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Growing in Math Fact Fluency-Planning and Delivering Interventions that Work

  • by Kelly Harmon
  • Nov. 11, 2020, 9:35 a.m.

By Ann Elise Record

In my consulting work, I’m frequently asked about how interventionists can structure their limited time with students to be the most impactful. There are two areas of content that I think are often not given enough instructional time that can be incredibly powerful and positively affect students’ achievement as well as their disposition: fluency and word problem structures. It’s all about finding out the students’ strengths and then building on them. In this post, I’ll be focusing on fluency and next month I’ll delve into word problem types.


Beginning to Learn Math Facts

Traditionally, students’ math fact journeys have begun with our students in the counting phase of reasoning. So, when asked to add two amounts, they will use objects or fingers to show both of the amounts and then begin counting them all beginning at 1. Then, students develop the understanding of groups. They begin to “count on” starting with the amount of the larger group and counting up to the other addend. A big step at this stage is recognizing the efficiency of counting on from the larger addend. At this point, many students are then asked to memorize the math facts using games and activities with all their facts. Unfortunately for many, they aren’t able to memorize the facts, so they continue counting on and thus are only in a counting phase of reasoning. This is actually extended to their work typically when working with multi-digit computation if they are using algorithms.


What is Fluency?

When teachers are expected to report out to parents on the progress of their children on mastering their math facts, often the students are given timed tests, because fluency has been narrowly defined as speed and accuracy. There are many issues with this, not the least of which is that it has repeatedly been shown to be the start of math anxiety. There are many long lasting effects on self-efficacy throughout students’ lives. Fluency is so much more than speed and accuracy. It includes flexibility and efficiency as well. The more we provide opportunities for students to flexibly work with numbers and use derived facts to help them solve the ones they don’t know, the more their number sense will develop and their speed and accuracy will naturally improve as well. Additionally, they will be moving from using counting strategies into additive reasoning.


Using Math Running Records to Determine Starting Points and Growth

But where do we start with our students who have been identified as being “behind”? My favorite assessment tool for knowing exactly where a student needs to begin working is a Math Running Record created by Dr. Nicki Newton. After 10 years of pouring over the math fact research, as well as her own action research, the Dr. Nicki has developed a math interview that provides us data on all 4 aspects of fact fluency: accuracy, flexibility, efficiency, and relative speed (although the students have no idea we are keeping track of the time it takes to say an answer). With an interview protocol for each operation, the Math Running Record allows us to zoom in on exactly which set of facts are causing super slowdown, inaccuracies, or inefficient strategies and then to determine where the students are on the levels of strategies such as counting, mentally using counting strategies, using derived facts, or having mastery with understanding.


Benefits of a Math Running Record

Armed with the information gained during the interview, we can then provide targeted explorations and activities that will meet the students where they are and help move them forward. The huge bonus to this is that not only will students be mastering their math facts, but they will be developing a foundation of strategic thought that can then be applied to the content expectations of their grade level. If you want to learn more, the free Math Running Record recording sheets can be downloaded at www.mathrunningrecords.com. I also facilitate the Facebook group called Math Running Records with hours of content and support available to you. Here’s a video of me administering an addition interview one with an adorable first grader.


Now What?

During your intervention time, you will want to explore these strategies in concrete, pictorial, and abstract ways. Dr. Nicki Newton, Dr. Alison Mello, and I have written a book called Fluency Doesn’t Just Happen with Addition and Subtraction (we are currently writing the companion Multiplication and Division one) that provides you tons of ideas.


I have created a fluency padlet full of explanatory videos, resources, and links to lots of free websites with fabulous activities and games. You can access it at www.anneliserecord.com/free-resources. Just this week, the KY Center for Mathematics released a companion website to Jennifer Bay-Williams and Gina Kling’s Math Fact Fluency book. There are games to print as well as Jamboard versions! You can find that site here: http://kcm.nku.edu/mathfactfluency/


I provide virtual trainings on Math Running Records as well as Fluency Games and Activities. If you would like to know more, feel free to email me at [email protected].


Ann Elise is the co-author of Fluency Doesn't Just Happen with Addition and Subtraction. If you would like to learn more about fluency or problem solving and how we can implement them within the structure of Guided Math, please join Ann Elise in December for her all day seminar for the Bureau of Education and Research.



Kelly Harmon and Randi Anderson

About The Authors

Kelly Harmon & Associates began in 2001 with a mission of instructional coaching and providing rich literacy resources for educators and parents. Our work incorporates research-based best practices for teaching and learning.

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