Pupils are more likely to develop a positive attitude towards mathematics if they are successful in it, [footnote 42] especially if they are aware of their success. [footnote 43] However, teachers should be wary of the temptation to invert this causal pathway by, for example, substituting fun games into lessons as a way of fostering enjoyment and motivation. This is because using games as a learning activity can lead to less learning rather than more. [footnote 44] The unexpected finding from cognitive science is that practice does not make perfect… Practice until you are perfect and you will be perfect only briefly… What's necessary is sustained practice.”

Teachers and leaders should try to strike a balance between curricular approaches that enable pupils to keep up with their peers and reactive approaches that identify, help and support pupils after they have fallen behind. These reactive approaches are more likely to rely on assessment, diagnoses, personalisation and interventions. This contrasts with the view of problem-solving as a generic skill that pupils can transfer to multiple topics and sub-domains. [footnote 99] Applying generic strategies to find examples, look for relationships or weigh up features could yield accurate and inaccurate information. However, pupils who are struggling might not know which information to choose to use. Dowker, A. (forthcoming). Review of Mathematics Education Programmes. London: The Education Endowment Foundation.

20. Move!

This review seeks to make a clear distinction between mathematics curriculum and pedagogy. We have also classified mathematics curriculum content. We have used these classifications in our review of the available literature. We have drawn forms or categories of content from disciplines in which mathematics is applied. [footnote 21] These categories are informed by the way our minds work [footnote 22] and are intended to be easy to understand. These practices significantly improve proficiency in word problem solving and operations. 4. Use staff strategically

In the primary phases, pupils’ experience of problem-solving often involves solving word problems. The first barrier to overcome is language. Pupils therefore need to be proficient readers at the required level. [footnote 95]Terms also vary over time. For example, ‘tables’ has changed in meaning: it used to refer to number facts in all the operations that infant and junior pupils were expected to learn [footnote 23] but now it is shorthand for multiplication facts in the present day. [footnote 24] Examples of terms (and associated concepts) that have been used less and less over time include ‘mechanical drill’, ‘syllabus’ and ‘recall’. How the review classifies mathematics curriculum content

Teachers should therefore ensure that more pupils experience success in solving word problems, by sequencing the teaching of strategies to ‘convert’ the deep structure of word problems into simple equations. [footnote 96] Strategies for solving classes of problem Japanese lesson study is an example of a systematic approach to sharing subject-pedagogical knowledge that builds and shares subject-pedagogical knowledge at organisational, local and national scales. [footnote 198] The fact that lesson study is a system should also alert teachers and leaders to the dangers of adopting ‘surface features’ and not systems. This may also explain why attempts to install (the surface features of) ‘lesson study’ as a curricular or pedagogical intervention leads to somewhat less convincing results. [footnote 199] This really does not matter. The practice quizzes are designed to enable learning to take place. That is why pupils have two opportunities to respond. So long as the person supervising the session has a good knowledge of the content being covered – and knowledge of effective teaching strategies to help pupils overcome barriers – there is strong potential for very good pupil progress within sessions. When pupils obtain levels of proficiency, they look forward to and enjoy tests. [footnote 186] Competitive maths games are, for example, more effective for learning and retention than non-competitive games. [footnote 187] The goals of trying to achieve a personal best and doing well compared to the average mediate later attainment. [footnote 188] Therefore, in addition to ensuring pupils are well prepared for tests, leaders should ensure that benchmarks for success are understandable. Many pupils with autism have ‘normal to above average algorithmic thinking ability’ but can struggle with reasoning and problem-solving because of:Early interventions help pupils to catch-up and perform better across the curriculum. They also help with confidence and reduce maths anxiety. Early interventions are most valuable if you can find ways to build on the early gains interventions produce. 2. Use tried-and-tested strategies sometimes it refers to ease of recall and computation (which the review refers to as ‘automaticity’) In addition to highlighting approaches that could raise the attainment of all pupils, a core theme of the maths review is how to prevent struggling pupils from falling further behind their peers.