學生自學、教師教學與學生成就水準對 學生數學學習成效、態度及認知負荷之影響－以國中數學圓與角單元為例

Abstract

中文摘要 本研究以國中數學科圓與角單元為教材，以學生自學與教師教學兩種不同的教學法為焦點，探討這兩種教學方法在圓心角，圓周角，弦切角，圓內角與圓外角五種角的教學中，對於不同成就水準學生的學習表現，數學學習態度與認知負荷感受的影響。在研究實驗中，利用幾何變換中的平移，以平行弦截等弧為教學主軸，並且根據多媒體學習理論與認知負荷理論中的教學教材設計原則自編教材，以國立交通大學陳明璋教授-AMA簡報系統-所開發的弧角估算器為工具，設計可操作學習單，輔助教學。本實驗採用準實驗研究法，以新北市某國中九年級四個常態班共187位學生為研究對象，學生自學組的教學方法為受試學生自己操作由教師錄製好的影音教學投影片進行圓與角教學並完成學習單，教師教學組的教學方法為教師在課堂上親自講述同一分教學投影片並完成學習單。以二因子變異數進行實驗資料分析，自變項為教學方法與成就水準，依變項為後測表現、延後測表現，數學學習態度與認知負荷感受。後測與延後測分為「總分」、「知識」、「理解」與「應用」四個向度進行分析；以數學學習態度量表檢測受試學生「學習數學的樂趣」、「數學的重要性」、「學數學的動機」與「免於數學的恐懼」四個向度的表現，以及認知負荷感受量表中的「上課意願」、「困難度」、「花費心力」、「信心指數」與「投入努力」五個向度檢測認知負荷感受； 研究結果顯示： (1) 教學方法與成就水準兩個變項在後測、延後測各向度之表現沒有顯著的交互作用。 (2) 教學方法與成就水準兩個變項在數學學習態度之學習數學的樂趣上表現達到顯著的交互作用，其餘三個向度未達顯著的交互作用。 (3) 教學方法與成就水準兩個變項在認知負荷感受之各向度均未達到顯著的交互作用。 (4) 教學方法變項對認知負荷感受的主要效果，在上課意願與信心指數兩個向度上達顯著差異；成就水準變項對認知負荷感受的主要效果，在花費心力與信心指數兩個向度上達顯著差異。

Abstract The study was to utilize Self-learning and Teaching as two approaches in teaching the units of Circle and Angle, including Central Angle, inscribed angle, angle of contingence, interior angle of a circle, exterior angle of a circle, to investigate the influence among students’ learning performance with different learning achievements, different attitudes toward mathematics learning and perceptions of cognitive load. In the experiments, the teaching material was designed by the researcher with the elements of translation of geometric transformation, two parallel chords intercept arcs are congruent integrated with the principle of the theory of multi-media and the theory of cognitive load. The operational work sheet was taken by Professor Ming-Jang Chen of National Chiao Tung University as a tool to assist the teaching. A quasi-experimental design was adopted to the study. The subjects were the 187 students in ninth grade from four average classes in a junior high school in New Taipei City. The teaching approach for Self-learning was that target students operated the slides created and recorded by the researcher to learn Circle and Angle and completed the work sheet while the teaching approach for teaching was that teachers used the above-mentioned and slides to teach in classes and helped the target students to complete the work sheet. The results of the experiments were analyzed through a two-way ANOVA, in which teaching approaches and students’ achievements were independent variables, while scores in post-test, delayed post-test, mathematics learning attitude and the perceptions of cognitive load were the dependent variables. Scores in both post-test and delayed post-test were analyzed as four individual parts, including “Total scores”, “Knowledge construction” and “Understanding construction” and “Applied construction”. Mathematics Learning Attitude Scale were analyzed as five individual parts, containing “The enjoyment of learning of mathematics”, “The importance of mathematics”, “Motivation to learn mathematics” and “Freedom from fear of mathematics”. The perceptions of cognitive load scale were analyzed as five individual parts, which contain “The willingness of learning”, “Difficulty”, “Endeavor”, “Confidence” and “Efforts”. The results showed that: (1) In terms of the individual scores in post-test and delayed post-test, there was no significant interaction between the two independent variables: teaching method and learning achievement level. (2) In terms of the individual scores in the fun of mathematics of Mathematics Learning Attitude Scale, there was significant interaction between the two independent variables, teaching method and learning achievement level. (3) In terms of the individual scores in the perceptions of cognitive load scale, there was no significant interaction between the two independent variables, teaching method and learning achievement level. (4) The major effect the variable of teaching method had on scores in “The willingness of learning” and “Confidence” of the perceptions of cognitive load scale was found to significant; the major effect the variable of learning achievment had on scores in “Endeavor” and “Confidence” of the perceptions of cognitive load scale was found to be significant.