高職三年級學生微積分解題表現、類科與性別間關係之研究

A Study on the Relationship Between Calculus Problem-Solving Performance, Department and Gender of Senior High Vocational Students

本研究旨在探討不同類科、不同性別的高職生在微積分的解題表現是否有差異，了解是否存在交互作用並進一步比較不同程度學生之解題差異，期待研究結果提供教師未來教學參考。本研究採質量並重設計，以量的分析為主軸，質性分析晤談為輔，研究者選取雲林縣某高職學生共94人分成三個類科分別是商業經營科資料處理科與廣告設計科。樣本完成研究者自編的「微積分單元」成就測驗後，研究者利用SPSS 21.0分析資料包含敘述統計、單因子共變數分析、相依樣本t 檢定與二因子變異數分析；並透過半結構式晤談方法比較不同程度學生的解題差異。研究結果如下：

(1) 高職生在「微積分單元」的學習成就有一定的程度。

(2) 高職生在「微積分單元」的學習成就無顯著性別差異。

(3) 不同類科的高職生在「微積分單元」的學習成就有顯著差異。

(4) 不同類科、不同性別的高職生在「微積分單元」的學習成就有顯著的交互作用。

(5) 高職不同程度學生在「微積分單元」的解題策略有差異。

a.在導數與切線的題型中，不同類科高分組的男學生皆能理解題意。高、中、低分 組皆有學生犯相同的錯誤。

b.在微分的加減乘運算的題型中，廣設科中、低分組的男女學生皆將分子、分母微 分後當成答案。

c.在三次多項式的圖形的題型中，半數有著相同的錯誤答案，錯誤觀念以為微分後求得x=-3較小代入後即為極小值。

d.在多項式函數定積分的計算的題型中，廣設科只有高分組的女學生算對；高、中、低分組皆有學生犯相同的錯誤。

 

The purpose of this research was to discuss if vocational high school students with different majors or in both genders would perform differently in solving calculus and to understand whether there are interactions among them. Also, the research took a further step to compare students solving questions with different ways. The goal was to provide some teaching strateggies for teachers as the future reference. The methods of this study stressed both quantitative analysis and qualitative analysis of interviews. It was mainly conducted with quantitative analysis, supplemented with qualitative analysis of interviews. All participants in the research were selected from a national vocational high school in Yunlin County. The 94 participants included students with three different majors: Business Management, Data Processing and Advertising Design. After the participants completed the calculus test, the achievement test designed by the researcher, the researcher analized the data with SPSS21.0. The researcher chosed quantitative analysis with descriptive approach, One-way ANCOVA, paired-sample t-test, and Two-way ANOVA in the SPSS21.0 as the analizing methods. Also, the researcher used semi-structed interview methods to find the differences of students’ problems solving. The findings were as follows.

1. The result showed that vocational high school students could achieve to perform well in their learning of calculus.

2. With regards to the learing achievement of vocaitonal high school students, there was remarkable differences among the performance of students with different majors.

3. There were remarkable interaction effects on the learning achievement of calculus among students with different majors or of different genders.