A Hierarchy of Strategies for Solving Linear Equations

This paper describes an investigation of students ’ strategies for solving linear equations. The assessment techniques used for investigating algebra paralleled those used for investigating number in the New Zealand Numeracy Development Projects (NDPs). In this study of 621 Year 7 to Year 10 students oral interviews were used to investigate the strategies that students used to solve equations. Rasch analysis was used to investigate item difficulty and student ability, and then the strategies associated with each question were examined. The data suggest that there is a hierarchy of sophistication of strategies. Many students were unable to solve a lot of the equations as they were restricted to less sophisticated strategies. The most sophisticated strategy of solving equations by performing transformations was understood by very few students. A new curriculum for New Zealand schools was introduced in 2007 (Ministry of Education, 2007). The learning area of Mathematics and Statistics is now divided into three strands rather than the previous six, with Number and Algebra being one strand. The implementation of the curriculum in Number up to Year 10 of schooling is guided by the Numeracy Development Projects (NDPs), which provide a framework for children’s development in number. The achievement objectives of the new curriculum are grouped t