The relationships between visual and verbal working memory, working memory updating ability, Chinese language ability and different cognitive strategies for students with mathematics difficulties in solving percentage word problem

Abstract

Students with mathematics difficulties (MD) often face challenges in word problem solving due to their low working memory capacity (WMC). Past studies revealed that the use of cognitive strategies is an effective way to help students improve their word problem solving performance. As the effectiveness of cognitive strategies is closely associated with WMC, this study examined the effectiveness of different cognitive strategies from the perspective of WMC in solving simple percentage word problems. In addition, there are few studies which have examined the effectiveness of cognitive strategies from the perspective of WMC where the medium of instruction (MOI) is Chinese. This study attempted to fill this gap in research literature. This study examined 3 research questions: (1) what the effectiveness of the three types of cognitive strategies (namely verbal, visual and combined strategy) on the MD students’ word problem solving performance is; (2) how different working memory abilities of students interact with the intervention conditions on their word problem solving performance; (3) how the Chinese reading comprehension ability of students interacts with the intervention conditions on their word problem solving performance. The study consisted of two separate phases: A pilot study and the main study. The purpose of the pilot study was to validate the research tools and instructional materials created for the three experimental conditions while the main study was designed to explore the three research questions. Fifty-six students ranged from primary 6 to secondary 2 in Hong Kong participated in the main study. Their WM abilities (including visual WMC, verbal WMC and WM updating ability) and Chinese reading comprehension ability had been measured before the treatment. The study also included a pre-treatment mathematics test and a post-treatment word problem solving test. In an experimental design, each student was taught to solve the same set of problems with one of the 3 strategies including the visual strategy (n=16), the verbal strategy (n=15), the combined strategy (n=11) or the control group (n=14). The quantitative data of the 4 groups were analyzed with moderated regression model analysis, pick-a-point analysis, ANOVA, Kruskal-Wallis Test and correlation analysis. In addition, 11 post-treatment semi-structural interviews were conducted to explore the differences between high and low ability students with respect to the treatment and the problem-solving habits. The results of the pre-treatment mathematics test and the post-treatment test found that all three cognitive strategies could effectively reduce the differences in performance between high and low performing students. In addition, students with lower verbal WMC and/or WM updating ability benefited more from the three cognitive strategies. Conversely, visual WMC was found to have no main effect nor interaction effect with the intervention conditions on the post-treatment performance of the students. Lastly, although the interaction effect between Chinese reading comprehension ability and intervention conditions was not statistically significant due to the small sample size, it was found the students with weaker Chinese reading comprehension ability benefited more from the trainings. The interview results further explored the reasons behind these phenomena and revealed that students with higher ability did not find the strategies helpful, which is in line with the assumptions underpinning the compensation model. On a theorical level, this study has filled a research gap by providing support to the compensation model in describing the interaction effect between cognitive ability and cognitive strategy trainings in solving simple percentage word problems where the medium of instruction is Chinese. On a practical level, based on the results of the study, it is worthy to further explore how to incorporate these cognitive strategies into remedies for helping MD students.