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A Teacher Asks: Why the Renwick?

Vaija Wagle, former teacher at Washington International School. 

Welcome to the Renwick Gallery. I am Vaija Wagle. I have been a classroom teacher for the last 40 years. For 20 of those years, ideas from Project Zero , a research institute at Harvard Graduate School of Education influenced teaching and learning in my classroom. Upon retiring from the classroom, I took on the challenge of writing teacher resources for the Renwick Gallery.

As a teacher, my initial concern was that the Renwick Gallery would not be a teacher’s intuitive choice. Teachers have limited time and the artwork at the Renwick Gallery were not connected to any curriculum content. However, I soon recognized that the artwork at the Renwick Gallery presented a unique teaching opportunity.

Finding the Key

The artworks begged understanding. Using thinking patterns to understand and appreciate the artworks could offer students vital lessons to learn about critical thinking. If thinking about their thinking (metacognition) could be part of this experience, then the students might, in addition, transfer these thinking patterns across subject areas and to the world beyond.

If a visit to the Renwick, either through reproductions in the classroom or in-person, offered an opportunity to learn about using critical thinking skills and metacognition, teachers like me might find it quite valuable. With this in mind, I set to work on the units now available in the Resources section. They use a variety of trans-disciplinary thinking patterns to appreciate and understand the Renwick’s artworks such as:

• Uncovering Hidden Stories
• Taking Multiple Perspectives
• Getting to the Heart of the Matter
• Gleaning Context from Objects
• Making Connections

Learn more about Field Trips and School Tours at the Smithsonian American Art Museum.

The Units’ Philosophical Core

At Project Zero , I was profoundly drawn to the idea of making cultivating understanding through critical thinking as the goal of learning. This idea promised to benefit students’ learning in the classroom, but also for life long learning beyond the classroom.

You’ll notice that the units I created:

• Constructing an understanding of big conceptual ideas : Big conceptual ideas describe physical and social patterns that govern the world, how things work or why they are the way they are. They provide an enduring and universal lens through which to view subject matter but also the world around.
• Engage active student thinking . While knowledge may be dished out and delivered, understanding can only be cultivated through critical thinking, and through the units, students are guided to use a variety of thinking patterns to construct the desired understandings.

The units are designed for a variety of age groups; elementary to middle school students or middle to high school students.

Each unit takes between 60 and 90 minutes and can be accomplished during a visit to the museum or by displaying high definition photographs of the artworks available on the website.

Each unit uses a particular thinking pattern to look closely at a select artwork, and form informed and relevant interpretations.

There are metacognitive breaks along the way to help students become cognizant of the thinking pattern they are using to engage with the artworks.

A closing moment of reflection is built in to allow the students to revisit the experience and think about what they gained both in terms of ideas the artwork generated and patterns of thinking used.

Examples of how the various thinking patterns can be used to successfully teach curriculum content are also provided.

Practical Testing

As a teacher, I know that there is nothing better than a chance to actually teach the units and receive feedback. So, I took multiple opportunities to test the units in the gallery and at workshops across the city and gather feedback from participating students and teachers. I also reflected on what worked and what didn’t.

My highlight was when we presented the unit on Hidden Stories (the importance of seeking side and hidden stories to better understand the main story) to a high school art class at St. Alban’s School. Having visited the classroom some days before, my host teacher wrote to me and said that the students had returned from their art class and informed their teachers in the history and literature classes that they ought to be looking for side and hidden stories!! This, to me, is the ideal outcome. With all this feedback I set to revise the units.

Thinking Through Craft  resources were funded by a generous gift from the William R. Kenan, Jr. Charitable Trust.

Arts Academy

in the Woods

How Art Education Fosters Critical Thinking and Why It Matters

These days, the ability to grasp the logical connection between ideas is a necessary skill.

Unless you’re a hermit living in a cave, there is so much information coming at all of us at any given moment.

Being able to discern which information is of worth – and which is not based in reality – requires critical thinking.

So What Exactly Is Critical Thinking?

Critical thinking is often synonymous with reflective and independent thinking. It means knowing how to take in the data and then come to a reasonable conclusion. 

Those who engage in critical thinking are constantly questioning ideas and assumptions rather than just accepting what’s being peddled to the masses.

