ICME13 Papers

EXISTENTIALISM IN MATHEMATICS AND ITS EDUCATION
FROM ESSENCE TO EXISTENCE
DON’T PREACH ESSENCE – TEACH EXISTENCE

Contents

01. Proportionality and Integration in Preschool through IconCounting and NextTo Addition
02. Calculators and IconCounting and CupWriting in PreSchool and in Special Needs Education . 03. As PerNumbers, Fractions are Operators, not Numbers
04. From Essence to Existence in Geometry Education
05. Preschool, Middle school and High school Calculus
06. Essence and Existence in Conflicting Cognitive Theories
07. From Essence to Existence in Curriculum Development
08. From Essence to Existence in Math Teacher Education
09. From Essence to Existence in Mathematics Education

KopTæl_& OmTæl

text

KopTæl_OmTæl

CupCount & ReCount

Material to practice CupCounting and Recounting:

Contents

Preface

Introduction to the Chapters

1. From Sticks to Icons………………………………………………………………….. 1
2. Counting in Icons………………………………………………………………………. 3
3. CupCounting in Icons………………………………………………………………… 5
4. CupCounting with Dices……………………………………………………………. 6
5. ReCounting in the Same Unit…………………………………………………….. 7
6. ReCounting in a New Unit…………………………………………………………. 8
7. ReCounting in BundleBundles…………………………………………………… 9
8. ReCounting in Tens on Squared Paper or an Abacus………………… 10
9. ReCounting from Tens…………………………………………………………….. 11
10. ReCounting Large Numbers in Tens…………………………………………. 12
11. DoubleCounting with PerNumbers………………………………………….. 13
12. DoubleCounting with Fractions and Percentages…………………….. 14
13. ReCounting PerNumbers, Fractions…………………………………………. 15
14. Adding OnTop………………………………………………………………………… 16
15. Reversed Adding OnTop…………………………………………………………. 17
16. Adding NextTo………………………………………………………………………… 18
17. Reversed Adding NextTo…………………………………………………………. 19
18. Adding Tens……………………………………………………………………………. 20
19. Reversed Adding Tens…………………………………………………………….. 21
20. Recounting Solves Equations…………………………………………………… 22