Abstract
There is a strong consensus among mathematics educators, researchers and instructional designers that mathematical problem solving is among the central means—and ends—of school mathematics education. Different ideas, practices and studies in the field of mathematical problem solving are reflected in the volumes, chapters, and papers published over the course of the last 30-plus years (Felmer et al. 2016; Lester and Charles 2003; Schoenfeld 1985; Silver 1985). The problem-based approach to teaching mathematics assumes that students are presented with authentic problems that are meaningful for them, and that can be solved using mathematical tools available to them. The problem-based approach seeks to develop new mathematical knowledge and skills through solving such problems. Moreover, when solving these problems the students are assumed to develop appreciation for the power of mathematics to solve problems from different fields of life and science.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Brousseau, G. (1997). Theory of didactical situations in mathematics. Dordrecht: Kluwer.
Cai, J. (2010). Commentary on problem solving heuristics, affect, and discrete mathematics: A representational discussion. In B. Sriraman & L. English (Eds.), Theories of mathematics education, advances in mathematics education (pp. 251–258). Heidelberg: Springer.
Choppin, J. (2011). The role of local theories: Teachers’ knowledge and its impact on engaging students with challenging tasks. Mathematics Education Research Journal, 23(1), 5–25.
Felmer, P., Pehkonen, E., & Kilpatrick, J. (2016). Posing and solving mathematical problems. Dordrecht: Springer.
Leikin, R. (2007). Habits of mind associated with advanced mathematical thinking and solution spaces of mathematical tasks. In The fifth Conference of the European Society for Research in Mathematics Education – CERME-5 (pp. 2330–2339). Retrieved from http://ermeweb.free.fr/Cerme5.pdf
Leikin, R. (2009). Exploring mathematical creativity using multiple solution tasks. In R. Leikin, A. Berman, & B. Koichu (Eds.), Creativity in mathematics and the education of gifted students (pp. 129–145). Rotterdam: Sense Publisher.
Leikin, R. (2014). Challenging mathematics with multiple solution tasks and mathematical investigations in geometry. In Y. Li, E. A. Silver, & S. Li (Eds.), Transforming mathematics instruction: Multiple approaches and practices (pp. 59–80). Dordrecht: Springer.
Lester, F. K., & Charles, R. (2003). Teaching mathematics through problem solving: Pre-K–grade 6. Reston: National Council of Teachers of Mathematics.
Pehkonen, E. (1995). Introduction: Use of open-ended problems. ZDM-International Journal of Mathematics Education, 27(2), 55–57.
Schoenfeld, A. H. (1985). Mathematical problem solving. Orlando: Academic Press.
Silver, E. A. (1985). Teaching and learning mathematical problem solving: Multiple research perspectives. Mahwah: Erlbaum.
Silver, E. A., & Mesa, V. (2011). Coordinating characterizations of high quality mathematics teaching: Probing the intersection. In Y. Li & G. Kaiser (Eds.), Expertise in mathematics instruction: An international perspective (pp. 63–84). New York: Springer.
Silver, E. A., & Zawodjewsky, J. S. (1997). Benchmarks of students’ understanding (BOSUN) project [technical guide]. Pittsburgh: LRDC.
Steinbring, H. (1998). Elements of epistemological knowledge for mathematics teachers. Journal of Mathematics Teacher Education, 1(2), 157–189.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Leikin, R. (2018). Part IV: Commentary – Characteristics of Mathematical Challenge in Problem-Based Approach to Teaching Mathematics. In: Kajander, A., Holm, J., Chernoff, E. (eds) Teaching and Learning Secondary School Mathematics. Advances in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-92390-1_38
Download citation
DOI: https://doi.org/10.1007/978-3-319-92390-1_38
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-92389-5
Online ISBN: 978-3-319-92390-1
eBook Packages: EducationEducation (R0)