A Study of Problem-Solving Strategies in Linear Equations with One Unknown for Junior High School Students under the Different Understanding of the Equal sign

• Main Authors: Heng-tsu Pan, 潘亨足
• Other Authors: Shuk-kwan S. Leung
• Format: Others
• Language: zh-TW
• Published: 2010
• Online Access: http://ndltd.ncl.edu.tw/handle/11521157682018591266

碩士 === 國立中山大學 === 教育研究所 === 98 === The purpose of this study is to investigate students’ understanding of the equal sign, problem-solving strategies of equations with one unknown, and the strategies of solving equations with one unknown under different understanding types of the equal sign. To achieve this purpose, the investigator did a survey and development instruments. The participants were 203 seventh-grade students in a convenient sample. Descriptive statistics were used to analyze data in frequency and percentages. The main results was that participants with a relational definition of the equal sign were the most (close to 50%), and an operational definition of the equal sign was approximately 1/4. There was a higher successful performance associated with a relational definition than an operational definition. The primary strategy of operations on the left-hand side of equal sign is the mathematical operations; the main strategy of an unknown quantity on the right-hand side of the equal sign was by going to the parenthesis-reverse and bringing different denominators into a common denominator; the principal strategies of one number on the right-hand side of the equal sign, equations with operations on the right side of the equal sign and equations with operations on both sides of the equal sign are cover-up and transposing. To use the strategies of trial and error substitution and undoing is minority in a linear equation with one unknown. The strategy of an operational definition participant in five equal sign topics is similar to the strategy of one with a relational definition. However, those with a relational definition apply multiple strategies and exhibited varying particular and algebraic property. On the other hand, participants with an operational definition used arithmetic strategies more frequently than participants with a relational definition. From the above results, the researcher suggested instruction to include strategies with algebraic property to help learners to develop stable understanding of the equal sign in Algebra. In addition, the recommendation is to have teachers to encourage students to apply multi-dimensional thinking and different strategies in algebraic problem-solving.