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Mathematics Matters Lesson Accounts 13 - Investigation and Problem Solving

This page has been archived. The content was correct at the time of original publication, but is no longer updated.
Created on 27 May 2008 by ncetm_administrator
Updated on 23 July 2009 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 13 - Investigation and Problem Solving

Written by Edwards
Organisation Unknown
Age/Ability Range Key Stage 4

(a) What was the mathematical task(s)?
Set 10 of 10, group of 3 girls. Task: This is the final score in a hockey match, what are the possible half-time scores? Explain.

In the previous lesson, they have generated enough data to generalise and after considerable debate, arrive at the number of possible half-time scores being (x+1)(y+1) where x and y are the final scores. When challenged to explain why this expression ‘worked’, they argue, challenge, justify amongst themselves for half an hour. Eventually, they are able to describe why they need to add one to each score. Value of this is in: (a) being able to comfortably challenge each other; (b) achieving ‘hard’ maths (for them); (c) being aware that mathematics can describe situations d) being able to interpret a situation mathematically.

(b) What learning culture was created? How was this achieved?
A background of feminist epistemology.

The 10 school ‘classroom rules’ were abandoned in favour of 3 mathematics classroom rules:

  • everyone does mathematics
  • everyone does mathematics in a a way that enables others to do mathematics
  • everyone shares their mathematics (collaborates)

Small groups based on friendship, ethos of collaboration, feminist principles of connectedness. Understanding that a mathematics classroom is where thinking takes place.

(c) How could you tell that the task(s) achieved the intended purposes? Do you have any evidence?
Being able to communicate the outcomes and process both verbally and in writing. Pleasure expressed by the pupils about their achievement. (Despite being in set 10 of 10, this ‘diet’ of mathematics learning resulted in GCSE grades D,E,E for this group of girls)

(d) Is this example available to see/read about?
Graded Assessment in Mathematics (GAIM) Macmillan Education 1988 p68

(e) Can you say why you chose this example? What criteria were in your mind?

  • Level of enjoyment for pupils;
  • Level of challenge;
  • Potential for awareness that mathematics can describe ‘real’ situations;
  • Potential to develop confidence – ‘doing quadratics’ is for ‘good’ people

Downloadable PDF

Click here to download this lesson account in PDF format.

Values & Principles

Strategies for investigation and problem solving
Makes appropriate use of whole class interactive teaching, individual work and cooperative small group work
Encourages reasoning rather than ‘answer getting’

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Lesson Accounts Introduction


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