## March thinking together: What is computational fluency?

Posted on: May 12th, 2018 by jnovakowski

Computational fluency is defined as having efficient, flexible and accurate methods for computing.

-NCTM, 2000

Computational fluency develops from a strong sense of number.

(BC Math Curriculum, Big Idea, K-9, 2015)

In BC’s redesigned curriculum, computational fluency has been given a heightened emphasis. In mathematics, there are typically four strands of topics/content and in this iteration of our curriculum, a fifth strand – computational fluency –  has been added and this is reflected in the big ideas and curricular competencies and content.

The meta big idea around computational fluency in our BC K-9 Mathematics curriculum is:

Computational fluency develops from a strong sense of number.

There is a big idea for computational fluency at each grade level:

K: One-to-one correspondence and a sense of 5 and 10 are essential for fluency with numbers.
Grade 1: Addition and subtraction with numbers to 10 can be modelled concretely, pictorially, and symbolically to develop computational fluency.
Grade 2: Development of computational fluency in addition and subtraction with numbers to 100 requires an understanding of place value.
Grade 3: Development of computational fluency in addition, subtraction, multiplication and division of whole numbers requires flexible decomposing and composing.
Grade 4: Development of computational fluency and multiplicative thinking requires analysis of patterns and relations in multiplication and division.
Grade 5: Computational fluency and flexibility with numbers extend to operations with larger (multi-digit) numbers.
Grade 6: Computational fluency and flexibility with numbers extend to operations with whole numbers and decimals.
Grade 7: Computational fluency and flexibility with numbers extend to operations with integers and decimals.
Grade 8: Computational fluency and flexibility extend to operations with fractions.
Grade 9: Computational fluency and flexibility with numbers extend to operations with rational numbers.

As computational fluency with whole numbers is focused on in the earlier grades, it is expected that students will apply number sense and computational fluency and flexibility to their work with decimal numbers, greater numbers, integers and fractions.

For addition and subtraction and then multiplication and division, students develop computational fluency over three years – beginning with emerging fluency, then developing through proficiency and then moving on to extending fluency with increased flexibility and ability to apply strategies across contexts and content. For example, with addition and subtraction:

In Grade 3, the curricular content learning standard is “addition and subtraction facts to 20 (emerging computational fluency)“.

In Grade 4, it is “addition and subtraction facts to 20 (developing computational fluency)”.

And in Grade 5, it is “addition and subtraction facts to 20 (extending computational fluency)”.

It is also important to be aware of what comes before and after these three stages of development. In grades 1 and 2, students are introduced to the concepts of addition and subtraction as well as the related symbolic notation. They begin to practice mental math computational strategies building on their understanding of five and ten and decomposing numbers to work flexibly with addition and subtraction questions. In grades 6&7, students apply computational strategies that they have developed for addition and subtraction facts with greater whole numbers, decimal numbers and integers.

There is a similar progression for multiplication and division facts.

A note about memorizing…memorizing is one form of learning but is not necessarily related to students having computational fluency. Many teachers in our district report that their students have memorized their addition or multiplication facts but need support with thinking flexibly and fluently with numbers. In our BC mathematics curriculum, the expectation is that by the end of Grade 3 for addition and the end of Grade 5 for multiplication,  that most students will be able to recall their facts. In a previous curriculum, recall was defined as being able to compute within three seconds. For some students, there may be instant memory retrieval and for other students they may bring the sum or product to mind through an efficient mental computational strategy or associative retrieval process.

Number Talks are an essential instructional routine in developing strategies, mathematical discourse and creating awareness about computational fluency. Key resources include: Number Talks

BC_Computational_Fluency

So some questions to think about…

How would you define computational fluency? What does it look like? sound like?

What do your students need move towards more developed computational fluency?

What do you need to understand more about regarding a continuum of learning and specific strategies related to computational fluency?

What are different ways to develop computational fluency? What instructional routines, games or tasks could we use for practice?

How can we communicate the goals of computational fluency to parents?

~Janice