Critical thinkers want to know that the incoming information is representative of the bigger picture. If they determine that it’s not, they’ll take the necessary measures to get that additional information.

Critical Thinking Versus Being Critical

Critical thinking is not the same thing as being argumentative or critical/judgmental of other people. Sure, critical thinking can expose errors or poor reasoning.

But it’s also crucial for cooperative reasoning and then moving toward constructive tasks. Because acquiring more knowledge improves and strengthens one’s theories and arguments. And this subsequently leads to enhanced work processes.

How Art Improves Critical Thinking

Because critical thinking tends to incorporate logical and rational thinking and veers from instinct, many people see it as a hinderance to creativity.

After all, creativity requires breaking the rules, right? (Well, yes and no .)

Still, critical thinking truly requires out-of-the-box thinking. Rather than just taking popular approaches and swallowing them whole, critical thinkers challenge the consensus. This means they often have to pursue less popular thoughts or approaches.

So if you think about, critical thinking is an absolutely necessary component of creativity. Without it, how can the creative person continue to evaluate and improve upon his or her ideas?

It’s this very process of observation and study that teaches students of the arts to more intensely observe and analyze the world. And it gives them the skills that build the foundation of critical thinking.

But Why Does It Matter?

You might think that if your path leads you to work in research, law, education, management, finance or medicine, then you’ll absolutely need this skill. And you’re right.

But no matter what you   choose to do with your life, the ability to think clearly and rationally is important.

Knowing how to receive information, clearly consider it and then use it to systematically solve problems is an asset for any career. Especially in light of this new knowledge economy. To be successful in such an economy requires one to able to handle changes quickly and effectively.

There is an increased demand for workers to be able to analyze a lot of information from diverse sources, then integrate it in order to find solutions. Critical thinking promotes these skills.

It also enhances language and presentation skills. The simple act of learning to think in a more systematic and logical fashion can also improve the way one expresses ideas.

Furthermore, in having to analyze the structure of different information sources, critical thinking also improves one’s ability to comprehend.

And as we mentioned above, critical thinking actually promotes creativity. Coming up with creative solutions is more than just having new ideas. There has to be an understanding that the new ideas are useful and relevant to the required task.   Critical thinking plays an important role in this.

That’s right. Critical thinking is even important for this. It’s nearly impossible to structure a meaningful life without the ability to justify and reflect on our own values and decisions. And critical thinking provides the tools for this process.

So yeah, it’s safe to say that critical thinking definitely matters.

Learning Critical Thinking with an Arts Integration Education

Arts integration education merges the important skill of critical thinking achieved through art education and blends it in with academics.

There’s no disputing the importance of STEM. The above mentioned knowledge economy requires students to understand facets of science, technology, engineering and math.

With arts integration though, there’s the added importance of art – hence the term STEAM. Arts integration isn’t looking to bypass STEM. It strives instead to create an integrated program that includes all of those, while teaching the application of skills learned through the arts – such as critical thinking.

Arts integration helps students see the world from multiple angles, and to take a design-thinking approach in finding solutions.

Teaching young people to be careful and deliberate observers can go miles toward expanding their worldview. And this, in turn, can create a stronger democracy.

Do You Want to Explore An Arts Integration Education?

So take a look at what our students have to say . And/or request a tour of our school and see what we have to offer.

Then get ready to put those critical thinking skills toward a higher purpose.

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Inspire Thoughtful Creative Writing Through Art

A few years ago, I showed my sixth graders The Gulf Stream by Winslow Homer. It's an epic painting of a young black sailor in a small broken boat, surrounded by flailing sharks, huge swells, and a massive storm in the distance. I asked my students the simple question, "What's happening?" The responses ranged from "He's a slave trying to escape" to "He's a fisherman lost at sea." The common theme with the responses, though, was the tone -- most students were very concerned for his welfare. "That boat looks rickety. I think he’s going to get eaten by the sharks," was a common refrain. Then a very quiet, shy girl raised her hand. "It's OK, he'll be fine," she said. "The ship will save him."

The room got quiet as everyone stared intently at the painting. I looked closely at it. "What ship?" I responded. The young girl walked up to the image and pointed to the top left corner. Sure enough, faded in the smoky distance was a ship.

