Increasing Competence and Confidence in Algebra and Multiplicative Structures

Project summary


This collaboration between the Universities of Aberdeen, Glasgow, King's College London and Education Scotland explores the nature of issues surrounding students' understanding of algebra and multiplicative reasoning. In Scotland, there is a real scarcity of discipline specific research within mathematics education and an increasing need for more robust and rigorous evidence to evaluate impact of educational interventions and to inform policy. A pilot study using surveys and interviews will help establish the extent of similarities and differences between England and Scotland in terms of algebra and multiplicative structures. The pilot will enable a comparison of current achievement between the two countries and help outline policy to increase the competence and confidence in early algebraic and multiplicative structures.


International surveys such as the Trends in Mathematics and Science Study (TIMSS) and more recently the Programme for International Student Assessment (PISA) 2012 alongside Scottish specific surveys such as the Scottish Survey of Literacy and Numeracy (SSLN) 2011, and previously the Scottish Survey  of Achievement (SSA), collectively provide a very broad picture of achievement in mathematics within primary and secondary education over time. The SSLN provides a broad brush approach specific to Scotland, where PISA provides an international overview. Overall, Scotland's average performance in  the international surveys tends to be slightly higher in comparison to England (for example in the recent PISA 2012 the mean score for Scotland was 498 compared with 495 in England). However, where Scotland is maintaining its mean score over time other countries are moving forward. More worryingly, the SSLN continues to indicate a significant decrease in achievement between P7 and S2 where the proportion of students performing well or very well decreases from over 70% in P4 and P7 to 42% in S2. Alongside this, the proportion of students underperforming rises sharply from less than 2% in P4 and P7 to 32% in S2. The SSLN numeracy report (Scottish Government, 2012) suggests that levels of deprivation have a more significant effect than gender and that this effect is most prevalent in S2.

This period between P7 and S2 (11-14 year olds) is a crucial time which can create significant barriers to continuing to study mathematics for many students. All of these surveys indicate similar key areas of mathematics, in both Scotland and England, which students find more challenging: including measurement; fractions, decimal fractions and percentages; and chance and uncertainty. Most of the areas identified by the SSLN have been resilient over time; these are persistent areas of concern. Also, they are all predominantly built on a need to move from additive reasoning to multiplicative reasoning (Wright et al, 2012). By exploring this aspect of mathematical understanding a more informed position could be developed to address these concerns. Multiplicative reasoning and early algebraic structures are pivotal hurdles to students participating in mathematics post-16. Therefore a deepening understanding of the nature of these issues requires a strong evidence base. The adaptation of the ICCAMS survey and interviews for the Scottish context will allow us to explore the nature of these understandings and misunderstandings: to gather evidence of the situation within Scotland both to support our work and to inform national debate about how concerns about algebraic and multiplicative reasoning might be tackled.

View the ICCAMS project website.