探究國小三年級在周長及面積操作活動下的學習歷程

我國於各項數學國際評比中，學生於學習成就表現上皆名列前茅。但學生內部間的表現卻差異很大。此外，在這些大型測驗中可以發現，學生在幾何概念的表現皆遜於數與量方面，這樣的結果可能與現今台灣的教學現場及考試制度息息相關。此外，研究者於教學現場時，發現幾何學習中以周長、面積概念的表現最為低落。許多學生至高年級尚分不清楚自己計算的是周長，還是面積。因此，本研究雖採用個案研究法，但為了維持學生高度的操作動機，於前後兩次操作所配對的組原有做調整以國小三年級為對象，讓學生經驗以「周長」及「面積」為主的操作活動，再透過同試卷的前後測來檢驗學生學習的成效，並將結果進行分析。研究結果顯示，學生於操作活動時會受到遊戲規則、操作活動本身及人際的互動影響，而出現了四個現象：（1）學生於操作時受到遊戲規則的影響，導致操作常採取「先圍起來」的策略，造成大家的領土多集中於一側。（2）學生於拼扣條時，幾乎採取1根1根拼在地圖上的策略，少部分學生會先拼輪廓線再放置於地圖上。（3）學生對於土地的選擇，經常以眼前的土地為優先選擇。（4）學生藉由與同學的互動，提升主動思考的可能性。（5）學生透過與教學者的互動，增加學生思考的廣度。經過了多回合的操作活動，學生於前、後測的表現上出現以下的情況：（1）部分學生對於周長及面積的解讀尚無法將說明與圖示作連結。（2）部分學生對於周長及面積的解讀尚以典型例作輔助的說明。（3）學生於後測的表現優於前測。因此，根據研究結果的發現，提出以下的結論：（1）操作活動中的遊戲規則會影響學生的操作。（2）操作活動能夠建立學生周長與面積的概念。（3）操作活動能提升學生學習周長與面積的成效。（4）操作活動可以協助學生與周長、面積的連結。（5）操作活動可以提升學生的學習動機。（6）操作活動於教材設計上的侷限性。因此，針對日後的研究提出以下的建議：（1）研究對象方面：增加樣本數，以提升研究的信效度。（2）研究設計方面：將扣條替換成沒有寬度的工具，以減少學生對於周長的誤解、將地圖上土地的輪廓線調淺，平方公分的格線加深，以減少學生視覺上的混淆、增加功能卡牌使用的頻率，提升學生看見周長與面積改變的比例、修正圍土地只能根據地圖給予的界線，開放學生可以一次圍更多的小土地，引發學生更多的遊戲策略。（3）研究時機方面：將活動於周長學習之前進行，以探討操作活動對周長及面積教學的影響。

關鍵字

周長；面積；心像；操作活動

並列摘要

In international evaluation of mathematics, our students are among the best in terms of academic achievement.But the performance among students is very different. In addition, in these large-scale tests, students' performance in geometric concepts is inferior to quantity and quantity. Such results may be closely related to the teaching scene and examination system in Taiwan today. In addition, when the researchers were at the teaching site, they found that the concept of perimeter and area was the lowest in geometric learning. Many students are still unclear whether they are calculating the perimeter or the area. Therefore, although the case study method is used in this study,in order to maintain the students' high manipulation motivation, the group that was paired with the two operations before and after was originally adjusted to target the third grade of primary school,so that the student experience is "perimeter" and " area" manipulation activities, through the test papers before and after the test to test the effectiveness of student learning, and the results of the analysis. The research results show that students are affected by the rules of the game, the operation activities themselves and the interpersonal interactions when operating the activities. There are four phenomena:(1) Students are affected by the rules of the game during operation, resulting in the operation often adopting the first The strategy of getting up has caused everyone’s territory to concentrate on one side. (2) When a student flexes a piece, he or she takes almost one strategy of spelling on the map. A small number of students will first put the outline and then place it on the map. (3) Students' choice of land often takes precedence over the land in front of them. (4) Students enhance the possibility of active thinking by interacting with classmates. (5) Students increase the breadth of students' thinking through interaction with the teacher. After several rounds of operation activities, the following situations occurred in the performance of the students before and after the test: (1) Some students' interpretation of the perimeter and area cannot be linked to the illustration. (2) Some students' interpretation of the perimeter and area is supplemented by typical examples. (3) Students' performance in post-testing is better than pre-test. Therefore, based on the findings of the research, the following conclusions are drawn: (1) The rules of the game in the manipulation activities will affect the student's operation. (2) Manipulation activities can establish the concept of student perimeter and area. (3) Manipulation activities can improve the effectiveness of students' learning circumference and area. (4) Manipulation activities can assist students in connecting with the perimeter and area. (5) Manipulation activities can enhance students' motivation for learning. (6) The limitations of manipulation activities in the design of textbooks. Therefore, the following suggestions are proposed for future research: (1) Research object: increase the number of samples to improve the reliability and validity of the research. (2) Research design: replace the buckle with a tool with no width to reduce the student's misunderstanding of the perimeter, lighten the outline of the land on the map, and deepen the square of the square centimeter to reduce the visual confusion of the students. Increase the frequency of use of functional cards, increase the proportion of students seeing the change of perimeter and area, and correct the surrounding land only according to the boundaries given by the map. Open students can encircle more small land at a time, triggering more game strategies for students. (3) Research timing: The activities will be conducted before the perimeter study to explore the impact of manipulation activities on perimeter and area teaching.