A hot topic inside of the Build Math Minds Facebook group is always fact fluency. Recently, Lori posted asking about how children build automaticity in math, and that sparked some heated comments, let’s just say that. 

People are very passionate about helping kids become automatic with their facts. But there’s two very different sides to this debate. I’m definitely leaning towards one side, but I also think we need to find a balance. I’ll give you a little unpopular opinion towards the end, also, about my thoughts that you might not expect from me.

I’m Christina Tondevold, The Recovering Traditionalist and today, we’re going to take a look at How Children Build Automaticity in Math, 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.

Research articles about strategy development versus drill & memorization

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Lori had also asked about research, and I think that this is an important thing that we all become familiar with. So we will post some of the research articles and books that back up what I’m talking about today. 

But I also know, and let’s be brutally honest, most of you won’t do it. Most of us are pretty firmly based in our beliefs. And our belief is based in the way that we learned. You can read all the research you want out there, it’s probably not going to change your mind.

If you learned your facts through memorization, through drill and kill, through flashcards, and you were successful with that, then you believe that is the best way to help kids develop their facts. 

If you were one of those people who learned by memorization, drill and kill, time tests, but you did NOT have success with that, then you believe that there has to be a better way for students. 

Some of you might be like me. I learned through memorization, drill kill, all of that stuff, and I felt like I was good at math. That’s why I went into teaching. Then I realized that didn’t work for all of my kids and I needed to find a way to help those kids out. 

Just yesterday, I was listening to Jenny Bay-Williams and she was encouraging us to get past our personal experiences. 

Just because it worked for you, doesn’t mean it’s going to work for the whole class.

I think that this happens on both ends of the spectrum, whichever way you’re kind of viewing things. I really do want you to keep an open mind, check out the research, and then listen to your students. 

Two Views: Conventional Wisdom vs. Number Sense

So one of the articles that I’m gonna post a link to is by Arthur Baroody. It’s from 2006 and he talks about the two different views on how to help kids build automaticity. I’m going to read a direct quote from this article. 

These are the two views. You could see it in the comments of that post that there are definitely people who are very, very passionate and believe in conventional wisdom. They believe that the only way we get kids to master their facts is through memorization and repeated practice and reinforcements. People are very passionate about that. 

We also have the other side who are very passionate about helping kids look at patterns, build relationships, and seek connections between some of the certain types of facts to some of the harder facts. 

I’m definitely leaning towards the number sense view. You guys know that. I’m a number sense person, so you can guarantee my take is that we should be going the number sense route. But I think there’s a few points about why. In our standards, we say that kids need to be fluent, but what does ‘fluent’ actually mean? 

Memorization in math & making mathematical connections

There’s a line in one of the standards. I think it’s in 2nd grade. It says, ‘“know from memory.” People assume that means we need to get kids to memorize their facts. But memorization is conventional wisdom. 

I can memorize things for the short term. That’s the way we typically tend to memorize things. I’m memorizing it because I need to remember that phone number, which nowadays we don’t, we just type it into our phone, right?  Or I’m memorizing for a test that’s on Friday. 

That doesn’t necessarily mean I can pull it from memory when I need it. Pulling from memory is when you’re being able to recall information when you need it, and that ties to the number sense view. 

In order for our brain to recall information when we need it, the research behind how our memory works and how our brain works is that the more connections we make when we learn new information–if we can connect it to more things that we already have in our brains, the easier it is to recall that information. 

So if we are focusing our instruction with our students on just taking the fact, 6 + 7, and associating it with 13, the answer. That’s one piece, that’s one connection point. But if we are helping kids see connections between 6 + 7 and 6 + 6. Or 6 + 7 and how we can pull the 5s out of the 6 and the 7, and we can add the 5s together, and we’ve got 1 and 2 on the other side. Or maybe a “make it 10” connection. All of the things that we can help build connections to, the easier it is to recall that information. 

There’s an article by Constance Kamii. She did a study looking at kids who were being taught through play versus kids who were being taught to memorize (using) basic facts. 

One of the things I remember from that article was that she said 3 + 4 was the hardest fact for kids to be able to recall. She’d talked about how it was the hardest because it has the least connection points. 

So 3 + 4 = 7. That’s a connection point, but those strategies and how it connects to other numbers…it can be a double, it could be 3 + 3 + 1 more, it could be 4 + 4 – 1. But there’s no “make it 10” connection. 

If you were looking at 6 + 7 and you try to look at all the things that you could possibly connect 6 + 7 to, there’s a lot more connection points than 3 + 4. One of the things she talked about was the more connection points that we can help kids make, the easier it is for them to recall that information. She saw that the ones that had the least connection points were the hardest ones that kids kind of tended to get wrong more or took longer to get the answer to. 

“We want to focus on getting kids to recall information, not just memorize the facts. The end goal is to be able to quickly get answers.” 

There’s also another piece, and that’s why there are three parts of fluency.

Three Parts to Math Fluency

If you’ve ever heard me talk about those before, it comes from Susan Jo Russell, and she talks about that kids do need to be accurate, they need to be efficient, they need to be fast and quick. But the third part is they also need to be flexible. And that’s where those connection points come in. 

