| This mixed method study investigated the effect of three curricula for teaching multiplication facts on third graders' knowledge of multiplication facts, looking specifically at correct responses, errors and omissions, problem size effect, and strategy use. The study employed a pretest-treatment-posttest design.; Prior to the treatment, 49 students in three third-grade classes completed two pretest measures. Then intact classes were taught during their regularly scheduled mathematics sessions during a three-week period. Two groups were taught with an experimental curriculum, Multiplication Matters (Salvo, 2004). The Multiplication Matters group ( MM, n = 16) was taught the strategies in Multiplication Matters , while the Multiplication Matters without Strategies group (MM without Strategies, n = 18) was not. The Control group (n = 15) was taught using activities and methods from the Everyday Mathematics curriculum (University of Chicago School Mathematics Project, 2001). A single teacher, who was also the researcher for the study and author of Multiplication Matters , taught all three groups. Following the treatments, all participants completed a group posttest measure. Eighteen students individually completed a videotaped computer posttest with interview.; There were no differences in overall gains in correct responses among the groups. However, the MM group had greater gains among problems with larger factors and products than the Control group. The MM without Strategies and Control groups had greater gains among problems with smaller factors and products than the MM group. Consequently, the problem size effect was reduced for the MM group as compared with the other two groups. The results, therefore, indicate that the problem size effect was modified by instruction.; The MM group made more table-related errors after the treatment, attributable to one of the strategies that was taught. Omissions were reduced for the MM group while remaining near pretest levels for the other two groups, attributable to the strategies taught. Videotaped interviews revealed potential emotional consequences of omissions for students.; The findings, taken as a whole, suggest tailoring multiplication fact teaching methods to the specific facts being taught. A more complete model for multiplication fact knowledge is proposed in the discussion based on these results. |
