Mastery is and continues to be a significant topic of conversation in the teaching of primary maths. How we support our students to unpick and develop understanding of mathematical concepts is something which primary school teachers experiment with regularly. We all endeavour to come up with the best solution for the children we teach.
Recently, I sought to explore the use of arrays in primary maths teaching and how they enable a connection between multiplication and division. Arrays are visual representations of these operations using rows and columns. The use of arrays in teaching is something that I feel personally confident with. As such, I was excited to explore what might be the ‘best solution’ in supporting my Year 2 children to understand the complex relationship between multiplication and division.
What I quickly realised was that through the visual use of an array I had already, in teaching multiplication in isolation, created a barrier. The visual use of an array in the teaching of multiplication at once masked the intricate connection between multiplication and division. The children had established an understanding that an array would help them with multiplication but were less likely, upon observation, to cross-connect their learning to the mathematical processes of division. In other words, while arrays supported the development of fluency in multiplication, the same could not be said about supporting student understanding of division. I had hit my first stumbling block.
I started to wonder if, when the array was created by the multiplication sentence, children might be able to discuss other forms of mathematical calculation, such as what they could share the whole by. Such a leap would provide a strong foundation for them in understanding the relationship between multiplication and division. For a moment, I believed I had found the holy grail to teaching with arrays. Alas, this was not the case.
When asking the children to use an array to solve division, the nature of the representation was far too abstract. My project had to be stripped back to consider the cornerstones of mastery and therefore go back to which representation was being used. When I used concrete materials the children could manipulate the model and thus see that it could be divided, making the critical connection between multiplication and division.
In short, the array when used in particular ways did show the children the connection between multiplication and division. However, I realised something even more important than that. The developmental needs of the children were still very much in need of concrete and practical real life experiences. The array itself only came to life when it was applied in such a way.
It could be argued that the actual teaching method is always self-limiting, and that what is at the crux of successful maths teaching is its application (i.e.how it is revealed and represented to the children).
Is there a best solution? Possibly not. But what we do know is that, at the heart of primary maths, are our children who learn in many different ways. Maths teaching must meet this at the forefront. After all, the children are ultimately our next generation of mathematicians.
Rebekah Gear (NTU BA Primary Education alumnus)