A Study on Fourth grades’ Understanding of Symbol x and Parentheses for the Unknown values in Mathematics Sentences

• Main Authors: YANG, PIN-ROU, 楊品柔
• Other Authors: HSIEH, KAI-JU
• Format: Others
• Language: zh-TW
• Published: 2017
• Online Access: http://ndltd.ncl.edu.tw/handle/393bwh

碩士 === 國立臺中教育大學 === 數學教育學系 === 105 === The purpose of this study was to investigate fourth graders ideas of using two different symbols for unknown values in solving mathematical problems. This study adopts both qualitative and quantitative methods in two different stages. In the first stage, the researcher used self-constructed instruments to investigate participants’ thoughts on unknowns. In the second stage, a semi-structured interview was conducted in order to further understand the differences between the students and their ideas of writing mathematics sentences when using different symbols of parentheses or x for the unknown numbers. The results showed：(1) some students thought that there were errors in the listing forms using either x or parentheses to solve the same situation problems. (2) some students thought it was easier using x while others preferred to use parentheses for the unknowns. (3) some students used x or parentheses in their listing forms, but made mistakes in solving mathematical problems. (4) in computing the same operating structure, some students made higher correct answers percentage when using parentheses instead of x. Students tended to do better in computing the operating structure with addend unknown numbers, while divisor unknown numbers were the harder. From the semi-structured interviews, it was discovered that using two different symbols (i.e., x or parentheses) for the unknown values that (1) some students thought the symbols as an situation unknown condition, a certain number, or a position in which to fill answer. (2) some students expressed x as the unknown condition of the situation, a certain number, or the equation to be calculated, similar to the symbol of parentheses. (3) some students believed that there are differences between using two different symbols x and parentheses for the unknown. The key to solve the problem successfully was to fully understand the corresponding relationships between the operation forms and the problem conditions. (4) some students thought the unknown part should be located on the right side of the equation. Accordingly they converted the original meaning of the text problem into the exact inverse operation. (5) some students agreed that both using different symbols of parentheses or x for the unknown values had made the problem easier to solve. However, further investigation showed that reason they held were not the same. (6) after some students successfully solved the same operating structure problem, they found that the arithmetic method could be used to solve the algebra problem.