By Laura Tyler
41 pages of a research review to devour? All about maths?! Yes please! An unusual reaction, I’m sure some might say, but developing evidence based approaches to learning is something we get very excited about at Mathematics Mastery. So Ofsted’s research review on mathematics education was eagerly anticipated. We’re really happy that the review shares our core purpose of ‘highlighting approaches that could raise the attainment of all pupils’ (spoiler alert), however it falls short, appearing to miss some important elements and misinterpreting the literature in some key places. What we’ve found particularly surprising is the apparent ‘ideological messaging gap’ between the stance taken in the review and what’s found in our very own National Curriculum.
I’ll share my reaction to the research review this week – the highs and the lows. Detailing instances of where Ofsted have shone a light on the priorities and implementation barriers that we indeed face in schools nationwide, as well as instances where we recommend treading with caution in its implementation. I aim to fill in some of the missing pieces of the maths pedagogy puzzle, with gentle reminders and nods to some of our ‘maths giants’ who have been invaluable in influencing our approach to teaching maths in the UK for decades but sadly didn’t quite make the cut in Ofsted’s review….
Cutting to the chase, the review dives headfirst into highlighting the attainment gaps we face in the UK. A challenge our schools face, only intensified by the disruption of COVID. It pulls up a core theme to ‘prevent struggling pupils from falling further behind their peers’. Yes – ambition for all is certainly the intention here. An aside: This is something we’ve been thinking deeply about at Mathematics Mastery. How can we help close the gap? We’ve created a brand new bank of video-supported interventions aligned with the EEF best practice principles and DfE Ready to Progress Criteria which is available for all primary schools now.
‘Careful sequencing of content, instruction and rehearsal can also show pupils new and consistent patterns of useful information.’
It’s great to see cumulative, coherent curriculums being celebrated. Those which are well sequenced to encourage connections between ‘linked facts and methods’. ‘Systematic and clear teaching’ is also held high but unlikely to be achieved by curriculum alone. Which is why it was encouraging to read….
‘School-wide approaches to providing time and resources for teachers to develop subject knowledge and to learn valuable ways of teaching from each other.’
We wholeheartedly agree. Subject-pedagogical knowledge is power! For new and experienced teachers, it’s great to see ‘proactive professional development’ approaches illustrated such as collaborative planning, lesson studies and renewing & improving subject knowledge. The complexities of maths as a discipline demand this investment to achieve the ultimate aim of ambition for all.
The review refers to plenty of other important elements in maths education, from intelligent variation, pattern seeking, maths anxiety, early exposure to algebraic thinking, automaticity in recalling key facts and laying firm foundational knowledge with regular opportunities to rehearse and apply. So where does it fall short?
Putting research based practice into classrooms is what we are all about at Mathematics Mastery.
Over the next few days, I’ll be highlighting some of the evidence that we’ve interpreted to be under-represented in the Ofsted review. We’ll look at representation, talk and mathematical thinking. Firstly though, let’s take a look at problem solving.
Problem solving is at the heart of mathematics education for every child, whatever their home background or prior attainment. Every child can learn to solve complex problems in unfamiliar contexts.
It’s great to see repeated references to problem solving in the review. Only three sentences in, the reviews’ introduction revels a powerful message about the importance of mathematics for us to all ponder upon: It nurtures the development of a logical and methodical mindset, as well helping to inculcate focus and the ability to solve all manner of problems.
It’s helpful to note that problem solving at the heart of Singapore’s curriculum (Ministry of Education, Singapore, 2012), a country the review refers to as one where ‘all groups of pupils do well’. Problem solving also lies at the heart of the Mathematics Mastery approach (Drury, 2014). In fact, it is thoroughly embedded as a central part of our National Curriculum which aims for all pupils to ‘solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication’. Note the focus here on ‘non-routine’ and ‘sophistication’ – we’ll return to this.
I’ll be referring to the EEF maths review a few times in this blog series. However, the EEF maths review was very clear about how the research was sought, found, selected and evaluated.
What did the EEF find?
