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  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.

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.

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.

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.

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.

If not by the end of 4 th 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.