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…

Research studies have shown that students encounter difficulties in transitioning from arithmetic to algebra. Errors made by high school students were analyzed for patterns and their causes. The origins of errors were: intuitive assumptions, failure to understand the syntax of algebra, analogies with other familiar symbol systems such as the…

To probe beyond declarative knowledge about real numbers in secondary school, the authors interviewed students in Grades 9, 10 and 12. The main question seems to be whether the length of a decimal expansion is "indefinite" or "infinite." It blurs the mental representation of rational numbers as well. (Contains 3 footnotes.) [For complete…