Multiplication Nation

[00:00] SPEAKER_01:

Welcome to Principal Center Radio, bringing you the best in professional practice.

[00:05] Announcer:

Here's your host, director of the Principal Center, and champion of high-performance instructional leadership, Justin Bader. Welcome, everyone, to Principal Center Radio.

[00:14] SPEAKER_00:

I'm your host, Justin Bader, and I'm honored to be joined today by Alex Kajitani. Alex is a California Teacher of the Year and National Teacher of the Year finalist and the author of three books. A sought-after speaker, he is the founder of Multiplication Nation, an online program to help students master their times tables and have fun doing it.

[00:36] Announcer:

And now, our feature presentation.

[00:38] SPEAKER_00:

Alex, welcome to Principal Center Radio.

[00:40] SPEAKER_02:

Ah, thanks so much. It's an absolute honor to be here.

[00:42] SPEAKER_00:

Yeah, well, let's talk about Multiplication Nation. Where did that come from, that idea that you could help students, not just in your classroom, but around the world, master their times tables? What did you see as kind of the need and the impetus to create Multiplication Nation?

[00:56] SPEAKER_02:

Yeah, absolutely. You know, I was an algebra teacher for over 10 years, and year after year, I would see students come into my class, and It was very clear within the first week of class, and, you know, this is eighth grade algebra. If the students had a good mastery of their times tables, they usually went on to do really well in class and achieve pretty well. If they didn't, they really struggled and they really got stuck. and had a hard time progressing, and as I began to really look into this even more, what I found out is, you know, that not passing algebra is actually the number one reason why most students drop out of high school. And so, to me, it was this obvious progression as I started to look back at, okay, what was happening in middle school and then in elementary school, that if the kids weren't mastering their times tables, You know, early on in elementary school, they were getting to my algebra class and really, really struggling.

[01:51]

And so, I immediately saw this as just one of the critical foundational skills that is so very important. And it really happened, you know, when I started to see my own daughter, who was in third grade, start to struggle. And, uh, once I helped her with her times tables, she started doing really well. She started really becoming confident in math class. And so I thought, okay, you know what? Maybe I need to shift from it not being about one student mastering their times tables, but to about all students mastering their times tables.

[02:24]

And so now I'm on this mission to get every kid in America to master their times tables, because think about, if you're a teacher and you had every student in your class, or you're a principal and you have every student in your school, or for a superintendent, every student in your district mastering their times tables, It would be an absolute game-changer for the students' confidence in math and in life.

[02:47] SPEAKER_00:

And I want to zoom in on this aspect of your being an eighth-grade algebra teacher, because I think of algebra, you know, I think of mathematics in general as being a subject that's very cumulative in terms of the concepts that students learn. You know, one thing builds on another, and by the time you're at eighth-grade algebra, there are so many concepts that students are expected to have mastered as a foundation for algebra, and yet that subject itself is very conceptual. So I wonder, you know, for those of us who aren't math teachers, what is it that helped you pinpoint multiplication, you know, just knowing the times tables, as something that was important for a subject that is so conceptual? Because, you know, certainly there are hundreds and hundreds of concepts that students have also had to master. What is it about multiplication that makes such a difference, even, you know, years and years later in Algebra 1, in the 8th grade, that, you know, why does multiplication play such a critical role?

[03:38] SPEAKER_02:

You know, I think it really is the first spot in a lot of students' education where they start to actually have to combine, you know, bigger numbers than they're normally used to. Students generally understand, you know, addition and subtraction, that when you're adding things together, the number gets bigger, unless, of course, you're using negative numbers, but I won't get too math on you. And, you know, they generally understand subtraction. When you take things away, the amounts get smaller. Multiplication is sort of that first crossroads where they have to start to combine numbers quickly and in bigger and bigger amounts. And so, to me, it's almost like the reading of math.

