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Mathematics Matters Lesson Accounts 29 - Revision Session of Tree Diagrams

This page has been archived. The content was correct at the time of original publication, but is no longer updated.
Created on 28 May 2008 by ncetm_administrator
Updated on 16 June 2008 by ncetm_administrator

Mathematics Matters Lesson Accounts
A collection of memorable mathematics lessons that conference and colloquia delegates had observed or taught which they felt were successful.  Each account refers to one or more of the values and principles in the report.

Lesson Account 29 - Revision Session of Tree Diagrams

Written by Liz Durham
Organisation Southend Adult Community College
Age/Ability Range Adults 1 year GCSE class: revision session of tree diagrams, prior to module exam. About 14 students abilities A* - D

How was the session/task introduced?
Told learners I’d split them into 2/3s to revise tree diagrams and want them to produce at least one challenging probability question for another group to solve – but they had to solve it themselves first. Boardstormed as whole class for 5 mins on possible topics in case groups didn’t have own ideas. I chose groups: 2 groups of learners doing Higher level were asked to make their questions involve conditional probability.

How was the session/task sustained?
Learners spent 15-20mins in their groups creating and solving own questions, then wrote question up on poster for another group to solve. Swapped back and discussed answers.

Extension 1: 2 posters I’d put up on the wall with errors. Learners take post-its and try to identify errors but delay putting these on until all had chance to see.

Extension 2: Rewrite your question so you give the solution and try to deduce the question instead.

Didn’t intervene to help learners write the questions in understandable language (deliberately) so people had to go back to group that had set the question and ask them to articulate it more carefully. But did intervene to ensure questions set were appropriate for solving via tree diagrams.

How was the session/task concluded?
All posters put up on wall by learners. Plenary with one of my posters with errors discussing as whole group what they identified as errors.

What were the critical moments?
At this point in the course it was appropriate to group according to the GCSE level they were sitting.

Introducing the task – this group hadn’t done either poster work or setting exam style questions before – I needed to ensure they could see clear purpose.

Discussion times within original groups and when two groups amalgamated to share outcomes.

What mathematics was learnt? (on plan and off plan) and what is the evidence of learning?
All understood what sort of questions led to possible solutions by tree diagram and were able to recognise, pose and answer such questions. Helped increase level of class discussion in future sessions

Evidence: Masses of discussion, full participation. In following session learners went up and looked at other groups’ posters without prompting. All got A*-C in module exams.

How was that mathematics learnt?
Through discussion, questions and explanations among learners themselves.

Questions I posed to prompt further thought. Guidance I gave to stop them going off track in composing questions. Answers I gave to specific questions where they had disagreements between themselves that could not be resolved.

Other memorable outcomes
One learner had only wanted to be taught by the teacher but had a Eureka moment when another learner was able to explain to him how a question worked through. One learner with support help was able to work in a group of 3 without the support and this had great benefit for her for the rest of the year. Support was freed up more in subsequent lessons..


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Values & Principles

Fluency in recalling facts and performing skills
Conceptual understanding and interpretations for representations
Strategies for investigation and problem solving
Awareness of the nature and values of educational system
Appreciation of the power of mathematics in society
Builds on the knowledge learners already have
Exposes and discusses common misconceptions and other surprising phenomena
Uses higher-order questions
Makes appropriate use of whole class interactive teaching, individual work and cooperative small group work
Encourages reasoning rather than ‘answer getting’
Uses rich, collaborative tasks
Creates connections between topics both within and beyond mathematics and with the real world

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Lesson Accounts Introduction

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