Review: noun; a critical appraisal

An open book resting on a table with a magnifying glass on top of it. In the background is a blackboard with mathematics equations on.

Depending on how you see it, there’s a big push, or gentle encouragement, to persuade teachers to access and use research findings to support changes in their classroom practice. Here in the UK, the Education Endowment Foundation offers the Teaching and Learning toolkit¹ which is an “accessible summary of the international evidence on teaching 5–16 year-olds.” And there are dozens of such organisations around the world – the NCTM² in the US, Matematikksenteret³ in Norway, and Fundación “la Caixa”⁴ in Spain, for example. Closer to the classroom in the UK is the Research Schools Network,⁵ set up with the specific aim of leading the way in the use of evidence-based practice, some of this arising from teachers’ own action research.

But not all teachers have the time, or inclination, either to read the original research or to engage in action research, so here at Cambridge Maths we publish Espressos⁶ – “small but intense draught[s] of filtered research on mathematics education, expressly designed with teachers in mind” – to give busy teachers a quick way into knowing what research has to say about classroom practice. (The structure of Espressos was unashamedly borrowed from Mike Askew’s 1995 publication Recent research in mathematics education 5-16,⁷ which was innovative at the time in that it described the research and then indicated what the implications of the findings were for the classroom.)

Ofsted, the influential body which inspects English schools, recently published Research Review Series: Mathematics.⁸ This is the next in a series of subject reviews, informed by principles⁹ which are also intended to support teachers in linking research to practice, and ensure “an evidence-based ‘conception of subject quality.’”

The publication addresses:

scope, content and sequencing of the curriculum
specification and ordering of component parts that make up composite skills
the value of teachers’ subject knowledge
promotion of a range of quality interactions with pupils
quality and pacing of instruction
how to avoid overloading working memory
the value of deliberate practice, interleaving and regular low-stakes testing

These would seem to be extremely important aspects to which teachers of mathematics should attend. Ofsted reports are eagerly awaited by leaders of education in England because they point the way to successful school inspections – and school inspections are important because they can determine the success or otherwise (including forced closure) of a school. So the recommendations in an Ofsted paper are taken as an indication of the what, when and how teachers should teach.

Which makes it all the more important that the conclusions drawn, and the changes to classroom practice suggested, are well evidenced by the research. The maths education research community has been discussing the veracity of the report and several detailed critiques have been written elsewhere.¹⁰ Common criticisms are:

Linking research and conclusions
The Association of Mathematics Education Teachers (AMET)¹¹ has conducted a detailed analysis on the match/mismatch between quoted research findings and conclusions for classroom practice.

Problem solving, and the importance of talk
Anne Watson¹² has written about the misunderstanding of the role of problems and problem solving. There is nothing in the Ofsted paper about the research into the effects of a restricted diet of word problems, of the use of rich problems which model intriguing questions, or of the central use of non-routine problems in the classrooms of high-performing jurisdictions.

The Review states, “Studies have also shown that the ideal environment for periods of independent work is one that is not just quiet but is in fact near silent.” There is much research on the importance of dialogue in the mathematics classroom (between children and between teacher and child) – and yet the only reference to language in the Review is that children should be able to read fluently…

Connections and mathematical thinking
Maths Mastery¹³ has summarised the Review’s restricted view of research highlighting the importance of linking core facts and methods, and its lack of research findings into the importance of connecting different aspects of mathematics, or connecting and moving between different representations, including some interesting attitudes towards the use of manipulatives.

Mathematical thinking usually includes a variety of ways in which a student may be expected to act upon a mathematical idea, such as classifying, defining, representing, analysing, justifying, etc. However, research into the importance of these ways of thinking about maths is missing and the reader is left thinking that pattern seeking is the only type of “thinking mathematically.”

Here at Cambridge Maths we have some sympathy for the points made above. If you have the time, do read the report and the commentaries in full and come to your own conclusions. We’d love to hear what you think.

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