Mathematical Problem Solving
Current Themes, Trends, and Research
- © 2019
- Peter Liljedahl 0 ,
- Manuel Santos-Trigo 1
Faculty of Education, Simon Fraser University, Burnaby, Canada
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Department of Mathematics Education, Cinvestav-Instituto Politecnico Nacional, Mexico City, Mexico
- Brings together some of the latest research on problem solving
- Offers international perspectives on current themes, trends, and research on problem solving
- Presents multiple frameworks and views on problem solving
Part of the book series: ICME-13 Monographs (ICME13Mo)
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Table of contents (15 chapters)
Front matter, problem solving heuristics, “looking back” to solve differently: familiarity, fluency, and flexibility.
- Hartono Tjoe
Future-Oriented Thinking and Activity in Mathematical Problem Solving
- Wes Maciejewski
Problem Solving and Technology
A model of mathematical problem solving with technology: the case of marco solving-and-expressing two geometry problems.
- Susana Carreira, Hélia Jacinto
Mathematical Problem Solving and the Use of Digital Technologies
Manuel Santos-Trigo
The Spreadsheet Affordances in Solving Complex Word Problems
- Nélia Amado, Susana Carreira, Sandra Nobre
Inquiry and Problem Posing in Mathematics Education
Is an inquiry-based approach possible at the elementary school.
- Magali Hersant, Christine Choquet
How to Stimulate In-Service Teachers’ Didactic Analysis Competence by Means of Problem Posing
- Uldarico Malaspina, Carlos Torres, Norma Rubio
Assessment of and Through Problem Solving
The impact of various methods in evaluating metacognitive strategies in mathematical problem solving.
- Mei Yoke Loh, Ngan Hoe Lee
Assessing Inquiry-Based Mathematics Education with Both a Summative and Formative Purpose
- Maud Chanudet
Beyond the Standardized Assessment of Mathematical Problem Solving Competencies: From Products to Processes
- Pietro Di Martino, Giulia Signorini
Toward Designing and Developing Likert Items to Assess Mathematical Problem Solving
- James A. Mendoza Álvarez, Kathryn Rhoads, R. Cavender Campbell
The Problem Solving Environment
Creating and sustaining online problem solving forums: two perspectives.
- Boris Koichu, Nelly Keller
Conditions for Supporting Problem Solving: Vertical Non-permanent Surfaces
Peter Liljedahl
The ARPA Experience in Chile: Problem Solving for Teachers’ Professional Development
- Patricio Felmer, Josefa Perdomo-Díaz, Cristián Reyes
- Mathematical problem solving
- Problem solving heuristics
- Problem posing in mathematics education
- Problem solving environment
- Future-oriented Thinking in Mathematical Problem Solving
- Mathematical problem solving with technology
- Spreadsheet affordances in solving complex word problems
- Didactic analysis by means of problem posing
- Mathematical problem solving competencies
- Activating Problem Solving in the Classroom
- Creating and sustaining online problem-solving forums
- Methods in Evaluating Metacognitive Strategies
About this book
This book contributes to the field of mathematical problem solving by exploring current themes, trends and research perspectives. It does so by addressing five broad and related dimensions: problem solving heuristics, problem solving and technology, inquiry and problem posing in mathematics education, assessment of and through problem solving, and the problem solving environment.
Mathematical problem solving has long been recognized as an important aspect of mathematics, teaching mathematics, and learning mathematics. It has influenced mathematics curricula around the world, with calls for the teaching of problem solving as well as the teaching of mathematics through problem solving. And as such, it has been of interest to mathematics education researchers for as long as the field has existed. Research in this area has generally aimed at understanding and relating the processes involved in solving problems to students’ development of mathematical knowledge and problem solving skills. The accumulated knowledge and field developments have included conceptual frameworks for characterizing learners’ success in problem solving activities, cognitive, metacognitive, social and affective analysis, curriculum proposals, and ways to promote problem solving approaches.
“The volume will be a useful addition to the libraries of education researchers and to mathematics teacher educators who are charged with supporting preservice or inservice teachers’ development of capacities to incorporate problem solving into their instruction. … this volume offer interesting insights into the phenomenon of problem solving and the technological tools and learning environments that support students to engage in problem solving.” (Duane Gaysay, MAA Reviews, August 16, 2020)
Editors and Affiliations
Bibliographic information.
