Introduction to Charis Maths Units 10-19

by John Westwell and John Shortt Editors of Charis Mathematics


Why should mathematics teachers be concerned with spiritual and moral development?

Addressing spiritual and moral development across the curriculum has come much more to the fore recently as a result of the renewed emphasis placed upon personal development within both the National Curriculum and the OFSTED Framework for Inspection.

These facets of development are, of course, not new as goals of education. Indeed, many mathematics teachers would say that they are fundamentally concerned with the education of the "whole child". However, a shared understanding of what this means has proved to be elusive and, consequently, it has not always been seriously worked through by mathematics teachers. However, having developed these resources, the Charis Mathematics writers have become convinced that moral and spiritual dimensions should be and can be present in the teaching of their subject.


How can learning mathematics provide opportunities for such development?

The nature of the subject itself suggests a number of approaches for combining spiritual and moral development with the learning of mathematics.

The first of these approaches comes through recognising that mathematics has been developed and is applied in a wide range of human situations. Consequently, it is possible to choose contexts which allow students to develop their mathematics while, at the same time, reflecting upon and discussing the spiritual and moral dimensions arising from the human issues being examined. For example, Unit 18 'Could it be you?' uses the National Lottery as a context to develop probability and statistics skills. At the same time, it provides an opportunity to reflect upon what we really value and to discuss the impact, if any, of luck in our lives.

A second approach comes through recognising how people find that by exploring ideas within mathematics, they can also gain insight into broader areas. Mathematics could he seen to act as a metaphor for other areas of life. Unit 19 'Do you know where you are going?' is an example of this approach. The unit examines various aspects of the mathematics of navigation and also links this with the way we seek guidance and direction in our lives.

The third approach used in the resources comes through recognising that mathematics is used extensively to help us model and understand the universe. It is hoped that, through examining examples of this, students will develop a sense of wonder in response to the real world around them. For example, Unit 11 'The Designer Universe' offers opportunity for students to improve skills with standard form, while reflecting on the origin and amazing nature of our universe.


What the Pack Contains

The pack consists of a set of 10 free-standing units mainly aimed at Key Stage 4 students. Some units are more appropriate for students of particular tiers, but there are some units that can be used effectively with all GCSE students. Also, during trialling, some of the units were used successfully with younger students.

Each unit contains Teacher's Notes and photocopiable Student's Sheets. The Teacher's Notes contain information on:

  • the mathematical content within the unit
  • the aspects of spiritual and moral development addressed by the unit
  • background ideas and additional sources of resources
  • how the unit is structured and any special resources required
  • how to conduct the discussion and reflection activities within the unit


How can the units fit in with our existing scheme of work?

Teachers often express a desire to broaden the mathematical experience of their students, but feel under pressure to press on with the syllabus. The Teacher's Notes for each unit give an indication of how long the unit can take and also outline the mathematical content. Some units could either be used as a motivation for learning an area of mathematics or alternatively used to practise and apply knowledge, skills and understanding already developed:

The table shows the key mathematical content addressed by each unit and for which tiers of GCSE (Foundation, Intermediate or Higher) the unit would be suitable. The information below together with the further content details in each unit is designed to help you to identify where a unit can be usefully incorporated into your existing scheme of work.

Unit  Title GCSE tier Key mathematical content
 10 The literal facts  F/I Using fractions and percentages; working with large numbers; place value; interpreting tables; interpreting and constructing statistical diagrams
 11 The designer universe  I/H Standard form (positive powers of 10); rounding numbers to
significant figures; scale drawing.
 12 Believe it or not?  F/I/H Data collection methods; carrying out a statistics project; using percentages.
 13 Bucking the trend  I/H Correlation; lines of best fit.
 14 But can you afford it?  F/I Understanding and calculating with percentages; sensible use of a calculator.
 15 Mr Kepler's shapes  F/I/H Symmetry; nets and solids; construction of loci.
 16 The inside story  I/H Standard form (positive/ negative powers of 10); substitution in
formulae.
 17 What's the time?  F/I/H Complex calculations, negative numbers; large numbers; using
formulae; constructing graphs; calculating means.
 18 Could it be you?  F/I/H Calculating probability; interpreting tables; carrying out and interpreting surveys; combinations and factorials; number patterns.
 19 Do you know where you are going?  F/I Compass points; bearings; scale drawing

What preparation will I need to do?

Having decided when you want to use the unit with your students, we recommend that you study the Teacher's Notes closely. After this you will need to:

  • consider whether and how you wilt teach the students any relevant mathematics prior to work on the unit
  • photocopy the Student's Sheets and organise any other necessary resources
  • plan how to structure the unit over a series of lessons
  • consider the implications for classroom organisation
  • allow time for any preliminary activities with the students (units 12 and 18)

What if I am not used to teaching mathematics in this way?

Many teachers may be hesitant about organising lessons that stimulate discussion of issues not normally addressed during mathematics lessons. Also, students may initially find the experience strange if they have not done similar work in the past. However, it was found when trialling the materials that if the approach was appropriately introduced then students enjoyed engaging with the spiritual and moral dimension and that stimulating discussion did take place.

Guidance is given in each unit about possible areas for discussion and reflection. It is helpful to ask students to produce written responses prior to a class or group discussion of an issue. It is also important to realise that your role is not to provide answers but to enable students to think through the spiritual and moral issues raised by the unit.

Given the innovative nature of these resources, the project team would appreciate any feedback from teachers on their experience of using the materials. There is a form at the end of the book which you can use if you wish to respond, or you may prefer to send a letter/fax/e-mail. We trust that the resources will support you as you seek to promote both the personal and mathematical development of your students.


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