2s have similarly been reported by Birdsong and Molis [26] and are at odds with an L2-independent cph . One parsimonious explanation of such conflicting age trends may be that the overall, cross-linguistic age trend is in fact linear, but that fluctuations in the data (due to factors unaccounted for or randomness) may sometimes give rise to a ‘stretched L’-shaped pattern ( Figure 1, left panel ) and sometimes to a ‘stretched 7’-shaped pattern ( Figure 1 , middle panel; see also [66] for a similar comment).

Importantly, the criticism that DeKeyser and Larsson-Hall levy against two studies reporting findings similar to the present [48] , [49] , viz. that the data consisted of self-ratings of questionable validity [14] , does not apply to the present data set. In addition, DK et al. did not exclude any outliers from their analyses, so I assume that DeKeyser and Larsson-Hall's criticism [14] of Birdsong and Molis's study [26] , i.e. that the findings were due to the influence of outliers, is not applicable to the present data either. For good measure, however, I refitted the regression models with and without breakpoints after excluding one potentially problematic data point per model. The following data points had absolute standardised residuals larger than 2.5 in the original models without breakpoints as well as in those with breakpoints: the participant with aoa 17 and a gjt score of 125 in the North America study and the participant with aoa 12 and a gjt score of 117 in the Israel study. The resultant models were virtually identical to the original models (see Script S1 ). Furthermore, the aoa variable was sufficiently fine-grained and the aoa – gjt curve was not ‘presmoothed’ by the prior aggregation of gjt across parts of the aoa range (see [51] for such a criticism of another study). Lastly, seven of the nine “problems with supposed counter-evidence” to the cph discussed by Long [5] do not apply either, viz. (1) “[c]onfusion of rate and ultimate attainment”, (2) “[i]nappropriate choice of subjects”, (3) “[m]easurement of AO”, (4) “[l]eading instructions to raters”, (6) “[u]se of markedly non-native samples making near-native samples more likely to sound native to raters”, (7) “[u]nreliable or invalid measures”, and (8) “[i]nappropriate L1–L2 pairings”. Problem No. 5 (“Assessments based on limited samples and/or “language-like” behavior”) may be apropos given that only gjt data were used, leaving open the theoretical possibility that other measures might have yielded a different outcome. Finally, problem No. 9 (“Faulty interpretation of statistical patterns”) is, of course, precisely what I have turned the spotlights on.

Conclusions

The critical period hypothesis remains a hotly contested issue in the psycholinguistics of second-language acquisition. Discussions about the impact of empirical findings on the tenability of the cph generally revolve around the reliability of the data gathered (e.g. [5] , [14] , [22] , [52] , [67] , [68] ) and such methodological critiques are of course highly desirable. Furthermore, the debate often centres on the question of exactly what version of the cph is being vindicated or debunked. These versions differ mainly in terms of its scope, specifically with regard to the relevant age span, setting and language area, and the testable predictions they make. But even when the cph 's scope is clearly demarcated and its main prediction is spelt out lucidly, the issue remains to what extent the empirical findings can actually be marshalled in support of the relevant cph version. As I have shown in this paper, empirical data have often been taken to support cph versions predicting that the relationship between age of acquisition and ultimate attainment is not strictly linear, even though the statistical tools most commonly used (notably group mean and correlation coefficient comparisons) were, crudely put, irrelevant to this prediction. Methods that are arguably valid, e.g. piecewise regression and scatterplot smoothing, have been used in some studies [21] , [26] , [49] , but these studies have been criticised on other grounds. To my knowledge, such methods have never been used by scholars who explicitly subscribe to the cph .

I suspect that what may be going on is a form of ‘confirmation bias’ [69] , a cognitive bias at play in diverse branches of human knowledge seeking: Findings judged to be consistent with one's own hypothesis are hardly questioned, whereas findings inconsistent with one's own hypothesis are scrutinised much more strongly and criticised on all sorts of points [70] – [73] . My reanalysis of DK et al.'s recent paper may be a case in point. cph exponents used correlation coefficients to address their prediction about the slope of a function, as had been done in a host of earlier studies. Finding a result that squared with their expectations, they did not question the technical validity of their results, or at least they did not report this. (In fact, my reanalysis is actually a case in point in two respects: for an earlier draft of this paper, I had computed the optimal position of the breakpoints incorrectly, resulting in an insignificant improvement of model fit for the North American data rather than a borderline significant one. Finding a result that squared with my expectations, I did not question the technical validity of my results – until this error was kindly pointed out to me by Martijn Wieling (University of Tübingen).) That said, I am keen to point out that the statistical analyses in this particular paper, though suboptimal, are, as far as I could gather, reported correctly, i.e. the confirmation bias does not seem to have resulted in the blatant misreportings found elsewhere (see [74] for empirical evidence and discussion). An additional point to these authors' credit is that, apart from explicitly identifying their cph version's scope and making crystal-clear predictions, they present data descriptions that actually permit quantitative reassessments and have a history of doing so (e.g. the appendix in [8] ). This leads me to believe that they analysed their data all in good conscience and to hope that they, too, will conclude that their own data do not, in fact, support their hypothesis.

