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Arithmetic

Arithmetic. Is the study of relationships between numbers, through the actions of numbers on objects (including numbers themselves). The Place of Generality. A lesson without the opportunity for learners to generalise mathematically, is not a mathematics lesson. Conjecturing Atmosphere.

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Arithmetic

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  1. Arithmetic • Is the study of relationships between numbers, • through the actions of numbers on objects • (including numbers themselves)

  2. The Place of Generality • A lesson without the opportunity for learners to generalise mathematically, is not a mathematics lesson

  3. Conjecturing Atmosphere • Changing your mind is evidence of mathematical thinking! • Things are said with the intention of modifying them • Being ’stuck’ is an honourable state!

  4. Some Mathematical Powers • Imagining & Expressing • Specialising & Generalising • Conjecturing & Convincing • Organising & Characterising

  5. Some Mathematical Themes • Doing and Undoing • Invariance in the midst of Change • Freedom & Constraint • Extending & Restricting

  6. Affordances • What does that task offer? • Opportunity to … • Use and develop my powers • Encounter mathematical themes • Experience useful concepts (through suitable variation) • Experience effective procedures(through suitable variation)

  7. Concrete-Pictorial-Abstract • C-P-A • E-I-S • M-G-A

  8. Attention • Holding Wholes (gazing) • Discerning Details • Recognising Relationships • Perceiving Properties • Reasoning on the basis of agreed properties

  9. Inner & Outer Aspects • Outer • What task actually initiates explicitly • Inner • What mathematical concepts underpinned • What mathematical themes encountered • What mathematical powers invoked • What personal propensities brought to awareness

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