[04:15]

You know, you could have asked the same question of me for a history class, but if you don't read well, you're not really gonna progress in history class. Same with language arts or science. And reading is very important in math, but mastering those times tables and understanding it from a conceptual point of view. I'm not just talking about memorizing the facts. This goes beyond that. But really understanding the concepts behind multiplication and how numbers are combined in groups is such a critical foundation and concept that kids have to know in order to go forward.

[04:48]

And then once they do, It's something that is required in so many different levels of math, everything from finding the area of a rectangle to exponents, all the way through to calculus and beyond. It's really that foundational, critical skill, and I heard one of the Silicon Valley coders once say that, you know, in order to be a great coder, you don't actually have to have all that high-level math, you really just need to know your times tables, and then you can go on to really code, you know, some amazing things in technology.

[05:18] SPEAKER_00:

Well, and I wonder if you're encountering any backlash against this idea of, you know, knowing your times tables, because I feel like in the last, I don't know, decade or two, there's been a big pushback against the idea of rote learning, or of just factual knowledge, and I think especially against memorizing dates in history class and things like that. And when it comes to math, it seems like there's more of an integration between the facts and the concepts than maybe there is You know, I think it's a little bit of everything. I think, first of all, I haven't come across anybody who has disagreed that having the Times Table's facts mastered is, you know, a bad idea. Pretty much everybody agrees that it's a good idea, that it's a skill that propels you forward.

[06:13] SPEAKER_02:

I think, however, what the great debate in all of this is comes to whether or not we give timed tests, whether or not students have to be able to recall them, you know, within 3.5 seconds or 4 seconds and things like that. And I'm really on the side that this should never be a test of speed, this should not be something that is, you know, drilled into kids in terms of being able to fill out, you know, 100 math facts within Two minutes or things like that, and so, I totally agree that timing, um, should not be the most significant factor, or even a significant factor in mastering those facts. What I have found, though, is that the more comfortable kids get with memorizing them, the more comfortable they get and more masterful they get at understanding the concepts, then the timing just takes care of itself. the timing just sort of starts to come automatically and the kids get quicker at it as they deepen their knowledge conceptually and things like that.

[07:10]

I will say that, you know, one of the things that I think is very, very important is that we spend a lot of time trying to get kids, you know, really fired up about math, really making it cool. And I am no exception. You know, my claim to fame is as the Rappin' Mathematician, and I am the guy who makes math cool. But that can't be the only thing that we do. Sometimes, in order to be confident in math, kids have to first get competent in math. And that competence then leads to the confidence.

[07:39]

And so... We can spend all this time telling kids, you know, math is cool, math is cool, math is so fun, you're so good, but it's only when they get the real competent skills and see that they can do it, that they can do the operation, that's when their confidence really starts to grow.

[07:55] SPEAKER_00:

Yeah, absolutely. And I know a lot of the research around, say, self-determination theory, major field of research in psychology, says that competence really is at the heart of that confidence and students' willingness to try things. You know, and that's true, I think, of humans in general. When we feel competent in something, we're confident, we're willing to put forth effort, we're willing to tolerate risk and failure and persevere through that. And it's interesting to me thinking about multiplication as something that, as you said, Nobody really says kids don't need to learn their multiplication facts, and I think it occupies kind of an interesting place in mathematics instruction as kind of the last thing that parents remember mastering. Like, if you survey parents about their attitudes towards some particular aspect of math instruction, almost everything is controversial, right?

[08:41]

Because almost everything is different from how parents learned it, and, you know, we kind of hate that as parents. We want our kids to learn things the same way we did, even if it wasn't particularly effective. But I feel like learning your times tables is one of those things that everybody experiences and everybody gets intuitively that matters. And I appreciate your thoughts as to precisely why that is. What are some of your thoughts about, or what were some of your discoveries in helping students master those facts, including students who maybe had reached the eighth grade without learning them as they were supposed to in, say, third or fourth grade? So what are some of the how-tos for us in terms of

[09:19] SPEAKER_02:

Yeah, that's a great question, and before I answer that, I have to say what's been funny talking to adults about all this is every single adult has a specific memory of memorizing those times tables, or not memorizing them. Someone say, oh, I got sent to the retired teacher down the street who drilled them into me every day, or other people remember the songs or the chants or, you know, or a schoolhouse rock and things like that, and so it is fascinating that adults always have this memory of How they learn them. And so, you know, that's been fascinating. In terms of actually learning them, you know, what I see a lot of times is, there's a couple of challenges. The first challenge is just in the actual pedagogical practice of teaching the times tables. And so, a lot of times, I see educators skipping over the step of sitting down and learning them.

