The CAME research project (link to research page) directed by Professor Shayer resulted in the commercial publication of the 'Thinking Maths' file.

This file was the first CAME resource and comprises some 30 lessons or activities. CAME itself is an approach to mathematics and as such a paper-based resource can only serve to illustrate or exemplify a small aspect of what actually happens in the CAME classroom.

The lessons are arranged in strands (see below) and follow a spiral progression of allowing pupils to reach out towards ever higher levels of mathematical thinking and reasoning.

A few words of introduction, concerning the management of learning, to the CAME classroom is necessary at this stage.

Each lesson is structured around episodes of interaction which following the three lesson phases illustrated below. Each lesson ends with a general reflective time where the pupils are encouraged to reach out in their thinking and to reflect upon the ideas raised.

CAME lessons are characterised by a gradual rising degrees of cognitive demand with accessibility changing from full understanding to partial understanding to the recognition of challenges that remain beyond the lesson. It is helpful to keep the lower ability pupils working with the less challenging areas while the more advanced activities and episodes including the extension work are used with the more able.

A key feature that needs to come across within any class is that the teacher genuinely accepts that he/she is exploring concepts with the group, at least at the level of their formulations of the concepts in hand. This may involve accepting new kinds of mathematical learning, one that complements the formal curriculum yet is constantly engaging and challenging. Within this there needs to be a balance between dwelling upon the myriad misconceptions and reaching for higher challenges. Both are key elements to the CAME approach but time allocation is critical and conscious decisions need to be made about the balance within each lesson - care should always be taken to move any groups into areas of cognitive discomfort. Some misconceptions are technical and could be resolved by 'telling' or by training on what to do, or teachers avoiding busy work.

Lesson Phases

Each episode will generally follow a similar pattern, outlined below. Obviously in episode 1 the start will be longer and more concrete in nature. Later episodes, however, may only require the most simple of starts but the final sharing phase supported by a more reflective plenary may actually take 15 minutes or more.

The key characteristics of each phase are outlined below:

Whole class start

• Engagement of all usually via a story that gets over the idea without the need to record. There will be a gradual focusing so diversions can be minimised. Speed is of the essence.
• Decisions made on grouping of pupils (pairs and pairing of pairs) and the seating, table arrangements for later in the lesson.
• Cognitive and language preparation via knowing the context, agreeing the descriptions and language to be used.
• The first challenge is accessible for majority of the group.

Supporting independent peer work

• Step 1 = pupil generation of ideas.
• Step 2 = pairs of pupils sharing ideas, possible involvement of other groups.
• Step 3 = pupil recording of ideas (OHT, poster, whiteboard) in most efficient manner for presentation.
• Step 4 = preparation to share ideas/methods/thinking with rest of group.
• Teacher must have awareness of the range (may prompt to ensure appropriate range) of ideas. It is also necessary to think through how you will orchestrate the class sharing to come.

Sharing phase

• Begins with an ordered/structured time of recording pupil ideas, in their words, as they share in turn.
• It is usually productive and inclusive to begin with lower and mid range ideas. Tjis must be decided during the previous phase.
• This process will result in a gradual sifting and filtering of ideas as the class are focusing upon the emergent ideas present upon the board. Pupils are encouraged to comment, make connections, see patterns etc.
• There will follow a time of generalisation and the abstraction of ideas. A more reflective approach will encourage the pupils to focus upon the most appropriate and necessary.

"I am now waiting for an answer and not always giving a response when they don't answer - I now make them think and as a result they come up with some brilliant answers. It is giving them space and time to think and the end result is a focus upon the process of thinking."