When a half and a half are not a whole: putting word problems in context

Fitzpatrick, Cheryll (2018) When a half and a half are not a whole: putting word problems in context. Doctoral (PhD) thesis, Memorial University of Newfoundland.

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Abstract

Math word problems can be quite challenging to students. They learn early in their formal education that there is a proper “procedural recipe” to follow when solving words problems. Typically, it consists of taking the numbers and keyword(s) that indicate what mathematical operation should be used coupled with whatever lesson they happen to be learning at that moment. These word problems are usually very straightforward, applying one mathematical operation to all the numbers present in the problem, to a situation that largely ignores any inkling of reality, and does not include any extraneous information. This style of mathematical problem solving however is not conducive to applying mathematics in the real world. In the real-world situations are messy, there are often many unknowns, and there may not always be one correct answer. How does children’s formal education prepare them for applying their mathematical knowledge to real-world situations? The research examining this topic has consistently shown that students have trouble incorporating their real-world knowledge into their solution process for mathematical word problems that require realistic considerations. This dissertation investigates the relation between realistic problem solving and general academic skills while also testing procedures meant to improve realistic problem solving in Grade 6 students. After reviewing the literature on this topic in Chapter 1, Chapter 2 focuses on how general academic abilities play a part in children’s abilities to use their real-world knowledge. Chapter 3 examines interventions aimed at increasing students realistic responding to realistic word problems. The results of Chapter 2 indicate that general academic abilities are not predictors of success on realistic word problems; however, student’s ability to provide realistic responses to realistic word problems was an independent predictor of their performance on standard word problems (e.g., those seen in mathematics classrooms). This suggests that students’ general problems solving skills are benefitted by their ability to incorporate realistic reasoning and for this reason realistic reasoning is a skill worth nurturing. The result of Chapter 3 revealed that having students respond to realistic word problems with a response sentence was only helpful for boys and only on a particular type of word problem (Division-with-Remainder; see Experiment 1), using examples hinders students’ ability to use their realistic knowledge (Experiment 2), and creating a richer backstory in the word problem also does not increase student’s use of realistic knowledge. The experiments conducted in Chapter 3 indicate that students are extremely resistant to including realistic knowledge in their solution process. Chapter 4 provides more general discussion of the findings, and included some additional findings not discussed in Chapters 2 and 3. Future directions in this line of research, the implications of the dissertations findings, and some practical applications were also discussed, but the findings reported here point to the difficulty in teaching children to apply real-world information in problem solving situations and the importance of doing so.

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