Before you get into the video, I’d like you to download this image and if, after watching the video, you agree that we need to switch to these alternatives please share this image and tag me (@BuildMathMinds).
I’d also love to hear if you have any additions to these 10.

So we’ve all seen kids who can memorize and regurgitate math facts and solve multi-digit problems using algorithms with what looks like ease. But then you ask them to solve a problem like 100 minus 98, and they have to set it up using the algorithm.

I’m Christina Tondevold, The Recovering Traditionalist, and today we are going to talk about how fast does not mean fluent in our quest to build our math minds so we can build the math minds of our students. 

Watch the video or read the transcript below:

Here are links to products/activities mentioned in this vlog. (Some may be affiliate links which just means that if you do purchase using my link, the company you purchased from sends me some money. Find more info HERE about that.)

Build Math Minds Facebook Group

Building Math Fluency Through Games

Math Running Records video

Howard County’s website (click on your grade level and then browse around the ‘Course Essentials’)

Number Sense Routines books: K-3rd and 3rd-5th

Choral Counting & Counting Collections Book

Steve Wyborney’s site

Berkely Everett’s Math Flips Flashcards

Watch all the videos in this Fluency Series:
Video 1: Fast Does Not Mean Fluent (This video)
Video 2: Helping Kids Learn Their Math Facts
Video 3: Math Experiences That Build Fluency, Not Memorization 
Video 4: Students with Math Fluency
Video 5: The Importance of Visuals in Math
Video 6: The Root of Math Fluency 

The Pressure to Be Fast

I get why we all have this sense of associating the word fluent with fast. It is even in the Common Core Progressions. When you look into that document, they talk about how when they use the term fluent in the Standards, that means fast and accurate.

Now, they go on to describe how kids are using some facts that they just know, they’re using patterns, they’re using strategies, but they do use that term fast and accurate. Plus almost all assessments we have for mathematics are assessing those 2 things. Are the kids fast and are they accurate? But that’s really not what fluency is all about. Sure, those are 2 parts of being fluent, but the third part, which is honestly the most important part, is about flexibility.

Oh man, I was that kid, who when I grew up, I could regurgitate my math facts. I knew them memorized. I could solve any problem you wanted as long as I had an algorithm to be able to solve it, but when you would give me a contextual problem, like a word problem, I would shut down. If you asked me to solve it mentally, I really did not have any other way except the algorithm. Like I needed paper and pencil. I wanted to stack problems in my head to solve it mentally. I did not have any flexibility. If I knew it from memory or I knew the procedure to be able to solve it, I was fine, I was golden. But when it was a unique problem or one that I didn’t instantly know the answer to, I would shut down. And there are so many kids who are the same way and there are so many adults that have those same reactions, but in a bad way, because they weren’t able to memorize their facts, they weren’t able to remember these procedures and use them with “fluency.” 

But you can see these comments from people inside of the Build Math Minds Facebook group about how, when we are focused on that fast and accurate piece, through timed tests, through multiple problem worksheets where we are focusing on just getting kids faster and more accurate, it really makes them feel like they are not good at math. And so if it is harmful for just one student, is that really something we want to continue doing? Sometimes we are pushing this fast and accurate piece because we have that pressure of the testing that we have to get kids towards. Or in our Standards we see that term fluent. 

Every grade level, from Kindergarten to 6th grade, has at least one standard that uses the word fluent or fluently. So often we have associated, where it says fluent, we replace that instantly with fast. But I don’t want you to use that word fast anymore as a replacement for fluent. What really makes someone fluent is fast and accurate, but also that flexibility. In all things in our life, if we do not have all 3 of those, we are not truly fluent. 

I want you to take a moment and think about something you are fluent in and then something you are not in your personal life. It doesn’t have to be reading. It doesn’t have to be math. Okay, it needs to be something in your personal life. I’m going to give you an example of one that I am not fluent in. I am not a fluent chef. I am fast and I am accurate when I am cooking. I am quick with what I’m doing and I can follow a recipe to a T, but I am not technically fluent because the thing I lack is flexibility. If I see a recipe and I am missing one of those ingredients, I cannot make that recipe. I’m also not the kind of chef who looks at the recipe and says, “Oh if I just add a little bit of this “or a little bit of this, it would make it so much better.” I am not that kind of chef. So I am not a fluent chef. I can cook, but I have to follow a recipe and the same thing is true in all of our things in life. We are not truly fluent unless we have that 3rd piece of being flexible. 

I’ve heard another scenario of learning another language like if you are fluent in another language, it’s not just about how fast you are. Yeah, you do need to be accurate and you want to be fast so you can speak fluently, but the other piece of being fluent in a language is being flexible and knowing when to use certain words and in what situations. I could say words in French, but am I using them in the right instances? That’s a big piece of that flexibility. 

