A Study of 4th Graders’ Comprehension of Multiplication Principles

Author: Chia-Huang Chen(Center for General Education, Kun Shan University)

Vol.&No.：Vol. 55, No. 2
Date：June 2010
Pages：207-231
DOI：10.3966/2073753X2010065502007

Abstract：

The goal of this study was to investigate elementary school students understanding of the concepts and principles of multiplication, and to examine the students’ performance in solving distribution and associative law problems. Eighty fourth graders completed three stages of a task. Each task specified a learning goal. The data was analyzed using descriptive statistics, a goodness-of-fit test and a qualitative approach. The results show that the correctness ratio of partition or compensation strategies of students in one-factor is better than in two-factor. The selection of solving multiplication questions in “direct modeling to addition” and “doubling to complete number” is more than in “partitioning number strategies“ and “compensating strategies.” Four thinking paths were produced by these students and they showed that they could judge, apply the properties, and write down the appropriate expressions to solve mathematical problems. These findings can assist teachers as they engage students in opportunities to learn multiplication properties and can also be useful as teachers participate in instructional and curriculum design.

Keywords：distribution law, algebraic reasoning, associative law

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