Outline
Most young children see the equals sign as meaning "write the answer
here" rather than as a symbol of mathematical equivalence. This leads to
inflexible thinking about arithmetic notation and causes difficulties
when pupils meet symbolic algebra at the start of secondary school.
Recent studies have shown that teaching the equals sign means "is the
same as" helps reduce these difficulties. However, these studies neglect
that symbolic substitution is central to understanding mathematical
equivalence, and that the equals sign also means "can be exchanged for".
Our research will be the first to investigate the impact that teaching
an exchanging meaning in arithmetic contexts has on pupils' conceptions
of the equals sign, arithmetic notation, and the learning of symbolic
algebra. We will deliver a teaching intervention to Year 7 pupils at the
start of secondary school and measure their performance on a range of
arithmetic and algebraic tasks. We will focus in particular on the
impact of the intervention on the individual differences between pupils
in the target classes, and compare this with the performance of pupils
in control classes.
This site will be updated in due course with more information about our activities. Funding
Our work is supported by the Esmee Fairbairn Foundation via the New Approaches to Learning strand.
Staff
- Camilla Gilmore, Learning Sciences Research Institute, University of Nottingham.
- Matthew Inglis, Mathematics Education Centre, Loughborough University.
- Ian Jones, Learning Sciences Research Institute, University of Nottingham.
Related Papers
Jones, I. (2008). A diagrammatic view of the equals sign: Arithmetical equivalence as a means not an end. Research in Mathematics Education, 10, 119-133. [pdf]. Jones, I. (2009). Arithmetic equality statements: Numerical balance and Notational substitution. In M. Tzekaki, M. Kaldrimidou & H. Sakonidis (Eds.), Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 257-264). Thessaloniki, Greece.
[pdf].
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