I end this paper on an upbeat note. Even though I have argued that the analytical tools employed in cph research generally leave much to be desired, the original data are, so I hope, still available. This provides researchers, cph supporters and sceptics alike, with an exciting opportunity to reanalyse their data sets using the tools outlined in the present paper and publish their findings at minimal cost of time and resources (for instance, as a comment to this paper). I would therefore encourage scholars to engage their old data sets and to communicate their analyses openly, e.g. by voluntarily publishing their data and computer code alongside their articles or comments. Ideally, cph supporters and sceptics would join forces to agree on a protocol for a high-powered study in order to provide a truly convincing answer to a core issue in sla .

Supporting Information

Dataset s1..

aoa and gjt data extracted from DeKeyser et al.'s North America study.

https://doi.org/10.1371/journal.pone.0069172.s001

Dataset S2.

aoa and gjt data extracted from DeKeyser et al.'s Israel study.

https://doi.org/10.1371/journal.pone.0069172.s002

Script with annotated R code used for the reanalysis. All add-on packages used can be installed from within R.

https://doi.org/10.1371/journal.pone.0069172.s003

Acknowledgments

I would like to thank Irmtraud Kaiser (University of Fribourg) for helping me to get an overview of the literature on the critical period hypothesis in second language acquisition. Thanks are also due to Martijn Wieling (currently University of Tübingen) for pointing out an error in the R code accompanying an earlier draft of this paper.

Author Contributions

Analyzed the data: JV. Wrote the paper: JV.

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Original research article, critical period in second language acquisition: the age-attainment geometry.

• Teachers College, Columbia University, New York City, NY, United States

One of the most fascinating, consequential, and far-reaching debates that have occurred in second language acquisition research concerns the Critical Period Hypothesis [ 1 ]. Although the hypothesis is generally accepted for first language acquisition, it has been hotly debated on theoretical, methodological, and practical grounds for second language acquisition, fueling studies reporting contradictory findings and setting off competing explanations. The central questions are: Are the observed age effects in ultimate attainment confined to a bounded period, and if they are, are they biologically determined or maturationally constrained? In this article, we take a sui generis , interdisciplinary approach that leverages our understanding of second language acquisition and of physics laws of energy conservation and angular momentum conservation, mathematically deriving the age-attainment geometry. The theoretical lens, termed Energy Conservation Theory for Second Language Acquisition, provides a macroscopic perspective on the second language learning trajectory across the human lifespan.

Introduction

The Critical Period Hypothesis (CPH), as proposed by [ 1 ], that nativelike proficiency is only attainable within a finite period, extending from early infancy to puberty, has generally been accepted in language development research, but more so for first language acquisition (L1A) than for second language acquisition (L2A).

In the context of L2A, there are two parallel facts that appear to compound the difficulty of establishing the validity of CPH. One is that there is a stark difference in the level of ultimate attainment between child and adult learners. “Children eventually reach a more native-like level of proficiency than learners who start learning a second language as adults” ([ 2 ], p . 360). But this fact exists alongside another fact, namely, that there are vast differences in ultimate attainment among older learners. [ 3 ] observed:

Although few adults, if any, are completely successful, and many fail miserably, there are many who achieve very high levels of proficiency, given enough time, input, and effort, and given the right attitude, motivation, and learning environment. ( p . 13).

The dual facets of inter-learner differential success are at the nexus of second language acquisition research. As [ 4 ] once noted:

One of the enduring and fascinating problems confronting researchers of second language acquisition is whether adults can ever acquire native-like competence in a second language, or whether this is an accomplishment reserved for children who start learning at a relatively early age. As a secondary issue, there is the question of whether those rare cases of native-like success reported amongst adult learners are indeed what they seem, and if they are, how it is that such people can be successful when the vast majority are palpably not. ( p . 219).

The primary question Kellerman raised here is, in essence, a critical period (CP) question, concerning differential attainment between child and adult learners, and his secondary question relates to differential attainment among adult learners.

As of this writing, neither question has been settled. Instead, the two phenomena are often seen conflated in debates, including taking evidence for one as counter-evidence for the other (see, e.g., [ 5 ]). By and large, it would seem that the debate has come down to a matter of interpretation; the same facts are interpreted differently as evidence for or against CPH (see, e.g., [ 5 – 7 ]). This state of affairs, tinted with ideological differences over the role of nature and/or nature in language development, continues to put a tangible understanding of either phenomenon out of reach, let alone a coherent understanding of both phenomena. In order to break out of the rut of ‘he said, she said,” we need to engage in systems thinking.

Our research sought to juxtapose child and adult learners, as some researchers have, conceptually, attempted (see, e.g., [ 8 – 11 ]). Specifically, we built on and extended an interdisciplinary model of L2A, Energy Conservation Theory for L2A (ECT-L2A) [ 12 , 13 ], originally developed to account for differential attainment among adult learners, to child learners. In so doing, we sought to gain a coherent understanding of the dual facets of inter-learner differential success in L2A, in addition to mathematically obtaining the geometry of the age-attainment function, a core concern of the CPH/L2A debate.

In what follows, we first provide a quick overview of the CPH research in L2A. We then introduce ECT-L2A. Next, we extend ECT-L2A to the age issue, mathematically deriving the age-attainment function. After that, we discuss the resultant geometry and the fundamental nature of CPH/L2A, and, more broadly, L2 attainment across the human lifespan. We conclude by suggesting a number of avenues for furthering the research on CPH within the framework of ECT-L2A.

