完成問題教材形式與合作學習活動對國中生幾何問題解決成效與認知負荷之影響

Abstract

本研究目的是根據工作記憶容量有限的觀點及認知負荷理論，探討「問題形式」（含「完成問題」或「傳統問題」兩種呈現形式），搭配「教學活動」（含「個人學習」或「合作學習」兩種活動），對台灣國中學生理解幾何概念及解決問題之學習成效與認知負荷之影響。 研究對象為四個受試班級115位國中八年級學生，他們皆參與前測、教學、練習任務與後測四個階段。在練習任務階段，將受試班級分派至四個問題形式與教學活動組合的實驗情境，分別為「問題解決形式/個人學習」、「完成問題形式/個人學習」、「問題解決形式/合作學習」、「完成問題形式/合作學習」。各組在練習與後測階段，學生須完成每道題目（學習成就），亦須勾選單一題九點認知負荷量表。此外，為了瞭解教材設計的適當性，研究者進一步分析教材有效性分數，此公式結合了心智努力程度與表現分數，為教材設計良窳之指標。 本研究之結果為（一）四個受試班級先備知識程度不一致，（二）問題形式與教學活動對學生心智努力、學習成效與教材有效性的影響不大，（三）學生仍比較習慣「問題解決」的教材形式（四）採用「完成問題形式」學習的兩組學生，以系統結構化的方式學習到體積與表面積的觀念，在後測解題時表現出跟「完成問題形式」一樣有組織、步驟化的列式策略。相對的，採用「問題解決」學習的兩組學生，比較傾向自由列式，解題步驟不夠系統化，會急匆匆的合併(跳過)解題步驟，但也更願意自行繪圖解題。最後，研究者根據研究結果提供建議給未來研究者、教師與教材設計者。

According to the perspective of limited capacity of working memory and cognitive load theory (Sweller, Van Merriënboer, & Paas, 1998), the purpose of this study was to investigate the effects of “problem formats” (completion problem vs. problem solving) and “learning activity” (individual learning vs. collaborative learning) on problem solving achievement and cognitive load among Taiwan junior high school students in learning geometry concepts and problem solving skills. The participants were four-classes 8th graders (N=115). They all participated in four stages including pretest, instruction, learning tasks and posttest. In the learning phase, they were assigned to four experimental conditions in such a way that the first class had to learn individually from problem-solving tasks, the second class had to learn individually from completion-problem tasks, the third class had to learn in 3-person group from problem-solving tasks, the forth class had to learn in 3-person group from completion-problem tasks. The researcher analyzed the group differences of a 9-point cognitive load rating scale rated by participants after each learning task and posttest task, and posttest performance. Besides, in order to test whether instructional format were appropriate, researcher further calculated the instructional efficiency score which is an indicator of quality of instructional format. The major findings of the research were summarized as follows. 1. The levels of prior knowledge of four classes were not equal. 2. No significant effects of problem format or learning activity were found no matter on mental effort, performance or instructional efficiency scores, nor were there interaction effects between problem format and learning activity. 3. The participants seemed to prefer problem solving format to completion problem. 4. The participants in completion problem format groups learned concepts of volume and area in an organized way and then listed the formula step by step which was consistent with what they taught in completion problem process. Comparatively, the students in problem solving groups solved the problems in intuitive and less organized patterns. For example, many students collapsed several problem-solving steps into one as if in a hurry and others redrew the geometry figures to shape their understanding and problem solving steps. Finally, several suggestions were given for future researchers, teachers and instructional designers.