About cookies

The NCETM site uses cookies. Read more about our privacy policy

Please agree to accept our cookies. If you continue to use the site, we'll assume you're happy to accept them.


Personal Learning Login

Sign Up | Forgotten password?
Register with the NCETM

NCETM Secondary Magazine, Issue 2 - Professional Development activity - 2 hour learning module - Why do we teach mathematics?

This page has been archived. The content was correct at the time of original publication, but is no longer updated.
Created on 08 February 2008 by ncetm_administrator
Updated on 18 July 2012 by ncetm_administrator


Professional Development activity - 2 hour learning module
Each week the Secondary Magazine will include a Professional Development activity. Available in PDF format, this series of learning modules are ideal for giving a focus to a department meeting or inset session.
Each week we will publish a new learning module, which over the weeks will build up in to a shopping list of PD activities so that you can pick and choose the materials that best suit your own development needs.

The first twelve modules will cover the following areas: Self Evaluation, Why do we teach Mathematics?, Mathematics learning script, Pathways and option: KS3 to KS5, Mathematical vocabulary, AfL: Using the lesson objective - overview, Group Work, C/D Borderline, Revision latest, Technology for learning, Questioning script and AfL: Formative use of summative tests.

Why do we teach mathematics?
This module enables you to explore what you believe mathematics is. There are four activities which you can do with your department/group which are designed to encourage you to think about different types of mathematical understanding and their place in the classroom.
This unit addresses the question of why we teach mathematics and, in doing so, will explore what you believe mathematics is. The unit starts by looking at what mathematics is involved in a simple puzzle and then looks at different types of mathematical understanding as identified in an article by Richard Skemp and their place in the classroom. The unit closes by returning to the original question, by attempting to construct a definition of mathematics, and with some suggestions for further reading.

There are some large and challenging questions posed and the aim of this unit is not to provide you with definitive answers but rather to provide you with an opportunity to continue to develop the understanding and the answers that you already have.

Where are you now?
Individually for a minute or so then in pairs or small groups consider the question why do we teach mathematics? How do you answer the student who asks “why do I need to know about simultaneous equations?”

Take feedback from each pair or group.

Activity 1
Make a start on the mini Sudoku puzzles (handout 1 on the pdf file linked above). After a few minutes, individually at first and then in pairs or small groups, consider the skills that are involved in attempting a Sudoku. It may be useful to provide a list of possible skills such as:

Representing     Interpreting
Reasoning   Calculating
Selecting   Proving
Analysing   Deducing
Justifying   Modelling
Eliminating   Communicating

Many Sudoku puzzles come with a ‘disclaimer’ which says something like “there’s no maths needed to solve this puzzle, just problem solving and logical thinking”. In pairs or small groups discuss whether the Sudoku puzzle is a mathematical activity and, if so, what mathematics is involved.

Activity 2
Read the text on handout 2 (on the pdf file) taken from Relational Understanding and Instrumental Understanding by Richard R Skemp (first published in Mathematics teaching 77, 1976) and then, in pairs or small groups, give examples of relational and instrumental understanding in your classroom.

Activity 3
In pairs or small groups, considering both the Sudoku activity and the Skemp article, discuss the question: What does it mean to get better at mathematics?

Gather responses and consider what this suggests that the group believe mathematics to be.

Activity 4
In pairs or small groups cut out the cards on handout 3 (see attached pdf) and consider the type of understanding that the student on each card needs to work on to help them overcome their difficulty. How would you help them to achieve this?

Consider the following quote from “Making Mathematics Count”, the report of Professor Adrian Smith’s Inquiry into Post-14 Mathematics Education (February 2004)

Mathematics provides a powerful universal language and intellectual toolkit for abstraction, generalization and synthesis. It is the language of science and technology. It enables us to probe the natural universe and to develop new technologies that have helped us control and master our environment, and change societal expectations and standards of living. Mathematical skills are highly valued and sought after. Mathematical training disciplines the mind, develops logical and critical reasoning

Individually at first then sharing and refining your idea in pairs or small groups try to complete the sentence:

Mathematics is…

and consider how this might inform the answer from the year 11 student about why they need to know about simultaneous equations.

Implementing and continuing to learn
Individually complete handout 4 on the attached pdf file, giving strategies or ideas that you may use to continue your understanding of what mathematics is and why we teach it.

Further Reading
Relational Understanding and Instrumental Understanding
Richard R Skemp

Making Mathematics Count
The Smith Report

Mathematics and the mind gym
Guy Claxton

Don’t worry: you don’t need to know any maths to read this article; just problem solving and logical thinking!
Pete Griffin


Explore the Secondary Magazine
Issue 2
5 Things to do this week
Professional Development activity: Why do we teach mathematics?
Website of the week
Secondary Magazine archive

Browse Secondary Magazine
Issue 1 Welcome to the magazine
Issue 2 How much mathematics?
Issue 3 Pecking crows?
Issue 4 Unusual hobbies

PD Activities
Self Evaluation
Why do we teach mathematics?
Learning mathematics in my school
Pathways and options at KS3 to KS5



Comment on this item  
Add to your NCETM favourites
Remove from your NCETM favourites
Add a note on this item
Recommend to a friend
Comment on this item
Send to printer
Request a reminder of this item
Cancel a reminder of this item
Share |



There are no comments for this item yet...
Only registered users may comment. Log in to comment