The value of teaching mathematics in mixed- attainment groups
Teaching children mathematics in mixed-attainment groups is fundamental to providing all children with their access and entitlement to a common, statutory mathematics curriculum, as defined by HMG. However, teaching is complex and how anyone learns to teach is dependent upon many factors including the beliefs and values they hold and the ethos within the schools in which they practice. However, when we place our focus on learning then according to Gattegno [1971: ii] A radical transformation occurs in the classroom when one knows how to subordinate teaching to learning. It enables us to expect very unusual results from the students - for example that all students will perform very well, very early and on…
My experiences, initially as a young teacher and later as a HoD in a school, led me to believe in the value of teaching mathematics in mixed-attainment groups. These values were based upon:
How anyone might create the conditions for teaching mixed-attainment groups depends upon the range of strategies we use, the questions we ask and the types of resources we have access to and how we utilise these strategies and resources when planning lessons and designing tasks for use with our students. An earlier quotation from Gattegno (1963, 63) offers some insight into task design: All I must do is to present them with a situation so elementary that they all master it from the outset, and so fertile that they will all find a great deal to get out of it. Given the increasingly strong element of problem solving and reasoning emerging, from the 2014 National Curriculum and the subsequent impact of this upon assessment at GCSE and A-level, such strategies and resources need careful consideration with regard to subordinating our teaching to learning.
With regard to asking questions two seminal publication by the Association of Teachers of Mathematics (ATM) http://atm.org.uk) are: Questions and prompts for mathematical thinking andThinkers.
In terms of resources and task design http://www.inquirymaths.co.uk has the potential to make profound additions to supporting learning and teaching in mixed-attainment classrooms.
There are also a vast range of other resources published by the ATM and some are:
Gattegno, C. (1963) For the Teaching of Mathematics (Volume One), Great Britain, Lamport, Gilbert.
Gattegno, C. (1971) What We Owe Children: The Subordination of Teaching to Learning, London: Routledge & Kegan Paul.
Michael is a Freelance mathematics education consultant.
Students' Experiences of Learning Pythagoras.
The link below is to a a year 10 student's writing about her learning of Pythagoras in a mixed-attainment class (in 1991).
At the other end of the attainment 'scale' another student's work appears in chapter 6, titled: "John's access to Pythagoras' theorem:inclusion and entitlement in action, published in: Watson, A., Houssart, J., and Roaf, C., (2005) Supporting mathematical thinking, London, David Fulton Publishers, in association with NASEN. The link below is to this chapter.