During my time as an Advanced Skills Teacher (AST) I spent some time in primary schools, supporting Key Stage one and two maths coordinators as part of my role. Despite being there as a ‘maths specialist’, during my visits I learnt as least as much as the primary teachers I worked with - and what I learnt had a great impact in my own classroom.
The main change was how much equipment I used in lessons in order to help students explain their thoughts. Students in primary school were forever exploring mathematics through objects, and explaining what they had done using counters, multi-link cubes, pieces of card etc. To begin with, I introduced different equipment into Key Stage three lessons. All didn’t go well at first. Initially, students were more likely to use multi-link cubes to create toy guns than make linear sequences.
As their experience with using manipulatives in maths lessons increased, students slowly got used to the fact that the equipment was available in all lessons - not just in one-off ‘special’ lessons. Eventually my students became more confident in using the ‘manipulatives’ at hand to explain their thinking, to convince a friend or to show their working out.
Increasingly, the use of equipment was not seen as something for ‘those students who found maths hard’ or 'babyish. We began using cubes in Key Stage 4 classes to explain more and more advanced ideas, like how to complete the square, to find the difference of two squares and to factorise quadratics.
‘Manipulatives’ can come in a variety of forms. I think of them as any physical object that students can move around to help explain the mathematics: Interlocking cubes; counters; dominoes used to explore triangular numbers, square numbers and other number sequences; dice (did you know that dice can be left-handed or right-handed?); Pentominoes; Geoboards; Cuisenaire rods and even pieces of A4 paper.
Eventually, all of this equipment was used in my lessons not as a treat, or because it was Friday afternoon, but because students found it useful to help them learn, and I found it led to a deeper understanding in their mathematics. In my mind manipulatives were no longer restricted to primary classrooms, but played a vital part in my secondary maths teaching, too.