Mathematical modeling in algebra textbooks at the onset of the Common Core State Standards

Abstract

Student achievement in mathematics continues to be compared internationally, with the results indicating that students in other developed countries are outperforming students from the United States. Mathematical modeling is an expectation in both the new Common Core State Standards and the Programme for International Student Assessment (PISA). This study seeks to find the differences in expectations for students in mathematical modeling between the United States and Singapore, which is one country that regularly outperforms the U.S. on international assessments. Since teachers and students regularly use textbooks for curriculum, homework, and other resources, this study compares two textbooks from the U.S. with the high school series adopted in Singapore. More specifically, the aim of this study is to compare frameworks of mathematical modeling and code to-be-solved problems in algebra textbooks using characteristics common to all frameworks. While the U.S. textbooks explicitly state which word problems address the expectation of mathematical modeling, the Singapore program does not have this attribute. So, an equivalent chapter (in objective and number of to-be-solved problems) in all three textbooks will be coded for evidence of the expectations of mathematical modeling. The results of this study indicate that no standard framework for mathematical modeling exists, but there are multiple areas of overlap. This study found that the ratio of word problems to numerical problems was comparable in the three textbooks, although the U.S. algebra textbooks used in a one-year course had the same number of to-be-solved problems as the four-year Singapore series. Results also indicate that to-be-solved problems in the Singapore textbook series do not provide students with more explicit mathematical modeling instructions than do the U.S. textbooks. This study also found that the interpretation of to-be-solved problems differed according to the experience of the rater. None of the textbooks in this study provided to-be-solved problems that asked students to engage in the mathematical modeling cycle as delineated by any of the four frameworks