探究數學情意對工程數學學習成就的影響

Exploring Effects of Mathematical Affections on Engineering Mathematics Learning Achievements

10.30208/CGPS.202409_1(3).0002

蔡欣倫(Hsin-Luen Tsai)

工程數學 ； 多元教學法 ； 數學知識 ； 數學情意 ； 數學解題策略 ； 數學解題能力 ； engineering mathematics ； diversified instructional method ； mathematical knowledge ； mathematical affection ； mathematical problem-solving strategy ； mathematical problem-solving performance

諮商輔導與心理學研究

1卷3期（2024 / 09 / 10）

19 - 57

繁體中文;英文

本研究旨在探討透過多元教學方法探究數學情意對大學生數學解題表現的影響。研究對象為30位大學二年級學生，在先備知識和數學解題能力不足的情況下，修習工程數學時，必然面臨許多考驗。首先實施前測與溝通，了解學生的近側發展區與先備知識，因此先補強學生前備知識與解說數學應用性與價值，為期一學期十八周的多元教學，以期提升大學生在數學解題表現。研究工具為兩份量表和數學知識、數學解題表現（期中、期末考）試卷，經相依樣本t檢定後，數學程序知識、數學解題表現和前備知識應用都有顯著進步。路徑分析結果發現期中前測時數學知識能有效預測數學解題表現，也能經由數學情意間接影響數學解題策略，但數學情意與數學解題策略未能預測數學解題表現；期末後測時，則只有數學情意經數學解題策略間接影響數學解題表現。研究結果顯示，本多元教學方法先增強學生數學基礎知識，學期初的溝通讓學生了解數學價值與數學在內動機，開源軟體輔助計算能改善學生對數學的興趣與態度，能提升工數解題能力；再者經期末訪談得知部分學生擔心成績不及格，花更多時間練習，提升數學的外在動機，雖然數學情意的次構面沒有統計顯著性，最後數學情意能促進學生提升解題策略，經由數學解題策略中介影響數學解題表現，因此提升了工程數學的學習成效。

This study investigates the effect of mathematical affections on engineering mathematics on college students' mathematical problem-solving performance through the diversified instructional methods. The participants were 30 sophomores facing many challenges when studying engineering mathematics due to insufficient prior mathematical knowledge and mathematical problem-solving performance. First, we implement pre-test and communication to understand students' zone of proximal development and prior knowledge. Therefore, we first strengthen students' prior knowledge and elucidate the application and value of engineering mathematics. A one-semester and eighteen-week multi-teaching program is conducted in order to improve college students' mathematical problem-solving performance. The teaching lasted for 18 weeks in one semester and effectively improved the mathematical problem-solving performance of college students. Two questionnaires, mid-term and final exams were research instruments. Results of the paired sample t-test show that there was significant progress in mathematical procedural knowledge, mathematical problem-solving performance, and application of prior knowledge. The path analysis revealed that mathematical knowledge effectively predicted midterm pretest mathematical problem-solving performance and indirectly influenced problem-solving strategies through mathematical affection. However, neither mathematical affection nor problem-solving strategies predicted mathematical problem-solving performance. In the final posttest, only mathematical affection indirectly influenced performance through problem-solving strategies. The study suggests that diversified instructional methods enhance student's prior mathematical knowledge and communication before teaching help students to understand the mathematical values and improve their intrinsic motivation. The use of open-source mathematical software facilitates the improvement of habits and altitude towards mathematics learning, therefore improve the mathematical problem-solving performance. Further, interviews with teaching assistants revealed that students' concerns about grades motivated the increased practice, enhancing extrinsic motivations for learning mathematics. Although three sub-constructs of mathematics affection are not statistically significant, in the end, mathematics affection can promote students to improve problem-solving strategies and affect mathematics problem-solving performance through the mediation of mathematics problem-solving strategies, thus improving the learning effectiveness of engineering mathematics.

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