The following is an excerpt from the Building Fact Fluency: A Toolkit for Addition & Subtraction Facilitator’s Guide by Graham Fletcher, coming this fall.
To this day, I can still remember sitting in the back of my dad’s pickup truck, flipping through a stack of flashcards on the way to soccer practice. I must have been about seven or eight years old, because the cards were addition and subtraction facts, not multiplication. We were about twenty minutes away from soccer and I was done practicing facts for the day, so I placed a rubber band around the stack and tossed it to the side. Little did I know, I was not done practicing my facts.
Dad: Are you done?
Dad: Do you know them all?
Dad: Okay . . . Fourteen minus eight. (He always went for the hard ones first.) I held up eight fingers and began counting backwards from fourteen (“thirteen, twelve, eleven . . .”) as I knocked down a finger for each number I counted.
Dad: Way too long. You need to know these, Graham. Sixteen minus nine. I held up nine fingers, but I hid them behind the driver’s seat as I went to work.
Dad: Are you counting again? You need to work harder at memorizing your facts.
At that time in my life, “memorize harder” made complete sense. When I look back now, I think the Mission Impossible team had a far easier task than what my dad was asking of me. I was trying to learn each fact in isolation—more than two hundred individual addition and subtraction facts. I wasn’t encouraged to think about the relationships between the numbers, or make connections across different number combinations, or explore the properties of addition and subtraction. I wasn’t empowered to break those numbers up and put them back together in ways that made sense to me. I wasn’t celebrated for starting from what I knew or encouraged to build understanding from there. I was just supposed to know the answer and say it right away, without thinking.
Fast forward a few decades. As a teacher, I tried more than my fair share of activities, routines, gimmicks, and tricks to help my students learn their facts. From mnemonics to mad minutes, from flipping flash cards to spending hours at the photocopier printing class sets of worksheets, I tried it all. Sure, I would add new twists to old habits, but the results were always the same. Students seemed to know their facts on Friday, but they forgot them over the weekend and were back to square one on Monday. Some students would practice and practice, trying songs or tricks or endless sessions with the flashcards, but they just didn’t lay those facts down in their memories. Or students would recall their facts when quizzed on them but, when solving problems, they would count instead. They didn’t seem to trust those facts they’d memorized, no matter how often they wrote them on worksheets. Other students could spit out those memorized facts all day long, but then wouldn’t know whether to add or subtract in a word problem. Does any of this sound familiar?
I understand why I expected my students to learn their facts through memorization: because that’s the same way I was expected to learn my facts. Unfortunately, I struggled as a math student because my own understanding was built on a shaky foundation. When I asked my students to learn their facts using the same techniques that I had used, I was building the same shaky foundation for my students. I was repeating the cycle.
More recently, as an elementary and middle school coach, I have seen how that foundation collapses for kids later on. For years, teachers have been asking students to memorize their math facts, and to this day, the most common complaint I hear from intermediate and middle school teachers is, “My kids aren’t fluent with their basic facts.” After spending countless hours in classrooms across the grades, I have come to understand three things clearly:
- Students need to be able to know and use their facts in the midst of more complicated problems without losing track of their thinking (but you knew this).
- Many students who can say their single-digit facts don’t use them effectively or flexibly when solving problems.
- Students who aren’t given enough opportunities to uncover the properties of numbers and operations have trouble identifying relationships and making meaningful connections later on.
These observations aren’t new. Many educators and researchers have noticed these same things and studied them in depth. My editor, Tracy Johnston Zager, and I have learned a tremendous amount by reading articles and books and interviewing scholars as we built this toolkit. There is honestly a ton of research on fluency out there, and we’ll be summarizing and citing some of that research throughout this facilitator’s guide. Our goal with Building Fact Fluency is to create a resource that puts existing research to use in a practical and accessible way. I (Graham), am not a researcher—I’m a teacher, coach, and math specialist who has been creating multimedia classroom activities and tasks for several years now. Tracy is a coach, author, editor, and all-around nerd who loves digging into the literature. What you’re holding in your hands is our team effort to design comprehensive, user-friendly, engaging materials supported by research. We have had many wonderful conversations while building this toolkit, and we’ve captured our shared thinking by writing this facilitator’s guide together (hence the we you’ll hear most of the time).
As you take this journey with your students, we hope you’ll begin to see the development of fact fluency not as a chore, but as an opportunity for your students to engage in important mathematical thinking, and for you to listen to and build on your students’ brilliant ideas. This toolkit will help you develop your students’ deep conceptual understanding of the operations through rich tasks, strategy discussions, contextualized practice, reflection, and engaging games. That’s right—your students will be accumulating their number facts at the same time as they are working on the operations and discovering the fundamental properties of arithmetic. Fact fluency is not an add-on—it’s an integral part of learning arithmetic with deep understanding.
For more information and to download free samples of Building Fact Fluency: A Toolkit for Addition & Subtraction, visit Sten.pub/GrahamFletcherSignUp.
About the author
Graham Fletcher has served in education as a classroom teacher, math instructional lead, and currently as a math specialist. Graham's work with the math progressions and problem-based lessons has led him to present throughout North America and beyond.
Building Fact Fluency: A Toolkit for Addition & Subtraction