This revelation changed the tone and content of the conversation that followed. Some thought it was the ship that would save him. Others thought it was the ship that cast him off to his death. Would the storm, sharks, or ship get him? The best part of this intense debate was hearing the divergent, creative responses. Some students even argued. The written story produced as a result of analyzing this image was powerful.

Since this experience, I have developed strategies that harness the power of observation, analysis, and writing through my art lessons.

Children naturally connect thoughts, words, and images long before they master the skill of writing. This act of capturing meaning in multiple symbol systems and then vacillating from one medium to another is called transmediation . While using art in the classroom, students transfer this visual content, and then add new ideas and information from their personal experiences to create newly invented narratives. Using this three-step process of observe, interpret, and create helps kids generate ideas, organize thoughts, and communicate effectively.

Step 1: Observe

Asking students to look carefully and observe the image is fundamental to deep, thoughtful writing. Keep this in mind when choosing art to use in class. Look for images with:

• Many details: If it is a simple image, there's not much to analyze.
• Characters: There should be people or animals in the image to write about.
• Colors: Find colors that convey a mood.
• Spatial relationships: How do the background and foreground relate?

Lead your students through the image. "I like it" is not the answer we are looking for. Ask questions that guide the conversation. Encourage divergent answers and challenge them. Try these questions:

• What shapes do you see? Do they remind you of anything?
• What colors do you see? How do those colors make you feel?
• What patterns do you see? How are they made?
• Do you see any unusual textures? What do they represent?
• What is the focal point of the image? How did the artist bring your attention to the focal point?
• How did the artist create the illusion of space in the image?
• If you were living in the picture and could look all around you, what would you see?
• If you were living in the picture, what would you smell? What would you hear?

Keep your questions open-ended, and record what students say so that they'll have a reference for later. Identify and challenge assumptions. At this point, we are not looking for inferences or judgments, just observations.

Step 2: Make Inferences by Analyzing Art

Once they have discussed what they see, students then answer the question, "What is happening?" They must infer their answers from the image and give specific reasons for their interpretations.

For example, while looking at The Gulf Stream , one student said, "The storm already passed and is on its way out. You can tell because the small boat the man is on has been ripped apart and the mast is broken." That is what we are looking for in their answers: rational thoughts based on inferences from data in the picture. No two responses will be exactly the same, but they can all be correct as long as the student can coherently defend his or her answer with details from the image. When children express their opinions based on logic and these details, they are analyzing art and using critical thinking skills.

Here are some tips to model a mature conversation about art:

• Give adequate wait time. We are often so rushed that we don't give children time to think and reflect.
• Ask students to listen to, think about, and react to the ideas of others.
• Your questions should be short and to the point.
• Highlight specific details to look at while analyzing art (characters, facial expressions, objects, time of day, weather, colors, etc.).
• Explain literal vs. symbolic meaning (a spider's web can be just that, or it can symbolize a trap).

Step 3: Create

After thoughtful observation and discussion, students are abuzz with ideas. For all of the following writing activities, they must use details from the image to support their ideas. Here are just a few of the many ways we can react to art:

For Younger Students:

• Locate and describe shapes and patterns.
• Describe time of day and mood of scene.
• Describe a character in detail with a character sketch. Characters may be people, animals, or inanimate objects.
• Write a story based on this image including a brand new character.
• Give students specific vocabulary that they must incorporate into their story.

For Older Students:

• Write down the possible meaning of the image, trade with a partner, and persuade your partner to believe that your story is the correct one based on details in the image.
• Identify characters and their motives. Who are they and what do they want? Explain how you know based on details.
• Pretend that you are in the image, and describe what you see, smell, feel, and hear.
• Describe the details that are just outside of the image, the ones we can’t see.
• Introduce dialogue into your story. What are they saying?
• Sequence the events of the story. What happened five minutes before this scene, what is happening now, and what happens five minutes later? How do you know?
• Write from the perspective of one of the characters in the image.
• Explain who is the protagonist and antagonist. What is their conflict?

Thinking and Communicating

We don’t know what the future holds for our students, but we do know that they will have to think critically, make connections, and communicate clearly. Art can help students do that. During this year's commencement speech at Sarah Lawrence College, Fareed Zakaria said, "It is the act of writing that forces me to think through them [ideas] and sort them out." Art can be that link to helping students organize their ideas and produce coherent, thoughtful writing.

As you consider teaching writing through art, I recommend reading In Pictures and in Words by Kate Wood Ray and Beth Olshansky's PictureWriting.org website.