However, before we proceed, it is necessary to note two “boundary conditions” we have set for our work. First, the linguistic domain in which we theorize inter-learner differential attainment concerns only the grammatical/computational aspects of language, or what [ 14 , 15 ] calls basic language cognition, which concerns aspects of language where native speakers show little variance. As [ 2 ] has aptly pointed out, much of the confusion in the CPH-L2A debate is attributable to a lack of agreement on the scope of linguistic areas affected by CP. Second, we are only concerned with naturalistic acquisition (i.e., acquisition happens in an input-rich or immersion environment), not instructed learning (i.e., an input-poor environment). These two assumptions are often absent in CPH/L2A research, leading to the different circumstances under which researchers interpret the CP notion and empirical results (for discussion, see [ 7 ]).

The critical period hypothesis in L2A

To date, two questions have dominated the research and debate on CPH/L2A: What counts as evidence of a critical period? What accounts for the age-attainment difference between younger learners and older learners? More than 4 decades of research on CPH/L2A- from [ 16 ] to [ 17 ] to [ 18 ]—have, in the main, found an inverse correlation between the age of acquisition (AoA) and the level of grammatical attainment (see also [ 19 ], for a meta-analysis); “the age of acquisition is strongly negatively correlated with ultimate second language proficiency for grammar as well as for pronunciation” ([ 20 ], p . 88).

However, views are almost orthogonal over whether the observed inverse correlation can count as evidence of CPH or the observed difference is attributable to brain maturation (see, e.g., [ 5 , 7 , 21 – 35 ]).

For some researchers, true evidence or falsification of CPH for L2A must be tied to whether or not late learners can attain a native-like level of proficiency (e.g., [ 36 ]). Others contend that the nativelikeness threshold, in spite of it being “the most central aspect of the CPH” ([ 2 ], p . 362), is problematic, arguing that monolingual-like native attainment is simply impossible for L2 learners [ 37 , 38 ]. Echoing this view, [ 39 ] offered:

[Sequential] bilinguals are not “two monolinguals in one” in any social, psycholinguistic, or cognitive neurofunctional sense. From this perspective, it is of questionable methodological value to quantify bilinguals’ linguistic attainment as a proportion of monolinguals’ attainment, with those bilinguals reaching 100% levels of attainment considered nativelike. ( p . 121).

In the meantime, empirical research into adult learners have consistently produced evidence of selective nativelike attainment, that is, nativelikeness is attained vis-à-vis some aspects of the target language but not others. These studies employed a variety of methodologies, including cross-sectional studies and longitudinal case studies (see, e.g., [ 40 – 56 ]). Some researchers (e.g., [ 55 , 57 ]) take the selective nativelikeness as falsifying evidence of CPH/L2A; other researchers disagree (see, e.g., [ 36 ]).

Leaving aside the vexed issue of nativelikeness, 1 Birdsong [ 58 ], among others, postulated that CPH/L2A must ultimately pass geometric tests: if studies comparing younger learners and older learners yield the geometry of a “stretched Z” for the age-attainment function, that would prove the validity of CPH/L2A, or falsify it, if otherwise. The stretched Z or inverted S [ 20 ] references a bounded period in which the organism exhibits heightened neural plasticity and sensitivity to linguistic stimuli from the environment. This period has certain temporal and geometric features. Temporally, it extends from early infancy to puberty, coinciding with the time during which the brain undergoes maturation [ 1 , 36 , 59 – 62 ]. Geometrically, this period should exhibit two points of inflection or discontinuities, viz, “an abrupt onset or increase of sensitivity, a plateau of peak sensitivity, followed by a gradual offset or decline, with subsequent flattening of the degree of sensitivity” ([ 58 ], p . 111).

By the temporal and geometric hallmarks, few studies seem to have confirmed CPH/L2A, not even those that have allegedly found stark evidence. A case in point is the [ 17 ] study, which reported what appears to be clear-cut evidence of CPH/L2A: r = −.87, p <.01 for the early age of arrival (AoA) group and r = −.16, p >.05 for the late AoA group. As Johnson and Newport described it, “test performance was linearly related to [AoA] up to puberty; after puberty, performance was low but highly variable and unrelated to [AoA],” which supports “the conclusion that a critical period for language acquisition extends its effects to second language acquisition” ( p . 60). However, this claim has been contested.

Focusing on the geometry of the results, [ 58 ] pointed out that the random distribution of test scores within the late AoA group “does not license the conclusion that “through adulthood the function is low and flat” or the corresponding interpretation that “the shape of the function thus supports the claim that the effects of age of acquisition are effects of the maturational state of the learner” ([ 17 ], p . 79)” ( p . 117). Birdsong argued that if CPH holds for L2A, the performance scores of the late AoA group should be distributed horizontally in addition to showing marginal correlation with age. Accordingly, the random distribution of scores could only be taken as indicative of “a lack of systematic relationship between the performance and the AoA and not of a “levelling off of ultimate performance among those exposed to the language after puberty” ([ 17 ], p . 79)” ([ 58 ], p . 118).

Interpreting the same study, other researchers such as [ 20 ] did not set their sights as much on the random distribution of the performance scores among the late learners as on the discontinuity between the early AoA and late AoA groups, arguing that the qualitative difference is sufficient evidence of CPH/L2A.

If geometric satisfaction is one flash point in CPH/L2A research, explaining random distribution of performance scores or, essentially, differential attainment among late learners counts as another. Analyses of late learners’ ultimate attainment (e.g., [ 10 , 22 , 26 , 43 , 63 – 67 ]) have yielded a host of cognitive, socio-psychological, or experiential factors that can be associated with inter-learner differential attainment among late learners. The question, then, is whether or not these non-age factors confound, or even interact with, the age or maturational effect (see discussion in [ 2 , 68 – 72 ]. As Newport [ 7 ] aptly asked, “why cannot other variables interact with age effects?” ( p . 929).

