數學表徵及數學自我效能對國小學生樣式推理學習成效之影響

The Effects of Type of Mathematical Representation and Mathematics Self-Efficacy on Fifth-Graders' Pattern Reasoning

本研究旨在探討不同數學表徵設計之虛擬教具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。研究樣本為台灣中部121位國小五年級學生。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，數學表徵依教材所使用之表徵方式分為「圖形類型教材」及「數字類型教材」兩種；數學自我效能則依據數學自我效能量表之得分區分為高、低數學自我效能兩組。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含數字序列推理及圖形序列推理；數學學習態度則包括：學習興趣、學習動機、及數學焦慮等三個面向。研究發現：（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；及（3）高數學自我效能者具有較正向的數學學習態度。

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 located in the middle part of 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 more positive mathematics attitudes.