How have you used the arts to inspire creative thinking in your students? Please tell us about it in the comments.

Top 7 Benefits of Art Education for Critical Thinking

If you're an art student, you understand how dynamic art education is! Art is a learning that comes in various forms. For a long time, there has been a great value in art education in enhancing analytical skills.

If you're an art student, you understand how dynamic art education is! Art is a learning that comes in various forms. For a long time, there has been a great value in art education in enhancing analytical skills.

Studies show that developing thinking skills through visual art is an excellent approach to developing critical thinking skills in students. When an image is perceived, it develops a critical thinking ability in students, which has been proven to nurture analytical skills.

Like assignment writing services , art education relies on critical thinking as its foundation, aiming to assist students in producing high-quality work. In this article, we will delve into the significance of art education and its role in fostering creativity and critical thinking among students. Importance of Art Education to Develop Critical Thinking

Art education is a dynamic field with numerous essential elements that contribute to the broader educational landscape. Beyond aiding students in acquiring analytical skills, art education provides a multitude of benefits. It's accurate to assert that art and critical thinking are interconnected.

To cultivate analytical skills and articulate them through visual expression, art education becomes indispensable. This parallels the necessity of college paper writers , crucial for enhancing writing skills during your college journey, enabling success in exams and assignments.

Let's explore the myriad advantages that art education offers, including the development of creativity, critical thinking, emotional intelligence, and proficiency in various disciplines.

1.   Creativity and Critical Thinking

Art has its base in various forms; it could teach painting, drawing sketches, or anything else.

Whatever it is, art education lies in enhancing creativity, a skill that must be in today's changing world. When you encourage students to engage in such creative experiments, you allow them to explore the creativity and unique perspective art education offers.

It goes hand in hand with critical thinking as well. When students indulge in any form of art, they are prompted to analyze, interpret, and critique the artwork.

This practice enhances their ability to assess information, form their viewpoint, and make an informed judgment about it. The whole process builds a thoughtful perspective in both complex and interconnected ways.

2.   Cognitive and Emotional Development

Art students are liable to build strong cognitive and emotional skills. With the creation of art, they enhance the skills of observation, pattern recognition, and reasoning.

They can abstract these concepts into a form, holding their thinking ability accountable to form perspective and thoughts. When further enhanced, these skills grow into an ability to solve problems and analyze.

Emotional development is yet another aspect that art education touches. Art is a power of expression. Through it, students can explore their creativity and mental health.

3.   Promoting Cultural Understanding

Art is a unique ability to promote a country's or regional cultural understanding among the students. They will learn to have an appreciation for the work they perform.

Art education touches on various cultures and periods, and students gain insight into the value and histories surrounding the art. It has no language barrier, communication issues, or anything. It allows the student to go beyond their understanding and into the world of imagination to understand and appreciate the art.

Students learning art education learn about different artists and their backgrounds. This learning allows them to develop empathy and open-mindedness. They can appreciate the diversity of art and recognize the themes that connect the universe.

It goes against the stereotypes and fosters a culture of respect in cultures and celebrates them rather than fear. This equips them with global empathy and respect for different traditions and viewpoints.

4.   Integration in Curriculum

Including art in the school or education curriculum is an excellent approach to maximizing its benefits. While art is seamlessly woven into any subject, students experience firsthand connection with the knowledge.

Students studying art from a specific time can enhance their knowledge of history and gain insight into a political-social context. Art has also proven to be beneficial for science education.

This approach allows students to learn art in their own curriculum and helps enhance their learning ability.

It helps them build connections between the disciples and the complexities of real-world challenges. By integrating art, the school can prepare its students to become innovative thinkers who can apply creative and critical skills in various contexts.

5.   Embracing Versatility

Painting, drawing, sculptures, painting, photography, and other art education forms can experiment with various materials and approaches. Students could be learning digital art, fine art, or ceramics, but one thing in common is their ability to explore.

Art is not limited to a particular aspect and has various forms. Students who are involved in art education can select from a wide range of course approaches and learn about them.

We now live in a world where transdisciplinary is highly valued, so in this context, flexibility becomes priceless. Art education provides a medium for students to explore their field of want and interest and get educated in it.

