Changing Mathematics Teaching in the Elementary School Jack Easley and Elizabeth Easley Published by Deakin University, Geelong, Victria, Australia 3217 First Published 1992 ISBN 0 7300 1330 8

1. Primary school mathematics: the crucible of our technological society

   • Can we improve primary-school mathematics?
   • The problem of equity
   • Five stages of American primary-school mathematics
   • What is wrong?
   • Counting and the ‘base ten’ system
   • What hope is there?

2. Kitamaeno School as an environment in which children learn to study mathematics cooperatively

   • Why we went to Japan
   • Choosing Kitamaeno School
   • Classes observed
   • What we want to report
   • The school plant and grounds
   • School schedules
   • The staff
   • School contact with parents
   • Special events during the first trimester
   • Kitamaeno primary arithmetic
   • Priorities of teachers
   • The use of groups
   • Using challenging problems
   • The Kitamaeno School system for promoting discussion in mathematics classes
   • Reconceptualising arithmetic: the ‘water supply’ system
   • The wall
   • How teachers in Kitamaeno School operated on a meta- mathematical level
   • Learning to understand one another as an educational goal

3. Promoting independence and responsibility in working with American teachers on problems in teaching primary-school mathematics

   • Getting organised
   • Children who cannot keep up
   • Explorations with story problems
   • In retrospect

   1. The implementation of needed change in primary-school mathematics

   • Common problems in primary school mathematics
   • How does one improve in teaching?
   • Four changes needed in primary-school mathematics
   • Taking the guilt out
   • Dialogue

• Appendix 1 Examples of classroom deliberations: Grade I (Wantanabe sensei)
• Appendix 2 Examples of classroom deliberations: Grade 2 (Nakano sensei)
• Appendix 3 Observations from Susan Shadid’s class
• Appendix 4(a) Problems studied by Mrs Walters’ class
• Appendix 4(b) Additional problems used in Susan Shadid’s third and fourth grade class