These are undoubtedly complex questions for which sophisticated solutions are needed—beyond the methodological repairs many have thought are solely needed in advancing CPH/L2A research (see, e.g., [ 19 , 67 ]). In the remainder of this article, we take a different tack to the age issue, adopting a theoretical, hybrid approach, ECT-L2A [ 12 , 13 ], to mathematically derive the age-attainment function.

Energy-Conservation Theory for L2A

ECT-L2A is a theoretical model originally developed to account for the divergent states of ultimate attainment in adult L2A [ 12 , 13 ]. Drawing on the physics laws of energy conservation and angular momentum conservation, it theorizes the dynamic transformation and conservation of internal energies (i.e., from the learner) and external energies (i.e., from the environment) in rendering the learner’s ultimate attainment. This model, thus, takes into account nature and nurture factors, and specifically, uses five parameters - the linguistic environment or input, learner motivation, learner aptitude, distance between the L1 and the target language (TL) and the developing learner—and their interaction to account for levels of L2 ultimate attainment.

ECT-L2A draws a number of parallels between mechanical energies and human learning energies: kinetic energy for motivation and aptitude energy, potential energy for environmental energy, 2 and centrifugal energy for L1-TL deviation energy (for discussion, see [ 12 ]). These energies each perform a unique yet dynamic role. As the learner progresses in the developmental process, the energies shift in their dominance, while the total energy remains constant.

Mathematically, ECT-L2A reads as follows:

where ζ r denotes the learner’s motivational energy, r the learner’s position in the learning process relative to the TL, η the distance between L1 and TL, and ρ the input of TL. According to Eq. 1 , the total learning energy, ∈ , comes from the sum of motivation energy ζ r , aptitude (a constant) Λ , deviation energy η 2 r 2 , and environmental energy - ρ r .

The energy types included in Eq. 1 are embodiments of nature and nurture contributions. The potential energy or TL traction, - ρ r , represents the external or environmental energy, while the kinetic or motivational energy, ζ r , along with aptitude, Λ , and the centrifugal or deviation energy η 2 r 2 represent the internal energies.

Under the overarching condition of the total energy being the same or conserved throughout the learning process, ϵ = constant , each type of energy performs a different role, with one converting to another over time as the position of the learner changes in the developmental process.

For mathematical and conceptual convenience, (1) is rewritten into (2) which contains the effective potential energy, U eff (r) .

where U e f f r = η 2 r 2 − ρ r . In other words, the effective potential energy is the sum of deviation energy and the potential energy (see further breakdown in the next section).

The L2A energy system as depicted here is true of every learner, meaning that the total energy is constant for a single learner. But the total energy varies from learner to learner. Accordingly, different learners may reach different levels of ultimate attainment (i.e., closer or more distant from the TL), r 0 . This is illustrated in Figure 1 , where r 0 and r 0 ′ represent the ultimate attainments for learners with different amounts of total energy, ϵ >0 or ϵ <0.

FIGURE 1 . Inter-learner differential ultimate attainment as a function of different amounts of total energy: ϵ >0; ϵ < 0; ϵ = ϵ min [ 12 , 13 ].

Key to understanding Figure 1 is that it is the individual’s total energy that determines their level of attainment. Of the three scenarios on display here, ECT-L2A is only concerned with the case of ϵ ≥0, which represents the unbound process (r 0 , ∞), ignoring the bounded processes of ϵ < 0; ε = ϵmin.

The central thesis of ECT-L2A, as expressed in Eq. 1 , is that the moment a learner begins to receive substantive exposure to the TL, s/he enters a ‘gravitational’ field or a developmental ecosystem in which s/he is initially driven by kinetic or motivational energy, increasingly subject to the traction of the potential or environmental energy, but eventually stonewalled by the deviation energy or centrifugal barrier, resulting in an asymptotic endstate. This trajectory is further elaborated below.

The developmental trajectory depicted and forecast by ECT-L2A

The L2A trajectory begins with the learner at the outset of the learning process or at infinity (r = ∞). Initially, their progression toward the central source, i.e., the TL, is driven almost entirely by their motivation energy and aptitude, as expressed in Eq. 3 .

As learning proceeds, but with r still large (i.e., the learner still distant from the target) and the deviation energy much weaker than the environmental energy, η 2 r 2 ≪ ρ r (due to the second power of r ), the motivation energy rises as a result of its “interaction” with the environmental energy− ρ r , in which case the environmental energy transfers to the motivation energy. Mathematically, this is expressed in Eq. 4 .

As learning further progresses, the environmental energy - ρ r becomes dominant before yielding to the deviation energy η 2 r 2 . Eventually, the deviation energy overrides the environmental energy, as expressed in Eq. 1 , repeated below as Eq. 5 for ease of reference.

The deviation energy is so powerful that it draws the learner away from the target and their learning reaches an asymptote, where their motivation energy becomes minimal, ζ ( r 0 ) = 0, as expressed in Eq. 6 .

At this point, all other energies submit to the deviation energy, including the initial motivation energy ζ (∞) and some of the potential or environmental energy. Consequently, further exposure to TL input would not be of substantive help, meaning that it would not move the learner markedly closer to the target.

