Research School Network: Using metacognitive strategies to improve pupils’ mathematical problem-solving Alastair Gittner of the Hallam Teaching School Alliance, explores how metacognitive thinking can support pupils’ problem-solving

“A packet contains 1.5 kilograms of guinea pig food. Remi feeds her guinea pig 30 grams of food each day. How many days does the packet of food last?”

Even before the pandemic, this type of question was often challenging for pupils. Teachers can sometimes avoid setting questions like these, both because of this difficulty they present for pupils, and because teachers may not always have a well-defined strategy for teaching them.

It is unsurprising given teachers were reporting less resilience among pupils when attempting questions of this nature, perhaps due to fewer opportunities for peer discussion, lack of access to manipulatives or due to children being exposed to fewer strategies.

The EEF’s Maths content specialist, Kirstin Mulholland, also commented that, ​‘I feel as though every time I have a conversation about maths with a teacher or school leader, problem-solving is identified as something we want to work on’[i]

Clearly, this issue may be widespread.

As a result, when we were offered the chance to take part in the EEF’s Early Project pipeline, it seemed an obvious choice. Working together with 10 schools, we set out to use metacognitive strategies to improve pupils’ resilience and motivation during mathematical problem-solving.

The IES ​‘What Works Clearing House’ defines problem-solving as ​‘the movement from a given state to a goal state with no obvious way or method for getting from one to the other’ (2012, p. 7) [ii]. This highlights the intrinsic difficulty of problem-solving: pupils need to read and decode instructions, identify the nature of the task, choose the correct mathematical principle, and then work out their own route from question to answer! There are many possible routes, and this means that problem-solving can seem challenging, thereby affecting pupils’ levels of resilience. As a consequence, pupils may only perform simple processes, or even avoid attempting the problem altogether.

To try to overcome this, we used a series of prompts developed from the Australian educationalist, Anne Newman [iii]. Newman proposes that there are five stages where mistakes could be made during problem-solving, and that by prompting students to self-monitor their progress, these mistakes can be prevented or pupils’ can develop skills of self-regulation to encourage independent checking and correction. The five prompts are:

1. Read – the question (out loud.)
2. Comprehension – What is the question asking you to do?
3. Transformation – manipulating the words of a question into an appropriate mathematical equation.
4. Process – What must they actually do to get the answer?
5. Encoding – Write down the answer to the question.

We used these prompts to develop metacognitive talk in the classroom. The five prompts became titles for laminated cards, coloured so that the teacher could refer to them easily. On each card, we added other questions to extend pupils’ thinking, such as ​‘Which information in the problem is relevant?’, ​‘Can you draw an image to help you understand what the problem is asking?’, and ​‘Can you check your answer using a different strategy?’

These cards prompted teachers to model their thinking. As this became embedded, teachers could fade their input so that pupils took increasing ownership over monitoring and discussing their approaches to problem-solving, using the prompts to help them.

In the ten schools who are piloting this approach as part of the EEF’s Early Pipeline work, it is great to see the enthusiasm pupils have for this way of working, and hear the detailed conversations they engage in as they grapple with problems.

It is early days in this pilot and we must await a more thorough analysis, but so far teachers and pupils of all abilities have reported that these metacognitive prompts seem to be making a real difference.

If you would like to find out more about this project, please contact Alastair: agittner@​hallamtsa.​org.​uk

References:

1. Mulholland, K. (2021). The problem with problem-solving. Available at: https://educationendowmentfoundation.org.uk/news/eef-blog-the-problem-with-problem-solving-in-maths[Accessed 27.4.22]

2. Woodward, J., Beckmann, S., Driscoll, M., Franke, M., Herzig, P., Jitendra, A., Koedinger, K.R. and Ogbuehi, P. (2012). Improving Mathematical Problem Solving in Grades 4 through 8. IES Practice Guide. NCEE 2012 – 4055. What Works Clearinghouse. Available at: https://ies.ed.gov/ncee/wwc/Docs/PracticeGuide/MPS_PG_043012.pdf(Accessed 27.4.22)

3. Newman, M.A. (1977). An analysis of sixth-grade pupils’ errors on written mathematical tasks. In M. A. Clements & J. Foyster (Eds.), Research in mathematics education in Australia, Vol. 2, pp. 269 – 287. Melbourne: Swinburne College Press.