: Maths: Problem Solving or Problem Solved? Where are the moments within the maths process that allow children to realise and see their successes, or struggles?

Let’s take some time to look back to when RUCSAC facilitated problem solving in classrooms across the UK. On the face of it, it provided a scaffold, a safety net and, for teachers, a tool to show what they did to support children in maths with reasoning and problem solving. Expert teachers see and represent problems on a deeper level as opposed to focusing on superficial aspects but it is superficial aspects that ​“tools” such as RUCSAC focus on. Read, Underline, Choose/​Calculate, Solve, Answer, Check. However, this simply assumes that students can do all of these things independently and that it will actually help. But where is the thinking? The questions to deepen understanding? The thinking aloud? Where are the moments within this process that allow children to realise and see their successes, or struggles for that matter? The answer: they aren’t there.

Of course, education has come a long way in the intervening years. We have a national curriculum that has reasoning and problem solving as two of its three key strands and there are a plethora of companies offering resources and a whole host of other things to help teachers deliver high-quality maths lessons. Sure, teachers have access to more maths problems than ever before, but what use are these materials if we don’t utilise them well?

We found ourselves here a few years ago and so, as part of the NCETM Mastery Programme, we put together a lesson study involving several local headteachers and maths leads, setting out with the aim of answering the question ​‘How well do children actually approach unseen problems? Figure 1 is from that lesson study workshop.

We had further nagging questions too: Would a ​‘guide’ or ​‘set of steps’ assist this process? Would this make partner talk more effective? The ​‘guide’ we initially put together (see figure 2) was focused on children planning to approach a problem and questioning themselves as they did so – at least, that’s what we hoped.

Further developments followed in our approach to teaching maths specifically, utilising elements of both the Shanghai and Singapore approaches to mastery along with adjustments to our ​‘guide’ and other areas of our pedagogy. All aiming to improve children’s ability to approach unseen problems and reason mathematically. Figure 3 shows the interactions of our approach as we developed and refined over a period of time.

Along the journey, we learned a few things: there is no ​“one way” to develop problem solving and reasoning; a mixture of approaches is absolutely key; metacognition should be central; children need questions to help guide their thinking; children need experts (you) to show them how, using think-alouds and models – just as you would when teaching a new process; and they also need time and opportunities to face ​‘desirable difficulty’.

So, we continued to develop to best serve our pupils. We have a new ​‘guide’ (figure 4) now that the children were involved in, helping us connect our learning behaviours, reading skills, maths skills and metacognition. It focuses on the stages of metacognition and provides children with key thinking questions at each step, linking these to familiar comprehension skills. But this is one tool in a box of many. We model and use think-alouds to show pupils how to apply the guide; we offer independent and paired opportunities to monitor and evaluate; we provide completed problems that are both correct and incorrect to encourage reasoning; and we use hedging and goal-free problems to promote open thinking and discussion.

Like I said, no ​“one way” but having something that remains central and allows the children to frame their thinking and explore the depths of maths has been vital in our journey to where we are now.

References:

Education Endowment Foundation (EEF). (2021). Metacognition and Self-Regulated Learning Guidance Report.
Education Endowment Foundation (EEF). (2022). Improving Mathematics in Key Stages 2 and 3 Guidance Report.