Engaging (with) Mathematics and Learning to Teach : An Integrated Approach to Mathematics Preservice Education

Mathematics education research indicates the value of a meaning-making and problem-solving approach to the teaching mathematics in primary and lower secondary classrooms. Yet teachers, most of whom have not experienced such pedagogies in their own mathematics learning, often find it difficult to imp...

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Verfasser: Povey, Hilary
Dokumenttypen:Buch
Medientypen:Text
Erscheinungsdatum:2017
Publikation in MIAMI:21.12.2017
Datum der letzten Änderung:21.12.2017
Verlag/Hrsg.: WTM-Verlag für wissenschaftliche Texte und Medien
Angaben zur Ausgabe:[Electronic ed.]
Schlagwörter:Zahlentheorie; Polygon; Polyeder; Gruppentheorie; Mathematikunterricht; Grundschule; Sekundarstufe 1
Fachgebiet (DDC):370: Bildung und Erziehung
510: Mathematik
Rechtlicher Vermerk:© 2017 WTM – Verlag für wissenschaftliche Texte und Medien, Münster
Lizenz:InC 1.0
Sprache:English
Anmerkungen:Druckausgabe: Povey, Hilary: Engaging (with) Mathematics and Learning to Teach : An Integrated Approach to Mathematics Preservice Education. Münster : WTM, 2017. ISBN 978-3-95987-051-1
Format:PDF-Dokument
ISBN:978-3-95987-052-8
URN:urn:nbn:de:hbz:6-10219398258
Permalink:https://nbn-resolving.de/urn:nbn:de:hbz:6-10219398258
Onlinezugriff:wtm_isbn-978-3-95987-052-8.pdf
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Inhaltsverzeichnis:
  • CONTENTS
  • Acknowledgements ..... i
  • Links to software ..... ii
  • Introduction ..... 1
  • SECTION ONE
  • Introduction ..... 7
  • 1. What we are about ..... 9
  • 1.1. Our approach to mathematics subject knowledge for teaching ..... 10
  • 1.2. Our pedagogical principles ..... 13
  • 1.3. Troubling the account ..... 19
  • 2. Doing mathematics ..... 22
  • 2.1. “Big ideas” in mathematics ..... 23
  • 2.2. Mathematical thinking ..... 25
  • 2.3. Models of thinking ..... 28
  • SECTION TWO
  • Introduction ..... 33
  • 1. Place value ..... 36
  • 1.1. Number systems in history ..... 38
  • 1.2. The role and meaning of zero ..... 41
  • 1.3. Counting in other bases ..... 43
  • 2. The four rules ..... 46
  • 2.1. Alternative algorithms ..... 48
  • 2.2. Problems in other number scripts ..... 50
  • 2.3. Working in other bases ..... 51
  • 3. Polygons ..... 53
  • 3.1. Properties of quadrilaterals ..... 55
  • 3.2. Semi-regular tiling patterns ..... 57
  • 3.3. Triangles from folds ..... 59
  • 3.4. The four centres of a triangle ..... 61
  • 3.5. From circles to polygons ..... 62
  • 3.6. Polygon symmetries ..... 63
  • 3.7. Four tiles ..... 64
  • 4. Natural numbers and beyond ..... 66
  • 4.1. Patterns on grids ..... 67
  • 4.2. Make 17 ..... 69
  • 4.3. Flipping a coin ..... 69
  • 4.4. A problem of power ..... 70
  • 4.5. Diophantine equations ..... 72
  • 5. Rational numbers and beyond ..... 74
  • 5.1. Early Egyptian fractions ..... 75
  • 5.2. Counting camels ..... 76
  • 5.3. Bicimals and other numbers ..... 76
  • 5.4. Beyond the rationals ..... 79
  • 6. Polyhedra ..... 80
  • 6.1. Spinning the cube ..... 81
  • 6.2. Slicing the cube ..... 82
  • 6.3. Filling the cube ..... 83
  • 6.4. What are the Platonic solids? ..... 83
  • 6.5. Symmetries of the Platonic solids ..... 84
  • 6.6. The symmetries of a marked cube ..... 88
  • 6.7. Semi-regular solids ..... 88
  • 7. Group theory ..... 93
  • 7.1. Dancing squares ..... 95
  • 7.2. Isomorphism ..... 96
  • 7.3. Four properties defining a group ..... 7
  • 7.4. The Latin Square property ..... 98
  • 7.5. Subgroups ..... 99
  • 7.6. Cosets ..... 100
  • 7.7. Lagrange’s theorem ..... 101
  • 7.8. Revisiting the marked cube ..... 101
  • 7.9. Cyclic groups and cyclic subgroups ..... 102
  • 7.10. Two proofs ..... 103
  • 7.11. Hexagon symmetries ..... 105
  • 7.12. More about inverses ..... 106
  • 7.13. Groups with six elements: how many are there? ..... 106
  • Conclusion ..... 111
  • References ..... 113
  • APPENDICES
  • Appendix 1 Mayan number puzzle ..... 125
  • Appendix 2 Symbol sequence cards ..... 126
  • Appendix 3 Grid multiplication puzzle ..... 128
  • Appendix 4 Squares, triangles and hexagons – from Smile 1734 ..... 130
  • Appendix 5 Proof that there are only eight semi-regular tilings ..... 131
  • Appendix 6 Proof for two tiles ..... 133.

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