The research and development of two-tier computerized diagnostic test in the “Ratio, Proportion and Direct Proportion” unit of the sixth grade.

• Main Authors: Siou-Ru Cao, 曹秀如
• Other Authors: Shu-Chuan Shih
• Format: Others
• Language: zh-TW
• Published: 2011
• Online Access: http://ndltd.ncl.edu.tw/handle/10128931479683119587

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 === 99 === Abstract In this research, the two-tier diagnostic test of “Ratio, Proportion and Direct Proportion” unit was developed using knowledge structure, and Bayesian network was integrated to establish the computerized two-tier diagnostic test later. Finally, the effectiveness of paper-and-pencil two-tier diagnostic test and computerized two-tier diagnostic test were evaluated. There were 285 students participating in the paper-and-pencil two-tier diagnostic test. The results of test were used to correct two-tier multiple choice items, establishing the reliability and validity of the test, and combined students’ responses in two-tier test with three different Bayesian modules to assess the effectiveness of the combined diagnosis models. Next, the optimal combined diagnosis model was used to construct the computerized two-tier diagnostic test. The computerized version of two-tier test was administered to 303 sixth grade students from Taichung County, Taichung City and Nantou County. The research results were shown below: 1. The Cronbach α of the computerized two-tier test was 0.76, it was better than the computerized one-tier test with the Cronbach α was 0. 71. 2. The combined diagnosis model that integrating two-tier test with Bayesian network could effectively increase the diagnostic accuracy. 3. In the paper-and-pencil two-tier diagnostic test, combining binary scoring in the two-tier joint judgment result to Bayesian network model got better diagnosis result. 4. In the computerized two-tier diagnostic test, combining binary scoring in the two-tier joint judgment result to Bayesian network model also got better diagnosis result. 5. In paper-and-pencil two-tier diagnostic test and computerized two-tier diagnostic test, the identification rates of three combined diagnosis models were in the same order. 6. Less than 35% of the students possessed the following mathematic concepts: using the multiplication relationship between similar numbers to calculate the ratio; determining whether any two numbers are in direct proportion; finding the relationship between two direct proportional numbers or two numbers of the same ratio and solving problem; drawing the relation chart for two sets of direct proportional numbers; determining the relation chart for two sets of direct proportional numbers and finding the unknown number from the relation chart of two direct proportional numbers. 7. More than 50% of the students made those six misconceptions described as the following: unclear about the proportion concept - mistake ratio for proportion; calculation mistake when converting integer ratio- mistake in decimal digits; proportional misplacement; wrong proportional formula; unable to determine the same ratio relation when two variables are in direct proportion; and unaware the relation chart will be a straight line that runs through the origin if two variables are in direct proportion. 8. According to the analysis of the questionnaires that were done by students who received computerized two-tier diagnostic test, the result showed that students have no difficulty in using the computerized two-tier test developed in the research. Keywords: “Ratio, Proportion and Direct Proportion”, Bayesian network, two-tier test, computerized diagnostic test