Aren't addition facts cool?! By this point you've learned some amazing relationships and strategies to help your students make real sense of and automatize the single digit addition facts. But sometimes learning and applying are two different things. In this episode Pam and Kim detail how to help your students get out of counting mode and actually apply the relationships they've learned to become fluent with single digit addition facts.
Pam Harris 00:01
Hey fellow mathematicians. Welcome to the podcast where Math is Figure-Out-Able. I'm Pam.
Kim Montague 00:08
And I'm Kim.
Pam Harris 00:09
And we make the case that mathematizing is not about mimicking steps or rote memorizing facts. But it's about thinking and about reasoning, creating and using mental relationships. We take the strong stance that not only are algorithms not particularly helpful in teaching, but that mimicking algorithms actually keep students from being the mathematicians they can be, we answer the question, if not algorithms and step by step procedures, then what?
Kim Montague 00:40
So for the last few weeks, we've been chatting about addition facts, and how to help students become fluent with these facts. Today, we're going to wrap up this series with a few final thoughts about how to put these ideas into practice.
Pam Harris 00:53
Yeah, So Kim, told me once about a group of students who were not using relationships, the strategies, but they were counting one by one. And I was like, "What, like, how was that a thing?" Because I was really convinced once we sort of open the vision, open their minds to the fact that they could just use them. I was like, "Then it's magic. It's just gonna happen automatically." So how is that a thing? And then we tell us all about that. What's the scenario? What was going on? Yeah, go.
Kim Montague 01:26
Yeah. So I spent some time on a campus for quite some time, actually, that was really into numeracy and really into relationships. And I got to because I was there quite a while, I got to know the teachers well enough that we had a relationship. One day I was planning with the first grade team and a few of the teachers said to me, "Kim, we are working on that stuff, we're working on the Doubles, we are working on like the Partners of 10. They're still counting, what do we do?" So I said, "Okay, let's take a look at what's happening." And so I scheduled some time in their classes. And I sat down with the kids as they were working on problems, right? Some problems that they were supposed to be solving, problem solving, whatever.
Pam Harris 02:05
There were some word problems. There were some problems.
Kim Montague 02:07
Pam Harris 02:08
All different kinds of problems.
Kim Montague 02:09
Pam Harris 02:10
You sat down with it. So that's a noteworthy thing. I'm just going to point out right now that what you didn't do was just kind of like glance or whatever. But you sat down and interacted with kids.
Kim Montague 02:19
Yeah. Didn't look at the work afterwards, right? Because then it's too late to know what they did. So I sat down with the kids. And listen, they were just so quick at counting on their fingers, or to 8, 9, 10, 11, 12, right? That kind of like, say it really fast.
Pam Harris 02:35
You said that so fast, I didn't even understand. Say that again. Do that again. I dare you.
Kim Montague 02:40
8, 9, 10, 11, 12.
Pam Harris 02:41
Kim Montague 02:42
And so the kids were quick, right at what they had been doing for quite some time. And so we needed to find out first who owned their Doubles, and who owned their Partners of 10. Before we could kind of interrupt that flow, before we could kind of say, "Wait, wait, don't do that." And so I talked with the teachers specifically about Doubles and Near Doubles, and Partners of 10. And they kind of thought they knew who owned them, but they couldn't really name specific names. And so that was kind of our first, that's where we started, that was our first job.
Pam Harris 03:16
Let me just be clear. You said to teachers, "Which of your students own Doubles, Near Doubles? Which of your students own Partners of 10? We need to sort of know that."
Kim Montague 03:26
Pam Harris 03:27
And your teachers might had some ideas, but they weren't actually sure of their, they didn't know which students own those relationships and which didn't.
Kim Montague 03:35
Pam Harris 03:35
Kim Montague 03:36
So that was kind of the first thing we needed to figure out is who could we say, own them? And who do we still need to work on and give them more experience. And so that's where we started. We, um, I say 'we'. I didn't they pulled kids too quickly, here's what we did. We flashed, and I say 'flashed'', that's probably not the right word. We flashed Doubles. So we held up for a couple of seconds, each of the doubles up to 10. So showed them a card with nine plus nine, give him a few seconds, slide it to the side. Show them a card with five plus five, and we just sorted them into 'ones I know right now', 'ones I don't know yet' to get a feel for which of the students owned their Doubles. And then we did the same thing with Partners of 10. And it literally took about 30 to 45 seconds per kid because there's only so many Partners of 10, and only so many Doubles. And so we just had these cards ready. And it was really just about kind of sorting the kids. Can I rely on the fact that they own them in isolation at this point. And so what I said to them was, "We're going to make a list of these kids and we're going to commit those names to memory. We're going to write them down somewhere. We're going to know in our heads which kids we can identify as ones that know these two categories are these groups of facts." And then we call those kids out. Right? When we say saw them doing...
Pam Harris 05:01
What do you mean by that? You didn't embarrass them to be clear.