[10:08]

We often want to move right to the fun game, or we often want to move right to the cool video game, where if you, you know, you get the math fact right, you get to blast the Martian kind of thing. And I think sometimes what we need to do, and certainly what I try to emphasize in MultiplicationNation.com is really stepping back and saying, okay, before we play the game, before we work on really getting these things down, let's stop and let's break up the learning, just like in any other learning, And let's have a really good system for actually getting these things mastered. And so what I do is, let's say we're working on the sixes, right? Instead of just giving them a bunch of six flashcards or sitting down with them, we break it up. And so we do what I call the first half.

[10:50]

So we're gonna memorize six times one, two, three, four, and five. And we're gonna do that forwards. We're gonna do that backwards. We're gonna mix it up. And we're just gonna get that first half memorized. Then we're gonna do the second half.

[11:02]

six times six, six times seven, times eight, times nine, and times ten, for example. We're gonna get those, we're gonna mix them up, right forwards, backwards, mix them up, then we're gonna put them together, and then we're gonna mix them all up, and then, you know, within a few times, kids are really gonna start to have those memorized, because they're learning to depend on and lean on an actual systematic system of learning. We can't just Throw things at kids, expect them to memorize it, and then move straight on to the game. We've got to get a system for input into them, and so that's been really powerful. I also think the order that we teach them in, it doesn't have to be one, two, three, four, five, you know, in numerical order. I've got a great system for mixing them up, because it's really important that we do that, in addition to which, consistency is super, super important.

[11:52]

I see parents struggling all the time with, you know, do I help my kids with their flashcards, or do I do the dishes? And if I help the kids, I'm gonna have to do the dishes at 10 o'clock at night, right? That's where real life actually gets in the way of, you know, learning the math that students need to learn. Teachers have 30, sometimes more kids. It's very hard to get to them You know, one, one-on-one, or all in a day, things like that, and so, really, with this program, I created it so every kid can log in, I'm there, I take them through, mastering their times tables in a really fun, engaging way, which focuses on the procedural and the conceptual and the application, but sort of like getting to clone me 30 times, bring me in and sit down and work with every student one-on-one, And I won't leave until they have them mastered. They can watch the videos as many times as they want.

[12:43]

It's very interactive, got assessments, and brings the real world learning. Like I said, I can talk about this all day. I'm on a mission to help every kid master their times tables, and I won't stop until I do.

[12:55] SPEAKER_00:

It seems like such a no-brainer that, you know, these are skills that are valuable throughout life, you know, that are foundational to everything students will learn in math from that point on. And, of course, we know math is often a gatekeeper subject when it comes to getting into college and... access to, you know, professional work later in life. So, certainly, this is one of those things that we can just decide as educators.

[13:17]

Non-negotiably, all students are going to master this, you know, at a certain point in their educational career. I wonder if we could talk just a little more. I know we've touched on this a bit, but if we could talk about the kind of conceptual side that makes learning the multiplication tables more than simply kind of drill and kill. And it's funny because, again, learning the times tables is one of those places where...

[13:38]

As educators, no matter how progressive we are in our pedagogical philosophies, we're okay with drill and kill when it comes to learning the times tables. But it sounds like you're saying that it's a mistake to only focus on drill and kill. Like, there's more to it conceptually. So I wonder if we could talk just a little bit more about that. Like, what are some of the conceptual elements? You mentioned going in order and then going in reverse order and mixing it up.

[13:59]

Talk to me a little bit more about that.

