不同數學學業成就高一生選修GeoGebra軟體動畫課程的學習表現之研究

本研究旨在發展「GeoGebra軟體動畫課程」的歷程，訂立課程目標、規劃課程設計與活動日程，自編教學講義，在課程實施中以教室日誌記錄課堂活動與學生問題並省思，以提供日後教師做本課程發展的參考。發展課程的同時，根據研究目的，分析選修本課程之學生的數學學業成就與本課程學習表現之間是否相關？差異較大的個案學生，其作品有何特徵？研究者收集選修學生該學期三次期中考的數學成績平均作為數學學業成就，以及本課程所繳交的動態幾何作品成績作為本課程學習表現，作品成績滿分為100分，期中基礎操作佔60%、美觀佔20%、創意佔20%，將兩個成績做量的分析。再從兩個成績中，找出正差距與負差距最大的學生各三位，根據個案作品、個案訪談錄音記錄和教室日誌作質的分析，本研究得到以下結論： (一) 「GeoGebra軟體動畫課程」實施後，選修學生的數學學業成就與本課程學習表現之間沒有關聯，數學學業成就的高低，並不會影響本課程的學習表現。 (二) 動態幾何作品成績中的「美觀」與「創意」相關達顯著水準，即美觀成績愈高，創意成績也愈高。 (三) 正差距較大的前三位個案H1、H2、H3學生，皆是數學成就中下的學生，但在本課程的學習表現為中上，學習成就感較高，作品美觀程度略高於負差距的三位個案學生。 (四) 負差距較大的前三位個案L1、L2、L3學生，皆為數學成就頂尖的學生，在本課程的學習表現雖較普通，但其作品數學思維程度較高，偏向單一的創意。綜合言之，選修學生的數學學業成就與本課程學習表現之間沒有關聯，學習表現取決於學生的學習態度。對於高數學學業成就的學生，研究者建議給予更難的挑戰與獎勵，讓其在本課程的學習表現能夠再提升；對於低數學學業成就的學生，則建議在課堂公開表揚其作品，給予適時的鼓勵，激勵其持續向上、永不放棄的學習精神。

關鍵字

動態幾何；學業成就；學習表現

並列摘要

The purpose of this study was to develop the "GeoGebra Software Animation Course," including setting course objectives, designing courses and event schedules, compiling handouts, recording the classroom activities and students’ problems in the classroom journal, and making a reflection as a reference for future researchers in the subject area. Based on the purpose of the study, the researcher examined the correlation between participants’ academic achievements in math and their performance in this elective course in order to finding out the characteristics of the works by the individual student with bigger difference at the same time of the development of the course. The average of the scores in two midterms and one final exam in math served as students’ academic achievements in math; the grade on the work of dynamic geometry served as their performance in this elective course, whose full marks were 100%, composed of 60% for the basic operation, 20% for the aesthetic, and 20% for the creativity. The quantitative analysis of the two kinds of scores was conducted. And then the researchers selected three students with each biggest positive and negative gap from the results for qualitative analysis,including analyzing their works, conducting interviews, and examined the classroom journal. The conclusions were drawn as follows: (1) After the implementation of the "GeoGebra Software Animation Course," there was no correlation between the participants’ academic achievements in math and their performance in this elective course. That is, students’ academic achievements in math did not affect their learning performance in the course. (2) In addition, the results showed a significant and strong relationship between the aesthetic and the creativity in students’ works of dynamic geometry. In other words, as the score on the aesthetic went up so did that of the creativity. (3) The first three cases of H1, H2, H3 students with the biggest positive gap, were all students who did not have a high level of academic achievements in math but had a moderate and high level of the learning performance in the elective course. Furthermore, they had a higher sense of accomplishment in learning and the level of the aesthetic in their works was slightly higher than the other three students with the negative gap. (4) The top three cases L1, L2, L3 students with the biggest negative gap were all among the top students who had high academic achievements in math. Although the students did not have outstanding performance in this elective course, they have a higher level of mathematical thinking in their works, focusing on single creativity. In conclusion, the researchers found out that there was no correlation between participants’ academic achievements in math and their performance in this elective course. The students’ learning performance were mainly based on their learning attitude. The researcher suggested to offer the student who had the better academic achievement in math the more difficult challenges and prizes in order to improve their learning performance in the course. For the students who had the lower academic achievement in math, the researcher suggested to praise their work in public, and timely encourage them to arouse their positive and continuing learning attitude.