Book Title : Mathematical Problem Solving
Book Subtitle : Current Themes, Trends, and Research
Editors : Peter Liljedahl, Manuel Santos-Trigo
Series Title : ICME-13 Monographs
DOI : https://doi.org/10.1007/978-3-030-10472-6
Publisher : Springer Cham
eBook Packages : Education , Education (R0)
Copyright Information : Springer Nature Switzerland AG 2019
Hardcover ISBN : 978-3-030-10471-9 Published: 21 February 2019
eBook ISBN : 978-3-030-10472-6 Published: 12 February 2019
Series ISSN : 2520-8322
Series E-ISSN : 2520-8330
Edition Number : 1
Number of Pages : XI, 362
Number of Illustrations : 30 b/w illustrations, 82 illustrations in colour
Topics : Mathematics Education , Teaching and Teacher Education , Study and Learning Skills , International and Comparative Education
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Mathematical Problem Solving
This book covers twelve different problem-solving topics including Looking for a Pattern, Making the Problem Simpler, Making a Table and Working Backwards.
It is designed to assist teachers in teaching problem solving with students in years 4 to 8 and includes fully worked examples and questions with full solutions.
It is presented ready to be photocopied for classroom use.
Author: David Kennedy
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Writing, Mathematics, and Metacognition: Looking for Connections through Students' Work in Mathematical Problem Solving.
2001, School Science and Mathematics
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Mathematical problem solving is considered as one of the many endpoints in teaching Mathematics to students. This study looked into the performance in mathematics problem solving among fourth year students of Central Mindanao University Laboratory High School and their relationship with students’ attitudes towards Mathematics. The attitudes measured were Attitude towards success in Math, Mother’s mathematics attitude, Father’s mathematics attitude, Motivation, Usefulness of Math, Teacher’s mathematics attitude, Confidence in learning math, and mathematics anxiety. It also investigated the metacognitive processes of students considering varying levels of their mathematics anxiety. It used the responses of 127 students. Of the 127, (nine) 9 were selected according to their mathematics anxiety levels to determine and compare their metacognitive processes. Results showed that students consider Mathematics as useful and they have a positive attitude towards success in Mathematics. The students’ fathers, mothers, and teachers also have positive attitudes towards their mathematics learning. However, overall, the students’ performance in mathematics problem solving is considered poor. Among the eight (8) mathematics attitudes only confidence in learning Math and mathematics anxiety were correlated with performance in mathematics problem solving. Confidence in learning Math was positively correlated, while mathematics anxiety was negatively correlated with performance in mathematics problem solving. Students with high mathematics anxiety tend to confirm their solutions with their classmates. Students with moderate anxiety are test-anxious and those with low anxiety are distracted by external factors, but can readily shift their focus back to problem solving. The three (3) cases showed that students with low, moderate, and high mathematics anxiety employed mostly orientation and execution procedures. There were only few instances of verification and lesser instances of organization procedures. Self-questioning was the most observed metacognitive skill. Furthermore, students from the three (3) cases were unable to correctly answer two (2) problems, both of which are non-routine due to unfamiliarity and ‚experiential interference‛.
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This book contributes to the field of mathematical problem solving by exploring current themes, trends and research perspectives. It does so by addressing five broad and related dimensions: problem solving heuristics, problem solving and technology, inquiry and problem posing in mathematics education, assessment of and through problem solving, and the problem solving environment.
Author: David Kennedy. More from this collection. Mathematics Contests: The Australian Scene 2014-2022 PDF ... This book covers twelve different problem-solving topics including Looking for a Pattern, Making the Problem Simpler, Making a Table and Working Backwards. It is designed to assist teachers in teaching problem solving with students in ...
Description. Mathematical Problem Solving provides information pertinent to the nature of mathematical thinking at any level. This book provides a framework for the analysis of complex problem-solving behavior. Organized into two parts encompassing 10 chapters, this book begins with an overview of the four qualitatively different aspects of ...
8 The assessment of mathematical problem solving Siemon (1986) has criticised such an ''appendage in Australia mentality'' in relation to problem solving: During the 1990s, a consistency could be seen in the trends 'To spend the majority of one's time ''doing mathe- in mathematics assessment in communities as geographi- matics ...
on life and on mathematics is different now than it was when I was 15. I have not been involved in problem-solving competitions for a very long time now, and if I were to write a book now on the subject it would be very different from the one you are reading here. Mathematics is a multifaceted subject, and our experience and appreci-
All content in this area was uploaded by David Kennedy on Feb 03, 2022 . ... mathematics, and philosophy through spontaneous and planned activities with ... Problem solving activities.
Therefore, high-quality assessment of problem solving in public tests and assessments1 is essential in order to ensure the effective learning and teaching of problem solving throughout primary and secondary education. Although the focus here is on the assessment of problem solving in mathematics, many of the ideas will be directly transferable ...
