Exploring the Connection between Word Problem Structure and Problem Posing

Abstract

Word problems are an essential part of mathematics curriculum. However, prior research indicates that the semantic structure of a word problem can impact the difficulty of the problem solution. In the present study, I examined word problem structures through three key components – mathematics textbooks, problems posed by second-grade students, and the work of preservice teachers. In Chapter 2, I conducted a content analysis using three widely-distributed mathematics textbooks. Using the Common Core taxonomy for one-step addition and subtraction word problems for coding, I analyzed the frequency of the word problem structures in the addition and subtraction chapter for each textbook. Then using chi-square analysis, I compared this across textbooks. I determined that the different word problem structures do not appear proportionately within the textbooks, and these proportions were similar across all three textbooks. In Chapter 3, I compared 110-word problems posed by second-grade students using the same coding system as in Chapter 2. Although the students were not directed to write specific types of problems, many posed similar problems. Out of the 12 possible semantic structures, students only posed word problems within five of the categories. In Chapter 4, I compare preservice teachers’ test scores and survey results before and after an intervention on problem posing and the Common Core taxonomy. After the intervention, the preservice teachers’ scores and perceptions of self-efficacy and student ability statistically significantly increased. Additionally, their perceptions of variation of difficulty among the different word problem structures decreased. Their open-ended responses indicated that different word problem structures had varying levels of difficulty, they felt more confident after the intervention, and that student success would depend on other factors such as provision of instruction and practice. The combination of these results and prior research suggests that the types of word problems previously found to be the hardest for students to solve also appear less frequently in textbooks and student work. Furthermore, preservice teachers believe semantic structure is also connected to connected to the difficulty of posing problems, though less so with experience.