The effect of instruction in alternative solutions on Taiwanese eighth grade students' problem solving performance

The purpose of this study was to investigate the effect of the use of Alternative-Solution Worksheet (ASW) on Taiwanese eighth-grade students' problem solving performance and to determine the extent to which instruction in the formulation of alternative solutions promotes "look back" strategies. Based on and expanded from Polya's (1973) ideas, "look back," in the present study, means "examination of what was done or learned previously." The Alternative-Solution Worksheet was developed to promote students' use of "look back" strategies by generating alternative solutions to the problem presented on the worksheet.;The design of this study integrated both quantitative and qualitative approaches with one intact eighth-grade class of thirty-four Taiwanese students. The thirty-four participants received instruction in alternative solutions utilizing ASW techniques for fifty minutes, two days a week for a period of four weeks. Data for this study were collected by pre and post testing, Alternative-Solution Worksheet use, and interviews.;Descriptive statistics and a t-test analysis were used to examine differences between scores on the pre and post tests. The findings indicated that the students improved problem solving performance on the posttest, but this improvement was not statistically significant. From correlation analysis, a positive, statistically significant, correlation was shown between the average ASW problem solving performance and the difference of pre and post test problem solving performance, which suggested that students who performed better on ASWs tended to improve more on the posttest.;Interviews were conducted individually with six subjects to explore the extent to which they reported use of "look back" strategies while completing ASWs using think-aloud techniques. The think-aloud protocols were analyzed based on an investigator-developed coding scheme. The data indicated that students who looked back more tended to perform better on ASWs. The results of this study suggested that the use of "look back" strategies was positively related to success in mathematical problem solving.