[14:01] SPEAKER_02:

Yeah, you know, I almost liken it to learning how to spell, right? You can learn, you can drill and kill and learn how to spell certain words and things like that, and maybe when you need to spell that word, you know, you've got good recall. But it really is when we understand, you know, how to take words apart, how words are formed, you know, why the I comes before the E and things like that. It's really when we understand the concepts behind the words that we really start to gain a sense of what it means to compose sentences, to be a writer, things like that. And so, yes, we can, you know, just have students memorize, you know, nine times seven or six times four, and maybe they'll recall it, maybe they won't. But it's when they understand, you know, that five times seven is actually five groups of seven, or could be seven groups of five.

[14:48]

It's when we actually are able to have students, and students are able to, by themselves, pull numbers apart and understand the concepts behind that, understand skip counting and how we're actually skipping over, you know, if you're picturing a number line and you're learning to skip count by eights, where you're actually, you know, going eight, 16, 24, 32, we have a great character called the skip count who just, you know, skip counts. But, um, it's when we understand those concepts behind it that we can pull those numbers apart, put them back together, and then do the higher-level stuff. When we do order of operations, we don't want students stuck on, you know, just getting what six times six is. We want them to be able to free up their brain to access that quickly so that they can get to doing the higher-level math. I love what Lisa Delpit, who wrote Multiplication is for White People, says.

[15:39]

She says that one cannot divorce... the demands of critical thinking from the teaching of basic skills. When we have those basic skills, then we can go on and really hit the demands of critical thinking. We don't want kids coming to a seventh or an eighth grade or beyond math class and having to deal with complex word problems when they're really just getting stuck on not having the math facts memorized.

[16:03]

And so, I don't think in any way that it holds people back. I think it just propels them forward. And the deeper that they can understand the concepts behind multiplication, that it is adding equal groups of a certain amount of numbers, or a certain number, then they're really gonna understand that. And, you know, really, multiplication is just the ability to add numbers very quickly. And so, when we've got that concept down, it opens up the whole world of math to you.

[16:29] SPEAKER_00:

Well, for our audience of educational leaders, you know, curriculum-wise, I'm just going to confidently say that every elementary school has a curriculum that teaches multiplication, right? I mean, that's in the curriculum. But often the situation we're dealing with as leaders is we've got a group of students, maybe at the upper elementary level, or maybe even at the middle school or high school level, who, for whatever reason, did not master those facts at the time that they were initially taught. So they might arrive in your 8th grade algebra class not knowing their facts. They might arrive in 10th grade geometry not knowing their facts. What's some of your guidance for leaders as far as how we can identify and effectively support those students in closing those gaps, just knowing how important it is to catch up quickly if they've missed that in their career thus far?

[17:11] SPEAKER_02:

Yeah, that's a great question. That's sort of a question about where reality actually hits standards and curriculum and things like that. The first thing that I recommend to, you know, education leaders, teachers, parents, whoever, is when the conversation turns to, you know, hey, a lot of my students don't know their math facts, to stop and say, okay, which students? And to actually get their names and identify them as real people, as real students with real struggles and issues. And let's get rid of this blanket, you know, So many kids don't know their math facts. That may or may not be true, but next time you hear that, so many of my students don't know their math facts, the next question should be, really, which students and what can we do for them?

[17:55]

And let's really actually start to systematically identify students, who they are, and what they need. The other thing that I think is really important, you know, one of the things that I did as primarily an eighth grade math teacher, And then I got a chance to do some academic coaching at an elementary school. So I thought, okay, this is a great opportunity for me to figure out what's really going on. And so I went to, you know, the fifth and sixth grade teachers and said, hey, you know, how come so many kids don't know their, you know, don't know their times tables? Of course, knowing what I know now, they should have said, really, which kids and what can we do for them? But they said, you know...

[18:29]

Well, we don't know what to do. We're supposed to be teaching this curriculum, but a lot of the kids get stuck, and so we have to either teach our curriculum, and they never really grasp it because they don't know their times tables, or we teach the times tables, and then they're way behind. I said, okay, well, when do they learn their times tables? Third grade. So I went to the third grade teachers. Oh, well, we don't know what to do.

