In a recent Math-U-See webinar our founder Steve Demme took some time to talk about Math-U-See’s philosophy in his own words. He also provides some great strategies for nailing down those math facts. Here’s what he had to say:
I’m going to start with a quick summary of the Math-U-See philosophy. This will be helpful for those who don’t know about Math-U-See, as well as current customers.
One of the goals of Math-U-See is to teach students to understand math as well as know how to do it. In Math-U-See, we have 30 lessons per level. In what I would call the general math or the elementary level, we start in Alpha, which is just single-digit adding and subtracting. I’ll be referring to that book a lot today. And then we do Beta, which is multiple-digit adding and subtracting. And then we teach Gamma, which is all multiplication from facts all the way through multiple-digit multiplication. Those three books, though, are the first three in our series, and each of those books have 30 lessons; Math-U-See typically only teaches one topic per lesson.
What we want you to do is to master the material in each lesson, so you move through the book progressively. You’re moving from a position of confidence, because you’ll have mastered this, and then you’re only going to learn one new thing each lesson. Some textbooks give you three or four topics per lesson, and they’ll go all over over the place, and we’re not going to do that. We’re going to give you one thing at a time, and usually, those are pretty bite-sized chunks. If you can focus on one lesson at a time, get the material in that lesson before you move to the next lesson, you’re going to have a happy kid, you’re going to have a confident kid, and you’re going to have a student that really has had a chance to build up his self-esteem.
When we teach math facts (download free math facts activities here), we spread out the addition facts over several different lessons. I’m going to go through the addition sequence, but this whole concept of Math-U-See is line upon line, precept upon precept, here a little, there a little, that’s exactly what we’re trying to do. Math-U-See provides several different ways that we can teach math fact memorization; I’ll be showing you this later.
One question I get a lot is what the parent is responsible for in the math instruction. Math-U-See is just a curriculum, and you are the teacher. What Math-U-See does is give you the information and the tools so that you can present them to your student for the best success; I think this is a cooperative effort. You can even have your kids watch the Math-U-See videos with you, if you like. You know your child, and you know best how they learn, how fast or how slow you should go, and where they need help and reinforcement. I’m counting on your expertise to apply it properly, and you’re counting on our expertise to give you the tools to each math.
One of the things that we do at Math-U-See is to give you several different ways to teach, and you have to choose which one fits your student the best, which one clicks. Teach to a child’s strengths, but build up their weaknesses.
How would I apply this?
If I have a child that’s an auditory learner, I would be doing a lot of auditory input. Instead of just using blocks all the time, I’d be doing a lot of verbalizing the information. I would say, “3+3 is the same as 6. 3+3 = 6. 6 is the same as 3+3.” I’d be putting that into their ears, because if they learn better with the ear, then you want to teach that way.
If a child is a visual learner, the same thing happens. I would teach them visually. I’d find something that works for them and they go, “Oh, I get it. That’s just really helpful.” But I would continue to verbalize, at the same time.
If the building helps your child the most, maybe lean a little bit that way, when you’re emphasizing the new material. If verbalization is helpful, great. But most math that children are going to see is going to be written, and that’s why you need to take this, verbalize it, and illustrate it. Whichever one of these is going to help you the most, great, and maybe your child learns better. We have a family where I live, and they’re a singing family; they make songs out of everything, whether they’re studying geography, grammar skills, etc., and it seems to work for them. You might have a family that you can’t do anything with, unless there’s some kind of a story. For example, one of the facts that I teach, I learned from a boy named Josh, who said, “I ate and ate ’til I was sick on the floor. 8×8 is 64.” I wish I could make a poem up, and I spent hours one day trying to think of poetry for 7×7, 7×6, some of the hardest facts that you teach, and didn’t some up with anything. If you can think of little mnemonics or poems for math that really works for you, post them in the comments.
Memorizing Math Facts Video
Let me just show how we teach in a short 19-minute video; I’m going to go through the addition facts.
Probably the biggest obstacle I find among parents, is the pressure to conform to what their peers or educators think they should be covering, and when. Let your child have the time that he needs and to learn the information that he needs. It’s much more important that you move at the child’s pace than to conform to outside influences. Don’t worry about being behind; focus on teaching your child at their pace.