“Problem solving is crucial to the use and application of mathematics in the world beyond school (e.g., Hodgen & Marks, 2013; see also ACME, 2011, 2016). As a result, problem-solving skills are an important aim of school mathematics education as set out in the National Curriculum for England…mathematical problem solving takes place when a learner tackles a task for which they do not have a suitable readily-available solution method (NCTM, 2000). In practice, this means that a classroom task could be regarded as a “problem” if the teacher has not, immediately prior to the task, taught an explicit method for solving it. Typically, guidance on problem solving recommends the use of a wide range of problem types (e.g., NCTM, 2000; Woodward et al., 2012)…. There is some evidence to suggest that primary learners may benefit more from representing problems than from necessarily solving them or being taught problem-solving heuristics.”
(Hodgen et al. 2018, page 60-61).
The EEF calls for us to ‘select genuine problem-solving tasks that pupils do not have well-rehearsed, ready-made methods to solve’. These rich interpretations of problem solving seem at odds with the review which warns us of using open-ended problems: “Learning through participating in similarly open-ended problem-solving activities might be enjoyable for both teachers and pupils, but it does not necessarily lead to improved results”.
Actually, we feel the Ofsted review goes on to conflate problem solving with word problems. This is the ‘type’ of problem that repeatedly crops up in the review and is predominantly referred to and advocated: “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”.
It’s great to see converting word problems into simple equations is being flagged as significant challenge for pupils in this Ofsted review (see Duval’s seminal work on this, which involves harnessing the power of multiple representations, another aspect of maths which is discouraged by the report – more on this in a later blog!) However, this over-simplification of problem solving – focusing on word problems - feels risky. Where’s the references to rich problems involving intriguing starting points, low threshold-high ceiling tasks, those which allow learners to pose their own problems and allow for different methods and responses? Opportunities for learners to identify elegant or ‘efficient’ (more on this word ‘efficient’ in a later blog too!) solutions? I could go on…. but I’ll round it up with an observation. It seems a shame that Malcolm Swan’s (one of the most respected figures in maths education in the UK and internationally) research-based principles on task design and ‘non-routine’ problems (a nod back to the NC phrasing here) aren’t cited anywhere in Ofsted’s review.
And if we are being warned about the use of open-ended problems, where is the balanced warning for pupils being fed a diet of word problems alone? Experiencing problem solving through imitating and performing procedures - ‘practising solving similar types of problems’, based on a previously learnt strategy determines their perception of what maths is. Maths is far more creative than this rather rigid approach to problem solving: “Pupils need to be fluent with the relevant facts and methods before being expected to learn how to apply them to problem-solving conditions”. I think Anne Watson summarises it beautifully “Mathematics can be terrific fun; knowing that you can enjoy it is psychologically and intellectually empowering.”
Problem solving is central to learning maths. Regardless of their starting point, every child deserves to be equipped and encouraged to confidently solve unfamiliar problems in novel contexts.
Next up, we’ll take a look at the review’s approach to representation and conceptual understanding. How does the review shine light on important areas such as making connections and relational understanding? But also, where do we feel the review has overlooked some key areas of evidence? We’ll delve into this with a focus around visual imagery and the power of manipulatives.
Drury, H. (2014). Mastering Mathematics. Oxford University Press.
Duval, R. 2006. A Cognitive Analysis of the Problems of Comprehension in a Learning of Mathematics. Educational Studies in Mathematics. 61: 103-131.
EEF Guidance Report: Improving Mathematics in Key Stages Two and Three. (November 2017)
Hodgen, J., Foster, C., Marks, R., & Brown, M. (2018). Evidence for Review of Mathematics Teaching: Improving Mathematics in Key Stages Two and Three: Evidence Review. London: Education Endowment Foundation, accessed at: https://educationendowmentfoundation.org.uk/evidence-summaries/evidencereviews/improving-mathematics-in-key-stages-two-and-three/
Ministry of Education, Singapore (2012) Mathematics Syllabus Secondary One to Four
Swan, M. (2006). Collaborative Learning in Mathematics: A Challenge to our Beliefs and Practices. London: NRDC and NIACE
Watson, A. (2006) Raising Achievement in Secondary Mathematics. Maidenhead: Open University Press
As teachers ourselves, we understand how extraordinarily difficult this period has been for all schools. We have made some important changes to our mastery programmes this year to help support you in the months ahead.