By: Amy Bilek, K-8 Math Instructional Coach at The Frances Xavier Warde School in Chicago
Think back to your elementary years: Do you remember flashcards, timed tests, or the Around-the-World math game? Most of us learned our basic addition and multiplication facts through rote memorization. Today, we’ll talk about fact fluency programs and how they can drastically help your students with learning.
It is true that mastering math facts is important, however research shows that “drill and kill” memorization is not the best route for students. Focusing on speed and memorization often causes math anxiety for students and may lead them to developing a negative math identity. Students falsely conclude, I’m bad at math because I’m bad at my math facts.
Check out “Fluency without Fear,” to learn more from Professor Jo Boaler on the potential negative effects arising from teaching math facts through speed focused memorization.
What Should We Expect? - Grade-level Fluency Expectations
Below is a chart of the grade-level fluency expectations according to the Common Core Standards. These fluency standards are very tricky to teach because they can not be mastered in a day’s lesson or even one chapter.
These are year-long goals for the students and require consistent, effective instruction and practice.
CCSS Fact Fuency Expectation
Add and Subtract
Add and Subtract
Multiply and Divide within 100
In this blog post, I’m going to outline key steps to setting up a school-wide or classroom-wide fluency program.
3 Steps for a Perfect Fluency Program
First - Create a Shared Understanding of What Fact Fluency Is
It might also help to think about math fluency as meaning the same thing as when we say that somebody is fluent in a foreign language: when you’re fluent, you flow without having to give attention to the process.
Yet, I think it is important to go beyond that and ensure teachers, administration, parents, and students all understand the many facets of fluency. Fluency is not only about speed, it includes being able to flexibly, accurately, efficiently, and appropriately solve problems.
At my school we agreed on the following requirements for fluency:
- Flexibly – learners understand and can execute various ways to solve problems
- Accurately – learners arrive at the correct answer
- Efficiently – within 3 seconds
- Appropriate Strategy Selection – students select a strategy with minimum steps that makes sense for the given problem
Second - Understand the Research on Math Fact Fluency
Arthur Baroody (2006) has done extensive research on fact fluency and outlined the following three phases of a student’s progression when learning the facts:
Our job as teachers is to provide instruction and assessment that helps students through these phases without rushing them. Number talks, basic fact games, and other experiences provide engaging and diverse opportunities for students to use and talk about their strategies.
A good fact fluency plan allows students to move to more efficient strategies over the course of the year, become quicker at applying them, and eventually will develop mastery.
Third - Make A Fact Fluency Plan Rooted in the Research
Help Students Master a Strategy for a Specific Set of Facts
Do not subject any student to fact drills unless the student has developed efficient strategies for the facts being practiced. Thus, begin your work with number talks and discussions on a targeted strategy.
For 1st/2nd graders, you may start with the strategy of “counting on from higher” when adding 1 or 2 more. For 3rd graders, you may start with “doubles” when multiplying by 2.
Practice to Gain Automaticity
Once the student has an understanding of the targeted strategy, practice will strengthen the approach and make students increasingly automatic in their thinking. Whenever possible, make practice engaging and fun.
Utilize games and high-interest activities, and I suggest using games that focus on speed sparingly.
Be sure to organize the practice problems and activities according to the student’s current selected strategy.
Assess to Track Progress and Support When Needed
When we think about assessments on the basic facts our mindsjump to timed tests, yet these often do more harm than good. They can be anxiety provoking and cause students to have negative views of themselves as mathematicians.
I have experienced more success through interviewing. In these mini-interviews, I am making sure to check on a specific set of facts for student’s accuracy and efficiency, but I also ask a strategy question.
After sufficient practice with the “Doubles plus 1” strategy, I may hand a student a notecard like the one below and listen for their accuracy and efficiency.
Then, I would check in on their flexibility and strategy selection by asking, “ If a friend did not know how to solve 6 + 7, what would you recommend?”
2 + 3
3 + 4
8 + 9
For a third-grader completing practice on their 9s strategy, I would check in with this card during a one-on-one brief interview:
3 x 9
5 x 9
9 x 8
6 x 9
9 x 4
What strategy is good for x 9?
Have Students and Teachers Monitor Growth
As this is a year-long goal for students’ learning, I have found it very beneficial if both students and teachers monitor and track progress.
For students, this may be a tracking sheet in which they receive stickers for each strategy mastered and highlight the addition or multiplication table in accordance with the facts mastered. For teachers it may be having each student listed on a row and checking off each fact strategy mastered.
Mastering the facts is not easy for the students or for the instructing teacher. It seems most manageable when you can find about 15 minutes outside the typical math lesson to have students focus on their fluency. This time may be spent with number talks, practice games, or checking in on progress.
In my experience, the benefits of students learning their math facts through a fact fluency program are far-reaching. In working with number talk and strategy selection, students develop deeper number sense. They view the practice games as engaging and fun, and through them develop a more positive view of mathematics.
Further, students enjoy tracking their progress and come to know that hard work leads to growth – thus supporting their growth mindset. While it does take time and effort to roll out a math fact fluency program of this caliber, the benefits do seem to far outweigh the costs.
Van de Walle, John A.; Karp, Karen S.; Bay-Williams, Jennifer M.. Elementary and Middle School Mathematics (p. 192). Pearson Education. Kindle Edition.