國小四年級學生對乘法算則理解之研究   免費試閱

A Study of 4th Graders’ Comprehension of Multiplication Principles

本研究旨在探索學生對結合律與分配律等乘法算則概念理解的情形，研究樣本為國小四年級的學生80人，進行三階段之調查作業，研究工具包含「算則概念辨識判斷」、「算式選擇與解釋」、「算式表徵與解題」等三項測驗，配合紙筆作答、實作排列與訪談方式蒐集資料。採百分比、χ2適合度考驗與質性方式進行資料分析，歸結研究發現：學生對單因子合成設計的乘法算式較兩因子設計的分解或補償策略算式正確判斷比例高；選擇「直接加法」與「整體合成」之算則策略進行解題，較選擇「數字分解」與「補償策略」者多；依據對算則策略的理解，學生產出四種解決乘法問題的思考路徑，並能根據問題情境形成算式表徵，利用合成算則策略解決問題。根據學生乘法算則概念理解的發現，可協助教師瞭解影響學生乘法算則學習的要素，作為改善代數推理教學設計和輔導學生數學學習機制的建立。

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.