So, I want you to be able to see it beyond just mathematics, that that flexibility piece is really really important. But so much of the instruction that we do in mathematics is very well-intentioned, right. We are doing the best we can with the knowledge we have at the time to help our students. And I know that if I had a struggling student or if one of my own personal kids was struggling, I would do anything in my power to help them. But sometimes, we just don’t know what to try and so we’re left with these ideas and activities that have been around awhile, but are sometimes harmful for our students.

Alternative Ways to Build Math Fluency 

So I’ve created this little infographic that I want you to share out there about what it actually means to be building fluency. What are the kinds of activities that we do that build fluency and what are the things that we’re doing that do not build fluency?

Now, do not feel bad if you have done things that are in the column of the does not build fluency because I have done every single one of these things. They were all, again, well-intentioned. I was doing the best that I could for my students with the knowledge I had at the time. But when I became well-informed, along with my well intentions, things changed dramatically for me as a teacher and me personally as a learner of mathematics. 

I want you to share this out, but I’m also going to talk just really briefly about each one of these and I’m sharing 10 alternatives. This is not meant to be an end all, be all document. This document is meant to be the start of a conversation. So what I would really love to see is to have you share this out and then make a comment about what you would add onto this. Do you see something out of this document that’s maybe not on there? What would you like to see added into it? It’s the start of the conversation, not the end of the conversation.

Building Number Sense NOT Memorization

Alright, let’s take a look at each one of these. So the first one is about memorization. Now, what’s very interesting is I want you to take a look at your Standards because oftentimes, we think that kids need to memorize, but what the Standards say is know from memory and there is a big difference between know from memory and memorize. 

I can memorize something for a short period of time, but knowing something from memory is being able to recall it easily when I need that information and one of the best ways to be able to do that in mathematics is building a sense of numbers for students. The more connections they have around numbers, the easier it is to pull that information from our mind when we need it. That’s the way that we are able to recall information is by the more connections that we have, associated with that content. So instead of memorization, we want to encourage kids to know from memory by helping build their number sense.

Hands On Manipulatives NOT Bare Equations

Okay, the next one that I see a lot and I’ve done a ton too is having kids only solve equations, just the bare like problems on a piece of paper. And instead, what really helps build fluency is doing lots of hands-on activities for our students. It doesn’t matter if you’re working on addition, subtraction, multiplication, division, working with fractions, decimals. To build true fluency, build that flexibility, kids need to get in there and see it in a concrete form, not the abstract form of just the equations. 

Games NOT 100 Problem Worksheets

Another piece is that once kids start learning this stuff and we want them to practice, one of the old behavior that we, that I used to do is that I would give them worksheets that was just a bunch of bare problems, like 100 problems on a worksheet and have them just go through and solve it and practice it. But instead, I want to encourage you to find games and I’ve got other posts out there about games, but games are a quick way to do practice and in 5 minutes, kids might be solving 100 problems and it’s the same 100 problems that they might’ve solved on a worksheet, but they’re engaging with their peers, they’re talking with their peers, and they’re having fun while doing it. Okay, so if you need practice, instead of the worksheets, let’s try games. 

Formative Assessments NOT Timed Tests

Another thing that we have done in the past is timed tests. Yes, we need to assess students and ensure that they are becoming fluent, but timed tests only assess fast and accurate. All it looks at is how many are they getting in a certain amount of time? If we really want to assess true fluency, then we also need something that assesses that flexibility. There’s a lot of stuff out there about using formative assessments even when it comes to fact fluency, things like math running records, there’s stuff on Howard County’s website. 

We’ll link to some of that stuff below, but there are definitely some wonderful alternatives to timed tests because times tests really put that pressure on kids and we do want them to become faster and more accurate, but we also want them to see that their flexibility and their thinking strategies do matter and that needs to show up in our assessments as well.

Number Sense Routines NOT Singing Songs & Skip Counting

Another common practice is singing songs, doing skip counting and while these are fun and they, you know, they’re fun to do in class, it really does promote just this rote memorization. So instead, I want to encourage you to do a number sense routine in place of those. There’s wonderful routines in the Number Sense Routines books. You can Google them. Some of my favorites are counting collections and choral counting, anything by Steve Wyborney. There’s all kinds of wonderful number sense routines that can be great alternatives to singing songs and skip counting.

Interactive & Visual Flashcards NOT Traditional Flashcards

Another thing that I know I used to do and personally I used to love in school because I was good at this memorization, I loved the flashcards and any activity that had to do with flashcards like that Around the World when the teacher would flash the card and we would be racing, you know, with the person next to us in the chair, but that was so damaging to some of our students, right. I think back to some of the kids that were in my class who never got to move forward in those Around the World activities. I was the kid who always would move across because I could memorize and I was fast, but I was not a good thinker. 

