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Computation Fluency

Computation Fluency. A spectrum of learning over grades. The Goal. The goal of computational fluency is to become proficient at solving everyday problems. . What it takes.

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Computation Fluency

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  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 one’s 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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