素養導向下的數學解題研究:眼動追蹤分析試題類型與作答時間的影響

Abstract

素養題是台灣課綱中的一個重點導向，旨在培養學生的知識、態度及跨領域解決問題的能力，並促使他們將知識與生活情境整合應用，進而提升素養能力。素養的融入，有助於學生了解數學在生活中實際的應用，提升他們學習數學的動機。然而，過多的文字是否會加重學生的認知負荷，進而影響他們問題解決的能力？因此，有必要探討數學素養題中融入情境對學生的影響。此外，若給予較長的時間，是否能改善學生作答素養題的表現，也是本研究的另一個重點。本研究將分析素養導向（數學素養題與非數學素養題）與作答時間（短時間五分鐘與長時間十分鐘）兩個變項，將學生分為四組，並透過分析每組學生的眼動軌跡及解題歷程，探討素養導向試題與作答時間差異對學生數學題解題表現與解題歷程的影響。因此本研究招募113學年度臺灣北部的76位九年級普通班學生，藉由眼動儀與手寫板分析學生的閱讀歷程與解題歷程，並使用二因子變異數分析與t-test探討素養導向與作答時間對學生的解題表現、閱讀歷程與認知負荷的影響。研究發現素養導向對於學生在題目的解題關鍵文字的眼動指標有顯著影響，但對解題關鍵圖片的眼動指標沒有顯著影響；此外，素養導向與作答時間對於學生的作答分數與認知負荷皆無顯著影響。最後，討論研究結果以及背後意涵，並將閱讀歷程可視化，比較低解題表現與高解題表現學生的解題歷程，根據研究結果給予數學素養題對於教育上的建議，以及探討學生面對素養題時面臨的最大困難點。Literacy questions are a focus of Taiwan curriculum guidelines, aimed at cultivating students’ knowledge, attitudes, and cross-disciplinary problem-solving skills, as well as encouraging them to integrate knowledge with real-life scenarios to enhance their literacy. Literacy helps students to understand the practical applications of mathematics in daily lifes and increases their motivation to learn mathematics. However, an excessive amount of words may increase students’ cognitive load, thereby affecting their problem-solving skills. Therefore, it is necessary to explore the impact of literacy questions. In addition, whether providing longer answer time for solving problems can improve students’ performance on literacy questions is another focus of this research. Two variables—question types (mathematical literacy vs. non-mathematical literacy) and answer time (five minutes vs. ten minutes)— were tested by dividing students into four groups. Using eye-tracking and handwriting tablets, students’ reading and problem-solving processes were analyzed, the effects of literacy orientation and answer time differences on their mathematical problem-solving performance and strategies were tested. The participants of this research consisted of 76 ninth-grade students recruited from regular classes in northern Taiwan during the 113th academic year. Two-way ANOVA and t-tests were conducted to examine the effects of literacy orientation and response time on students’ problem-solving performance, reading processes, and cognitive load. The results revealed that literacy orientation had a significant effect on students’ eye movement indicators related to key words information in the problems, but no significant effect on indicators related to key picture information. Moreover, literacy orientation and answer time showed no significant effects on students’ scores and cognitive load. Finally, the study discusses the findings and their implications, visualizes students’ reading processes, compares the problem-solving processes of high-performing and low-performing students, and provides educational suggestions for mathematical literacy questions, as well as insights into the main difficulties students face when dealing with such questions.