Again, remember these are well-intentioned things. We’re doing the best we can with the knowledge we have at the time, but there’s some great new alternatives to the traditional flashcards. There’s some great flashcards out there that are very interactive and very visual. If you’re not familiar with Berkeley Everett’s Math Flips, grab the link below the video. It’s one of my favorite new alternatives to traditional flashcards. 

Students Exploring Strategies with Visuals NOT Teachers Describing Strategies to Kids

Now another thing that happens where we’re trying to build fluency is that we describe these strategies. So an example for basic facts, but this works even when you’re doing multi-digit addition, subtracting, multiplication, division, we will see something like 6 + 7. We’ll tell kids like when you see 6 + 7, it’s a 6 + 6 + 1 more. It’s a doubles plus one. Let’s learn it, know it, let’s use it. 

Kids don’t get it from just us describing those strategies. They need to explore those strategies through visuals by using ten frames, by using Rekenreks, and yes you can use ten frames and Rekenreks to help with multiplication strategies as well. By using the area model and arrays. Those visuals make those strategies come to life for students so we aren’t the ones describing it. They can visually see it right there in front of them and help them make sense of those strategies. 

Using Number Relationships NOT Using Tricks

One thing that I know I used and I just think back and think, oh my gosh, what did I do to my students? But now I know better. One of the big things was using tricks like when you’re telling kids to multiply by 10. Just add a zero to it, but then when they go to multiply with decimals, adding a zero does nothing. Or the finger trick for the 9. What do you do when you have to do 9 x 12, right? 

These tricks last for a moment, but they don’t last long-term. So instead, I want to encourage you to use strategy-based activities. There are strategies for developing your x 9 that will last even when they’re doing 15 x 9. So really look into these strategies and do activities that help build these strategies for your students.

Strategy Based Activities NOT Learning Facts in Numerical Order

And that leads us into having students do strategy-based activities instead of learning their facts in numerical order. Now what I mean by this is typically when we’re learning addition facts, we will have kids learn it in a way that is like let’s learn our plus ones, our + 2, our + 3. And instead, I want to encourage you to focus in on strategies. 

So here’s a chart for addition that highlights ones that students tend to gravitate more towards and they learn faster than others. So like the doubles, the facts that make a 10, the 10 plus somethings are the blue ones. Those are things that kids will naturally learn first and then we can focus in on helping kids build strategies around those, so if they know 3 + 7 is 10, 4 + 7 can be derived from that by using strategies. So it helps kids see connections instead of seeing things in isolation. And the same thing holds true when you’re working with multiplication. There are certain facts that kids will gravitate towards and they’ll be able to know faster, but we can use those to help them use the other facts. 

So the darker colored ones are the ones that kids gravitate more towards and then the lighter versions of those are the ones that we can help use those strategies and build connections instead of having kids just learn their times zero, x 1, x 2, x 3, x 4, x 5, have them learn x 5. I’m not saying you have to start with 5, but once they learn their x 5, how does that help them with knowing x 6 and x 7? That’s really what we want to focus in on is helping them have strategy-based activities instead of just learning their facts in numerical order.

Personal Journal of Student’s Development NOT Public Displays of Goal Progress

The last one is the public display of students who have or have not met a goal. And I’m talking about the ice cream sundaes, the race car to the end, meeting your goal. Those kinds of displays of students’ success and non-success just help to reinforce this idea of I’m bad at math and that kid is good at math all because they know their times tables and I don’t know my times tables or whatever the goal is that you’re wanting them to get. 

It is totally fine to have goals, but the alternative I want to recommend to you is have each child have a personal journal that documents their development. I am not against having a chart for each kid and having them graph their growth along the way, but it needs to be private, between you, them, and even their parents, right. We want each kid to feel that success, but when they are being always kind of comparing themselves to the other kids in the class, it’s hard to acknowledge their own personal development along the way. 

So let’s keep that private. Put it into a journal for them to know the things that they have mastered and the things that they have not mastered. And again, what is that mastery? It comes back to our alternative. It’s not about the timed tests. It’s about those formative assessments, looking at the strategies and really encouraging kids to build their flexibility and the by-product of them building their flexibility is that the fluency will come from it. But if we are focusing on just building fast and accurate kids in mathematics, they start to divide themselves between those who are good at math and those who are bad at math and they’re also not building their flexibility. Those kids who are seen as good at math are just fast and fast does not mean fluent. 

So let’s change our definition of what fluency is and let’s start using some of these alternatives in our classrooms. And again, share this out on social media. Tag me @BuildMathMinds on Instagram and Twitter. Share it out there on Facebook. I want to see what other alternatives you guys have as well because remember, this is not the end of the conversation. This is just the start of how we start changing our instruction to build more flexibility and put the emphasis of fluency on the flexibility part of fluency, not just the fast and accurate. Alright, I hope that this helped you build your math mind so you can go build the math minds of your students. Have a great day.

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