Skip to main content
SpringerLink
Log in
Book cover

Encyclopedia of Mathematics Education pp 686–693Cite as

Problem-Solving in Mathematics Education

  • Reference work entry
  • First Online:

Introduction

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...

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   499.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   699.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  • Artigue M, Houdement C (2007) Problem solving in France: didactic and curricular perspectives. ZDM Int J Math Educ 39(5–6):365–382

    Article  Google Scholar 

  • Cai J, Nie B (2007) Problem solving in Chinese mathematics education: research and practice. ZDM Int J Math Educ 39(5–6):459–473

    Article  Google Scholar 

  • Common Core State Standards for Mathematics (CCSS) (2010) Common Core State Standards initiative. http://www.corestandards.org/

  • Devlin K (2002) The millennium problems. The seven greatest unsolved mathematical puzzles of our time. Granta Publications, London

    Google Scholar 

  • Dick TP, Hollebrands K (2011) Focus in high school mathematics: technology to support reasoning and sense making. The National Council of Teachers of Mathematics, Reston

    Google Scholar 

  • Doorman M, Drijvers P, Dekker T, Van den Heuvel-Panhuizen M, de Lange J, Wijers M (2007) Problem solving as a challenge for mathematics education in the Netherlands. ZDM Int J Math Educ 39(5–6):405–418

    Google Scholar 

  • English LD, Gainsburg J (2016) Problem solving in a 21st-century mathematics curriculum. In: English LD, Kirshner D (eds) Handbook of international research in mathematics education. Routledge, New York, pp 313–335

    Google Scholar 

  • Hadamard J (1945) An essay on the psychology of invention in the mathematical field. Dover Publications, New York

    Google Scholar 

  • Halmos PR (1980) The heart of mathematics. Am Math Mon 87(7):519–524

    Article  Google Scholar 

  • Halmos PR (1994) What is teaching. Am Math Mon 101(9):848–854

    Article  Google Scholar 

  • Hilbert D (1902) Mathematical problems. Bulletin of the American Mathematical Society, 8:437–479

    Google Scholar 

  • Hoyles C, Lagrange J-B (eds) (2010) Mathematics education and technology: rethinking the terrain. The 17th ICMI study. Springer, New York

    Google Scholar 

  • Krutestkii VA (1976) The psychology of mathematical abilities in school children. University of Chicago Press, Chicago

    Google Scholar 

  • Lester FK, Kehle PE (1994) From problem solving to modeling: The evolution of thinking about research on complex mathematical activity. In: Lesh R, Doerr HM (ed) Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching. Mahawah: New Jersey, pp 501–517

    Google Scholar 

  • Lesh R, Zawojewski JS (2007) Problem solving and modeling. In: Lester FK Jr (ed) The second handbook of research on mathematics teaching and learning. National Council of Teachers of Mathematics. Information Age Publishing, Charlotte, pp 763–804

    Google Scholar 

  • Lester F, Kehle PE (2003) From problem solving to modeling: the evolution of thinking about research on complex mathematical activity. In: Lesh R, Doerr H (eds) Beyond constructivism: models and modeling perspectives on mathematics problem solving, learning and teaching. Lawrence Erlbaum, Mahwah, pp 501–518

    Google Scholar 

  • Liljedahl P, Santos-Trigo M (2019) Mathematical problem solving. Current themes, trends and research, https://doi.org/10.1007/978-3-030-10472-6 Cham, Switzerland: Springer

  • NCTM (1989) Curriculum and evaluation standards for school mathematics. NCTM, Reston

    Google Scholar 

  • NCTM (2000) Principles and standards for school mathematics. National Council of Teachers of Mathematics, Reston

    Google Scholar 

  • NCTM (2009) Focus in high school mathematics. Reasoning and sense making. NCTM, Reston

    Google Scholar 

  • Perkins DN, Simmons R (1988) Patterns of misunderstanding: An integrative model of science, math, and programming. Rev of Edu Res 58(3):303–326

    Google Scholar 

  • Polya G (1945) How to solve it. Princeton University Press, Princeton

    Book  Google Scholar 

  • Santos-Trigo M (2007) Mathematical problem solving: an evolving research and practice domain. ZDM Int J Math Educ 39(5, 6):523–536

    Article  Google Scholar 

  • Santos-Trigo M, Reyes-Martínez I (2018) High school prospective teachers’ problem-solving reasoning that involves the coordinated use of digital technologies. Int J Math Educ Sci Technol. https://doi.org/10.1080/0020739X.2018.1489075

  • Santos-Trigo M, Reyes-Rodriguez, A (2016) The use of digital technology in finding multiple paths to solve and extend an equilateral triangle task, International. Journal of Mathematical Education in Science and Technology 47:1:58–81. https://doi.org/10.1080/0020739X.2015.1049228

  • Schoenfeld AH (1985) Mathematical problem solving. Academic, New York

    Google Scholar 

  • Schoenfeld AH (1992) Learning to think mathematically: problem solving, metacognition, and sense making in mathematics. In: Grows DA (ed) Handbook of research on mathematics teaching and learning. Macmillan, New York, pp 334–370

    Google Scholar 

  • Schoenfeld AH (2015) How we think: a theory of human decision-making, with a focus on teaching. In: Cho SJ (ed) The proceedings of the 12th international congress on mathematical education. Springer, Cham, pp 229–243. https://doi.org/10.1007/978-3-319-12688-3_16

    Chapter  Google Scholar 

  • Selden J, Mason A, Selden A (1989) Can average calculus students solve nonroutine problems? J Math Behav 8:45–50

    Google Scholar 

  • Wertheimer M (1945) Productive thinking. Harper, New York

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centre for Research and Advanced Studies, Mathematics Education Department, Cinvestav-IPN, Mexico City, Mexico

    Manuel Santos-Trigo

Authors
  1. Manuel Santos-Trigo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Manuel Santos-Trigo .

Editor information

Editors and Affiliations

  1. Department of Education, Centre for Mathematics Education, London South Bank University, London, UK

    Stephen Lerman

Section Editor information

  1. Department of Science Teaching, The Weizmann Institute of Science, Rehovot, Israel

    Ruhama Even

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

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

Download citation

Publish with us

Policies and ethics

Search

Navigation