I do the 1s first, then I do the 2s, then I do the 9s, then the 8s, and the doubles, doubles +1 making 10, making 9 and there you go. Now, I’m going to through it.
This is just something I came up with, but when we’re learning to use the blocks, one of the first things that we learn in Primer, in Alpha, is that we can replace. Instead of having three individual pieces, we want to use a three bar. Keep going here. If I were to show 3+3 with just individual pieces, some students will say, “One, two, three, four, five.” First of all, I have to define addition. To me, that’s not addition, that’s counting. And addition is when you say, “3+2 is the same as or equals 5. 3+2 = 5.”
To help with that concept, that’s why we have blocks that represent the different quantities. There’s the 2 block, there’s the 3 block, so 3+2, and that would be the same as 5. And we build it, and then we notice that it’s even two lines the same length, which is why we explain, “We have two lines the same length,” to show that they are equal or the same. 3+2 is the same as 5.
[1:48] Once a child can count to nine, he learns all of his unit pieces. There’s 2, 3, 4, 5. There’s 6, 7, 8. There’s the one 1-9 pieces. When you’re teaching +1, we just take this and we say, “Oh, 2+1 is 3. 4+1 is the same as 5.” And for each time you do it, you build it, you write it, you say it. But usually, the ones are not too difficult to teach, but this is a good time to learn the symbolism. Here, we have 6+1, two lines the same length, is the same as 7.
You build it, write it, say it. And as you’re teaching this, start looking for patterns, to see how your students are learning better. From you saying it, or from them watching it, or from them writing it? And try to figure out what works best for your child.
[3:01] Once we’ve done the 1 facts, then we’re going to do the 2s.. We have 2+4 and we can see that’s the same length as 6. 4+2=6. We can do all the different facts that way. 6+2 is the same as 8. 3+2 is the same as 5. 2+2 is four. You build it, you write it, you say it. Now, we’re going to have a whole lesson, just the 2 facts, which if we’ve already learned the 1 facts, means there’s only 1, 2, 3, 4, 5, 6, 7, 8 facts. And that shouldn’t be difficult. Take the time that you need. When you’re learning the 2s and the 1s, focus on the symbolism. You can do that horizontally. You can do it vertically. I forget exactly what lesson I teach this incredible concept of commutative property. Here it is. Don’t blink. 3+2 is the same as 2+3. And this is something that’s important for kids to learn, though, because if they don’t have that visual, sometimes they think that 2+3 and 3+2 are two different math facts, so this is going to save them a lot of work.
[4:27] There were nine of these facts, eight of these facts. And in our textbook, we have these graphs of all of the possible combinations of facts. And up in the corner, we have the 1+1, 1+2, 1+3, all the way down to 1+9. And then, across, we have the grid. We have 2+1, 2+2, 2+3. And then we have 3+1, 3+2, 3+3, and they’re all the way down, and all the way over. And it turns out there’s about 100 addition facts.
[5:06] Now, after you learn these one facts, which we did first, we want to encourage the kids to color them, to see what they’ve accomplished, and we’re going to quickly take chunks out of this chart, to show how much we’ve accomplished. Something else we have on the website, is we have a free worksheet generator. Let’s say that you do all the practice pages in the lesson on +2 and it’s not enough, you can generate more worksheets for practice, but that’s just written. Some of ’em, you want to just talk about for the auditory learner. Some, you want to make sure that they’re building them.
[5:41] And we have an online drill program. Let’s say that your child knows their facts. You know that he knows that 7+2 is 9, but maybe he’s not quick enough, or maybe he just needs a little bit more confidence or competition. We have an online drill program, where you can design it according to your student’s needs. These are things that we’re just giving you more and more tools. Find out what works for your students and go from there.
[6:12] Now, once they’ve done the 1s, the 2s, they’ve learned the commutative property, they know how to write an addition problem horizontally, vertically, the 9s are next. And what I tell the story of the 9s is…See, 9, I don’t know if you can tell, but he’s…This is one of the customers, gave us this great story, and they said, “9 is green with envy, ’cause 9 really wants to be 10.” ‘Cause in the base 10 system, that is the kingpin. Everybody wants to be 10, which is why we call it the base 10 or decimal system. 9 needs one more to be a 10. Knowing that, we say, “9, every time I turn around, he sneaks over and grabs one from the units.” So we had 9+4, and now, we have 10+3.
