Representation Matters By Jasmine Ellis
Ending a great day of getting to know fellow scholars and alumni, the final Maths Scholars Celebration workshop was ‘Representation Matters’ by Aidan Gollaglee (Maths Hub Lead for London South East Plus Hub).
Scholars were first asked to calculate 22 x 32 using 21 x 31 = 651. With many of us employing the distributive law in our solution, we were prompted to consider instead how our calculations could be represented visually. After a brief brainstorming session with my tablemates, we collectively agreed on a diagram – a representation known as an array. Building on the earlier question as a model, we attempted a similar problem yet this time incorporating algebra, where the effectiveness of arrays certainly became clear to me.
Before delving deeper into arrays specifically, we discussed the foundational principles of representations and structure, and their role in teaching for mastery. Some of the practical examples of representations we saw included Deines blocks, place value charts, Gattegno charts, and stem sentences. Despite these tools being commonly used in primary schools, why do we rarely see them in secondary classrooms? Many of the techniques taught in secondary maths lose their relevance as the subject progresses, teaching memorisation as opposed to developing deep understanding.
We continued to examine the use of arrays, in concepts from KS1 all the way to KS4. We began by exploring how to represent the multiplication and division of fractions, the diagram for division admittedly taking me some time to produce. I think most of us could have reached solutions to the given questions in just a few minutes, resulting in a much shorter workshop, yet the challenge was in showing the reasoning behind our solutions. Extending this understanding to expanding brackets using algebraic tiles, completing the square, and then ultimately to factorising quadratics, we explicitly tracked the application of arrays across the entire curriculum. Representations like this are called ‘forward-facing,’ and after this seminar I can see why.
While I thoroughly enjoyed the problem-solving exercises of this workshop, the concepts explored have real applications for all educators. I am reminded of the saying ‘essential for some, harmful to none, helpful for all.’ Though not every student requires visual aids to grasp abstract concepts, incorporating them into our teaching will do them no harm. However, if, for example, using tools like arrays can help even one student understand how to multiply fractions, it will have been worthwhile. I am keen to practice incorporating representations into my teaching as a trainee, and to help with this, Aidan directed us to several online resources - Polypad, MathsBot, and Underground Maths.
Being both fun and informative, experiencing this workshop makes me look forward to the future CPD events available to us as scholars.
By Jasmine Ellis
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