A study on nine-graders'' main error types on quadratic equation with one unknown and its remedial teaching

• Main Authors: Pei-Ying Ni, 倪佩瑛
• Other Authors: Pei-I Chou
• Format: Others
• Language: zh-TW
• Published: 2013
• Online Access: http://ndltd.ncl.edu.tw/handle/15699424134261156094

碩士 === 國立中山大學 === 教育研究所 === 101 === The aim of this study is to investigate the types of errors students may make on the unit of the conception and calculation of quadratic equation with one unknown. This study conducts a quasi-experimental design. Self-made tests was used to classify and analyze the types of errors by which remedial teaching materials and activities will be designed and then conducted to correct students’ errors. According to the study, four error types which can be found are shown as follows. A. The conception of comprehending and calculating quadratic equation with one unknown. (1)Wrong judgment or unfamiliarity with the application of solution and roots. B. Solution by factorization of polynomial (2)Unfamiliarity with the solution: if AxB=0, then A=0 or B=0 (3)Unfamiliarity with the method of extracting common divisor or misusing an equal division axiom leading to reduced root (4) Unfamiliarity with, mixing up, left out and forgetting multiplication formula (5)Errors on the solution to cross deposit multiplication. C. Applying the method of completing the square to solve quadratic equation with one unknown (6)Wrong conception on square root (7)Unable to find suitable, correct complete square form (8)Unclear steps or principles on the method of completing the square to solve quadratic equation with one unknown. D. Using formula to solve quadratic equation with one unknown. (9)wrong memorization on the formula (10)Difficulties in dealing with related questions on discriminant and solution. The reasons for these error types are: 1. Not enough background knowledge or basic concepts. 2. The interference of new experience on old one. 3. Not enough ability of calculation or carelessness. 4. Wrong memorization or application on formula. 5. Emphasis more on memorization but less on comprehension. 6. Wrong concept or calculation on the solution of cross deposit multiplication. As far as the effect of the remedial teaching is concerned, the percentage of post-tests is higher than that of pre-tests. Among the participants, there is only one who gets full grades on both tests. For the rest of them, the percentage of post-tests is higher than that of pre-tests. Apart from answering the questions by the conception of square root, the effect of the remedial teaching program on the participants is quite satisfying.