Kim Montague 05:03
No, no, no. So I'm gonna explain. So when the teachers were sitting down next to them, and they saw them pull out their fingers, we gently covered their hands. And we reminded them, "You know, these Doubles." And when we heard them 8, 9, 10, 11, 12, then we tapped them on the arm, we started speaking to them in the middle of the count. We did some things to interrupt the method that they had been doing for so long that it was a natural habit, right? So if you have a habit, something has to interrupt the habit that you have to replace it with something new.
Pam Harris 05:40
So you literally gently stopped them mid count?
Kim Montague 05:43
Yes, absolutely. Physically by, you know, covering their fingers a little bit softly, of course. Just kinda tapping them on the hand. Or verbally, if they were a verbal outloud counter or mouthing it, then we would speak to them in the middle of the count. So sometimes we realized the kids weren't even aware that they were doing it. So we just reminded them, "Hey, Double. Oop, Partner, 10." And they would go, "Oh, I know this one." Because we needed to correct the habit that they had gotten into for quite some time.
Pam Harris 06:15
can you really lay it out for me? So I'm a kid, and I'm like, "8, 9, 10, 11, 12." You would have said...?
Kim Montague 06:23
I would have said their name.
Pam Harris 06:25
Kim Montague 06:26
And I would have said, "Oh, it's a double." Or if it was like, like eight plus seven, right? And they were about to "8, 9, 10, 11, 12, 13, 14."
Pam Harris 06:33
Kim Montague 06:33
Then I would say, "Oh, eight and eight." And they would go, "16, 15." Or I might say, "Seven and seven." And they would go, "14, 15." So I would suggest a 10, or a double that they could use to help them with the fact that they were working on. And often it would be the fact that were the leftovers, that were not clearly a double like eight and eight or seven and seven. It was the ones that were a little bit off from the Double. And they just needed help recognizing that because you know that Double, then it can help you with the one that's right beside it.
Pam Harris 07:15
Hey, Kim, am I remembering correctly that you told me that before you started interrupting the kids, that you actually sat him down and had a conversation with them?
Kim Montague 07:23
Pam Harris 07:23
Can you tell us about that?
Kim Montague 07:25
Oh, if I can remember? Well, and so I think it's just kind of what I said was, "Hey, you've been working on Doubles, and you know, your Doubles. And you've been working on Partners a 10. And you know, those." And so I wrote a couple of them on a whiteboard, you know, pull those students off to the side. And I said, "If you have this problem, eight plus seven, how might a Double help you with this problem?" And somebody would have suggested, "Well, 8 and 8, if I know that is 16, then I just need one less. So that's 15." And another student might have said, "Well, it's eight and seven, but I know the Double seven and seven is 14. So then one more would be 15." Another student might have said, "Well, I know my Partner's of 10. So if it's eight and seven, I know that eight plus two is 10. And so then I have five leftover." So we generated ways that the Partners of 10 and the doubles could help, that just brought that again to the forefront of their awareness. Short conversation, just reminding them that one of the reasons that we care that we know Partners of 10 and Doubles is to help us with the unknown facts that we are not as comfortable with.
Pam Harris 08:35
So actually bringing to light, your like brain to the top of their heads. It's not just about knowing Partners of 10, about knowing Doubles. It's using them to figure out these other ones.
Kim Montague 08:45
Right. And I think that's the part that's missing sometimes, is we go through these motions of like, oh, Double seem important, and in 10s seem important. They're important because they can help us with other things.
Pam Harris 08:56
Do I also remember, this is the part that really sticks in my memory is I think, I think you and I had a conversation about you said to them, "So from now on... "
Kim Montague 09:05
Pam Harris 09:06
Yeah, "From now on, use these relationships. From now on no more counting by ones."
Kim Montague 09:10
Pam Harris 09:10
And I kind of went (gasps). I was like, "You told him what to do." And you were like, "Yes." In fact, I think the word you used was 'absolutely'. Sometimes Kim will say that to me.
Kim Montague 09:19
Pam Harris 09:20
I'll say, "Kim, really?" And you're like, "Absolutely." And then I know you're like serious.
Kim Montague 09:23
Pam Harris 09:23
And you said to me, "They know the relationships, they own these, they can use them. They're just in this habit. So I'm just going to be clear with them." In fact, we've been saying on the team lately, "Clear is kind." I'm going to be clear, that's quoting Brene Brown, "Clears kind and so I'm going to be clear with them. Hey, we want you to use these relationships, not counting so we might interrupt you. Like this is gonna be a thing from now on that we're gonna, like, have these moments where if we see you counting and you're just reverting into habit, it's okay. It's not bad. We're not, you're not ugly or whatever. But we are going to like gonna make you aware you." Yeah, I thought that was fascinating. I was like, "Oh, yeah." Because if you make the kids aware you make it a thing, then we can interrupt those habits. And Kim, why is this important?
Kim Montague 10:11
Well, so one of the teachers, and I had a conversation because she was like, "I don't know, like they're so quick at it." And so we got to have another conversation.
Pam Harris 10:20
But why is that important, right? They're quick. They're getting right answers. Why is it important?
