Polya解題策略融入八年級數學課程之行動研究

Abstract

本研究探討Polya解題策略融入數學課程在學生數學學習成效、解題行為和數學學習動機是否有提升。研究方法採用行動研究法。研究對象為17名國中八年級B組學生。在課程設計方面，採用Polya解題策略搭配同儕觀摩進行教學，配合教學進度做策略融入。行動研究時間共計八週。研究工具方面，量化研究工具為「前測與後測的試卷」、「數學解題行為問卷」、「數學學習動機量表」，質化研究工具為「Polya解題策略提問單」、「同儕觀摩單」、「解題策略融入課堂問卷調查」、「教師省思札記」、「訪談紀錄」。研究結果顯示，Polya解題策略融入數學課程後，學生於解題行為的學習成效有提升；學生於解題策略四階段中的「瞭解問題」、「擬定計畫」、「執行計畫」階段的解題行為有提升；學生的數學學習動機，於解題策略教學前後沒有顯著差異；教師嘗試解題策略融入教學後，教師自身數學教學與教學專業知能上獲得成長。

Using the action research approach, this paper investigated whether the integration of Polya’s problem-solving strategies into the mathematics curriculum improved students’ learning effectiveness, problem-solving behaviors, and motivation to learn mathematics. The participants were 17 eighth-grade students in Section B. In terms of curriculum design, Polya’s problem-solving strategies were used in conjunction with peer observation for teaching, and the strategies were integrated according to the teaching schedule. The action research spanned 8 weeks. The quantitative research instruments used were pretest and posttest papers, mathematics problem-solving behavior questionnaires, and the mathematics learning motivation scale. The qualitative research instruments used were Polya’s problem-solving strategies questionnaires, peer observation sheets, problem-solving strategy integration questionnaires, teacher reflection notes, and interview transcripts. The results showed that students’ learning effectiveness regarding problem-solving behaviors improved after integrating the Polya’s problem-solving strategies into the mathematics curriculum. Among the four stages of problem solving, students’ problem-solving behaviors improved in three of the stages, namely, “understand the problem,” “devise a plan,” “and carry out the plan.” There was no significant difference in students’ motivation to learn mathematics before and after integrating the problem-solving strategies. Teachers’ knowledge of teaching mathematics and their own teaching expertise improved after integrating problem-solving strategies into their teaching.