Abstract

There are many different types of research done on algebra learning. In particular, word problems have been used to analyze students’ thought process and to identify difficulties in algebraic thinking. In this thesis, we show the importance of quantitative reasoning in problem solving. We gave 14 mature students, who were re-taking an introductory course on algebra, four word problems of different types to solve: a connected problem, a disconnected problem, a problem with contradictory data and a problem where students were asked to assess the correctness of a fictional solution. In selecting these types of problems we have drawn on the research of Sylvine Schmidt and Nadine Bednarz on the difficulties of passing from arithmetic to algebra in mathematical problem solving. We present the students’ solutions and a detailed analysis of these solutions, seeking to identify the sources of the difficulty these students had in producing correct solutions. We sought these sources in the defects of quantitative reasoning, arithmetic mistakes, and algebraic mistakes. The attention to quantitative reasoning was inspired by the research of Pat Thompson and Stacey Brown. Defects of quantitative reasoning appeared to be an important reason why the students massively failed to solve the problems correctly, more important than their lack of technical algebraic skills. Therefore, teaching procedures and algebraic technical skills is not enough for students to develop problem solving skills. There should be a focus on developing students’ quantitative reasoning. Students need to have a good understanding of relations between quantities. Defects of quantitative reasoning create obstacles that prevent mature students from successfully solving any type of word problem.