Quantitative Reasoning as a Framework to Analyze Mathematics Textbooks

Abstract

AbstractWe consider quantitative reasoning as a possible venue to analyze textbooks in order to identify the kind of reasoning students are likely to be engaged in learning mathematics. In this chapter we attempt to extend previous research by using quantitative reasoning as a framework to provide a cross-national textbook analysis. We analyzed how quantitative reasoning is embedded within Japanese curricular materials. We did this in the context of the elementary school curriculum, especially in introducing and developing whole number multiplication and division between Grades 2 to 4. In our analysis, we identified tasks, problem situations and representations likely to trigger students’ quantitative reasoning. We also investigated the kind of questions students are asked to think about regarding quantities and quantitative relations. Results pointed that in the Japanese curricular materials quantitative reasoning has been given a great place for the concepts of multiplication and division. Particularly, taking students’ attention to the quantities and their relationships in the problem situations, an understanding of multiplication multiplicatively and division as relative size seem to be the focal points in these curriculum materials.