Use Production Rules to analyze the use of addition algorithm for Elementary School First Grade students

• Main Authors: Teng,Chiachen, 鄧佳珍
• Other Authors: Huang,Yihung
• Format: Others
• Language: zh-TW
• Published: 2012
• Online Access: http://ndltd.ncl.edu.tw/handle/98572946665987456966

碩士 === 國立臺中教育大學 === 數學教育學系在職進修教學碩士學位班 === 100 === 　　The main object of this study was the 99 school year grade one students who used the lower grade math textbooks written by National Academy for Educational Research. These students were from an elementary school located in central Taiwan. This study used ACT-R production rules to carry out the experiment and analysis. The procedure of the experiment was after giving lessons of two addition operation processes, the students were divided into group A and group B, each with 13 students. After having some practice, the groups received the first test and the second test given seven days later. The result of the test takers’ performance on the use of horizontal multi-step addition or vertical addition to calculate the problem of carrying a number to a greater place value or not to carrying a number is as followings: 1.In horizontal multi-step addition, the mistakes students made are: not understand the format of addition operation process, insufficient in the number concepts of tens and units, and insufficient in the cognitive concepts of addition. 2.In vertical addition, the mistakes students made are: not understand the format of addition operation process, insufficient in the number concept of value, not understand the cognitive concept of decimal notation, and insufficient in the cognitive concepts of tens and units place value. 3.The students in Group A used horizontal multi-step addition in their first test, among them eleven students still used it in their second test; the students in group B used vertical addition in the first test, all of them still used it in the second test. 4.In the first test, Group A’s accuracy rate is 80% and Group B’s is 71.54%. In the second test, Group A’s accuracy rate is 91.54% and Group B’s is 79.17%. 5.The most mistakes students made are the two-digit plus two-digit carrying to a greater place value problems and the mistake rate is higher in the use of vertical addition than the use of horizontal multi-step addition. Finally, this study is also aimed at the mistakes in horizontal multi-step addition and vertical addition, and provides some teaching suggestions for the field teachers’ reference.