視覺引導在代數教材設計之探討－以解二元一次聯立方程式為例

Abstract

本研究探討不同的視覺引導教材設計於示例教學上，對學生學習成就表現與認知負荷差異的影響；以七年級數學二元一次聯立方程式單元為教材設計主題，採準實驗研究法於七年級常態班級進行實驗。並藉此研究初步發展認知負荷量表以及觀察專業知識反轉效應。 實驗結果分析得到： 1.不同的視覺引導教材設計於示例教學上，對於低先備知識學生(未學過學生)的學習成就有顯著的差異。融合代數教材設計原則的視覺引導教材設計，有助於低先備知識學生的學習成就表現。 2.不同的視覺引導教材設計於示例教學上，對於低學習成就學生的學習成就有顯著的差異。融合代數教材設計原則的視覺引導教材設計於示例教學上，有助於低學習成就學生的學習成就表現。 3.不同的視覺引導教材設計於示例教學上，對於高先備知識學生(已學過學生)的困難度認知負荷有顯著的差異。視覺引導教材皆能降低高先備知識學生的困難度認知負荷，而融合代數教材設計原則的教材，能降低更多。 4.不同的視覺引導教學設計於示例教學上，以效應值和學習者投入學習的觀點判斷，有專業知識反轉效應的產生。但對於高先備知識學習者和高學習成就學習者無負面影響。 關於初步發展的認知負荷量表，未臻成熟，有待未來繼續發展。

In this study, we use different visual guiding materials to the worked-example teaching. The purpose is to discuss how the visual guiding materials can have effect both on students’ performance and their cognitive load. Our study designed the unit of systems of first-order algebraic equations in variables of mathematics for the seventh grade, and with quasi-experimental design, the experiment targets the classes of normalized class assignment. Meanwhile, we try to develop the rating scales of the cognitive load as a pilot study and explore the expertise reversal effect. The results are as follows. Firstly, the worked-example teaching with different visual guiding materials remarkably encourage learners of low prior knowledge. The material with the algebra material design principles is really helpful to the learners in their performance. Secondly, the worked-example teaching with different visual guiding materials remarkably encourage learners of low achievement in their performance. The material with the algebra material design principles is also helpful to the learners. Thirdly, the worked-example teaching with different visual guiding materials cause significant effect on the cognitive load of the difficulty from the learners of high prior knowledge. Visual guiding materials, especially those by algebra material design principles, can reduce the cognitive load of the difficulty more prominently. Finally, the worked-example teaching with different visual guiding materials principles lead to expertise reversal effect in view of the effect size and learners’ involvement. However, there is no negative impact on the learners of high prior knowledge and of high achievement in their performance. Nevertheless, there are still problems for the pilot study of the rating scales of cognitive load, and thus it remains to be improved with future studies.