Getting under the skin of different representations in Mathematics
Why a picture tells a thousand words
This famous phrase is something many of us can relate to – how do you prefer to take in your information …. from a single picture or pages of text?
The plethora of infographics and visuals in our world demonstrates the reality of why imagery is so important to the human brain. With one infographic we can get across a huge amount of data in a manageable form that is easy to digest and remember. It creates a framework for our long-term memory and makes it much easier for us to recall the detail when we need it. The art of creating easy visual representations is a valuable one and if it can be used in multiple scenarios to help us grasp many different concepts, it becomes even more powerful.
Visuals are just as important in mathematics as in many other subjects. Can you imagine how hard it would be to help young children understand basic number concepts without concrete materials or visual representations? And they’re not just great for our early years’ learners. If we have a variety of visuals at our fingertips, it is much easier to grasp something more complex – understanding the relationships between the numbers we see in front of us so that we can solve really challenging problems. We can use them to make better decisions about what is relevant and what we need to do with them to find a solution.
Mixing and matching representations
There are many different representations we can use in Mathematics:
So, is it just a case of evolving from one type of representation to the ultimate goal of the symbolic or abstract? We talk about moving from the concrete to the visual and finally into the abstract, but this does not mean that we should leave the concrete and visual behind when we’ve become confident with symbolic calculation strategies. The best teaching strategies involve carefully sequenced steps through different representations so that the same concept can be deeply understood and therefore much more easily applied to any new problem. It’s definitely not the case that we put the images and manipulatives away at the end of Key Stage 1 and forever after rely on written methods – let’s keep them to hand to help deepen our students’ understanding of increasingly challenging and complex concepts.
Choosing the right visual representation
Number lines, place value grids and 100-squares have been used by teachers since time immemorial to help with numerical understanding. So, should we be throwing these out and only focusing on the newer more fashionable part/whole and bar models? These have been developed as part of the mastery approach to mathematics from the early years all the way through to secondary school. The goal for us as teachers is to have a wide range of models and representations at our fingertips so that we can choose the best one to uncover a new mathematical concept, keeping some in reserve for those students who need an alternative view to aid their understanding.
When you are questioning which ones to use and how many to uncover, you may want to think about:
- How your choice of visual representation can help students to understand the structure of the Mathematics.
- How familiar your students are with different representations. If you would like to introduce a new one, students will need explicit instruction on what it is and how it works.
- How you verbalise your use of the representation to help you solve an example problem and how you want to develop your use of this through a careful sequence of worked examples.
- How you are going to integrate the use of accurate mathematical language and STEM sentences with your representation so that they can make the link between the language and the image for a key concept.
Visual representations are also a great way for students to challenge each other and you – building their own understanding along the way as they think carefully about what information to give you and what they want to hold back. It’s a great way to get everyone thinking and passing ownership of learning back to where it needs to be – in the hands of your students.
Rachel Tilden Walker is a consultant, guest author and writer for Thirsty Scholars Partnership. Rachel has written our Primary Maths: Visual representations in Mathematics course