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Cognitively Guided Instruction

Cognitively Guided Instruction. Using Story Problems to Develop Mathematics Knowledge. Operation Sense. Developing meanings for operations Gaining a sense for the relationships among operations Determining which operation to use in a given situation. Operation Sense.

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Cognitively Guided Instruction

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  1. Cognitively Guided Instruction Using Story Problems to Develop Mathematics Knowledge

  2. Operation Sense • Developing meanings for operations • Gaining a sense for the relationships among operations • Determining which operation to use in a given situation

  3. Operation Sense • Recognizing that the same operation can be applied in problem situations that seem quite different • Developing a sense for the operations’ effects on numbers • Realizing that operation effects depend upon the types of numbers involved

  4. What factors influence how students reason in story problem contexts? • Types of problem structure • Types of numerical relationships within problems, and • Context of the problem and of the number choices (sizes of numbers/kinds of quantities) used

  5. Cognitively Guided Instruction Looking at Problem Structures and Numerical Relationships

  6. Which of These Problems Would be Most Difficult for First-grade Students? Examine the problems on Appendix B. • Assume the problems are read aloud to the child as many times as needed. • Assume the child has a set of counters they can use to help them. • Assume the child has a much time as they wish to solve the problem.

  7. Which of These Problems Would be Most Difficult for First-grade Students? Examine the problems on Appendix B. • Circle “A” if Problem A is harder than Problem B. • Circle “B” if Problem B is harder than Problem A. • Circle “E” if the problems are of equal difficulty.

  8. Which of These Problems Would be Most Difficult for First-grade Students? • E • B • B • B • A • E • B • E

  9. How are these three problems alike? Different? • Lucy has 8 fish. She wants to buy 5 more fish. How many fish would Lucy have then? • TJ had 13 chocolate chip cookies. At lunch she ate 5 of them. How many cookies did TJ have left? • Janelle has 7 trolls in her collection. How many more does she have to buy to have 11 trolls?

  10. Willy has 12 crayons. Lucy has 7 crayons. How many more crayons does Willy have than Lucy?

  11. 11 children were playing in the sandbox. Some children went home. There were 3 children still playing in the sandbox. How many children went home?

  12. Reflect • How do these last two problems compare in difficulty to the three problems we just saw and discussed?

  13. Problem Structures • Examine the set of “Marble Problems”. • Sort the “Marble Problems” into sets of problems that seem to be related. Be able to explain how you think the problems are related.

  14. JOIN – The action in these problems is a joining of two sets. Start ------>Change------>Result The unknown quantity can be either the result, the change, or the start.

  15. SEPARATE: The action in these problems is taking a subset out of a set. Start ------>Change------>Result The unknown quantity can be either the result, the change, or the start.

  16. Part-Part Whole: There is no action. A set (whole) with defined subsets (parts) is described. The unknown quantity can be either one of the parts or the whole. Whole Unknown Part Unknown

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