6.   Exploring Career Opportunities

Along with developing analytical and emotional skills, art education has its own roots in defined career paths. Contrary to the stereotype in our society that fine art only leads to struggling artists, it opens the door to various career paths.

Students interested in art and a graduate degree can practice various occupations. When studying art, students exhibit their work and explore other avenues of art like art education, art therapy, museum curation, graphic design, art conservation, and more.

When more refined, this skill allows them to be a successful worker in this field. Further, art students are also creative, critical thinkers, and visual communicators. These skills are highly demanded in the world.

7.   Personal Achievement

While studying art has benefits and advantages, like helping in critical thinking and developing analytical skills, it is also about personal fulfillment. Students are on their journey to self-discovery and are on a road of continuous growth.

Art education provides students with an opportunity to learn about themselves and about art.

They get a feeling of fulfillment from creative, beautiful, and thought-provoking pieces. Art allows you to explore your own areas of identity, passion, and values.

Other than subject matter, art education also teaches students to learn more about themselves, the culture, work, and the values behind the artwork. This leads them to a path of personal fulfillment and self-expression that goes beyond traditional education.

In conclusion, art education is a medium that enhances various aspects of human development in students. It allows them to develop their critical thinking ability. It leads them to nurture their analytical skills through visual expression. Further, it's mentioned to be a great way to enhance creativity and promote emotional intelligence.

By including art education in the regular curriculum, students learn to be more self-aware and authentic to art's value, from cultural appreciation to its impact. Students are equipped with the tools they need to thrive in the world, like innovation, empathy, and knowledge.

In this article, we mentioned the top 7 benefits of studying art and how it positively impacts a student's mindset and creates positive learners in life.

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Anna Melnykova, "Palace of Labor (palats praci), architector I. Pretro, 1916", shot with analog Canon camera, 35 mm Fuji film in March 2022.

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Strengthen Your Students’ Critical Thinking Skills by Playing Art Detective

We all know that Critical Thinking is a vital 21st Century Skill for our students. However, sometimes it’s difficult to think about presenting the concept to very young students. The good news is that with a little imagination, anything is possible. Today I’m sharing a simple activity you can use with your youngest students to begin to develop their critical thinkings skills.  

The activity is called Art Detective and is super simple to pull off.

  It would be perfect for an introduction to a project or theme, or an excellent option to pull out when you have 15 extra minutes of class. Here’s how to do it.  

Help your students become art detectives.

1. get into costume..

2. Choose a piece of art for students to “investigate.”

If you’re using this as an introduction to a project or theme, you may want to use a specific piece of art. Most likely, your choice will only be available in poster form. However, if you’re doing this activity outside of a specific project, why not bring in a real, physical piece of art? This could be a painting you’ve done (don’t tell them!), a piece of work done by a high school student in your district, or something you have hanging in your home. There is something about a real piece of art that truly engages students. In addition, don’t feel as though you have to limit your choices to 2D works. Ceramic pieces, sculptures, weavings, and artifacts also all work well. In fact, if you don’t know anything about the piece yourself, it can lead to a much more authentic discussion.    

3. Set the stage.

Explain the premise of the activity: You have just discovered the piece of art you are holding (or showing) and you have no idea what it is or what it’s about. You need the students help to figure it out!    

4. Guide the discussion without judgment.

If students are coming to different conclusions than the artist or different conclusions than you, it’s OK! Ask follow-up questions to reveal their thought processes. “What makes you think the person feels angry?” or “What about the picture makes you think it was made with fabric?” are two examples of these types of questions. I guarantee you will be blown away by their ideas and insights.

The beauty of this activity is that just by participating, students are developing critical thinking skills. The NEA has a helpful document available for download called “ An Educator’s Guide to the ‘Four Cs’ ” which details how part of critical thinking is making judgments and decisions. Specifically, students should develop skills to “Effectively analyze and evaluate evidence, arguments, claims, and beliefs,” and, “Interpret information and draw conclusions based on the best analysis,” and finally, “Identify and ask significant questions that clarify various points of view and lead to better solutions.”

Over time, providing your students with opportunities like playing Art Detectives will do just that! For even more insight into helping students analyze art, check out the following articles and lesson plan.  

• Slow Looking and 5 Other Simple Activities to Enhance Your Students’ Ability to Analyze Art 
• Five Easy Steps for Talking with Children About Art (via Tinkerlab )
• Artists Analyze: Free Lesson Plan Download

How do you get young students to begin to think about artwork in a critical way?

