由研究者自身的教學經驗與文獻中發現，台灣國小四年級的學生在學習周長與面積單元時，容易出現相互混淆的情形造成學習單元表現不佳。因此本研究利用合作學習法針對小四學生進行為期一週，周長與面積單元的教學，研究能否對概念的理解產生正面的影響效果，並且在合作學習的過程中，加入學生學習投入情況交叉比對，藉以了解學生合作學習、學習投入與其學習表現的關係。本研究採取準實驗研究法進行教學研究，教學時間為五節課。研究對象為宜蘭市某國小的四年級兩個班級的學生，人數共35位，其中一班接受合作學習教學法為實驗組，另一班則接受傳統講述式教學法為控制組。
研究者利用自行編製的前測概念診斷試卷，針對兩個班級的學生進行預試，了解兩班學生在教學前對於周長與面積概念的掌握程度。依照合作學習教學法設計教材，針對實驗進行教學。教學後再進行後測，以檢視兩組學生的學習表現是否有差異。另外在教學前後利用研究者自行編製的「學習投入量表問卷」經信、效度考驗以進行正式施測。藉以了解教學前後學生學習投入改變情形，以及學習投入對於學習表現之影響。本研究主要結果顯示如下:
(1) 根據實驗組與控制組學習投入問卷的前、後測結果顯示，實驗組的學生在接受合作學習法教學後，在行為投入與情意投入面向上，後測有提升，控制組的學生則為下降。控制組的學生在認知投入面向上，後測有提升，實驗組則為下降。
(2)兩班學生的周長與面積成就測驗後測成績皆高於前測。接受合作學習法的學生與接受傳統講述法的學生，對於周長與面積單元學習成就上並沒有顯著的差異，但從後測成績的平均分數來看，控制組的學生表現優於實驗組。
(3)將學生的周長與面積單元成就測驗結果、學習投入問卷、學生合作情形進行交叉比對，發現學習投入越高的學生或高合作的學生在後測的表現相對較高。
(4) 分析實驗組學生問卷以及學生的訪談內容，喜歡合作學習法的學生多過不喜歡的學生，多數人認為合作學習法可以增進上課時與同學的互動關係，藉由同學間彼此教學，可以提升學生的學習動機。

Based on personal teaching experience and on review from the literature, it is noticed that some Taiwanese students have difficult in learning the topics on perimeter and area. They are prone to be confused between the two concepts and perform unsatisfactorily in subsequent assessments. In order to help students learn better these important topics, this study attempted to incorporate cooperative learning as a means to promote conceptual understanding by fourth grade students on perimeter and area. This study adopted a quasi-experimental non-equivalent groups design as its method of study. Two classrooms were randomly chosen with a total of 35 students from an elementary school in Yilan city. One class was randomly assigned as the control group which was taught under the lecturing method. The other class was assigned as the experimental group the students of which were taught under a cooperative learning environment. The purpose of the study is to find out if there is a relationship between students’ cooperative learning, their engagement in learning and academic performances.
Information pertaining to students’ engagement as well as performances on the subject matters was collected from both groups of students prior to and after the study. Both groups were administered a test instrument designed by the researcher that measured their understanding of basic mathematics and whether they had prior knowledge on perimeter and area. Instruction was then given accordingly, with the students in the experimental group given the opportunity to participate in group discussion within every class. Afterwards, post-test was administered to identify if there were differences in performances between the two groups. In addition, the Learning Engagement Questionnaire, which was developed and validated by the researcher, was administered to both groups at the beginning and end of the study. This instrument tapped into students' learning engagement with respect to the cognitive, emotional and the behavioral domains.
First, based on the results from the Learning Engagement Questionnaire, it was found that the scores increased on both the behavioral and emotional aspects of engagement for the experimental group yet decreased for the control group. In contrast, the scores on the cognitive aspect of engagement increased for the control group yet decreased for the experimental group.
Second,it was found that the post-test scores on perimeter and area for both groups were better than the scores from the pre-test. Though no significant difference was identified between the two groups on the post-test, the average score of the cooperative learning group outperformed that of the traditional lecturing group.
Third, it was found that, in general, students with higher post-test scores on the Learning Engagement Questionnaire demonstrated significantly improvement in their performances on the post-test on perimeter and area. It was further observed that students with higher learning engagement scores or higher scores on cooperation had also performed better in the post-test on perimeter and area.
Fourth, with reference to the questionnaire data and interviews from selected students in the experimental group, it was observed that there were more students who preferred cooperative learning than those who did not prefer it. Most students indicated that cooperative learning could enhance learning motivation as well as interaction with their classmates through the act of teaching each other.

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