本研究旨在探討國小二年級學童以不同的整數乘法教材學習之表現，研究方法採準實驗研究法，實驗組以乘法替代性教材學習，對照組則以陽光教材（匿名）學習，並透過前測、前後測、後測以及延後測的統計分析與晤談結果，比較兩組學童在乘法意義與解題上的表現。實驗組和對照組各為103和104人，在前測沒有統計上的顯著差異，因此兩組學童學習乘法的起點相當。在節數方面，實驗組和對照組各上63和62節課程。
主要研究結果如下：
1.對於乘法意義的表現：
（1） 在倍的語言轉換方面：實驗組在幾個幾的表現顯著優於對照組，在幾有幾個和幾的幾倍的表現則沒有顯著差異。
（2） 在單位量轉換方面：實驗組在乘法算式表徵的表現顯著優於對照組，在複製集聚單位而後相加的表現則沒有顯著差異。
2.對於乘法問題的解題表現：
（1） 在數字大小方面：實驗組在Ⅰ×Ⅰ和1×Ⅰ的解題表現顯著優於對照組，在Ⅱ×Ⅰ的解題表現則沒有顯著差異（Ⅰ表示一位數，Ⅱ表示二位數）。
（2） 在限制解題型式方面：實驗組在開放解題和乘法算式的解題表現顯著優於對照組，在乘法算式填充題的解題表現則沒有顯著差異。
（3） 在乘法情境方面：實驗組在等組群的解題表現顯著優於對照組，在陣列的解題表現則沒有顯著差異。
3. 解題的錯誤類型與解題困難：
本研究發現的解題錯誤依加法算式、乘法算式和乘法算式填充題分為數種類型，且每一種錯誤類型出現的次數皆是實驗組少於對照組。此外，本研究發現學童的解題困難包含欠缺基本的語文知識、對幾有幾個和幾個幾的語言描述不易理解、對乘法算式記錄感到困難、忽視單位量與單位數位置的意義性、受限於九九乘法表的限制等。
4.延後測與後測表現之比較：
（1） 在乘法意義方面：實驗組在幾個幾和幾有幾個的表現有顯著退步，對照組的表現則保持穩定。兩組學童在複製集聚單位而後相加都有顯著進步，在乘法算式表徵的表現則是改變不大。
（2） 在解題方面：兩組學童在數字大小、乘法算式解題和等組群的解題表現並無顯著差異，在乘法算式填充題方面都有明顯的退步。此外，實驗組在開放解題的表現比對照組明顯退步，對照組則在陣列的表現上比實驗組明顯進步。

The purpose of this study was to explore the performance of the different whole number multiplication of teaching materials learned by second graders of the elementary school. The research method was adopted with quasi-experimental design. The experiment group used the alternative materials and the contrast group used the issued textbook. To compare the performance of the two groups in terms of the meaning of multiplication and solving problems, the researcher analyzed the result of the pretest, the middle test, the post test, the retention test and interviewed with students. The experiment group consisted of 103 students and the contrast group consisted of 104 students. There were no obvious variance between the two groups in statistic of the pretest, therefore they had the similar ability. The experiment group was taught 63 activities and the contrast group 62 was taught.
The main study results were shown as follows:
1. In the meaning of multiplication:
(1) In multiplicative language translation: The experiment group was prior to the contrast group significantly in the performances of the language(such as three of fours). These two groups had no significant difference in the performances of the language(such as three had fours) and the other language(such as three times as much as four).
(2) In unit translation: The experiment group was prior to the contrast group in multiplicative representation significantly. These two groups had no significant difference in copying unit and adding.
2. In solving problems:
(1) The experiment group was prior to the contrast group in solvingⅠ×Ⅰand 1×Ⅰproblems significantly. These two groups had no significant difference in solvingⅡ×Ⅰproblems.(Ⅰis represented as one digit number and Ⅱ is represented as two digits number. )
(2) The experiment group was prior to the contrast group in solving the opening and multiplication problems significantly. These two groups had no significant difference in solving fill-in the blank in multiplication problems.
(3) The experiment group was prior to the contrast group in solving the equal group problems significantly. These two groups had no significant difference in solving rectangular array problems.
3. The error pattern and difficulties: The study found that there were several error patterns classified in terms of addition, multiplication and fill-in the blank in multiplication. The number of each one of the error pattern were the experiment group less than the contrast group. In addition, the study also found that students lacked basic language knowledge. They don't understand the description of languages(such as three had fours and three of fours). They felt difficult with multiplicative representation record. They ignored the meaning of the position of unit and the number of unit, and their solving performance was restricted to multiplication table.
4. In comparing the retention test with the post test:
(1) In the meaning of multiplication: The experiment group made no progress in languages(such as three had fours and three of fours)significantly, but the contrast group remained stable. These two groups both made progress in copying unit and adding significantly, but had no obvious difference in multiplicative representation.
(2) In solving problems: The performances of these two groups had no significant difference in number, multiplication and equal group problems, but they both made no progress in solving fill-in the blank in multiplication problems. Besides, the experiment group was inferior to the contrast group significantly in the performances of solving opening problems, and the contrast group was prior to the experiment group in the performances of solving rectangular array problems.

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