Do you have any favorite art pieces for them to analyze?

Magazine articles and podcasts are opinions of professional education contributors and do not necessarily represent the position of the Art of Education University (AOEU) or its academic offerings. Contributors use terms in the way they are most often talked about in the scope of their educational experiences.

Amanda Heyn

Amanda Heyn is AOEU’s Director of K–12 PD & Media and a former AOEU Writer and elementary art educator. She enjoys creating relevant and engaging professional development just for art teachers.

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College minor: everything you need to know, 14 fascinating teacher interview questions for principals, tips for success if you have a master’s degree and can’t find a job, 14 ways young teachers can get that professional look, which teacher supplies are worth the splurge, 8 business books every teacher should read, conditional admission: everything you need to know, college majors: everything you need to know, 7 things principals can do to make a teacher observation valuable, using the arts to develop children’s critical thinking skills.

It’s no doubt that critical thinking is essential to education and, ultimately, success in life, but does developing this skill have to be so hard ?

As parents and teachers, we can get caught up in the “critical” aspect of critical thinking, often turning the acquisition of complex processing and problem-solving abilities into an overly serious matter of assigning elaborate math and science problems or forcing our kids to try to think in ways that their brains are not developed enough to understand. Although the development of these right-brained skills is part of the critical thinking process, we spend a meager amount of time and effort teaching the equally important creative, inquisitive thought patterns that the arts encourage.

Using Art to Harness Innate Curiosity

Children have unmatched levels of curiosity by nature, and strengthening our schools’ arts programs could be the solution to teaching the critical thinking skills that are necessary to keep the world functioning for future generations.

Think back on your elementary school experience for a moment when math, science, and the more “practical” classes were largely theoretical endeavors involving unknown variables and untouchable subject matter. The arts, however, provide students with hands-on learning, real-time problem solving and the ability to bring the hypothetical down to earth.

According to Dictionary.com , critical thinking is “disciplined thinking that is clear, rational, open-minded and informed by evidence.” When employed, critical thought enables us to make objective judgments about stimuli and information to find a solution to a given problem. With art education, students learn to take a slower, more observant approach to the world, giving them greater access to the clues that make solving complex problems possible.

Researchers at Walden University agree that guiding children to observe, examine and reflect on pieces of art, translates to a more careful analysis when problem-solving in other situations. Not to mention, growing students’ appreciation for art helps to improve tolerance, empathy, and resiliency, which are crucial to producing solutions that benefit society as a whole.

How to Implement Art in the Classroom

It’s one thing to understand the importance of art in critical thinking, but how can we take this, again, theoretical evidence and apply it in classrooms? Arts integration is a powerful method that employs the arts in every subject. When teaching history, for example, encourage students to draw upon their creative, left-brain functioning to act out important events, create theme-appropriate music, or illustrate interpretations of your lesson.

STEM (Science, Technology, Engineering, and Math) programs get most of the attention these days, but recent movements make a place for art within this framework by creating STEAM (STEM + Arts) classrooms, which utilize self-expression and other arts integration techniques to create a balanced learning experience.

After all, careers in STEM fields – like computer programming and engineering – boil down to precise applications of artistic solutions to real-world problems. STEAM proves that creativity and practical knowledge can (and should) coexist in schools. Historically speaking, art drives science and science drives art . Therefore, the arts more than deserve a place in every classroom’s curriculum. How else would we nurture our kids’ curiosity and develop the critical thinking skills necessary to ponder, digest, and solve all of the world’s abstract problems?

How do you integrate the arts into your classroom? Drop a comment below to keep the conversation going!

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Critical thinking definition

Critical thinking, as described by Oxford Languages, is the objective analysis and evaluation of an issue in order to form a judgement.

Active and skillful approach, evaluation, assessment, synthesis, and/or evaluation of information obtained from, or made by, observation, knowledge, reflection, acumen or conversation, as a guide to belief and action, requires the critical thinking process, which is why it's often used in education and academics.

Some even may view it as a backbone of modern thought.

However, it's a skill, and skills must be trained and encouraged to be used at its full potential.