Figure 2 gives a geometric expression of the L1-TL deviation η, which is akin to the angular momentum of an object moving in a central force field [ 73 – 75 ]. The deviation from the TL, signifying the distance between the L1 and the TL, varies with different L1-TL pairings. For example, the distance index, according to the Automated Similarity Judgment Program Database [ 76 ], is 90.25 for Italian and English but 100.33 for Italian and Chinese.

FIGURE 2 . Geometric description of the deviation parameter η .

Figure 3 illustrates differential ultimate attainment (indicated by r 0 ) as a function of the deviation parameter η. As η increases, the level of attainment is lower or the attainment is further away from the target ( r = 0).

FIGURE 3 . Effective potentials U eff with different values of η [ 12 , 13 ].

For adult L2A, ECT-L2A predicts, inter alia , that high attainment is possible but full attainment is not. In other words, near-nativelike attainment is possible, but complete-nativelike attainment is not. ECT-L2A also predicts that while motivation and aptitude are part and parcel of the total energy of a given L2 learner, their role is largely confined to the earlier stage of development. Most of all, ECT-L2A predicts that the L1-L2 deviation is what keeps L2 attainment at asymptote.

For L2 younger learners, ECT-L2A also makes a number of predictions to which we now turn.

ECT-L2A vis-à-vis younger learners

As highlighted above, the deviation energy is what leads L2 attainment to an asymptote. It follows that as long as η (i.e., the L1-TL distance) is non-zero, the learner’s ultimate attainment, r 0 , will always eventuate in an asymptote. As shown in Figure 3 , the larger the deviation r 0 , the more distant the ultimate attainment r 0 is from the TL. Put differently, a larger η portends that learning would reach an asymptote earlier or that the ultimate attainment would be less native-like. But how does that work for child L2A?

On the ECT-L2A account, it is the low η value that determines child learners’ superior attainment. In child L2 learners, the deviation is low, because of the incipient or underdeveloped L1. However, as the L1 develops, the η value grows until it becomes a constant, presumably happening around puberty 3 , hence coinciding with the offset of the critical period [ 1 ]. As shown in Figures 1 , 3 , the smaller the deviation, η, the closer r 0 (i.e., the ultimate level of attainment) is to the TL or the higher the ultimate attainment.

From Eq. 6 the ultimate attainment of any L2 learner, irrespective of age, can be mathematically derived:

where ε = ϵ – Λ (i.e., total energy minus aptitude). r 0 here again denotes ultimate attainment. The upper panel in Figure 4 displays the geometry of ultimate attainment as a function of deviation, η.

FIGURE 4 . Double non-linearity of r 0 η [ (A) : first non-linearity] and η t [ (B) : second non-linearity] at early AoA.

For a given child learner, η is a constant, but different child learners can have a different η value, depending on their AoA . Herein lies a crucial difference from adult learning where η is a constant for all learners because of their uniform late AoA or age of acquisition and because their L1 has solidified. Adult learning starts at a time when the deviation between their L1 and the TL has become fixed, so to speak, as a result of having mastered their L1 (see the lower panel of Figure 4 ).

Further, for child L2 learners, η is simultaneously a function of their AoA, a proxy for time ( t ), and can therefore be expressed as η(t). This deviation function of time varies in the range of 0 ≤ η t ≤ η max . Accordingly; Eq. 7 can be mathematically rewritten into (8):

Assuming that as t grows or as AoA increases, η increases slowly and smoothly from 0 to η max until it solidifies into a constant, which marks the onset of adult learning, η( t ) can mathematically be expressed as (9).

where a is a constant. The geometry of the deviation function of time is illustrated in the lower panel of Figure 4 .

Figure 4 displays a double non-linearity characterizing L2 acquisition by young learners, with (A) showing the first order of non-linearity of r 0 η , that is, ultimate attainment as a function of deviation or the L1-TL distance (computed via Eq. 7 ), and with (B) displaying the second order of non-linearity, η (t), that is, η changing with t , age of acquisition (computed through Eq. 9 ).

Figure 5 illustrates ultimate attainment as a function of AoA, r 0 (t), and its derivative against t , d r 0 d t , which naturally yields three distinct periods: a critical period, t critical ; a post-critical period, t p-critical ; and an adult learning period, t adult . Within the critical period, t critical , r 0 ≅ 0 , meaning there is no real difference in attainment as age of acquisition increases. But within the post-critical period, t p-critical , r 0 changes dramatically, with d r 0 d t peaking and waning until it drops to the level approximating that of the adult period. Within the adult period, t adult , r 0 remains a constant, as attainment levels off.

FIGURE 5 . Ultimate attainment (the blue line) as a function of age of acquisition ( t ) and its derivatives giving three distinct periods (the orange line).

ECT-L2A, therefore, identifies three learning periods. First, there is a critical period, t critical , within which attainment is nativelike, r 0 ≅ 0. Notice that the blue line in Figure 5 is the lowest during the critical period, signifying that the attainment converges on the target, but it is the highest during the adult period, meaning that the attainment diverges greatly from the target. The offset of the critical period is smooth rather than abrupt, with the impact of deviation, η , slowly emerging at its offset. During this period, the L1 is surfacing, yet with negligible deviation from the TL and weak in strength.

Key to understanding this account of the critical period is the double non-linearity: first, ultimate attainment as a function of L1-TL deviation ( r 0 ( η ), see (A) in Figure 4 ); and second, L1-TL deviation as a function of AoA ( η ( t ); see (B) in Figure 4 ). Crucially, this double non-linearity extends a critical “point” into a critical “period” .

