This case study looks at one mixed ability year 7 class investigating what algebra is taught and what algebra is learnt over the period of their first term at secondary school. The motivation for the study is to explore the challenge inherent in the quote: 'Can we develop a school algebra culture in which pupils find a need for algebraic symbolism to express and explore their mathematical ideas?' (Sutherland 1991).
Four teachers work with their Y7 classes to develop an algebraic activity and their pupils are interviewed before and after taking part in these activities.
Dave begins this article with a refutation of Vygotsky’s claim that “… algebra is harder than arithmetic” by asserting that “Arithmetic is impossible without algebra”. He then goes on to analyse what it means to work algebraically, how algebraic structures can support arithmetic and how you can help students develop their own structures.
[N.B. you need to be a member of ATM to access this article]
In this detailed and systematic review of how students learn algebra, Anne Watson describes understandings and misconceptions in algebra and offers a series of recommendations; about mathematical learning, for teaching and for research.
- Little, C. (2008) The role of context in linear equations questions: utility or futility?, Southampton, The British Society for Research into Learning Mathematics (BSRLM)
This paper considers the role of context in four linear equation questions, concluding that the purpose of the context is not utility, but concept formation and abstraction. Paper presented at the British Society for Research into Learning Mathematics day conferences held at Southampton University, 26 and 27 June 2008
- Ronda, E. (2009) Growth Points in Students’ Developing Understanding of Functions in Equation Form, University of the Philippines, Mathematics Education Research Journal, Vol. 21, No. 1, 31-53
This article is about functions in Key Stages 3 and 4 and about how students shift from seeing functions as a collection of data points to seeing them as objects that can be transformed.
Originally written for a research audience, this paper is presented within the NCETM ‘Accessing Research’ micro-site and is accompanied by a study module (module 7) in the form of a set of PowerPoint slides to support and guide you through the paper.
- Gould, L., Ikhinmwin, S., Walley, A., Clark-Wilson, A., & Hoyles, C. (2013). Embedding dynamic technologies in the key stage 3 curriculum – The Cornerstone Maths approach. Mathematics Teaching, 235, 44-47.
In this article, the authors describe some of the outcomes of the ‘Cornerstone Maths’ project. Cornerstone Maths is a USA/UK collaboration that offers teachers of Key Stage 3 mathematics some technology-enhanced units of work. The first of the Cornerstone units on linear functions is ‘Sand Circle Mobile Games’ in which students are put into the role of a mobile game software designer for which they need to understand the different ways that linear motion can be described. The article gives a snapshot of the ‘Cornerstone’ approach and 3 project teachers give an account of their experiences.