A study of elementary students'' ability in the representation translation of fractional multiplication-division problems and meta-cognition

• Main Authors: HUANG, YUEH-PING, 黃月平
• Other Authors: LIN, YUAN-HORNG
• Format: Others
• Language: zh-TW
• Published: 2005
• Online Access: http://ndltd.ncl.edu.tw/handle/59676241132860260624

碩士 === 臺中師範學院 === 教育測驗統計研究所 === 92 === The purpose of this study was to explore elementary students´ ability in translation of representation between word problems and algorithms, which were fractional multiplication-division. In this study, the sample, totally four hundred and eighty, were six-graders students from Taichung country seaport area. The main research tool was “ The Problem Posing Test”, which was pencil-paper form designed by the researcher. From the test, the ability of posing in word problems was collected. Furthermore, in the test, the meta-cognition for translation of presentation would also be realized. According the performance in this test, eighteen students were selected for semi-structural interview. By this way, the researcher could realize the thoughts and concepts while they processed posing of word problems. According to the analysis of the above data, there were some results as follows: 1. Description of Students´ ability in problem posing (1) The posing percentages was 94.6﹪and the percentages of success is 73﹪. It showed that students could respond “ The Problem Posing test” . (2) As to the ability of problem posing, there was not significant difference between multiplication and division problems. Difference in ability of problem posing is significant between numerical kinds. There was the highest ability for integers of multiplicand and dividend, and there was the lowest ability for mixed fractions of multiplicand and dividend. (3) As to the structure of multiplication and division problems, no matter which numerical kinds in these problems, most of all was “the rule of two“. (4) As to the performance for all dimensions of problem-posing, the dimensions of ”operation applicability” and “denomination integrity” were the best, and ”situation rationality” was the worst. Furthermore, multiplication is better than division in “maxim fineness”, ”operation applicability”, ”situation rationality”. For difference numerical kinds, the order of “ maxim fineness”, ”operation applicability” and ”situation rationality” are integer, fraction less than 1, mixed fractions. Only the order of “denomination integrity” is fraction less than 1, integer, mixed fractions. 2. There was significant canonical relation between ability of linguistic reasoning and problem posing. There was no significant difference in ability of problem posing with various kinds problems. 3. The more ability of meta-cognition the students had, the more ability of problem posing they had. There was no significant difference of meta-cognition with various kinds problems. In conclusion, the results of this study offered some suggestions for the improvement of instructional materials and pedagogy in mathematics. Some recommendations for further research were discussed.