Second, there is a post-critical period, t p-critical , 0 < r 0 ≤ r 0 ( η max ), within which, with advancing AoA, the L1-L2 deviation grows larger and stronger, resulting in ultimate attainment that is increasingly lower (i.e., increasingly non-nativelike). The change rate of r 0 , its first derivative to time, d r 0 d t , is dramatic, waxing and waning. As such, the post-critical period is more complex and nuanced than the critical period. During the post-critical period, as the learner’s L1 becomes increasingly robust and developed, the deviation becomes larger, resulting in a level of attainment increasingly away from the target (i.e., increasingly non-nativelike).

Third, there is an adult learning period, t adult , η = η max ≅ constant, where, despite the continuously advancing AoA, the deviation reaches its maximum and remains a constant, as benchmarked in indexes of crosslinguistic distance (see, e.g., the Automated Similarity Judgment Program Database [ 76 ]). As a result, L2 ultimate attainment turns asymptotic (for discussion, see [ 12 , 13 ]).

The three periods mathematically produced by ECT-L2A coincide with the stretched “Z” slope that some researchers have argued (e.g., [ 17 , 58 , 59 ]) constitutes the most unambiguous evidence for CPH/L2A, and by extension, for a maturationally-based account of the generic success or lack thereof (i.e., nativelike or non-nativelike L2 proficiency) in early versus late starters. For better illustration of the stretched “Z,” we can convert Figure 5 into Figure 6 , using Eq. 10 .

where a t t stands for level of attainment. According to Eq. 10 , the smaller the r 0 is, the higher the attainment is.

FIGURE 6 . Level of attainment as a function of AoA.

In sum, ECT-L2A mathematically establishes the critical period geometry. That said, the geometry, as seen in Figure 6 , exhibits anything but abrupt inflections; the phase transitions are gradual and smooth. The adult period, for example, does not exhibit a complete “flattening” but markedly lower attainment with continuous decline (cf. [ 7 , 23 , 28 ]). 4

Explaining CPH/L2A

As is clear from the above, on the ECT-L2A account of the critical period, η (i.e., L1-TL deviation) is considered an inter-learner variable and, at once, a proxy for age of acquisition, t . More profoundly, however, ECT-L2A associates η with neural plasticity or sensitivity (cf [ 77 ]). The relationship between plasticity, p ( t ), and deviation function, η (t) , is expressed as (11):

Thus, the relationship between plasticity and the deviation function is one of inverse correlation. During the critical period, η = η min (i.e., minimal L1-TL deviation) and p = p max (i.e., maximal plasticity); conversely, during the adult learning period, η = η max (i.e., maximal L1-TL deviation) and p = p min (i.e., minimal plasticity). In short, an increased deviation, η (t) , corresponds to a decrease of plasticity, p (t) , and vice versa , as illustrated in Figure 7 .

FIGURE 7 . Plasticity as a function of age of acquisition.

Illustrated in Figure 7 is that neural plasticity, first proposed by [ 78 ] as the underlying cause of CP, is at its highest during the critical period and, as [ 79 ] put it, it “endures within the confines of its onset and offset” ( p . 182). But it begins to decline and drops to a low level during the post-critical period, and remains low through the adult learning period. 5 It would, therefore, seem reasonable to call the first period “critical” and the second period “sensitive.” It is worth mentioning in passing that the post-critical or sensitive period has thus far received scant empirical attention in CPH/L2A research.

Temporally, following the [ 59 ] conjecture, the critical period should last through early childhood from birth to age six, and the sensitive period should offset around puberty (see also [ 2 , 20 , 36 , 67 , 71 ]). Crucially, both periods are circumscribed, exhibiting discontinuities, with the critical period exhibiting maximal sensitivity, the sensitive period declining, though, for the most part, still far greater, sensitivity than the adult learning period. This view of a changing underlying mechanism across the three periods of AoA and attainment resonates with the Language as a Complex Adaptive System perspective (see, e.g., [ 80 ]). [ 81 ], for example, noted that “the processing mechanisms that underlie [language development] … are fundamentally non-linear. This means that development itself will frequently have phase-like characteristics, that there may be periods of extreme sensitivity to input (‘critical periods’)” ( p . 431).

ECT-L2A as a unifying model

ECT-L2A, by virtue of identifying the L1-TL deviation, η, as a lynchpin for age effects, provides an explanation for the differential ultimate attainment of early versus late starters. Essentially, in early AoA, η is a temporal and neuro-functional proxy tied respectively to a developing L1 and to a changing age and changing neuroplasticity. In contrast, in late AoA, η is a constant, due to the L1 being fully developed and the brain fully mature. This takes care of the first facet of inter-learner differential attainment. What about the second facet, viz., the inter-learner differential attainment among late learners?

ECT-L2A (as expressed in Eq. 1 ) is a model of an ecosystem where there is an interplay between learner-internal and environmental energies. In line with the general finding from L2 research that individual difference variables are largely responsible for inter-learner differential attainment of nativelike proficiency in adult learners (see, e.g., [ 27 , 35 , 77 , 82 , 83 ]), ECT-L2A specifically ties motivation and aptitude to kinetic energy, only to provide a more nuanced picture of the changing magnitude of individual difference variables.

