Multiplicative Reasoning

The project is continuing into 2015-16 in Key stage 2 and 3 through lesson study. For further information about how to get involved please contact

Multiplicative Reasoning Project by Clare Hill, Twynham School 2014-15

Multiplicative ReasoningOver the last few years we have felt increasingly strongly within the Twynham Maths department that some of our students simply do not develop a secure and deep understanding of key aspects of mathematics, such as fractions and proportional reasoning. This is despite students appearing to be able to perform calculations with fractions. Subsequently we were delighted to become involved with the National Centre for Excellence in the Teaching of Mathematics Multiplicative Reasoning project last year in which two of our teachers attended high quality CPD to examine resources developed from university research to enable teachers to enhance and deepen students understanding of ratio and proportion.

An exciting aspect of this was to support the concept of Lesson Study between colleagues which we see as a potentially powerful way in which to engage teachers in professional development which is focussed on students understanding of mathematics. Alongside this, over the past year we worked with Heidi Whitney, Dorset Mathematics Advisor, to develop the use of concrete resources such as Numicon and Cuisenaire rods. This work involved all ability levels over a range of topics; from basic number work, to ratio, proportion and algebra. We shared our work last year with one of our primary schools but felt that we could raise the professional engagement within the work in addition to simply disseminating the work further.

Subsequently, as soon as the Maths Hubs were announced, we placed a bid to run a project which would disseminate the work of the Multiplicative Reasoning Project to three of our feeder schools, introduce concrete resources to them and develop the practice of Lesson Study between colleagues. We met for our first session recently and although our primary school teachers openly admitted they were slightly dismayed to be joining a project dryly entitled Multiplicative Reasoning – we all had a thoroughly enjoyable afternoon and learnt an enormous amount from each other – about how we understand fractions as adults and how we might be able to develop this understanding between each other – be it colleagues or students.

We were joined later in the session by colleagues from the University of Southampton and are in conversation with them about how we develop this relationship since the University brings a wealth of knowledge about the existing research surrounding students conceptual understanding of mathematics as well as a rigorous methodology with respect to how we evaluate the effectiveness of our work.