Student Enrollment in Classes with Frequent Mathematical Discussion and Its Longitudinal Effect on Mathematics Achievement

Abstract:Mathematical discussion has been identified as being beneficial to students' understandings of mathematics (Goos, 1995; Lee, 2006). Students in classrooms with more effective math discussion have been observed to engage more frequently in discussion (e.g. Hiebert & Wearne, 1993), but the converse is not necessarily true (e.g. Manouchehri & St. John, 2006). Utilizing hierarchical linear modeling, the present study examined student enrollment in classes with more and less frequent discussion and such enrollment's effect on mathematics achievement over time. Results indicated that students enrolled in classes that discuss math "almost every day" consistently have higher math achievement than students enrolled in classes that discuss math "never or hardly ever." These results and their implications are discussed in depth.Keywords: Mathematical discussion, mathematics achievement, hierarchical linear modeling.(ProQuest: ... denotes formulae omitted.)IntroductionAccording to Silver, Kilpatrick, and Schlesinger (1990), "mathematics deepens and develops through communication" (p. 15). Students gain a better understanding of the meaning of mathematics when they communicate with others about it. Mathematics discussion in the classroom involves students in describing, explaining, defending, and justifying their ideas about mathematics. By doing so, mathematics discussion deepens students understanding of mathematics (Goos, 1995; Lee, 2006; Pimm, 1987) and has been shown to have a positive impact on mathematical achievement (D'Ambrosio, Johnson, & Hobbs, 1995; Grouws, 2004; Hiebert & Wearne, 1993; Koichu, Berman, and Moore, 2007; Mercer & Sams, 2006). Yet, there is evidence that discussion does not always have a positive impact on mathematics achievement (Shouse, 2001), which may imply that either discussion is not consistently effective in deepening mathematical understanding or that it is not consistently implemented to maximize its effectiveness. Perhaps this inconsistency in the research concerning the effectiveness may explain why Pimm (1987) identifies mathematical discourse as a topic that is continuously advocated by researchers but rarely implemented by teachers.In addition to the contradictory results of research on the impact of mathematics discussion on math achievement (e.g. Mercer & Sams, 2006; Shouse, 2001), there are few examples of such research. Of the studies that focus on discussion's impact on math achievement, all are cross-sections of the samples evaluated. To date, the author has yet to find a longitudinal study to investigate the compound effects of discussion on mathematics achievement. Given that many teachers do not engage their students in mathematical discussion (Pimm, 1987), it may very well be that positive benefits of more frequent discussion may not be statistically evident within one iteration of its implementation.The current study seeks to investigate whether students' presence in a classroom with frequent mathematical discussions has any longitudinal effect on their mathematics achievement. Students who are in classrooms where their peers frequently talk about mathematics should be more likely to be able to meaningfully and skillfully discuss mathematics than students who have not been in such classroom environments. Likewise, this ability should have a positive influence on their mathematics achievement. Therefore, students who are more exposed to classroom environments with frequent discussion about mathematics should demonstrate more growth in mathematics achievement than students who are less exposed to such classroom environments.Mathematical Discussion and Mathematics AchievementDescribing effective teaching strategies for increasing mathematics achievement, D'Ambrosio et al. (1995) suggested that engaging students in discussions about mathematics would improve their mathematical understanding of it. …