Session Information
24 SES 10, Arithmetics and Number Sense. Proportions, Fractions and Multiplication
Paper Session
Contribution
Proportional reasoning involves the ability to distinguish proportional relationships from those that are not, and understanding the multiplicative nature of proportional relationships (Silvestre & Ponte, 2011). This reasoning is fundamental to solve daily problems and also for learning advanced mathematical topics as well as other fields of study, including natural and social sciences (Post, Behr & Lesh, 1988). Several researchers indicate the presentation of ratio and proportions are mechanical and textbooks leave pre-service teachers with the same proportional reasoning abilities they had when they finish college (Sowder, Bezuk, & Sowder, 1993; Lamon, 1999). In result many teachers, as other adults, cannot reason proportionally (Lamon, 1999).
The proportionality notion is one of the basic notions of the Portuguese elementary mathematics curriculum (grades 6-9), which has been an obstacle to the Mathematics learning, because the teachers teach this notion in a very formal way, emphasising the memorisation of the rules (Monteiro, 2007).
This paper analyses the proportional reasoning of pre-service elementary teachers, mainly when they are engaged in problem solving. The purpose of this study is to examine teacher preparation course, using the developmental shifts described by Lobato and Ellis (2010), in order to empower the teacher education course to provide both a profound mathematics understanding of the basic concepts of mathematics and the capacity of future teachers to be aware of the difficulties and the misconceptions of the students (e.g. National Council of Teachers of Mathematics, 2001).
Method
Expected Outcomes
References
Lamon, S. (1999). Teaching fractions and ratios for understanding: Essential content knowledge and instructional strategies for teachers. Mahwah, NJ: Lawrence Erlbaum. Monteiro, C. (2007). Prospective elementary teachers’ misunderstandings in solving ratio and proportion problems. In N. Pateman, B. Dougherty & J. Zilliox (Eds.), Proceedings of the 25th Conference of the IGPME (Vol. 3, pp. 317-325). Honolulu: PME. National Council of Teachers of Mathematics (2001). Curriculum and Evaluation Standards for School Mathematics. Reston, Va. Post, T., Behr, M., & Lesh, R. (1988). Proportionality and the development of prealgebra understandings In Algebraic concepts in the curriculum K-12. Reston, VA: NCTM. Silvestre, A. I., & Ponte, J. P. (2011). Missing value and comparison problems: What pupils know before the teaching of proportion. In B. Ubuz (Ed.), Proceedings of the 35th Conference of the IGPME (Vol. 4, pp. 185-192). Ankara: PME. Sowder, J. T., Bezuk, N., & Sowder, L. K. (1993). Using principles from cognitive psychology to guide rational number instruction for prospective teachers. In T. Carpenter, E. Fennema, & T. Romberg, Rational numbers: An integration of research (pp. 239–259). Hillsdale, NJ: Erlbaum.
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