[7:16] And if you do several of these problems, and what’s neat is…I always felt a little badly that I wasn’t teaching this to the student myself just because one of the neat things is discovery education, which the big word for it is inductive. Deductive is when you continue to give facts, and then they parrot them back. But inductive is when you let the student discover patterns for themselves. A nicer way… I don’t know if it’s just nicer, but it’s just my nature. I would rather discover something, than to have everybody tell me everything all the time. People in my family know this. If you have 9+4, and then you do 9+7, and he figures out that that’s 16, and you have 9+5, and they figure out that’s 14, it won’t be long before he’s going to discover that this number’s always one less than this number. Notice that? A little pattern there. You can teach it or let them discover it.
[8:16] Another way to teach this, which is what we try to make it fun, we tell the students that’s a vacuum nozzle, and it makes a…
Because Mr. Nine is…
He’s always taking one from the units. This makes a little learning device. Another way…See, I told you, we’re going to give you multiple ways. Nine plus four… You can also teach it, not with the unit pieces, but with the unit bar, and nine plus four is the same as 10 plus three. And if you do several of these problems with this, you’re going to discover the same concept, right?
[9:00] Once we’ve done the nines, if you need more practice sheets, go to the online drill. We’ve done the word problems in the book. Then you’ve done seven more facts on our grid. We color it to encourage ourselves and encourage our students. Then we’re going to do the eight facts, which I’m not going to take a lot more time with that, because it’s the same way we teach the nines, except, I don’t know if you can tell this, but eight, we call Chocol-8, eight needs two to be 10, and I don’t know if it’s providentially or what, but there’s two vacuum nozzles here, and eight needs to…
From the other number. If you had 8+5, for example, you have 8+5 is the same as 10+3. That’s always two less. 8+5 is one 10, three units. You could use the individual pieces. You could use the unit bars. Build it, write it, say it. I hope that works.
[10:07] Now, we even have songs in the “Skip Count,” an addition facts songbook, which we recommend that you get when you buy Alpha through Gamma, if you haven’t already. And there are even songs for these. And fortunately, oh, I just saw the songbook sitting there. I was hoping I wouldn’t have to sing one of these songs, but I’m going to do it, just because you’re online today. Let’s see if we can find the songs for adding plus eight. I need my spectacles. The tune is “London Bridge is Falling Down.” “Eight plus three is onety-one, 10 plus one, onety-one. Eight plus three is onety-one, isn’t adding fun?” Okay, that’s the verse. The chorus is, “Chocolate-8 is taking two, not from me, just for you. Chocolate-8 is taking two with his vacuum.” Now, I wrote these songs, so don’t be too critical. This is not going to make the Emmys or whatever, but we do have songs, if that will help you. And there’s even… See? It’s like a vacuum cleaner on wheels and he’s always taking two. You have some coloring book to go with it. If I could make these scratch and sniff blocks, if they would help you, I’d do that. I’m just always trying to think of ways to help you learn math better.
[11:36] Okay, so that takes care of the 8s. We’ve done 6 facts now. By the way, if you add these up, you’ve done 30 of the 55 facts, because there’s not really 100, because since you’re learning the commutative property, you don’t have to learn…If you’re learning 8+3 over here, you don’t have to learn 3+8 over there. If you look on our big chart in our books, you really only have to learn 55 facts. We’re over half done. Then we do the doubles. Oops, shouldn’t have erased that. Let me go back to my thing here. The doubles, and I have my own theories on this, but I don’t have a research paper to document it. But I think the doubles might be the easiest facts to teach, because…My theory is, is because of board games and games that we play that have dice, that have dominoes. And for some reason, if you’ve already learned two plus two, nine plus nine, eight plus eight, there’s only five facts to be teaching, and that would be three plus three, four plus four, all the way up to seven plus seven.
