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Computation Fluency

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Computation Fluency ... Adaptive Reasoning Capacity for logical thought, reflection ... Multiplying and dividing Learn about area and array models for ... – PowerPoint PPT presentation

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Title: Computation Fluency


1
Computation Fluency
  • A spectrum of learning over grades

2
The Goal
  • The goal of computational fluency is to become
    proficient at solving everyday problems.

3
What it takes
  • To become proficient at solving everyday
    problems, students must recognize the operation
    that is required to solve the problem they must
    understand the concepts of operations and place
    value.
  • They must also develop fact fluency.

4
Five Components of Mathematical Proficiency
  • Conceptual Understanding
  • Comprehension of mathematical concepts,
    operations, and relations.
  • Procedural Fluency
  • Skill in carrying out procedures flexibly,
    accurately, efficiently, and appropriately.
  • Strategic Competence
  • Ability to formulate, represent, and solve
    mathematical problems.
  • Adaptive Reasoning
  • Capacity for logical thought, reflection,
    explanation, and justification.
  • Productive Disposition
  • Habitual inclination to see mathematics as
    sensible, useful, and worthwhile, coupled with a
    belief in diligence and ones own efficacy.

5
Students go through stages in their computational
fluency
  • Recognize situations that call for adding,
    subtracting, multiplying or dividing (for
    situations involving fractions and decimals too).
  • Use simple counting strategies to solve these
    problems.
  • Develop more efficient strategies based on number
    sense (compensating, estimating, etc.)
  • Pick up some combinations fluently before others
    using a mix of recalled facts with strategies.
  • Learn about place value.

6
Adding and subtracting
  • Use place value strategies (counting the tens,
    counting the ones)
  • Learn the multi-digit algorithms (based on place
    value and sophisticated strategies)
  • The Concrete-Representational-Abstract sequence
    works well here (Objects-Pictures-Symbols)
  • See CGI Problem Sets, CRA for Multi-digit
    Subtraction.

7
Multiplying and dividing
  • Learn about area and array models for
    multiplying.
  • Generalize area models from 1 digit to 2 digit
    factors.
  • Connect area models to the distributive property.
  • Learn the multi-digit algorithms (based on the
    distributive property).
  • See Multi-digit Multiplication Learning
    Progression, examples resources, and
    Multi-digit Division with examples.

8
If not by the end of 4th grade
  • Teach strategies explicitly and provide at least
    10 minutes per day of additional support if
    needed Math Facts packet, ORIGOMath, PALS Math
  • Practice fluency in middle school and high school
    within all content areas.
  • See IISD Developing Fluency Packets, Origo and
    PALS Math overviews, and math across the
    curriculum ideas.
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