Research School Network: Improving mathematics learning: Becoming a metacognitive role model Improving mathematics learning: Becoming a metacognitive role model

Metacognition and self-regulation is one of the most impactful approaches featured in the EEF’s Teaching and Learning Toolkit. A review of 246 studies demonstrated an average impact of 7 additional months of progress, with evidence suggesting that impacts are particularly strong in maths and science.

Metacognition and self-regulation develop from a young age, and are evident in pre-school aged children (Whitebread et al, 2009, Whitebread and Coltman, 2010). However, some sources suggest that children facing disadvantage are less likely to use metacognitive and self-regulatory strategies without explicit teaching to promote these. Metacognition and self-regulation are often also ​‘hidden in plain sight’ (Quigley & Stringer, 2018, para. 3) due to educators’ uncertainty around the different ways in which metacognition can be manifest in different subjects and age phases.

It is therefore important for educators to develop a shared language around what metacognition is and how it relates to other learning behaviours. Through understanding the processes underlying this concept, educators can support children explicitly through conversation, scaffolding and reflection, building knowledge and motivation for maths learning. Some studies also indicate that, as educators become metacognitive role models, they provide authentic and transparent insight into their own learning processes, supporting pupils’ understanding of the expectations, successes – and challenges – that can accompany the development of knowledge and skills (Wall & Hall, 2016).

The EEF’s ​‘Metacognitive Process’ resource provides a useful summary of the components that comprise this: metacognitive knowledge, and metacognitive regulation. These themselves can be broken down further, as represented in the diagram below

In addition to the EEF’s Metacognition and Self-regulation guidance report, the Department of Education for New South Wales (2020) has also generated a useful evidence review, providing teachers with actionable guidance about potential strategies to promote the use of metacognition in classroom contexts.

In maths, this evidence demonstrates that stronger mathematicians know and use more metacognitive strategies than their less-successful peers. This review particularly highlights the IMPROVE model, explored in the research of Mevarech & Kramarski. Designed for use across primary and secondary age-phases, evidence suggests that this model can have long-lasting impacts upon pupil attainment.

The IMPROVE model draws upon four types of metacognitive questions:

• Comprehension questions: what is the problem all about? 
• Connection questions: how is the problem at hand similar to or different from problems I have already solved? Please explain your reasoning. 
• Strategic questions: what kinds of strategies are appropriate for solving the problem, and why? Please explain your reasoning. 
• Reflection questions: does the solution make sense? Can the problem be solved in a different way? Am I stuck? Why?’ (NSW, 2020)

To have impact, successfully integrating questions like these into maths lessons requires secure subject and curriculum knowledge, careful modelling and guidance, as well as opportunities to practice and receive feedback over time. Through modelling our own thinking – asking and responding to questions like those featured within the IMPROVE model, as educators, we can become metacognitive role models, supporting pupils to understand the hidden and often inaccessible processes of thinking.

For educators seeking to learn more about strategies for modelling metacognition in maths, we recommend the following resources:

This short blog explains how to use ​‘Think Alouds’ to scaffold pupils’ problem solving in maths: EEF blog: Thinking Aloud to support mathematical problem-solving | EEF

This blog explores the importance of ​‘debrief’ questions in encouraging the development of habits of metacognitive thinking: EEF blog: Using the debrief to support structured reflection on… | EEF

For further information on the metacognitive process, EEF has produced a helpful animation, which can be accessed here: Metacognition: a Brief Explainer.

References

Quigley, A., & Stringer, E. (2018). Making sense of metacognition. Impact (3). Available at: https://my.chartered.college/impact_article/making-sense-of-metacognition/

State of NSW (Department of Education) (2020). Metacognition: A key to unlocking learning. Available at: https://education.nsw.gov.au/content/dam/main-education/teaching-and-learning/education-for-a-changing-world/media/documents/Metacognition_Full_Report_FINAL.pdf

Wall, K., & Hall, E. (2016). Teachers as metacognitive role models. European Journal of Teacher Education, 39(4), 403 – 418.

Whitebread, D., Coltman, P., Pasternak, D. P., Sangster, C., Grau, V., Bingham, S., Almeqdad, Q. and Demetriou, D. (2009). The development of two observational tools for assessing metacognition and self-regulated learning in young children. Metacognition and Learning, 4(1), 63 – 85.

Whitebread, D., and Coltman, P. (2010). Aspects of pedagogy supporting metacognition and self-regulation in mathematical learning of young children: evidence from an observational study. ZDM: The International Journal on Mathematics Education, 42 (2), 163 – 178