以電子圓形釘板為輔具的開放式問題數學教學設計研究

Abstract

本研究主要是使用由Flash開發的圓形釘板數學電子軟體，依據開放式問題教學模式，對國中學生實施圓形釘板探索數概念的教學活動，來探討開放式問題教學模式在國中數學教學實施的可行性，並從教學歷程中觀察國中學生的解題表現與不同年級的國中學生在接受圓形釘板探索數概念的開放式問題教學活動後，解題表現的差異。 本研究以台北縣某私立完全中學國中部的國中一、二年級兩個班級的學生為研究樣本，兩班學生均接受圓形釘板探索數概念的開放式問題教學活動，並以研究者自行設計之圓形釘板教學個人學習單與團體學習單及數學學習問卷為主要研究工具。教學研究主要發現如下： 一、開放式問題教學模式在國中數學教學上實施是可行的。 二、在實施圓形釘板探索數概念的開放式問題教學活動後，國中學生提出多數的樣式猜測，但個人猜測結果仍十分有限。 三、在實施圓形釘板探索數概念的開放式問題教學活動後，學生發現了「因數與倍數」、「正比與反比」、「互質」、「最大公因數」、「最小公倍數」、「短除法」、「圖形的變化」與「等量公理」的數學概念。 四、不同年級的國中學生在接受圓形釘板探索數概念的開放式問題教學活動後，解題表現有差異。 最後根據研究結果與發現，提出若干建議以做為教師教學改進與未來研究之參考。 關鍵字：開放式問題、圓形釘板、電子教具、國中生

The purpose of this study was, by using the electronic circular geoboard software developed by Flash and open-ended approach, to find out whether the open-ended approach was feasible in teaching basic concepts of number theory to junior high students. Furthermore, by observing the problem-solving performance and the acceptability of the open-ended approach, the study also wanted to find out the differences between students from different grades.

This study was conducted to one junior first and one junior second class respectively at a complete school in Taipei County. All the students learned the basic concepts of number theory by the open-ended approach, and completed the self-designed learning sheets, individually and in a group, and learning questionnaire. And the findings of the study were as follow:

1. The application of open-ended approach in teaching mathematics to junior high students is feasible. 2. During the application, by using the electronic circular geoboard, more pattern conjectures were brought up by students than personal conjectures. 3. By using open-ended approach, students learned the mathematic concepts of the following: divisor and multiple, direct ratio and inverse ratio, relative primes, the greatest common divisor, the least common multiple, short division, graph diversity, and equality axiom. 4. There was difference between two different grades in problem-solving performance.

At the end of this study, some suggestions were made for future application and further study.

Keyword: open-ended questions, circular geoboard, electronic manipulatives, junior high school students