Abstract

The transition from arithmetic to algebra is a well-known difficulty in school mathematics. In order to succeed, learners require inter alia a better understanding of algebraic symbols, equality, equations and working with negatives/subtraction. This article reports on a response pattern analysis (RPA) of learners’ responses to six test items involving arithmetic equivalences and algebraic equations. The participants were 106 Grade 10 learners from two township schools in Johannesburg, South Africa. The key finding was that success in solving linear equations does not imply success in solving arithmetic equivalences, and vice versa. Methodologically, the study showed that an RPA is an accessible, simple and time-efficient means of conducting initial analyses of larger data sets that is well suited to studies conducted by novice researchers.

摘要

从算术到代数的过渡是学校数学中众所周知的难点。为了取得成功，学习者尤其需要更好地理解代数符号、等式、方程以及使用负数/减法。本文报告了学习者对涉及算术等价和代数方程的六个测试项目的反应的反应模式分析 (RPA)。参与者是来自南非约翰内斯堡两所乡镇学校的 106 名 10 年级学生。关键的发现是，求解线性方程的成功并不意味着求解算术等价的成功，反之亦然。在方法论上，该研究表明，RPA 是一种易于访问、简单且省时的方法，可以对较大的数据集进行初步分析，非常适合新手研究人员进行的研究。