If I’ve memorized 6 + 7 is 13 but I forget it in a moment, do I have another way to figure that out quickly? That’s what flexibility is all about. That’s where that number sense view that Arthur Baroody was talking about comes in. 

If we’re just focused on conventional wisdom, the “let’s memorize and do repeated practice,” they might have it memorized and they might be able to get an answer quickly and get the correct answer, so they’ll be accurate and efficient, but they won’t be flexible thinkers. 

That’s really the kind of learner I was. I could get you an answer, but I wasn’t a flexible thinker. 

The main part that we need to focus on if we want to build kids who are flexible thinkers, and we aren’t just focused on answer-getting, is building their number sense. That’s where the number sense view comes from, helping kids be able to see connections between numbers which helps them build more connection points. 

The way that we do that though, is through lots of experiences. You can’t just directly teach a kid that 6 is 1 more than 5, 6 is 1 more than 5, 6 is 1 more than 5. Learn it, know it, let’s use it now to help you to solve 6 + 7, because you can grab the 5s out. 

If you try to just directly teach that to kids, it just becomes another rule and procedure. But if you’re building their number sense through experiences and they’re playing a game, and their partner gets a 6, and they get a 5, and their partner gets to go one space further than them on the game that they’re playing, they notice that 5 is 1 less than 6. 

The more they have experiences with numbers and seeing relationships between numbers, the more they will use those experiences to help them build their fluency and flexibility through number sense, not through memorization. 

“So we want to start with that solid foundation of a number sense of view. And then yes, we do want to help solidify their understanding through practice.” 

That’s also how our brain works, right? That if “we don’t use it, we lose it,” that’s the saying. If we don’t use it, we lose it. So if all we’re doing is number sense stuff and we’re just letting kids play and explore with numbers, it’s not enough. 

That’s why I really hate that in education where we go “all in” on one idea. It’s drill and kill, practice, practice, memorization, practice, practice, memorization. Then we’re like, “no that’s not working.”  So we just let kids play and explore and build number sense. And that doesn’t work (alone) either, it’s gotta be some of both. 

Yes, I want to lay a foundation. I want to help kids build a sense of numbers. I want them to use their number sense to see connections and build those connection points in their brain so it’s easier to recall, but they also need more practice with it. Practice should be purposeful, not a worksheet of 50 random problems.

It’s using those connection points. What am I wanting kids to practice? What connection points do I want to help them build? And let’s practice those connection points. It can be fun. I am a firm believer in gameplay.  Practice doesn’t have to be filling out a worksheet. It can be playing a game that you’re going to do 100 problems while you’re playing that game. That’s way more fun than doing 100 problems on a worksheet. 

Kids do need to be building their number sense, playing and exploring with numbers, but we also need practice. 

For kids who need direct correlations in math

And my final point is that unpopular opinion that you may not expect from me. So here’s the deal. You heard everything I just said, number sense needs to be the focus. We want to build that foundation, we want to build their flexibility. But if I have done that for years and I’ve got a kid who’s still struggling and counting on their fingers to do 6 + 7 and they’re in 4th grade? Push comes to shove. I’m probably moving towards memorization. 

Because if that was my child, and I know that if we aren’t quick with things, it can hinder their ability. I’m not going to be forcing it. I’m not going to be doing time tests and making it anxiety ridden, but I might be doing a lot more practice of just straight, “here’s the fact here’s the answer, let’s practice” so that they hear that repetition. But that is if I know that they have had years of that foundation trying to be built, and those connections just aren’t being made. 

It is a very small percentage of your kids, but let’s be real, there are those kids. 

So I’m not saying you never go to memorization. You don’t go to memorization with 1st graders when they’re still developing an understanding of numbers. That’s not our first avenue. It’s our last avenue if we’ve tried everything else and those connections aren’t being built, what do you think? Do you agree? Do you disagree? Let me know in the comments on that. 

Let’s be real, if that was my kid, I would want to make sure that they could quickly come up with an answer so that they can use their brain space to help hopefully see other things. Too often, their inability to be able to add and subtract quickly hinders their ability to think through a problem because they’re stuck in that first part of something. 

So I want to be realistic and I’m not taking that off the table. If I see a kid who really needs it, then I may resort to that. I’m not saying I wouldn’t try a lot of other things before we ever get there. I’m not saying that it should never be an option for kids because some kids need that direct correlation. For some kids, having too many things can be confusing for them. However, that is not the majority of kids.

Final Words

As my parting thought, we don’t want to just teach kids to memorize facts. They will become automatic if we focus on memorization. But automatic does not mean fluent. They might become automatic, but at what cost does that come? Do we build their automaticity through memorization but that also builds a hatred for math? Do we build their automaticity through memorization and it builds math anxiety? That’s not the route we want to go, right?

So we want to help kids build that love of math, become flexible thinkers, and not just answer-getters. I hope that this video has helped you build your math mind so you can build the math minds of your students.

Want help with balancing number sense and repetition in your classroom?  Come join one of The Flexibility Formula courses.  The courses are online professional development for elementary educators that give you an understanding of how to build your students’ flexibility with numbers while also helping them build their fluency.  

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