探討學生對HCK 取向與解題取向教學的知覺

Abstract

本研究旨在整合眼界數學知識(Horizon Content Knowledge, [HCK])之模型，進而探討學生對於具有HCK 取向與解題取向教學的知覺(perceptions) 。針對HCK 模型中的基礎數學知識(Fundamental mathematical knowledge) ，我們設計IHCK 取向」與「解題取向」的教學方式，對68 位高一學生分別進行這兩種不同取向的教學，講學生比較何種取向最能幫助他們學習。研究結果發現(1)學生普遍認為HCK 取向的教學較能幫助他們瞭解整個問題的思考脈絡(73.5%) ，對低成就學生更是如此(85.7%) ; (2)不同數學成就學生存在不同偏好教學取向你2(2)=8.37 ， p<.05) ; (3)1數學成就」與「偏好HCK 取向教學」呈現中度負相關(r=-.292 ， p<.05) 。整體而吉，研究結果顯示HCK 取向的教學較能幫助學生學習，尤其是中、低程度的學生，而高成就學生似乎較偏好「解題取向」的教學。

The pupose of this study is to investigate the high school students' perceptions on the HCK and non-HCK (problem-solving) teaching approaches. According to the fundamental mathematical knowledge in the HCK model, we design the HCK and non-HCK teaching approaches in the shortest distance problem.The study included 68 high school students with high, medium and low mathematics achievement. These students were exposed in the HCK and non-HCK teaching, respectively. The results showed that: (1) HCK teaching approach could help students better understand how to solve the problem conceptually (73.5%). (2)The relation between mathematics achievement and teaching preference was significant (χ，2(2)=8.37 ， p<.05).(3) There was a significant negative correlation of -.292 (p<.05) between mathematical achievement and HCK teaching approach. In the summary, the HCK teaching approach seems to better help the medium and low mathematics achievers to learn the problem; the high mathematics achievers seem to more prefer non-HCK teaching approach.