# 1 Thinking Maths: A contribution to teaching

Cognitive Acceleration in Mathematics Education (CAME) began as a research project funded at King’s College, University of London. CAME aims to contribute to the teaching of mathematics in the lower secondary school, where youngsters have a ‘window of opportunity’ for rapid intellectual development.

**The Thinking Maths approach**

The CAME approach behind the Thinking Maths (TM) activities is to provide cognitive stimulation using challenging classroom tasks with an emphasis on ‘big ideas’ or organising conceptual strands in mathematics. It helps to underpin the notations and algorithms stipulated in the mathematics syllabus with real understanding, through pupils effectively reconstructing the underlying concepts for themselves. This approach complements the other ingredients in pupils’ mathematical experience (instruction and practice and/or investigations) and significantly raises pupils’ thinking capacity, creating a stable basis for higher achievement in later school years.The aim, therefore, is permanent and general cognitive development, as well as meaningful learning of mathematics here and now.

**Structure of Thinking Maths lessons**

In mathematics teaching, instruction and practice focus on a given objective and assume the ability of the whole class to benefit. Thinking Maths recognises a range of levels of ability in any class in any one context, of which only one may properly process the lesson objective. Hence Thinking Maths lessons propose agenda to be addressed rather than objectives to be reached by all.

Investigation and open-ended problem-solving, the other key elements of mathematics teaching, allow pupils to proceed in their own direction within their own capabilities. TM corrals the pupils within the mathematical context, and asks all to collaborate, from wherever they are, in constructing insight at all levels of understanding.

When pupils learn facts and practise procedures they often do not understand the underlying maths. Repetition and assessment can lead to pupils getting anxious and switching off when they repeatedly fail to meet expectations in terms of `right answers. Thinking Maths lessons allow pupils time to handle ideas and objects freely – mathematical symbols, drawn images, objects such as a rotating arm relating degrees in the four quadrants to the sides of triangles, etc.- so that every idea is valued and combined with others, leading gradually to higher levels of thinking as appropriate to the class and the topic. Pupils are then more likely to gain lasting understanding, but more importantly they develop powers of understanding.