Figure 8 illustrates the twin facets of inter-learner differential attainment. First, attainment varies as a function of AoA. Second, attainment varies within and across the three learning periods as a function of individual learners with different amounts of total energy, ϵ 1 < ϵ 2 < ϵ 3 . As shown, individual differences play out the least among learners of AoA falling within the critical period but the most within the adult learning period, consistent with the general findings from L2 research (see, e.g., [ 2 , 3 , 43 , 63 , 65 , 67 , 84 , 85 ]). During the post-critical or sensitive period, individual differences are initially non-apparent but become more pronounced with increasing AoA. 6

FIGURE 8 . Level of attainment for total energies ϵ 1 < ϵ 2 < ϵ 3 .

ECT-L2A thus offers a coherent explanation for variable attainment in late learners. First and foremost, it posits that individual learners’ total energy or “carrying capacity” [ 86 ] is different, which leads to different levels of attainment. Second, although the internal (motivation and aptitude) and external (environment) energies interact over time, ultimately it is the deviation energy η 2 r 2 that dominates and stalls the learner at asymptote (see Eq. 6 ). This account provides a much more nuanced perspective on the role of individual differences than has been given in the current L2A literature.

Extant empirical studies investigating individual difference variables through correlation analysis have mostly projected a static view of the role (some of) the variables play in L2A. In contrast, ECT-L2A gives a dynamic view and, more importantly, an interactive view. In the end, the individual difference variables are part of a larger ecosystem within which they do not act alone, but rather interact with other energies (i.e., potential energy and deviation energy), waxing and waning as a result of energy conservation.

In this article, we engaged with a central concern in the ongoing heated debate on CPH/L2A, that is, the geometry of age differences. Within the framework of ECT-L2A, an interdisciplinary model of L2 attainment, we mathematically derived the age-attainment function and established the presence of a critical period in L2A. Importantly, this period is part of a developmental trajectory that comprises three learning periods: a critical period, a post-critical or sensitive period, and an adult period.

ECT-L2A has thus far demonstrated a stunning internal consistency in that it mathematically identifies younger learners’ superior performance to adult learners’ as well as the differential attainment among adult learners.

ECT-L2A, while in broad agreement with an entrenchment-transfer account from L2A research that essentializes the role of the L1 in L2 attainment (see, e.g., [ 5 , 11 , 87 – 90 ]), provides a dynamic account of that role and its varying contributions to the different age-related learning periods. Furthermore, ECT-L2A offers an interactive account whereby the L1, as part of the deviation energy, interacts with other types of learner-internal and learner-external energies. Above all, ECT-L2A, by virtue of summoning internal and external energies, gives a coherent explanation for the twin facets of inter-learner differential success—as respectively manifested between younger and older learners and among older learners.

Validation of ECT-L2A is, however, required. Many questions warrant investigation. On this note, Johnson and Newort’s view [ 17 ], in particular, that the goal of any L2A theory should be to account for three sets of facts—a) gradual decline of performance, b) the age at which a decline in performance is detected, and c) the nature of adult performance—resonates with us. Although ECT-L2A shines a light on all three, further work is clearly needed. More specific to the focus of the present article, three sets of questions can be asked in relation to the three learning periods ECT-L2A has identified.

In the spirit of promoting collective intelligence, we present a subset of these questions below in the hope that they will spark interest among researchers across disciplines and inspire close-up investigations leveraging a variety of methodologies.

First, for the critical period:

1. When does the decline of learning begin?

2. How does it relate to the status of L1?

3. What is plasticity like in this period?

4. What does plasticity entail?

5. How is it related to a developing L1 and a developing L2?

Answers to these questions can, at least in part, be found in the various literatures across disciplines. But approaching these questions in relation to one another—as opposed to discretely—would likely yield a more systematic, holistic and coherent understanding. Or perhaps, in search of answers to any of these questions, one may realize that the existing understanding is way too shallow or inadequate. For instance, [ 18 ] cited “a lack of interference from a well-learned first language” as one of the possible causes of the age-attainment function in younger versus older learners. But what has not yet been established is the nature of the younger learners’ L1. What does “well-learned” mean? Is it established or is it still developing? At minimum, it cannot be a unitary phenomenon, given the age span of young learners.

Second, for the post-critical or sensitive period, ECT-L2A mathematically identifies two sub-periods. Thus, questions such as the following should be examined:

6. What prompts the initial dramatic decline of attainment?

7. How does each of the sub-periods relate to the status of L1?

8. How does the decline relate to changing plasticity?

9. How does it relate to grammatical performance?

Third, for the adult learning period, questions such as the following warrant close engagement:

10. How do learners with the same L1 background differ from each other in their L2 ultimate attainment?

11. How do learners with different L1 backgrounds differ from one another in their L2 ultimate attainment?

12. How is the trajectory of each type of energy, endogenous or exogenous, related to the level of attainment?

Investigating these questions, among others, will lead us to a better understanding not only of the critical period but also of L2 learning over the arc of human life.

The theoretical and practical importance of gaining a robust and comprehensive understanding of how age affects the L2 learning outcome calls for systematic investigations. To that end, ECT-L2A has offered a systems thinking perspective and framework.

Data availability statement

The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.

Author contributions

All authors listed have made a substantial, direct, and intellectual contribution to the work and approved it for publication.

Acknowledgments

We greatly appreciate the insightful and perceptive comments made by the reviewers on an earlier version of this article, and take sole responsibility for any error or omission.

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

1 Despite the centrality of “nativelikeness” to the Critical Period Hypothesis [ 1 ], studies in L2A have increasingly moved away from the use of the term in favor of “the level of ultimate attainment” [ 2 ].

