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.