“The Answer is Really 4.5”: Beliefs About Word Problems

In the course of a program of research into how students respond to typical word problems, it quickly became clear that patterns in their responses showing an apparent willingness to suspend sense making could not be explained in cognitive terms alone. Rather, it is necessary to consider the culture of the mathematics classroom and, in particular, the set of beliefs underlying the “Word Problem Game” that, largely implicitly, governs classroom practice. Findings from systematic research studies with students and teachers-in-training are reported that cohere with others in the literature and anecdotal evidence to elucidate the nature of practices surrounding word problems. Further, initial teaching experiments are reported which suggest that it is possible to change beliefs about word problems. However, these beliefs cannot be considered in isolation. Rather, they form part of more general beliefs about the nature of mathematics and its relation to the real world. Moreover, beliefs about word problems shaped by classroom culture are embedded within the nested and interacting contexts of school culture, the educational system, and society in general. We argue for the reconceptualization of word problems as a vehicle for promoting early awareness of the relationship between mathematics and aspects of reality that it models. This proposal reflects our own beliefs about the nature of mathematics and the proper goals of mathematics education.