[12:48] Each one of those, you build it, you take two threes, that’s the same as six. You take two sevens, it’s the same as 14. You build it, write it, say it, practice it, apply it, and it comes out. You learn those. Then you have doubles plus one. Now, doubles plus one is, if you know that three plus three equals six, and you’ve mastered that in one lesson, and two lessons later, we’re going to come in and say three plus four, that’s one more than three plus three, so there are the… You’re going to learn three plus four, you’re going to learn four plus five, five plus six, and six plus seven. You’re going to have four facts there to learn using that method.
[13:41] And then we have making 10. Now, there’s only three new facts here, that you haven’t learned with the previous methods, the plus twos, nines, eights, and all that. But this making 10 might be one of the most important fact sets, or sets of facts that you teach. And this is, “How many different ways can you make 10?” Which I usually do, by saying, “Well, we’re building a wall and it’s gotta be 10 units long. And we’ve run out of the 10 bars, so what two pieces can we stick together… ” The blocks do snap together… “That will make 10?” Well, eight plus two will work, seven plus three will work, nine plus one will work, six plus four will work, five plus five will work. Oh, so then we can say, “Five plus five.” Well, we’ve already learned that, because of the doubles. We have eight plus two here, we have nine plus one here. We’ve already learned those, because of adding plus one and plus nine. The only new ones, really, are four plus six and three plus seven. Just two new facts. But learning all of them, using this method, sometimes this is called the family method. This would be called the 10s family, some books will use that. And we’re going to do all of our 10 facts that way.
[15:19] And then you have making nine. And making nine, you have five plus four, you have three plus six, two plus seven, one plus eight, there’s a couple facts there. When you go through all of these little different patterns, these families of facts, there’s only three facts left. And it’s been a while since I’ve looked, but I’m pretty sure they are three plus five, three plus six… Ugh, I forget the last one. It might be four plus seven. If I’m not mistaken, that might be the only three. And get out your blocks, and build a four plus a seven. You could do three plus five. You could say, “Well, that’s two more than three plus three.” This is actually the fun part, because I like to give those to kids and say, “How are we going to do this? Mr Demme doesn’t have any tricks for this one. We’re on our own,” and let them start to develop their own strategies for problem solving.
[16:21] Now, I teach the addition facts, and while I’m teaching the addition facts, I also, simultaneously, in our books, teach solving for an unknown, which sounds algebraic and complicated, but it’s really not… Let’s say we’re teaching our doubles, or, well, make it tougher… Try doubles. If I’m teaching the doubles, I know that they’re learning three plus three equals six, so I might say, “Something plus three is the same as six.” And then I build it, by pulling out the six, and pulling out a three, and re-verbalizing it, and saying, “Something plus three is the same as six.” Have the students go find the piece that goes in there… Until they do. And now, they’re successful, and they find out, “Oh, it’s a three.” I just have ’em put the three there.
[17:18] Now, at this level, I am not asking a child to find solving for the unknown, by subtracting three from both sides, and doing the additive inverse, da, da, da, da, da. We’ll do that later in Pre-Algebra. But there’s three things that I’m accomplishing, hopefully, by teaching this. Number one, I’m laying a concrete, visual, hands-on foundation for Algebra, that we’ll build on later. Number two, I’m reinforcing addition, just doing it a different way. And the more ways we can do it, sometimes it fills in the gaps in our brain, helps us to remember it better. And the last thing is, every subtraction problem can be re-written as an addition problem. Even though it looks like subtraction, I could say, “What number plus three is the same as six?” Like I just did here, “What number plus three is the same as six?” I’m laying a foundation for Algebra and I’m laying a foundation for subtraction, which is why I personally have chosen not to teach subtraction, until after I’ve mastered addition facts.
[18:25] This is what we’re going to do in Alpha. Most of the book is just teaching the addition facts. Once they’ve been mastered, once you can say, “Hey, what plus three makes 10?” Well, if they already know that seven plus three makes 10, they go, “Oh, seven. Duh.” And then [chuckle].. They don’t say, “Duh,” anymore, that’s an old one. But anyway, you get the point. So Alpha, we’re going to teach single digit addition, and then single digit subtraction. When you finish Alpha, you should have memorized all your addition facts.