2 The potential energy in ECT-L2A is akin to gravitational potential energy. As such it defines the central source field, serving as the primary energy that dynamically converts to other types of energy: kinetic energy and centrifugal energy. Similarly, the potential energy of L2A defines the field of learning. It stands for TL environment or input, serving as primary energy, dynamically converting to motivational and L1-TL deviation energies. An essential premise of ECT-L2A is the existence of potential energy. This premise is consistent with that underpinning L2A studies on CPH and ultimate attainment.

3 That is when the L1 becomes entrenched.

4 Looking back on the [ 17 ] study, [ 7 ], taking account of developments in the intervening 3 decades in understanding changes in the brain during adulthood, updated the earlier assertation about the stability of age effects in adulthood, noting that “it is more accurate to hypothesize that L2 proficiency SHOULD continue to decline during adulthood” and that “a critical or sensitive period for language acquisition is not absolute or sudden” ( p . 929, emphasis in original). She further argued that “[t]he lack of flattening of age function at adulthood in many studies does not mean that learning is not constrained by biologically based maturational changes” (ibid).

5 The plasticity never completely disappears, but rather becomes asymptotic.

6 Age and attainment function appears to follow a power law in that age effects are greatest during the critical period, less so during the post-critical or sensitive period, and weakest during the adult learning period (see Figure 8 ). Similarly, Figure 7 exhibits a power law relationship between age and plasticity: Plasticity is at its peak during the critical period, declines during the post-critical or sensitive period, and plateaus in the adult learning period.

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Keywords: ultimate attainment, critical period, second language acquisition, physics laws, energy conservation, angular momentum conservation, inter-learner differential attainment

Citation: Han Z and Bao G (2023) Critical period in second language acquisition: The age-attainment geometry. Front. Phys. 11:1142584. doi: 10.3389/fphy.2023.1142584

Received: 11 January 2023; Accepted: 02 March 2023; Published: 20 March 2023.

Reviewed by:

Copyright © 2023 Han and Bao. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: ZhaoHong Han, [email protected]

This article is part of the Research Topic

Social Physics and the Dynamics of Second Language Acquisition

• The Critical Age Hypothesis and Literacy Skills

by Lori Au | Nov 25, 2020 | Blog | 0 comments

The Critical Age Hypothesis states that children need to be intelligible or possess clear, understandable speech by 5½ years of age, or they are likely to have difficulty with decoding and spelling (Bishop and Adams, 1990).   Decoding is the ability to apply knowledge of letter-sound relationships and knowledge of letter patterns, to correctly pronounce written words. Children with severe/profound speech-sound difficulties frequently demonstrate poorer phonological awareness skills than their typically developing peers.  Poor phonological awareness skills negatively affect literacy acquisition (Gillon, 2004).  Therefore it is imperative for children to be intelligible before entering school.  It should be noted that phonological awareness refers to an individual’s awareness of and access to the sound structure of his or her oral language.  The spoken words of a language represent strings of phonemes that signal differences of meaning.

A guideline for expected intelligibility (originally proposed by Caplan and Gleason, 1988) can be calculated by dividing the child’s age in years by four and converting that number into a percentage:

• 2-year-old: 50%
• 3-year-old: 75%
• 4-year-old: 100%

For example, the 4-year-old who is 50% intelligible is considered to be “delayed” by two years. Intelligibility is a much more meaningful measure for young children than are phoneme acquisition normative data, which vary greatly from study to study (Smit,1986).

The Critical Age Hypothesis is linked to normal development of reading (Bishop and Adams, 1990).   Children who have speech difficulties that persist to the point at which they need to use phonological skills for learning to read, are at high risk for reading problems. In contrast, children whose speech difficulties resolve before 5½ years old  will be at low risk. In line with this hypothesis, Carroll and Snowling, 2004  reported that 5- and 6-year-old children receiving speech therapy for expressive speech difficulties performed less well than typically developing children matched for verbal ability.  These same children performed as poorly as children at family-risk of dyslexia, on tests of rime, phoneme awareness, and early word recognition. The Critical Age Hypothesis therefore emphasizes the importance of the phonological skills that underpin reading development (Hodson, 2011).

The results of a study by Nathan, Stackhouse, Goulandris, and Snowling posted in the Journal of Speech, Language, and Hearing Researsh (April 2004) suggest that a child’s oral language skill in preschool is predictive of their later literacy development. Literacy is basically defined as the ability to read and write.  However, it also encompasses 4 main elements for reading and writing.  These elements include the following:

• Phonology: the ability to recognize and reproduce speech sounds.
• Orthography: the ability to recognize and reproduce spelling patterns.
• Semantics: the ability to pick out the meaning of words.
• Morphology: the ability to recognize and reproduce the patterns of word formations.

The development of phoneme (the smallest unit of sound in a language that holds meaning) awareness is also a critical factor. Children with speech difficulties, especially children with more severe and persistent problems, are more likely than children with normal speech development to struggle with literacy acquisition. These children represent an important group, some of whom may be dyslexic.  However, they are hard to identify among others with expressive speech difficulties who go on to develop literacy normally. It is important to identify these children so that intervention programs that target the development of phonological awareness and letter knowledge, can be implemented to reduce the risk of literacy difficulties by better preparing these children for learning to read. The reason these high-risk children develop literacy more slowly needs further research and perhaps qualitative assessments of their speech system (Nathan, Stackhouse, Goulandris, and Snowling, 2004).

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