People turn up to various approaches in improving their critical thinking, like:

• Developing technical and problem-solving skills
• Engaging in more active listening
• Actively questioning their assumptions and beliefs
• Seeking out more diversity of thought
• Opening up their curiosity in an intellectual way etc.

Is critical thinking useful in writing?

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The liberal arts math revolution: how math is more than just numbers

Whether we know it or not, math is integrated into many aspects of our daily lives. This article answers the question, “What is liberal arts math?” and explores how math concepts are incorporated into other core disciplines. Learn how liberal arts math can help you build your analytical, critical, and problem-solving skills and help you prepare for a variety of career paths.

What is liberal arts math?

Liberal arts math typically includes a comprehensive interdisciplinary approach, meaning courses are designed to align with other foundational subjects to build the mathematical know-how to solve real-world issues.

For example, liberal arts math courses can help you develop skills in quantitative reasoning, statistics, sampling bias, and exponential growth, which can be applied to disciplines including economics, political science, psychology, and social sciences.

Common topics in liberal arts math include applied statistics, linear algebra, logic and probability, geometry, game theory, philosophy of math, problem-solving, and everyday applications for mathematics.

Liberal arts math vs. traditional math

Traditional mathematics tends to focus on standard math sequences or calculations that are taught in isolation. For instance, when you were a child, you may have relied on memorization to learn your multiplication tables.

On the other hand, the goal of liberal arts math is to increase your understanding of mathematical basics and develop high-order reasoning skills that you can apply in practical contexts.

For instance, in MTHS 2000: Mathematics All Around You at Penn LPS Online, you’ll learn how math and logic provide the framework for everything—from quickly calculating a discount in your head to writing a story or presenting a persuasive argument in court.

Is math for liberal arts easy?

Easy is a relative term. If you find traditional mathematics easy, then you’ll likely feel the same way about liberal arts math. Conversely, if you struggle with traditional math, the same may be true with math designed for liberal arts students—although likely to a lesser extent.

That’s because rather than focusing strictly on numbers, concepts, equations, or calculations, liberal arts math incorporates real-world learning scenarios that draw from other disciplines. To that end, the concepts you learn in MTHS 3000: Linear Algebra are critical to the study of fields such as physics, chemistry, economics, computer science, and data science.

Liberal arts math concepts

Once you discover how frequently mathematical models are featured in other liberal arts disciplines, you’ll likely gain a greater understanding of why math is called “the language of the universe.”

Math and art

The connection between math and art can be seen throughout history. Pre-Columbian cultures demonstrated knowledge of geometric patterns in many of their aesthetic artifacts. Early and High Renaissance artists also used mathematical concepts, such as perspective and symmetry, to make their paintings and sculptures appear more realistic.

Examples of well-known art and artists that showcase mathematic principles include:

• The Parthenon: Phidias used the golden ratio (1.618) in his designs for sculptures in this grand architectural feat of Antiquity.
• Vitruvian Man and Mona Lisa: Leonardo Da Vinci used math to calculate the ideal proportions of the human body for the Vitruvian Man, which was drawn within geometric shapes. He also utilized the golden ratio to create proportions for the face, head, and neck of the Mona Lisa.
• Abstract modernist artwork: Bauhaus artist Wassily Kandinsky used mathematical forms like concentric circles, triangles, and open and closed lines in his paintings. Although it may not be readily apparent, abstract expressionist Jackson Pollock used the repetition of the geometric model of fractals in his work.

Math and literature

You may be surprised to learn that the underlying structure, pattern, and uniformity of math can also be found in literature. This makes sense when you stop to think about it, given that good writing relies on the same types of arrangement and form inherent to successful math equations.

There are metaphors related to cycloids (or mathematical curves) in Herman Melville’s Moby-Dick . Other famous authors such as James Joyce and Leo Tolstoy include references to geometry and calculus in their respective works. And, interestingly, Julio Cortazar encourages readers to traverse the maze of chapters in the novel  Hopscotch by picking a linear or non-linear structure of reading, which changes the story’s perspective.

Principles of algebra (or formulas) also prescribe the number of syllables that define different forms of poetry including:

• “Fib” poems, based on the Fibonacci sequence in math (1,1,2,3, 5, 8, 13, 21)
• Haikus, which include three lines with a total of 17 syllables
• Sonnets, which have 14 lines with 10 syllables per line
• Cinquain verses of five lines that don’t rhyme  

Math and philosophy

Not only does a branch of philosophy called metaphysics rely on advanced math concepts to help us understand the universe, the philosophy of mathematics is also a distinct area of study. The philosophy of math is a branch of epistemology, which is the investigation of how humans know things.

