What Exactly is Math Fluency Anyways?

Written by Shelly Read, Curriculum & Instruction Facilitator

"Guided Math and Running Records" session with Dr. Nicki Newton through CRC

A few years ago, as part of our curriculum redesign journey, I had the opportunity to meet with math professors from the University of Lethbridge to discuss student learning. The conversation centred around their valid concern that students were struggling in university math courses, mainly due to a lack of number fluency. As Bjorklund et al found back in 1990, “student brains are exhausted with these ‘small things’ and so can't work on the more complex problems”. This conversation has stuck with me and is one lens I use when designing math with a focus on conceptual learning. Although we know not ALL students go to university,  we also recognize the importance of understanding numbers in our everyday lives and the world of work.

So, what are these ‘small things’ that provide evidence that students know and understand
the ‘basics’ of basic facts?

There are four pillars around math fluency that teachers should consider:

1. Automaticity

• Can students recall the answer instantaneously or do they have to stop and

think?

• As a general rule, automaticity is answering in 2-3 seconds without thinking

about it or hesitating.

• No actual timer should be used by the teacher.
• 
  

2. Accuracy

• Teachers should consider both a student’s oral and written responses.
• Does the student self-correct if they provide an incorrect answer?
• Be aware of counting strategies a student may use to solve facts mentally,

such as finger counting or counting in their head.

3. Flexibility

• Flexible thinking about numbers reveals a student’s depth of understanding.
• Does the student have a variety of strategies at their disposal?
• Teachers and students, as mathematicians, should know the names of the

strategies they are using.

4. Efficiency

• Students have a repertoire of strategies to choose from and choose the best

one for the situation.

• Students may have more developed strategies but often resort back to simple

methods.

• Both the teacher and the student should monitor progress and use of the most

appropriate strategies.

Together, these four criteria are used by students when they develop their individual
mathematical disposition. Having math talks with individual students is invaluable, as it
“provides teachers with a richer portrait of who they are helping to learn.” (p. 17)

In her book, Math Running Records in Action,Dr. Nicki Newton has created a framework
teachers can use to assess basic fact fluency that goes beyond memorization or speed and
instead helps to make students’ thinking visible by providing evidence of the child’s
computational thinking. “Designed to go way beyond merely capturing answers, these
assessments reveal how students are arriving at solutions, where they are breaking down,
and how they feel about themselves in the context of math. Ask yourself, can a timed test
do all that?” (page xiii)