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Enhancing Mathematics Understanding Through Story Problems and Operation Sense

Explore how story problems help develop mathematics knowledge and operation sense in students by understanding problem structures, numerical relationships, and types of operations. Identify factors influencing student reasoning in mathematical contexts. Examine problem sets to determine difficulty levels and similarities. Classify problems based on their structures such as Join, Separate, and Part-Part Whole.

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Enhancing Mathematics Understanding Through Story Problems and Operation Sense

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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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