Fourth Graders’ Solving Process in Solving Two-Step Multiplication and Division Word Problems

• Main Authors: Huang, Chiao-Yin, 黃巧瑩
• Other Authors: Fu, Feng-Rung
• Format: Others
• Language: zh-TW
• Published: 2013
• Online Access: http://ndltd.ncl.edu.tw/handle/02872970882344081760

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 === 101 === This research was to explore fourth graders’ problem solving process in solving two-step multiplication and division word problems based on the theory of problem solving process by Mayer (1992, 2006) and Wittrock (2006), and Multiplication -division word problems classification by Greer (1992) and Vergnaund (1988). A test of two-step word problems was created and used as the instrument by the researcher. The test was divided into thirteen kinds of problems, based on the semantic structure and unknown quantities, and was executed on fourth graders from two schools in Taichung city. Two hundred and ten effective samples were collected and analyzed by quantitative statistical analysis. To find out students’ typical error types, an investigation was applied by surveying each of the students individually after the test. The major findings were as follows： 1.Students performed best in processing “translation”, better than “planning and monitoring”, “execution” and “integration” respectively. Among self-regulating in metacognition, students performed best in “understanding the problems”, better than “listing the correct equation” and “giving the answers” respectively. 2.The scores of different problem solving processes and students’ performances were highly correlated. 3.As to the pass rate among the four semantic structure problems, students performed best in “multiple-proportions”; “comparison in multiple”, “equivalent groups” and “quantity-isomorphism” were followed respectively. As to the pass rate among the three unknown number problems, students performed best in final-amount unknown type. The varying-amount unknown and the initial- amount unknown types were followed respectively. 4.Students with higher mathematical abilities used problem-solving approach to identify problems types, but students with lower abilities were influenced easily by problem structure and size of numbers. 5.Students with lower mathematical abilities performed worst in “execution” .They felt difficult in “quantity-isomorphism” types and “comparison in multiple” types (basic-amount unknown). 6.Students’ typical error types could be defined within each problem solving process.