This philosophy is focused on cognition, including determining how mathematical knowledge fits into the wider scheme of things. Mathematics philosophers also question how we can refer to or know of mathematical objects if they don’t have causes or effects.

Four schools of thought in the philosophy of math include:

• Logicism: Supposes that mathematical truths are logical truths
• Intuitionism: Argues that math is a creation of the mind
• Formalism: Reduces math and logic to rules for manipulating formulas without reference to meaning
• Predicativism: Supposes that math should be restricted to the study of objects that can be quantified predicatively

Math as a language

As the most fundamental type of logic possible, mathematics is routinely referred to as “the language of science” and “the language of the universe.” Generally, to be considered a language, there must be vocabulary, syntax, grammar, narrative, and people who use and comprehend it.

Math meets these criteria as a universal language whose symbols and organizations comprise equations that are recognized and understood worldwide. Additionally, mathematicians, scientists, educators, and others use math to communicate both real-world and abstract concepts.

The importance of liberal arts math

Without a basic understanding of math, it would be difficult to function effectively in the world. Math is involved in everything from baking and telling time to setting and keeping a budget and filing your taxes.

If you wish to attend college, not only do you need to meet the necessary math prerequisites, but math skills are also critical to doing well on standardized tests such as the SAT, ACT, GRE, GMAT, and LSAT.

Read on to explore other ways that math can be beneficial to your ability to thrive.

Critical thinking and problem-solving skills

Did you know that reading and solving arithmetic problems has been shown to improve brain health and cognitive function? Starting with word problems in elementary school, math forms the groundwork to help students develop critical thinking and problem-solving skills with real-world applications.

Later in life, a strong understanding of algorithms and other math concepts provides the basis for analytical and logical reasoning skills that are essential to finding solutions to personal, professional, and academic issues. This may include navigating an argument, preparing a work presentation, or authoring a persuasive essay.

Creativity and innovation

Flexible thinking and creativity spur innovation. Research shows that math training can enhance investigative skills, resourcefulness, and creativity. Creativity involves combining ideas that have no obvious relationship to develop new forms of expression or unique solutions to problems. Mathematicians routinely use existing knowledge to find new connections within the mathematical world that can be used to address real-world issues. For example, statistics and probability are utilized to make predictions for scenarios involving financial markets, climate change and weather patterns, or the spread of disease and viruses (such as with COVID-19).

Preparation for a wide range of careers

Building a strong foundation in math can also help prepare students for their future career paths, whether they are related to math or not.

Math courses are typically included in the general education requirements for most bachelor’s degree programs. The ability to identify and analyze patterns and use logic, critical thinking, and problem-solving skills are valued in industries including business, healthcare, marketing, finance, psychology, social sciences, manufacturing, and more.

There are also many jobs that rely heavily on math concepts such as scientists, architects, and accountants. Examples of in-demand STEM roles and their predicted job growth rates by 2031 include:

• Data scientists (36%)
• Information security analysts (35%)
• Logisticians (28%)
• Statisticians (33%)
• Web developers (30%)

Explore the future of liberal arts math at Penn LPS Online

Interested in combining the analytical tools of data science with a practical understanding of the social sciences? Read more about the Data Analytics and Social Sciences concentration for the Bachelor of Applied Arts and Sciences (BAAS) degree at Penn LPS Online.

In this program, you’ll develop statistical and data programming skills to solve everyday issues, learn how to make and communicate data-driven decisions, and customize your credential with Ivy League courses in organizational anthropology, global and area studies, leadership, and other social sciences.

Develop the expertise to:

• Implement and analyze surveys and basic regression models
• Understand predictive modeling and machine learning
• Create experiments and A/B tests to solve real-world problems
• Obtain skills in statistical programming and data analysis in R
• Use visualization to make complex information more accessible
• Develop rhetorical strategies to effectively persuade audiences

If you haven’t already, apply to Penn LPS Online today, and enroll in the Data Analytics and Social Sciences concentration for the BAAS degree . You can also register for individual classes or view our course guide to see what’s available in any upcoming term.