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2023, Article

Doing mathematics means that students are engaged in learning mathematics through reasoning and problem solving (NCTM, 2014). Prospective mathematics teachers need to learn about how to engage students in solving and talking about tasks that can be tackled in different ways by different students. Mathematically, proficient students are able to make sense of a situation, select solution paths, consider alternative strategies and monitor their progress (CCSSO, 2010). Before we can be effective in teaching mathematics, we need to have a good knowledge about what we are supposed to be teaching and how students learn mathematics. We are familiar with why we teach mathematics at the basic and high schools.

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Problem Solving in Mathematics Education

by Peter Liljedahl, Manuel Santos-Trigo, Uldarico Malaspina, Regina Bruder

Problem Solving in Mathematics Education

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Problem-solving approaches appear in all human endeavors. In mathematics, activities such as posing or defining problems and looking for different ways to solve them are central to the development of the discipline. In mathematics education, the systematic study of what the process of formulating and solving problems entails and the ways to structure problem-solving approaches to learn mathematics has been part of the research agenda in mathematics education. How have research and practicing problem-solving approaches changed and evolved in mathematics education, and what themes are currently investigated? Two communities have significantly contributed to the characterization and development of the research and practicing agenda in mathematical problem-solving: mathematicians who recognize that the process of formulating, representing, and solving problems is essential in the development of mathematical knowledge (Polya 1945 ; Hadamard 1945 ; Halmos 1980 ) and mathematics...

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Santos-Trigo, M. (2020). Problem-Solving in Mathematics Education. In: Lerman, S. (eds) Encyclopedia of Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-15789-0_129

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    The aim of the present paper is to present and discuss the recent progress of the. problem solving process in mathematics education. 1. Introduction. Problem - Solving (P-S) is a principal ...

  2. PDF Problem Solving in Mathematics Education

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    2012. In Bergqvist, T (Ed) Learning Problem Solving and Learning Through Problem Solving, proceedings from the 13th ProMath conference, September 2011 (pp. 5-16). Umeå, UMERC. 5 The solving of problems and the problem of meaning The case with grade eight adolescent students Sharada Gade Umeå Mathematics Education Research Centre, Umeå University

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    Problem Solving in Mathematics Education. Download PDF Viewer. Web Shop.

  8. [PDF] Problem Solving in Mathematics Education

    The importance for learners to formulate and pursue their own problems and the role played by the use of both multiple purpose and ad hoc mathematical action types of technologies in problem solving activities are reviewed. Problem solving in mathematics education has been a prominent research field that aims at understanding and relating the processes involved in solving problems to students ...

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    this study, problem-solving refers to the common situational problems in mathematics in a form of problem set or worded problems. The problems are composed of items in arithmetic and algebra, trigonometry, geometry, sets, probability, number theory and puzzle problem/logic. Hence, with the main goal of mathematics education to improve

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    Abstract and Figures. Problem solving in mathematics education has been a prominent research field that aims at understanding and relating the processes involved in solving problems to students ...

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    Singer et al. ( 2013) provides a broad view about problem posing that links problem posing experiences to general mathematics education; to the development of abilities, attitudes and creativity; and also to its interrelation with problem solving, and studies on when and how problem-solving sessions should take place.

  14. (PDF) The problem-solving process in a mathematics classroom

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    This framework was updated in 2009 (NCTM 2000, 2009) and conceptualizes a problem-solving approach as a way of fostering mathematical reasoning and sensemaking activi-ties. Throughout the proposal, there are different examples in which reasoning and sensemaking activities are interwoven.

  16. [PDF] Examples of Problem-Solving Strategies in Mathematics Education

    Teachers and educators are provided with methods, learning models, and strategies for developing 21st-century skills in students at all levels during classroom activities on Polya's heuristic. The overall aim of education is to train proactive, motivated, and independent citizens to face and overcome continuous challenges. Critical thinking—finding solutions to problems—is of primary ...

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    Doing mathematics means that students are engaged in learning mathematics through reasoning and problem solving (NCTM, 2014). Prospective mathematics teachers need to learn about how to engage students in solving and talking about tasks that can be tackled in different ways by different students.

  18. [PDF] Evaluating Problem Solving in Mathematics.

    1982. 1,061. PDF. In its Curriculum and Evaluation Standards for School Mathematics, the National Council of Teachers of Mathematics expanded the goals it developed in 1980 for promoting problem solving as a curricular focus (NCTM 1989). The first three stan dards — Mathematics as Problem Solving, Mathematics as Reasoning, and Mathematics as ...

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    He has led two large-scale mathematics education research projects on mathematical problem solving and continues to publish papers on this subject. Manuel Santos-Trigo is Professor at the Mathematics Education Department, Centre for Research and Advanced Studies, Cinvestav-IPN, Mexico.

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    Book Description This survey book reviews four interrelated areas: (i) the relevance of heuristics in problem-solving approaches - why they are important and what research tells us about their use; (ii) the need to characterize and foster creative problem-solving approaches - what type of heuristics helps learners devise and practice creative solutions; (iii) the importance that learners ...

  22. PDF EDUC 4301: Mathematical Problem Solving in EC6, Fall 2024 Monday 1:00-3

    2. th6 Grade Equivalency Test: Each student will complete two 6th Grade Equivalency Tests in Mathematics during the semester. The tests will have 40-50 questions and students will have 60 minutes to complete each test. One test will be during the first week of the semester, and the second test will be during the last week of the semester.

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