We all want students to become fluent in math, but there is something that we tend to do as educators thinking it’s helping the kids become fluent, but really it isn’t. 

I’m Christina Tondevold, The Recovering Traditionalist, and today I’d like to talk about A Big Mistake Educators Make When Building Math Fluency in our quest to build our math minds so we can build the math minds of our kiddos.

Watch the video or read the transcript below:

Here are links to products/activities mentioned in this vlog.

Flexibility Formula K-2 online PD course

Flexibility Formula 3-5 online PD course

Now, I can say this is a big mistake that a lot of educators can make because (A) I’ve made this very same mistake many times and for a long time, and (B) I’ve sat in so many classrooms of other educators and watched them do it as well. 

When I first started teaching in a way that was focused on helping students build their conceptual understanding of math, I made this big mistake and I want to share it with you in the hopes that you don’t make the same mistake that I did, or if you do it right now, I want to let you know that there is a better way.

The big mistake is that we are directly teaching strategies to kids.

I did this unintentionally, I thought I was doing the right thing, mainly because my textbook set it up that way. 

The textbook that I was required to use had a lesson on base-10 blocks to solve multi-digit multiplication. 

Then we did a lesson on partial products to solve multi-digit multiplication. 

Then a lesson on the lattice method for solving multi-digit multiplication. 

Then a lesson on the Box Method, which technically is the area model, but back then we didn’t call it that and it’s not proportional like the area model…but that’s a whole other topic. 

And then finally, we would get to the lesson on the traditional algorithm. 

And at the end of the chapter on multi-digit multiplication, I had maybe a handful of kids who understood the strategies, but I had the majority of my students who were just thoroughly confused and were mixing up all the steps of all the different strategies. 

So, I had spent all this time teaching five different strategies to solve multi-digit multiplication and most of my kids ended up having no strategies that actually made sense to them.

The big thing I hope that you can take away from this video is that strategies can’t be taught. Strategies are actually caught by kids when they understand how numbers work. 

I was teaching each of those strategies as a procedure to students, I taught them step-by-step, what to do. 

So they weren’t actually building an understanding, they were just “parroting” back to me what the steps were that I had taught them.  If they couldn’t remember those steps, they would just mix everything up. 

Now, it doesn’t matter if you teach older kids and you’re working on multi-digit multiplication, or you’re doing single-digit addition with young kids, this happens no matter what operation we’re working with or the size of numbers. 

So in the early grades, for example, a popular thing that we try to teach kids is using 10 frames to solve addition. So we’ll put 9 and 7 in a 10-frame and then we tell the kids step-by-step, how to solve this. 

“So we have 9 in one 10 frame and 7 in the other 10 frame and so let’s move one of the dots over to make the 10 frame full and then we have 10 and 6. Now figure out what 10 + 6 is.”

But that’s not what that’s meant to be. Ten frames are great for building relationships, there are so many things you can do with 10 frames, but don’t teach kids how to use a 10 frame. 

They need to make sense of it for themselves. They need to see, “Oh, if I just move one over here, I could make a 10 and a 6.” Because how many times have we taught lessons like, Make a 10 or Doubles Plus 1 to solve addition and then later the kids have no idea how to solve problems on their own, when there isn’t a 10 frame or we haven’t just done a lesson on doubles or doubles plus one. 

So if we directly teach these strategies to students, they just become a procedure that they need to learn and follow, but if students come up with these on their own, then it’s an actual strategy that they have internalized and they will use.

So how do we help kids come up with those strategies on their own? That’s a big topic. I’m actually doing a free webinar all about that because it isn’t something that can be covered in a 10-minute video. It won’t even be answered in the full one-hour webinar. 

I have online PD courses where we do a deep dive into how to build students’ math fluency by building their flexibility with numbers and those courses are 9- to 10-hours long. So it’s not like we’re going to cover everything you need to know in that hour, but I’m going to give you as much info as I possibly can in that one-hour webinar to help you get started on your journey to helping your students build their understanding of numbers and how to operate with them so that they can develop these strategies on their own in a way that actually makes sense to them, instead of you directly teaching your students a bunch of different strategies that they forget and confuse later. 

So use the link below this video to get registered for the webinar and as always, I hope that this video has helped you build your math mind so you can build the math minds of your students.

And I hope to see you on the webinar.

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