[18:48]

We're supposed to be teaching multiplication, but a lot of our kids are having trouble adding and subtracting. You know, well, when do they learn adding and subtracting? First grade. So I went to the first grade teachers. You already know what's coming, right? No more of this, hey, how come these kids aren't coming to me knowing what they need to know?

[19:05]

I'm saying, as educational leaders, as people who take responsibility for not just one kid, but for all of the students in our classrooms and our schools, let's stop and let's just get them, let's just solve the problem by getting them this one critical foundational skill, which will then allow us to get to, you know, the next even bigger, more important problem. But I'm saying, no more of this talk of, so many kids don't know them, let's stop, let's do something about them, and I'm on a mission to do that.

[19:35] SPEAKER_00:

I love it, because, you know, it is such a specific and solvable problem, yet that, as a profession, we've managed to not solve yet, but I really love that you're on that mission, to say, hey, like, there's a known solution to this, we know how to fix this, we have the ability, we just need to do it.

[19:51] SPEAKER_02:

Imagine if a teacher said, you know what, no more. No, I'm not sending any more students on

[19:56] SPEAKER_00:

So, Alex, if people want to learn more about Multiplication Nation and see your program, maybe try it for themselves, where can they find that online?

[20:06] SPEAKER_02:

Yeah, it's MultiplicationNation.com, and it's an online program. They can sign up for a free trial. They can try it out with their students. Happy to, you know, talk to them, answer questions about getting it for...

[20:18]

Whether it's for one kid, for their whole class, their whole district, we have districts and classes all over the country which are using it. Uh, and again, it's multiplicationnation.com. Check it out. And if you want to know more about me, you can check out alexkajitani.com.

[20:33]

That's A-L-E-X-K-A-J-I-T-A-N-I dot com.

[20:38] SPEAKER_00:

Fabulous. And we'll link to those in the show notes. Alex, thanks so much for joining me on Principal Center Radio.

[20:43] SPEAKER_01:

It's been an honor. Thank you so much. And now, Justin Bader on high-performance instructional leadership.

[20:50] SPEAKER_00:

So, high-performance instructional leaders, what did you take away from my conversation with the rap and math teacher, Mr. Alex Kajitani? I loved Alex's point about solved problems that we talked about toward the end. that when we know how to solve something in our profession, we have a duty, we have a professional obligation to solve that problem for our students. And I think it's increasingly becoming the case that virtually every problem our students face is a solved problem. Now, some of the biggest and most intractable problems may not yet be solved.

[21:26]

You know, poverty, for example, is not a solved problem. But when it comes to things that show up for us in the educational environment, such as students not knowing their math facts, or teachers who don't have classroom management under control, Those are solved problems in our profession. We know how to deal with them. And I think one of the most exciting things about the networking and the connecting and the sharing that happens online through things like Twitter chats, through things like professional learning networks, through things like our membership that we have at the Principal Center, one of the most exciting things there is the opportunity to share those solutions to those problems that perhaps are solved in some places, but not yet everywhere. So, it's part of my vision for the Principal Center, it's part of Alex's vision for Multiplication Nation, that we would do everything we can to spread the word about those solutions.

[22:20]

And when you discover a solution to a persistent problem in your school, I want you to recognize that other schools are facing that same problem every day. And I want to encourage you to exercise leadership, to reach out and share that solution with others in the profession. And one of the best ways to do that is by simply applying to present At conferences. Applying to present at conferences, uh, can get expensive if they're far away, but I'm guessing that your state or your, uh, even your district, even your city, uh, might have quite a few education conferences over the years. Typically...

[22:56]

There is an annual conference for educational leaders in every state. Often there are several. And they are starving for presenters. So I want to encourage you to present for your local principals' association, your state principals' association. Whatever conference they have coming up, I want to encourage you to apply and present and share your best strategies for solving the problems that you face and that others in our profession are facing in their work.

[23:24] Announcer:

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