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From Number Sense to Invented Strategies: Going the Extra Mile as a Teacher

Review of Concepts. Number Sense: Defined by the characteristics of those who possess It"Holistic examination of the problemLook for relationships and consider contextRely on their own understanding (choose or invent)Use BenchmarksRecognize unreasonableness. Attempt at Defining. Number sen

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From Number Sense to Invented Strategies: Going the Extra Mile as a Teacher

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    1. From Number Sense to Invented Strategies: Going the Extra Mile as a Teacher ACUMEN: Elementary Breakout June 25, 2005 David S. Allen Melisa Hancock

    2. Review of Concepts Number Sense: Defined by the characteristics of those who possess “It” Holistic examination of the problem Look for relationships and consider context Rely on their own understanding (choose or invent) Use Benchmarks Recognize unreasonableness

    3. Attempt at Defining “Number sense can be described as a good intuition about numbers and their relationships. It develops gradually as a result of exploring numbers, visualizing them in a variety of contexts, and relating them in ways that are not limited by traditional algorithms.” (Van de Walle, 2005)

    4. Gratuitous Quote “No substitute exists for a skillful teacher and an environment that fosters curiosity and exploration at all grade levels.” Hilde Howden Arithmetic Teacher, Feb., 1989, p.11

    5. Four Relationships for Early Numbers 0-9 Spatial Relationships

    6. One More/Two More/One Less/Two Less 6 7 8 Four Relationships for Early Numbers 0-9

    7. Anchors to 5 and 10 Four Relationships for Early Numbers 0-9

    8. Four Relationships for Early Numbers 0-9 Part-Part-Whole

    9. NCTM Stance on Facts “Knowing basic numbers combinations – the single-digit addition and multiplication pairs and their counterparts for subtraction and division—is essential.” NCTM, Principles and Standards, p.32

    10. A Three-Step Approach to Fact Mastery Develop a good understanding of the operations. Help students devise efficient strategies for fact retrieval. Practice the use of their efficient strategies.

    11. Basic Fact Remediation in the Upper Grades More drill is never the answer. Find out which specific facts are known and unknown. Diagnose to determine strengths, weaknesses, and current strategies. Provide hope. Build success into the remediation plan.

    12. Place-Value Triangle: Connecting Concepts with Oral and Written Forms.

    13. Close, Far, In-between

    14. Gratuitous Quote “Equally essential [with basic facts] is computational fluency – having and using efficient and accurate methods for computing. Fluency might be manifested in using a combination of mental strategies and jottings on paper or using an algorithm with paper and pencil, particularly when the numbers are large, to produce accurate results quickly.”

    15. Contrasts:

    16. Why Invented Strategies? Base-ten concepts are enhanced. They build on students’ understanding Fewer errors are made. Promote mathematical thinking. They serve students about as well on standardized tests.

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