## Or, are they just a piece of a massive, more complex problem?

This past Thursday for our MYCI Planning Meeting WSG Dan Meyer, there was quite a bit of discussion surrounding math facts as a **student learning need**. This is no surprise, as I think we can all agree that this is an area we would like to support our students in. The discussions at each table made it clear to me that we are all passionate about supporting our students in their mathematical journeys. Some of the discussions focused on math facts in general, while others were more specific such as being able to recall multiplication facts or working with fractions. All great discussion with great ideas being carved out along the way.

During our time debriefing the session, Justin Levack threw out a great question that I couldn’t find an answer for.

His question was:

If ______________ (math facts, multiplication tables, fraction fluency, etc.) is the most urgent student learning need in mathematics for a classroom/school/district, what exactly are students being held back from doing?

This was an “ah-ha” moment for me as we often think of our struggling students as those who do not know their math facts. However, maybe we need to zoom out a bit to discuss why these students struggle with math facts in the first place?

Does knowing times tables actually make students better in other areas of math, or is it a result of the students doing something else? Or just one piece of what makes a student strong in math? Sure, many strong math students know multiplication tables, but can we state without a doubt that knowing multiplication tables is the cause and being strong in math is the effect?

Maybe. Maybe not.

What if knowing multiplication tables is the effect of some other factor?

Could it be that having some other skills/abilities makes multiplication facts easier to recall? If so, can we somehow identify these skills/abilities and then spend some of our time focusing on them as well?

While I don’t have the answer, it could be worth a discussion with your MYCI Team, math department and/or professional learning network to determine whether we need to turn more stones to inform how we move forward.

With this, I’ll end with an article that really helped me better define what I would love for my students to be able to do once they leave my classroom:

Fluency Without Fear: Research Evidence on the Best Ways to Learn Math Facts by Jo Boaler, Stanford University.

I think this article does a great job summarizing some of the pieces of our discussion last Thursday and might serve as a starting point as we continue our journey to support students along the math continuum.

What are your thoughts? Let’s keep the conversation going!

## Interesting Tidbits:

After posting this article on Twitter, I liked this response:

```
```@MathletePearce Word up. Math facts are just the canary in the coal mine. Not that hard to master, so… what's the real problem?

— Tilton's Algebra (@tiltonsalgebra) December 8, 2015

Definitely an analogy I will be using in the future.

## Share With Your Tribe:

## About Kyle Pearce

I’m Kyle Pearce and I am a former high school math teacher. I’m now the K-12 Mathematics Consultant with the Greater Essex County District School Board, where I uncover creative ways to spark curiosity and fuel sense making in mathematics. Read more.

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Kyle,

As a teacher who has spent time in elementary and middle school math, this is a question that has dogged me, as well as my peers, for a long time. Does fluency lead to a better understanding of other concepts OR does it just allow us to compute more efficiently which helps us focus more on the task at hand? Also, why do some students commit the basic facts to memory quicker than others? Is it a conceptual understanding, or just memorizing. I have wrestled with these questions for what seems forever. I am currently trying to get my 3rd grade teachers to step away from timed tests because of the anxiety it creates….would love to hear your thoughts!

Jason

Hi Jason,

I’ll tell you, these past few years have had me flying from one end of the spectrum to the other. What I think it comes down to is balance. From what I understand currently, it would seem that having a balance of procedural/fact fluency and conceptual understanding is key to success rather than a one-sided debate.

I’m hoping to share some data I’ve collected soon that should be fun to explore.

Kyle – thanks for the great posts. I remember reading some research by Robin Rutherford in NZ years ago that found a high correlation between mathematical achievement and mental arithmetic skills. Surely some fluency in basic facts, vocabulary and skills give students more freedom to explore higher level problems without the mental burden of having to remember times tables when trying to solve a problem about proportional reasoning (for example)?

Hi Greg,

I think you’re right when it comes to number flexibility. The more digging through research and analyzing data in my own district, the more I see how important it is for students to have a good sense of number at a young age. The data I’ve explored would suggest that identifying gaps early (pre-school and primary grades) and addressing those gaps is our best bet to help students succeed later.

I believe there are two main reasons why many students struggle with fact fluency. First of all, many teachers in the early grades never received training in how to teach fact fluency beyond skip counting or memorization. Without an understanding of strategies that give students access to basic facts, teachers fall back on the way they were taught–skill and drill. This leads to the second reason students struggle–they are forced to “practice” facts that they have not yet learned in a timed situation that causes much stress and anxiety. We’ve tried to back up the train on all this a little bit. Our students and teachers start by watching video tutorials for each fact family that show 3 or 4 different strategies for recalling a fact. The students then choose worksheets that practice the strategies in the video, and then follow links to several internet games where the focus is on fun, not speed. Finally, after all of this practice, students are assessed on their facts, but instead of using a countdown timer, they are given an unlimited amount of time to complete 40 questions. The goal then becomes to improve efficiency. Our hope is with this process, all students can learn their facts–not just the students who are good at memorizing them.

Thanks for the comment, Donna.

I think you might be on to something regarding the strategies (or lack thereof) we use to teach fact fluency. It definitely is important and I think the key lies in how we go about trying to help students achieve that fluency. Balance is huge and being strategic about how we go about the learning is so important.

Thanks again for the comment!

I once took a university course in astronomy and, as part of the course, had to learn and memorize several formulae and facts. To this day, I can recite from memory the formula for calculating the force of attraction between two planetary objects. I can also recite the value of the gravitational constant (another “fact” I had to learn), as well as the masses of the Earth and Jupiter in kg. I can even apply these facts to accurately calculate the force of attraction between those two planets. That said, I really have NO deep understanding of what any of it means! I would argue, then, that simply learning the “facts” does not lead to deep conceptual understanding (in any area of study), and, consequently, cannot be the ‘urgent’ student learning need in math.

I once took a university course in astronomy and, as part of the course, had to learn and memorize several formulae and facts. To this day, I can recite from memory the formula for calculating the force of attraction between two planetary objects. I can also recite the value of the gravitational constant (another “fact” I had to learn), as well as the masses of the Earth and Jupiter in kg. I can even apply these facts to accurately calculate the force of attraction between those two planets. That said, I really have NO deep understanding of what any of it means! I would argue, then, that simply learning the “facts” does not lead to deep conceptual understanding (in any area of study), and, consequently, cannot be the ‘urgent’ student learning need in math.