數學表徵及數學自我效能對國小五年級學生 樣式推理學習成效之影響

Abstract

本研究旨在探討不同的數學表徵及數學自我效能對國小學生樣式推理思考表現和數學學習態度之影響。研究樣本為雲林縣某國小五年級學生，共121 位。研究設計採因子設計之準實驗研究法，自變項包含數學表徵和數學自我效能，依數學表徵的不同將教材分為「圖形類型教材」、「數字類型教材」兩種，數學自我效能依據數學自我效能量表總得分，將學習者分為高、低數學自我效能兩組，參與者於教學實驗前接受測量。依變項為「樣式推理思考表現」及「數學學習態度」，樣式推理思考表現包括(1)數字序列推理；(2)圖形序列推理，數學學習態度為學習興趣、學習動機、數學焦慮三個面向。 研究結果發現：(1) 樣式推理學習過程中使用圖形類型教材，可以促進學習者樣式推理思考表現；(2) 運用虛擬教具於教學中，可以提升學習者數學學習態度；(3)高數學自我效能者透過圖形類型教材進行教學活動，數學學習態度較正向。本研究結果與建議可供國小數學教學與未來相關研究參考。

The purpose of this study was to investigate the effects of type of mathematical representation and mathematics self-efficacy on fifth graders’ pattern reasoning and mathematics attitudes. Participants were 121 fifth graders from four classes of an elementary school in Yunlin, Taiwan. A quasi-experimental design with factorial design was employed in the study. The independent variables were type of representation (figural representation vs. symbolic representation) and self-efficacy toward mathematics (high mathematics self-efficacy vs. low mathematics self-efficacy). The dependent variables were pattern reasoning performance, including (a) number patterns and (b) figure patterns, and mathematics attitudes, including (a) enjoyment, (b) motivation, and (c) anxiety. The results showed that (a) the application of figural representation enhanced participants’ pattern reasoning performance, (b) the use of virtual manipulative for teaching mathematics enhanced students’ mathematics attitudes, and (c) students with higher mathematics self-efficacy obtained better mathematics attitudes.