Kim Montague 10:23
Because it's not about the answers only, right? So if we leave kids as counters, then what happens when they don't use those relationships, and we get into bigger problems, bigger situations, you can't leave kids counting 99 plus 37. But if they know Partners of 10, Partners, 100, then they can use strategies like Give and Take or Over Strategies. We're leading them into bigger strategies and more sophisticated thinking. If we just leave them counting, then that's all we're giving them. That's not helpful.
Pam Harris 10:56
Well, and literally, that's all they're going to be sort of capable of doing because their brain hasn't grown, their brain hasn't grappled with more sophisticated relationships, enough that their brain is now stronger, and able to then deal with even more sophisticated relationships and grapple with more simultaneity. We've sort of left them getting right answers in an unsophisticated way. Oh, bummer. Bummer, now that you can't think more sophisticatedly. No, no, like we have some, I don't know if 'power' is the right word, but we have some influence that we can have as we help students realize it's not about the right answer. It's not about fast. Because I think that teacher was saying to you, "Yea, they're really fast and they get the right answer." Not what's important. The important part is helping them become more sophisticated thinkers. Yeah, absolutely. So what are some things to do? Well you can do exactly what Kim did, but after you build the relationships. There is this part where we now need to use them. So when you see a kid counting, maybe gently say something like, finger, like what's going on? It's not that fingers are evil, it's that we want to help you use those other relationships. Include problems in center work. Give homework, where there's Doubles, and Near Doubles, and where they can use their Partners of 10. Also when you put kids together in partnerships in class, partner them strategically, so that sometimes kids are working with a student who also knows those relationships, and they can kind of egg each other on. But also partner kids, sometimes more heterogeneously, where you've got a student who knows Partners of 10, and a student who doesn't necessarily. And as they work together, they sort of share how they're solving problems, and they can both kind of learn to communicate about what they're doing better. So be strategic about how you partner kids. Do you want to anything more about that, Kim? Do they kind of knock that out? Yeah, you did. Yeah, cool. And then keep games going all year long. Play games, where kids have to sort of use facts. And so it becomes advantageous for them, to have them at their fingertips to have them sort of readily use, that they don't get bogged down in unsophisticated ways of refiguring those facts. We'd like to give a shout out to some other nice ways of developing relationships and getting some really thoughtful practice in. Berkeley Everett, our colleague, who we really appreciate the work that he's doing at berkeleyeverett.com has some really nice things that he does to help students really automatize single digit facts and some other things. But one of the things he does well, are his, what are they called, Kim?
Kim Montague 13:32
Pam Harris 13:32
Thank you. I was trying to say flip it. That's not, doesn't, no. So his Math Flips are definitely helpful. We'll give a shout out to Berkeley. Good work there. So you might be wondering, we've done a series on the podcast about multiplication facts. We've now just done a series about single digit addition facts. Anybody interested in subtraction facts? Well, maybe let us know. And we might do some work in the podcast in the future about single digit subtraction facts. If that interests you, maybe let us know. Y'all, right now registration is open for my deep dive workshops through February 4 of 2022. If you're listening to this some other time, you can still go to the link I'm about to give you and get on the waitlist. But if you're interested to know just a little bit more, I'm gonna take just a second and tell you about why I created online workshops. Well, a few years ago, a good colleague of ours really pushed me to think about how we could get this idea. this paradigm shift that Math is Figure-Out-Able out to more people? What could we do so that more people can have the opportunity to have their eyes and minds open to the fact that math isn't that rote memory stuff, but it really is Figure-Out-Able? And we've piloted and tried a bunch of stuff. Kim, could probably tick off things that we tried that actually didn't work. But we have found a way that works for teachers to get professional learning on their own time to really dive deeply into content they teach at their grade level. One way that we do stuff is the podcast where we're trying to get things out. But y'all, we can't be visual here on the podcast, you can't see things. Also, we don't dive as deep as we can. When you take a workshop that's just on say Building Powerful Multiplication, or Building Powerful Division or Building Powerful Proportional Reasoning, or backway. Up and Building Addition for Young Learners. Those are the four workshops that I have out right now. We're currently creating new workshops all the time, to give everybody an opportunity to dive deep into the content that they teach at their grade level. One of our participants who just took a workshop said, "My experience was amazing." Jennifer Harrison said, "I would tell not just a friend, but anyone who teaches math, to take this workshop. I learned to allow students to actually think. Honestly, I will be using all of the things we learned." If you'd like to hear from more participants and what they had to say about taking my workshops, you can go to MathisFigureOutAble.com/workshops, and choose one of those four workshops or however many we have out at the time that you're listening to this podcast, because we're just creating more as we go. I'm a K-12 math teacher educator. So we've been teaching teachers live, these deep dive workshops for quite a while, and we are now, we've created them virtually so that more teachers have access to the learning. It doesn't have to be that you travel somewhere to hear it or that your district brings me or my team in. Now anybody in the world can have access to this wonderful professional learning. And so I would invite you if you are interested to dive deeper into the content to check out MathisFigureOutAble.com/workshops. Y'all if you're interested to learn more mathematics and refine your math teaching so that you and your students are mathematizing more and more, then join the Math is Figure-Out-Able movement and help us spread the word that Math is Figure-Out-Able.