Reading Mathematical Texts as a Problem-Solving Activity: The Case of the Principle of Mathematical Induction

  • Ioannis Papadopoulos Faculty of Elementary Education, Aristotle University of Thessaloniki, Greece
  • Paraskevi Kyriakopoulou University of Western Macedonia, Greece
Keywords: mathematical induction, reading mathematical text, problem solving, secondary education students

Abstract

Reading mathematical texts is closely related to the effort of the reader to understand its content; therefore, it is reasonable to consider such reading as a problem-solving activity. In this paper, the Principle of Mathematical Induction was given to secondary education students, and their effort to comprehend the text was examined in order to identify whether significant elements of problem solving are involved. The findings give evidence that while negotiating the content of the text, the students went through Polya’s four phases of problem solving. Moreover, this approach of reading the Principle of Mathematical Induction in the sense of a problem that must be solved seems a promising idea for the conceptual understanding of the notion of mathematical induction.

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References

Adams, T. L. (2003). Reading mathematics: More than words can say. The Reading Teacher, 56(8), 786–795.

Allen, L. G. (2001). Teaching mathematical induction: An alternative approach. The Mathematics Teacher, 94(6), 500–504.

Avital, S., & Hansen, R. T. (1976). Mathematical induction in the classroom. Educational Studies in Mathematics, 7(4), 399–411.

Baker, J. D. (1996). Students’ difficulties with proof by mathematical reasoning. Paper presented at the Annual Meeting of the American Educational Research Association, New York. https://eric.ed.gov/?id=ED396931

Bell, E. T. (1920). Discussion: On proofs by mathematical induction. The American Mathematical Monthly, 27(11), 413–415.

Dubinsky, E. (1989). Teaching of mathematical induction II. The Journal of Mathematical Behavior, 8(3), 285–304.

Ernest, P. (1984). Mathematical induction: A pedagogical discussion. Educational Studies in Mathematics, 15(2), 173–189.

Freudenthal, H. (1983). The didactical phenomenology of mathematics structures. Reidel.

Grugnetti, L., & Jaquet, F. (2005). ‘Problem solving’, this is the problem! Paper presented at ICME 10, TSG 18. Denmark.

Konior, J. (1993). Research into the construction of mathematical texts. Educational Studies in Mathematics, 24(3), 251–256.

Leron, U. (1983). Structuring mathematical proofs. The American Mathematical Monthly, 90(3), 174–184.

Mamona-Downs, J., & Downs, M. (2005). The identity of problem solving. The Journal of Mathematical Behavior, 24(3–4), 385–401.

Mayring, P. (2014). Qualitative content analysis: Theoretical foundation, basic procedures and software solution. Beltz.

Mejía-Ramos, J. P., & Inglis, M. (2009). Argumentative and proving activities in mathematics education research. In F.-L. Lin, F.-J. Hsieh, G. Hanna, & M. de Villiers (Eds.), Proceedings of the ICMI Study 19 conference: Proof and proving in mathematics education (Vol. 2, pp. 88–93). National Taiwan Normal University.

Morgan, C. (1996). Language and assessment issues in mathematics education. In L. Puig & A. Gutiérrez (Eds.) Proceedings of PME 20 (Vol. 4, pp. 19–26).

Movshovitz-Hadar, N. (1993). Mathematical induction: A focus on the conceptual framework. School Science and Mathematics, 9(3), 408–417.

National Council for Teachers of Mathematics. (2000). Principles and standards for school mathematics. National Council for Teachers of Mathematics.

Ntzioras, I. (1979). Mathematics: Algebra for grade 11 (in Greek). School Textbooks Publishing Organization.

Österholm, M. (2006). Characterizing reading comprehension of mathematical texts. Educational Studies in Mathematics, 63(3), 325–346.

Österholm, M., & Bergqvist, E. (2013). What is so special about mathematical texts? Analyses of common claims in research literature and of properties of textbooks. ZDM, 45(5), 751–763.

Palla, M., Potari, D., & Spyrou, P. (2012). Secondary school students’ understanding of mathematical induction: Structural characteristics and the process of proof construction. International Journal of Science and Mathematics Education, 10(5), 1023–1045.

Papadopoulos, I., & Iatridou, M. (2010). Systematic approaches to experimentation: The case of Pick’s Theorem. The Journal of Mathematical Behaviour, 29(4), 207–217.

Polya, G. (1957). How to solve it (2nd ed.). Princeton University Press.

Raman, M. (2003). Key ideas: What are they and how can they help us understanding how people view proof? Educational Studies in Mathematics, 52(3), 319–325.

Schoenfeld, A. H. (1985). Mathematical Problem Solving. Academic Press.

Schoenfeld, A. H. (1985a). Metacognitive and epistemological issues in mathematical understanding. In E. A. Silver (Ed.), Teaching and learning mathematical problem solving: Multiple research perspectives (pp. 361–380). Lawrence Erlbaum.

Schoenfeld, A. H. (2013). Reflections on problem solving theory and practice. The Mathematics Enthusiast, 10(1&2), 9–34.

Selden, A., & Selden, J. (2003). Validations of proofs considered as texts: Can undergraduates tell whether an argument proves a theorem? Journal for Research in Mathematics Education, 34(1), 4–36.

Selden, J., & Selden, A. (1995). Unpacking the logic of mathematical statements. Educational Studies in Mathematics, 29(2), 123–151.

Vileniusâ€Tuohimaa, P. M., Aunola, K., & Nurmi, J. E. (2008). The association between mathematical word problems and reading comprehension. Educational Psychology, 28(4), 409–426.

Weber, K., Brophy, A., & Lin, K. (2008). Learning advanced mathematical concepts by reading text. Paper presented at the 11th Conference on Research in Undergraduate Mathematics Education. San Diego, CA. http://sigmaa.maa.org/rume/crume2008/Proceedings/Weber%20LONG.pdf

Yang, K. L. (2012). Structures of cognitive and metacognitive reading strategy use for reading comprehension of geometry proof. Educational Studies in Mathematics, 80(3), 307–326.

Published
2022-03-25
How to Cite
Papadopoulos, I., & Paraskevi Kyriakopoulou. (2022). Reading Mathematical Texts as a Problem-Solving Activity: The Case of the Principle of Mathematical Induction. Center for Educational Policy Studies Journal, 12(1), 35-53. https://doi.org/10.26529/cepsj.881