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 (ObjectsPictures-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 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.