數學軟體DERIVE應用於高中學生學習多項式概念的教學研究

Abstract

本研究乃是將數學軟體DERIVE應用於高中學生學習多項式概念的教學研究。以「多項函數的圖形」和「多項方程式」為單元主題，開發適合學生的學習素材和教學活動，了解學生對此試探性教學活動的看法與回饋，探究數學軟體DERIVE應用於高中數學教學之可行性。同時透過觀察與訪談，將探討數學軟體DERIVE的輔助學習對學生學習多項式概念的影響。本研究採行動研究的方式，以台北縣某完全中學8名高中一年級普通班學生為研究對象，依多項式之學習成就測驗前測的結果，將研究對象分為四組。前測階段8人同時進行二次共計110分鐘的電腦軟體教學課程，實驗階段中為時約7小時的教學活動則採分組分次進行，逐次地修正與調整教學活動，使教學模式能較佳化，在未來可作為大班教學的參考。藉由課堂觀察、學生電腦操作觀察、學習單、學生問卷、學生學習成就測驗以及訪談等資料之蒐集整理，來進行研究結果分析。 研究結果發現在合適的學習單循序漸進引導下，DERIVE免除學生作單調繁雜的計算，讓學生有更多的時間去作數學思考；當抽象的數學變成可具體操作時，學生心中的解題策略在DERIVE的輔助下得以延續；DERIVE有別於傳統教室教學的呈現，除了給學生新鮮感，亦激發學生學習數學的興趣。以DERIVE來輔助教學的模式，學生反應可以適應、接受，並不會因此而分心，並依學生學習成就之前後測的整體結果及學生給予的回饋，研究者相信數學軟體DERIVE應用於輔助高中學生學習多項式是具可行性的。惟教師以DERIVE輔助教學時，對於教學環境的限制、軟體可能帶來圖形錯誤解讀的迷思概念等，應有相對的應變與調適。 最後根據研究結果與發現，提出若干建議以作為教師改進與未來研究之參考。

This study applied an action research method to explore the possibility of applying Mathematics Software, DERIVE, to teach polynomials in high school. The researcher used DERIVE as the tool to design learning materials and activities for teaching and learning of "Graphs of polynomial functions" and "Polynomial equations". This study was based on observing classroom and interviewing students to discuss its effect on students' conceptual understanding of polynomials. Participates were 8 high school students in Taipei County. At the beginning, all students took an achievement test and based on the test results students were assigned to four groups of two. All students were given a 110-minute DERIVE exploration lesson at the same time. After the DERIVE lesson, the researcher designed a 7-hour polynomial exploration activity using DERIVE as the aid tool. Each group was taught by the research sequentially, and this gave the researcher a chance to modify the activity to improve the lesson plan for follow-up group teaching. It was found that using DERIVE could reduce the time on rigmarole tasks and students could spend much time on thinking mathematically. DERIVE was considered to make the abstract concept accessibility and manipulability, and this helped students continue their thought on solving problems. Unlike in the traditional classrooms, students were motivated by these novel presentations. Students responded that they liked to used DERIVE and it helped them focus on conceptual explorations. However, possible misconceptions might occur when using DERIVE in teaching mathematics. Suggestions for applying DERIVE into mathematics teaching and future research were provided.