Research on Problem-solving and Problem-posing Abilities of Fifth Grade Students-a Case of Tenths Decimal Multiplication

• Main Authors: YU-PING LI, 李玉萍
• Other Authors: 劉曼麗
• Format: Others
• Language: zh-TW
• Published: 2007
• Online Access: http://ndltd.ncl.edu.tw/handle/56007444921030144488

碩士 === 國立屏東教育大學 === 數理教育研究所 === 95 === The purpose of this study was to explore how the fifth-grade students apply problem-solving and problem-posing skills and strategies in the solution of decimal multiplication. Therefore, this research attempts to study how students’ abilities about problem-solving and problem-posing are related. This research involves a survey, comprised of two sets of questions concerning problem-solving and problem-posing. Questions were designed in five similar types, including integer × integer, integer × pure decimal integer, decimal integer × mixed decimal, pure decimal integer × integer, and mixed decimal × integer. Each type contains three situations, including of continuous quantity, the content of discrete unit as the single object, and the content of discrete unit as the multiple objects. Four southern elementary schools of 63 fifth-grade students participated in the study. Interviews were divided into three groups in terms of high, medium, and low-level, with an equal number of subjects (N=2) in each group in order to understand their thoughts. The data analysis of this study was conducted through descriptive statistics in order to determine the results in problem-solving and problem-posing of the students; also, through product-moment correlation by Pearson and personal interviews to study the relations between problem-solving and problem-posing. According to the results of the study, the students’ performance of problem-solving abilities in decimal multiplication is highly related to the multiplier. As the multiplier is integer, the outcome is well-performed; by the contrast, as the multiplier is decimal integer, it is poor-performed. When it comes to problem-posing abilities in decimal multiplication, the performances are generally poor in both conditions above.Additional studies showed that the performance of students in answering questions, integer × integer type was the best, followed by integer-multiple. The worst was decimal -multiple. In this case, performance in problem-solving was better than that in problem-posing. It is showed that the ability of the students in problem-solving is related to it in problem-posing through product-moment correlation by Pearson. According to the six cases of personal interviews, those who manage to problem-posing, their problem-solving tend to succeed; on the contrary, those who fail to problem- solving, their problem- posing tend to be defeated. Generalize the students’ strategies, they succeed mainly by means of unit quantity × unit numbers; they misconceive mainly due to failing to answer questions because of keywords. In problem-posing responses, three important reasons were used to explain failures, including less logic, misunderstanding of questions, and less familiarity with problem-posing type. To conclude, this study may be of importance in providing math teachers with a better understanding of how students’ beliefs about problem-solving and problem-posing in decimal multiplication.