Research School Network: There’s no Magic in the Plastic! Discover how the Forest Family of schools in Staffordshire skilfully use manipulatives to secure conceptual learning in Maths.

Donna Preston is a deputy headteacher of a primary school and Primary Teaching for Mastery Co-Lead at the North Mids Maths Hub. Here she writes about how she has put evidence to work with the help of the EEF’s Metacognition and Self-Regulated Learning andImproving Mathematics in Key Stages 2 and 3 Guidance Reports.

Why do we make changes to practice in our schools? If the data looks great, do we need to change? At our Forest Family schools in the John Taylor MAT, our data was strong, but collectively, we wanted to ensure our pupils were getting a rich diet of teaching that secured both procedural and conceptual understanding of concepts, and for some there had been more emphasis on the former than the latter. 

It is important to note that the journey I will describe did not happen overnight and we are still travelling! In order for implementation to be owned, developed and sustained by colleagues it takes time and this was reinforced to us as senior leaders through the EEF Implementation Guidance Report. As recommended in the report, we used our professional judgement through monitoring throughout our two schools to identify small, measurable targets for change. 

Alongside schools in our Multi-Academy Trust we were using research to develop metacognition and self-regulated learning within the classroom. Our initial starting point was the EEF Guidance Report on Metacognition and Self-Regulated Learning. Senior leaders launched the focus on these areas during an inset day in which action planning and a timescale were driven by staff to develop our colleagues’ understanding of these topics. As a result, we developed our desired Forest Family learner attributes and learning processes and these now feed into all our teaching and learning. 

As maths lead across the Forest Family I considered how the guidance report findings could be reflected in the development of my subject and the recommendation, ​‘model your own thinking to help pupils develop their metacognitive and cognitive skills’ was initially identified, with the aim of encouraging the children to be explicit about their thinking processes and in turn build their knowledge and understanding of strategies. The words of Bruner sprang to mind from my study days, ​‘We teach a subject not to produce living libraries on the subject but rather to get a student to think mathematically for himself’ and ​‘knowing is a process not a product.’ (1)

Initially teachers modelled their own thinking when tackling a mathematical problem with their class. Many teachers may feel that they frequently model maths to their class, but modelling how to solve a problem can be different to modelling your thinking through that problem. My colleagues at the Forest Family are reflective practitioners, keen to engage with new learning and continually improve in order to impact positively on pupil outcomes. As such, we developed this practice over a period of time. Now that we are further along our journey the children are often able to articulate their own thinking and indeed challenge the thinking of others in a non-threatening, collaborative manner. 

In addition, we have focused upon the ​‘answer’ only being the beginning of the learning process and emphasised the importance of understanding the structure of what is happening in the mathematics. Through my role with the North Mids Maths Hub, I was aware of the potential impact the use of manipulatives and representations could have on learning, which is echoed in the evidence found by the EEF’s guidance report on Improving Mathematics in KS2 and 3. The appropriate uses of these were crucial to further development in our maths teaching and learning. 

In school, our initial discussions concentrated on evaluating current practice, identifying resources we had and how they were used. This led to senior leaders delivering training for colleagues around less familiar manipulatives and representations. Over time, colleagues were supported to incorporate the appropriate and purposeful use of these in order for children to gain meaning from the exposed structure of the mathematics. This included manipulatives such as Dienes, place value counters, Numicon, ten frames, Cuisenaire rods and representations such as bar models, part-whole models, number lines and Gattegno boards. We have discovered that the manipulatives and representations, as well as revealing structure, allow the children to make links and connections across various concepts and therefore ​‘integrate their knowledge’ (2).

Although a number of studies have shown that children’s achievements in mathematics are related to teachers’ effective use of manipulatives (3), it is important to note that there is no magic in the plastic (or wood!). Pupils need to construct their own meaning about the mathematics from what they do with the tool as supported by the EEF’s Guidance Report and other studies (4). Different manipulatives have different strengths for different problems and procedures (5) and as a Forest Family we have now created a calculation policy with clear rationale for using particular manipulatives or representations for specific mathematical concepts.

In the past we may have only given the manipulatives to the children struggling with the mathematical concepts, but they are appropriate for all in the classroom, helping to clarify and secure children’s understanding of concepts. Conversely, we do not want our pupils to become over-reliant on their use, so once links have been made to pictorial and abstract representations, and learning is secure, these are removed to ensure they are not used as a constant crutch to learning, as recommended in the guidance report. 

Training Opportunities

Donna is leading training for the Staffordshire Research School where these strategies and conceptual thinking will be explored and modelled in more detail, alongside the Improving Mathematics in Key Stages 2 and 3 Guidance Report. Find out more and reserve your place on our free twilight and 1‑day Improving Mathematics in Key Stage 2& 3 course here. Don’t miss out, places are already limited!

References
(1) – BRUNER (1964: 335, cited in Bloomfield, 1998: 11). BLOOMFIELD, A.,1998. An Introduction to the Theories of Learning in Mathematics. Teaching Learning and Mathematics: Challenging Beliefs, pp.1 – 22. Derby: Association of Teachers of Mathematics.
(2) – CLEMENTS, D. H., 1999. ​‘Concrete’ Manipulatives, Concrete Ideas. Contemporary Issues in Early Childhood. 1 (1), pp.45 – 60.
(3) – MOYER, P.S., 2001. Are we having fun yet? How teachers use manipulatives to teach mathematics. Educational Studies in Maths. 47 (2), pp.175 – 197.
(4) – HIEBERT, J., Carpenter, T.P., Fennema, E., Fuson, K., Wearne, D., Murray, H., Olivier, A., & Human, P. (1997). Making sense: Teaching and learning mathematics with understanding. Portsmouth, NH: Heinemann.
(5) – BACK, J., 2013. Manipulatives in the Primary Classroom. NRICH. Available from: https://nrich.maths.org/10461

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