Views and Beliefs in Mathematics Education pp 183-195 | Cite as

# Beliefs and Mathematical Reasoning during Problem Solving across Educational Levels

## Abstract

In this paper the status of empirical mathematical reasoning during problem solving across primary, secondary and tertiary education is studied. The main aim is to see whether the very same beliefs influence the students’ performance in the same way across educational levels. The results show that despite sharing the same beliefs, the way these beliefs affect students’ performance (positively or negatively) is different for different ages. More precisely, as we move from primary grades to college, the students’ ability to employ empirical mathematical reasoning is inclined as they persist to ask for connections with more formal ways of working. Even though the students solved the same task and shared the same beliefs, the negative effects of these beliefs were stronger for older students.

### Keywords

Lester Rote## Preview

Unable to display preview. Download preview PDF.

### References

- Ball, D., Joyles, C., Jahnke, H., & Movshovitz-Hadar, N. (2002) The Teaching of Proof. In L.I. Tatsien (Ed.), Proccedings of the International Congress of Mathematicians, (v.II, pp. 907-920). Beijing: Higher Education Press.Google Scholar
- Bieda, K., Holden, C., & Knuth, E. (2006). Does proof prove? Students’ emerging beliefs about generality and proof in middle school. In Proceedings of the 28th Annual Meeting of the North America Chapter of PME, (v.2, pp. 395-402).Google Scholar
- Carlson, M. (1999). The mathematical behaviour of six successful mathematics graduate students: Influences leading to mathematical success. Educational Studies in Mathematics, 40(3), 331–345.CrossRefGoogle Scholar
- Crawford, K., Gordon, S., Nicholas, I. & Prosser, M. (1994). Conceptions of mathematics and how it is learned: The perspectives of students entering university. Learning and Instruction, 4, 331–345.CrossRefGoogle Scholar
- English, L.D. (1997) Intervention in children’s deductive reasoning with indeterminate problems. Contemporary educational psychology, 22, 338–362.CrossRefGoogle Scholar
- Fosnot, C., & Jacob, B. (2010). Young mathematicians at work. NCTM.Google Scholar
- Garofalo, J., & Lester, F.K. (1985). Metacognition, Cognitive Monitoring and Mathematical Performance. Journal for Research in Mathematics Education, 16(3), 163–176.CrossRefGoogle Scholar
- Hanna, G. (2000). Proof, explanation and exploration: an overview. Educational Studies in Mathematics, 44(1), 5–23.CrossRefGoogle Scholar
- Lithner, J. (2008). A research framework for creative and imitative reasoning. Educational Studies in Mathematics, 67(3), 255–276.CrossRefGoogle Scholar
- Maher, C., & Martino, A. (1996). The development of the idea of mathematical proof: A 5-year case study. Journal for Research in Mathematics Education, 27, 194–214.CrossRefGoogle Scholar
- Mamona-Downs, J. & Downs, M. (2011). Proof: a game for pedants? Proceedings of CERME 7, 213–222, Rzeszow, Poland.Google Scholar
- Mamona-Downs, J. & Downs, M. (2013). Problem Solving and its elements in forming Proof, The Mathematics Enthusiast, 10(1–2), 137–162.Google Scholar
- Schoenfeld, A. (1985). Mathematical problem solving. Orlando: Academic.Google Scholar
- Schoenfeld, A. (1992). Learning to think mathematically: Problem solving, metacognition and sense-making in mathematics. In D. Grouws (Ed.), Handbook of Research in Mathematics Teaching and Learning (pp. 334–370). New York: Macmillan P. C.Google Scholar
- Schoenfeld, A. (1989). Exploration of Students’ Mathematical Beliefs and behaviour. Journal for Research in mathematics Education, 20(4), 338–355.CrossRefGoogle Scholar
- Sumpter, L. (2013). Themes and interplay of beliefs in mathematical reasoning. International Journal of Science and Mathematics Education (to appear).Google Scholar
- Tsamir, P., & Tirosh, D. (2002). Intuitive Beliefs, Formal definitions and Undefined Operations: Cases of Division by Zero. In G.C. Leder, E. Pehkonen, and G. Torner (Eds.), Beliefs: A Hidden variable in Mathematics education? (pp. 331-344).Google Scholar