Arithmetic and Algebraic Knowledge in Student Learning of Concepts

Abstract

Current research deals with students' arithmetical and algebraical knowledge, with a focus on a conceptual connection, and the relationship between two aspects of knowledge. The content in question is rational numbers, rational equations, and problem-solving in terms of proportion and ratio in grades 7, 8 and 9. The method contains three tests given to 400 students in grades 7-9. Tools for analysis were theories of generalizing arithmetic into algebra (Kieran, 2004), and the relationship between arithmetic and algebra in a conceptual context (Kaput, 2008). Current research shows that student knowledge of algebra and arithmetic often has a limited conceptual connection, and a weak relationship. Their knowledge of arithmetic operations and solving rational equations used to be just procedural, and reliant on formulas learnt in a procedural way, and often mixed up. The study also shows that student procedural strategies for finding formulas suitable for solving the equations, as well as carrying out the corresponding calculations, were often insufficient. The study investigates shortcomings in students' conceptualization of arithmetic operations with rational numbers, and how to apply them to solving rational equations. One reason for this, is lack of continuity in instruction and learning.