Written by Helen Laflin
Helen Laflin is a UK based primary mathematics specialist and author, with twenty years of experience improving mathematics teaching and learning in schools. Helen currently balances her consultancy and training work with adults, with teaching children in primary schools.
Helen is passionate about the importance of teaching for conceptual understanding, and the use of models and images for all learners to both support and challenge mathematical thinking. Below she outlines the most effective approaches for meeting the learning needs of all children in the unsettled educational landscape.
The closures of schools and disruption to learning during the COVID-19 pandemic has brought into sharp focus the inescapable challenge that teachers are facing in meeting the needs of children with widening differences in attainment.
The Education Policy Institute (EPI) Education in England: Annual Report published in August 2020 found that in Primary schools the gap between disadvantaged learners and their peers has increased for the first time since 2007. The report also identified variation in educational attainment according to region and ethnicity, and a widening attainment gap for Black Caribbean children, Looked After Children, and children with English as an additional language who arrived late to the education system.
“What happens in the classroom makes the biggest difference“EEF Attainment Gap Report 2018
How can teachers ensure that whilst meeting the needs of those who may be struggling, they can stretch those learners who are ready for further challenge? The Education Endowment Foundation reports that high quality teaching and learning for all learners improves outcomes for those who are falling behind.
“The importance of good quality teaching cannot be underestimated … Additional intervention and support cannot compensate for a lack of good quality teaching.“EEF Special Educational Needs in Schools Guidance Report March 2020
The evidence is clear: attainment gaps are increasing, and learners’ needs are becoming increasingly varied and complex. Making a difference relies on high quality teaching using strategies which are known to result in the best learning for all. These practical strategies are explored in more detail below.
The EEF report highlights scaffolding as a key strategy in Quality First Teaching. Scaffolding builds more independence from the teacher by carefully structuring access to a task, using temporary supports and prompts which are then gradually removed as the learner becomes more independent.
The teacher may scaffold learners by thinking aloud as they answer a question, therefore modelling their approach and reasoning. The shift in focus from the answer to the process is a powerful message, especially in mathematical teaching and learning because maths is not about formulating an answer quickly. In fact, deeper learning goes on when we reason, justify and explore mathematical connections and to model this promotes the process rather than the solution.
Providing opportunities for children to think aloud
Modelling this ‘thinking aloud’ process helps learners to develop their metacognitive and cognitive skills whilst also promoting the importance of mathematical talk. Expecting children to think aloud also gives powerful assessment information and insight into the learner’s thought processes and understanding.
Encouraging children to work collaboratively in talking partners to discuss, formulate, explain and check their ideas together is a powerful scaffolding tool. Collaboration provides the opportunity for learners to explore their ideas with their peers while rehearsing and refining their thinking, before sharing it further.
“Asking children to ‘share what their partner said’ allows quieter children to have their answers shared without needing to feel exposed by having to share it themselves. Similarly, giving (children) warning time before sharing an answer, supports maximum participation.’“EEF Special Educational Needs in Mainstream Schools Guidance Report March 2020
Pairings should be carefully considered and regularly reviewed, but not based on the attainment of the children. Instead, consider whether the children will work together in a focused, collaborative and supportive manner. Being able to discuss and explain a maths concept to a peer is an excellent way of challenging understanding for higher attaining children, and really tests their true understanding of the concept. If you have children accessing work virtually, you can enable collaboration between children to not only reap these benefits but involve them in interactive and inclusive social opportunities as well.
Using a resource such as MathsBeat for teaching means that collaborative opportunities are integral to learning. ‘Listen for’ prompts and targeted questions are included to help identify misconceptions as well as to facilitate children’s reasoning.
Using models and images
An important element of scaffolding within mathematics is the use of models and images that enable learners of all ages to see structure, and therefore support children’s conceptual understanding of mathematics.
“Manipulatives and representations can be powerful tools for supporting pupils to engage with mathematical ideas.“EEF Improving Mathematics in Key Stage Two and Three Guidance Report 2017
Manipulatives can support children who are struggling. Alternatively, manipulatives can provide further challenge for expressing mathematical thinking through representation. The example below outlines the use of Numicon in a lesson to support and challenge Year Five children’s understanding of division in the context of decimals.
Learners were asked to calculate 27 ÷ 9. Some children were not able to do this mentally, so made use of Numicon shapes and a tens number line to support their calculation. This allowed children to focus on the structure of division rather than becoming caught up in calculating the answer. In talk partners children explored what the model represented, and what generalisations they could make next.
The following misconception became apparent when the teacher was circulating the room, so the whole class were asked to discuss and explain their thinking about the following:
Where children did agree, their reasoning included:
“Because it’s decimals, you need to add a decimal point to the answer to make it a decimal too.”
“The 27 and the 9 are ten times smaller so you need to divide the 3 by ten too.”
Those children who recognised that the answer was 3 were not able to come up with a clear explanation that demonstrated their own understanding. The teacher therefore presented the class with the following representation to discuss:
Learners were able to see that on the decimal number line the Numicon shape now represented 0.9 because both the decimal number line and the Numicon shape had been divided by 10 and were therefore ten times smaller. Therefore, three Numicon shapes representing groups of 0.9 fitted on the number line to make 2.7.
The teacher realised that language scaffolding was an important tool here to support children’s conceptual understanding of division so asked the children:
What does the 3 represent? (the number of groups)
What does the 0.9 represent? (the size of the groups)
Next, children worked together to represent division calculations using Numicon and Cuisenaire, and where appropriate, challenged to represent decimal calculations. Alongside the representation, children were tasked with writing the division as a calculation, and then what the calculation represented using the following sentence stem:
There are ________ groups of ___________ in __________.
Finally, children were asked to consider if there was another way to express this sentence as a calculation. The teacher circulated the room asking probing questions to see if learners were able to make the connection between the language and structures of multiplication and division.
Using manipulatives to allow children to see the structure of division and link to multiplication scaffolds the children by building their conceptual understanding and reasoning. Manipulatives can be gradually withdrawn or replaced with pictorial representations such as bar models to build the children’s confidence and independence.
While the recent disruption to education has adversely impacted the learning trajectory of many learners, it also provides an opportunity for teachers to prioritise excellent teaching and learning. Reuniting complete classes is in fact central to all learners making better progress, because by being together, children can benefit from talk for learning in the form of thinking aloud as modelled by their class teacher, conversations with their peers and talking through explanations using manipulatives and representations. Not only will they become more confident and independent, but they will have a deeper mathematical understanding too.
Helen is one of the expert authors behind MathsBeat, Oxford’s digitally-led Primary Maths mastery resource for Key Stage 1 and 2. MathsBeat is designed to give ALL children the depth of learning and support they need to participate in, make progress in, and enjoy maths. Based on clear progression, an easy-to-follow sequence of tasks develops children’s knowledge, fluency and understanding with suggested prompts, actions and questions to give all children opportunities for deep learning.
Find out more at www.oxfordprimary.co.uk/mathsbeat
Improving Mathematics in Key Stages Two and Three Guidance Report (EEF, 2017)
Special Educational Needs in Mainstream Schools Guidance Report (EEF, March 2020)
Attainment Gap Report (EEF, 2018)
Education in England: Annual Report (The Education Policy Institute, August 2020)