David Bradbard. 1977. Five papers from the Workshop cn Mathematical Problea Solving sponsored by the Georgia Center for the Study of Learning and Teaching Mathematics are included along with an overview of the interests and history of the Center and its organization cf the problem-solving workshop. One paper contains an overview of mathematical ...
Mathematical problem solving: An evolving research and practice domain. September 2007. ZDM: the international journal on mathematics education 39 (5):523-536. DOI: 10.1007/s11858-007-0057-9 ...
This book is about encouraging pupils to 'be mathematical' in the sense that they: think about and communicate ideas; engage in problem-solving activities; . create and identify mathematical problems within given contexts. . Clearly, being mathematical and doing mathematics in this sense involves some mathematical content knowledge.
The particular mathematical skills we need to use when problem solving are more than numeric, geometric and algebraic manipulation. They include ideas such as: l modelling; l visualising; l working systematically; l generalising. We would class these skills as elements of mathematical thinking that are needed to engage in mathematical problem ...
Loren Larson is professor of mathematics at St. Olaf College. His email address is [email protected]. "love and delight are better teachers than compulsion.". One means of promoting prob-lem solving is by organizing math contests, and there are now a variety of contests and plenty of opportunities for participation.
on life and on mathematics is different now than it was when I was 15. I have not been involved in problem-solving competitions for a very long time now, and if I were to write a book now on the subject it would be very different from the one you are reading here. Mathematics is a multifaceted subject, and our experience and appreci-
While visualization has been shown to play a crucial role in enhancing students' understanding of mathematical concepts and promoting problem-solving skills (Osman et al., 2018), research on the ...
Moreover a mathematical problem should be di cult in order to entice us, yet not completely inaccessible, lest it mock at our e orts. It should be to us a guide Reprinted from Bull. Amer. Math. Soc. 8 (July 1902), 437{479. Originally published as Mathematische Probleme. Vortrag, gehalten auf dem internationalen Mathematike-Congress zu Paris ...
Go back to the original problem later, and see if you can solve it in a different way. Many of the problems have multiple solutions, but not all are outlined here. All terms in boldface are defined in the Glossary. Use the glossary and the reading list to further your mathematical education. Meaningful problem solving takes practice. Don't get ...
• Problem solving strategies - Explicitly teach problem solving strategy - Once mastered, explicitly teach how to transfer to novel situations, structure - Explicitly teach categorization - Best when taught with self-regulated learning strategies (Fuchs and Fuchs in Berch, D.B. & Mazzocco, M.M. (Eds). 2009.)
236 Writing, Mathematics, and Metacognition: Looking for Connections Through Students' Work in Mathematical Problem Solving David K. Pugalee University of North Carolina at Charlotte This study investigated whether students' writing about their mathematical problem solving processes showed evidence of a metacognitive framework.
Pdf_module_version 0.0.18 Ppi 360 Rcs_key 24143 Republisher_date 20220618190636 Republisher_operator [email protected] Republisher_time 237 Scandate 20220617102515 Scanner station54.cebu.archive.org Scanningcenter cebu Scribe3_search_catalog isbn Scribe3_search_id 9780030928000 Tts_version 5.1-refactored-15-g1773b315 ...
In the book Thinking Mathematically that John Mason wrote with Leone Burton and Kaye Stacey, the term 'proof' never appears. On enquiring the reason for this, John expressed the deep fear that the word 'proof' engendered in his Summer School students. In this paper I will reflect on the development of mathematical thinking in the individual ...
Guzman Gurat M. (2018) "Mathematical problem-solving strategies among student teachers", Journal on Efficiency and Responsibility in Education and Science, Vol. 11, No. 3, pp. 53-64, online ISSN 1803-1617, printed ISSN 2336-2375, doi: 10.7160/ eriesj.2018.110302. MATHEMATICAL PROBLEM-SOLVING STRATEGIES AMONG STUDENT TEACHERS Abstract
David Patrick. Publication date 2005-11 Topics Combinatorics, Math, AOPS, Problem Solving Collection opensource Language English. Math, AOPS Combinatorics. Addeddate 2023-07-07 16:29:21 Identifier introduction-to-counting-probability Identifier-ark ... PDF download. download 1 file ...
It is not possible to learn math-ematics by reading a textbook like a novel. Good mathematics students, from elementary school to graduate school, read a math book with pencil and paper in hand. Mathematics is not a collection of independent topics. It is not \Algebra I," \Algebra II," \Trigonometry," \Plane Geometry," etc. All of mathematics is