A thinking skills approach

to learning maths (CAME)

Schools implementing cognitive skills in

maths saw:

over half participating classes achieve larger than

expected maths achievement from year 7 to year 8

significantly higher GCSE pass rates in maths than in

control schools (0.8 of a GCSE grade higher)

The impact of setting on student outcomes

Students in low ability sets gained

little from CAME lessons despite

being taught by experienced

CAME teachers

A CAME school with mixed ability

classes reported gains for

students of all abilities

Researchers believed the reason

was that higher-ability students

provide a range of insights that

help lower-attaining students

extend their thinking

Evidence of thinking skills developed in maths transferring to other subjects

CAME students achieved value-added gains of

0.30 of a grade in science and 0.32 of a grade in

English

this may be evidence for transfer of thinking

skills from maths to other subjects

The Cognitive acceleration in

mathematics education (CAME) project

The CAME project:

– is based on research and theory about students’

thinking

– aims to boost mathematical thinking of students aged

11 to 14 years and raise their attainment in standard

tests

The key ideas behind CAME are that:

through collaboration children who are further on in their

understanding of a problem can help move other

students forward too (from Vygotsky)

the teacher’s role is to prompt students thinking with

questions (mediation)

all adolescents have the potential to achieve in

mathematics

The key stages of a CAME lesson

CAME mathematics lessons follow a structure of:

– concrete preparation

– collaborative learning

– whole-class discussion

Concrete preparation

In the opening phase the teacher:

- introduces the task to the whole group

- asks students to explain to each other what they think

the task is about

Collaborative learning

Students work in pairs or

small groups on tasks which

challenge students’ existing

ideas

Students make notes from

discussion for feedback later

The teacher moves around

the class observing

interaction and prompting

with questions when

discussion falters

Whole-class discussion

The session closes with a

whole class discussion in

which the teacher:

– asks groups to report their

ideas

– encourages students to reflect

on their reasoning using

probing questions

– draw pupils’ attention to key

ideas and vocabulary

– encourages others to ask

questions

The tasks students tackle in a CAME session

In the ‘twigs and leaves’ task students describe

the pattern relating to the numbers of leaves on

some twigs

The teacher then asks students to express the

pattern in a word equation eg:

The total number of leaves = number of twigs

times 3 plus 2 leaves at the trunk

Students then replace the words by letter

symbols, in this case:

L = (3 x t) + 2

Who were the children in the study?

The intervention involved 78 classes of 11-12

year olds in 12 project schools

Project students received 30 CAME lessons

(called Thinking Mathematics) over two years

How was the information gathered?

Findings are based on:

– tests of mathematics understanding at the start of

Year 7 and end of Year 8

– GCSE results in mathematics, English and science

three years later

How might teachers use this evidence?

Group discussion was a key element in

developing students’ thinking skills, and the

teacher played an active role in ensuring this

happened effectively

In what ways could you support your students to

listen to each other’s ideas more effectively, and

reach a decision together? Could you weave in

opportunities to model effective dialogue for

them?

How might leaders use this evidence?

The CAME approach used a quite specific pattern of

delivery – preparation, collaborative task, whole class

discussion

How flexible, open to new approaches are teachers in

your school? If you were to introduce a new approach

like CAME which department or team of teachers is best

placed to develop the practice? What scope is there for

coaching partnerships to extend the practice?

Find out more

Study reference: Shayer, M and Adhami, M (2007)

Fostering cognitive development through the context of

mathematics: Results of the CAME project in

Educational Studies in Mathematics (2007) Vol. 64, pp.

265-291

You might like to read a summary of the work of

Vygotsky here: http://www.curee.co.uk/node/4883

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