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Chapter 02

Chapter 02. The Foundation of All Math Learning:. Representations of Early Number Concepts. Mathematical Routine: Tell me Fast. Mathematical Routine: Tell me Fast. Mathematical Routine: Tell me Fast. Mathematical Routine: Tell me Fast. Mathematical Routine: Tell me Fast.

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Chapter 02

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  1. Chapter 02

  2. The Foundation of All Math Learning: Representations of Early Number Concepts

  3. Mathematical Routine: Tell me Fast

  4. Mathematical Routine: Tell me Fast

  5. Mathematical Routine: Tell me Fast

  6. Mathematical Routine: Tell me Fast

  7. Mathematical Routine: Tell me Fast

  8. Conversation in Mathematics Discuss what the child’s misconception was around the use of tools.

  9. Concrete & Abstract Representations • Pedagogy

  10. What are Mathematical Tools? Often called manipulatives “Manipulatives” can be interpreted as something to play with in your hands whereas “tools” indicate that they are to assist in the learning of a math concept.

  11. Issues Regarding Tools Availability Knowing how to use them Management Free choice or teacher initiated

  12. Constructing Meaning for Tools A tool does not have meaning inherent in it. It must be constructed by the learner.

  13. Moving From Concrete to Abstract Representations

  14. Making the Connections Build Draw Record 27 + 4 (3+1) 10 20+10+1=31

  15. Moving Toward More Efficient Strategies Students share their work Students make connections between different strategies Students decide on most efficient strategies Students try on other students’ strategies

  16. Early Number Concepts • Content

  17. Emergent Phase Numbers Signify quantity Rote Count to 10 with words in order Identify by sight 1-5 objects Beginning to write numerals Know more/less/same and that a change will result in either bigger or smaller (but not by how much)

  18. Counting in the Matching Phase What we look for when assessing/observing 1-1 correspondence how they keep track? do they remember a quantity that they counted? can they pull out a quantity that you ask? cardinality principle direct modeling

  19. Student Interview We will assess the counting skills of two kindergarten students. Identify each of the student’s strengths What is the number range that each student should be working in?

  20. Counting in the Quantifying phase Counting on, counting back Counting in groups

  21. Number Relationships in the Matching Phase More / less - one more / one less Relating one number to another

  22. Number Relationships in the Quantifying Phase Part-Part-Whole (“There are numbers within numbers”) - grab bag subtraction - building 2 color trains - snap it - the tub game Number relationships (doubles/doubles plus one)

  23. The Continuum of Number Concepts Developing from Kindergarten to Algebra

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