Do increased opportunities to respond enhance generalization from multiplication to division

Haring and Eaton (1978) proposed four levels of skill development; acquisition, fluency, generalization, and adaptation. Many researchers and educators have focused on improving skill acquisition and fluency. This study was designed to investigate whether increasing a student's opportunities to respond (practice) would increase generalization of learning from multiplication to division. The participants were 31 students from two third-grade magnet classes in an inner-city school. The research design was a within-participants repeated measures ANOV A. Three levels of the independent variable, practice, were investigated (high, low, no). Outcomes were measured at three different times (Days 1, 8, and 10). Multiplication and division performance were the dependent variables. There were four measures of the dependent variables; number attempted, number correct, percent correct, and digits correct per minute. Three mutually exclusive sets of multiplication problems were generated for this study. Each set consisted of 10 one-digit by one-digit multiplication problems. These problems were used to generate three types of sheets (intervention sheets, multiplication assessment sheets, and division assessment sheets). The difference between the intervention and assessment sheets was that the intervention sheets had the answers with the problems. The study was conducted over a 10-day period. On the first day, the students were given the pretest. On the second day, they were taught how to perform the Cover, Copy, and Compare technique. On the third through seventh days, the students performed the Cover, Copy, and Compare intervention. On the eighth day, the students were given their first posttest. On the ninth day, the students were taught how to generalize their learning from multiplication to division. On the tenth day, the students were administered the second posttest. No significant interaction effects (interaction between time and practice) were found. In addition, the practice level did not increase the level of generalization. The results showed time increased the level of generalization. Time was a significant factor in fourteen of twenty-four comparisons across the three days (Day 1 to Day 8, Day 8 to Day 10, and Day 1 to Day 10). These results failed to support the hypothesis that increasing students' practice would enhance generalization. The discussion focuses on methodological problems of the current study and threats to the internal validity. Testing effects, spillover effects, history effects, and poor treatment integrity may have contaminated results.