Early algebraic thinking: links to numeracy

Funding year: 
1 year
University of Canterbury
School sector
Project start date: 
January 2006
Project end date: 
January 2007
Principal investigator(s): 
Chris Linsell
Research team members: 
Jan Savell, Noel Johnston, Melissa Bell, Eric McAuslan, and John Bell
Research partners: 
John McGlashan College; King’s High School; Otago Boys High School; Numberworks

Project Description

Many students struggle with introductory algebra and teachers have little to guide them in assisting students to learn this important component of high school mathematics. Little is known about the effect of students’ numeracy on the learning of early algebra, or about the strategies that students use to solve equations. There is widespread agreement that algebra is not easily understood by many students. The Cockroft Report in the United Kingdom highlighted the fact that algebra is a source of considerable confusion and negative attitudes among pupils (Cockcroft, 1982), while the title of Brekke’s (2001) paper, “School Algebra: Primarily Manipulations of Empty Symbols on a Piece of Paper?”, sums up the situation for many students.

The links between numeracy and readiness for learning algebra need to be investigated. Linsell (2005) suggested that only those students who have mastered multiplicative part–whole thinking are capable of solving equations by the formal process of inverse operations. We have available the diagnostic tool for assessing students’ stage of numeracy (Ministry of Education, 2003a). To determine how the students’ stages of numeracy have an effect on their learning of algebra, a diagnostic tool needs to be developed for assessing algebraic thinking in the domain of solving equations. This would allow a framework for algebraic thinking to start to be developed.