I’d like to think I’m pretty good at math. I did well on my AP exams and took Calculus for a few quarters at UCLA and in general, did a lot of math for chemistry and physics and my other science courses. I still remember a lot of useless geometric formulas for calculating the areas of triangles and circles and a ton of other crap.
So, you know. I thought, hey, teaching Cookie Monster math shouldn’t be hard. Last year was Kindergarten and we went through several books of Singapore math and ended the year somewhere in 3rd grade math around subtracting hundreds and borrowing/carrying, etc.
We took quite a few months off of subtraction and when we picked up where we left off, I was surprised to see how little Cookie Monster seemed to have retained or understood of even the THEORY of subtraction.
Also, it seemed like he didn’t understand ones, tens, hundreds, thousands, and columns and “borrowing” and what not.
I spent our first math session mostly yelling at him and then feeling bad because I know that his failure to understand the foundation of subtraction and units and anything was actually my failure. It’s not his fault he doesn’t understand something if I never actually taught it to him in a way that he integrated into his brain.
Eventually, I switched to manipulatives and I started super simple with unifix cubes and then moved onto the Base Ten Blocks that come in units, tens, and hundreds. (I don’t have the thousands, but I am thinking of buying them.) (Amazon affiliate links used.)
I had all these lofty thoughts of this magically changing how Cookie Monster understood math and subtraction and borrowing, etc.
I mean, I don’t think it hurt him. But I don’t think it translated.
Anyhow, on the first day of our official homeschooling, I spent 30-40 minutes with him on subtraction and I nearly died of frustration. As a result, I had a long conversation with Guavarama (and also a separate conversation with my other mama friends) and the result was something I found terribly interesting (particularly since it affects my life AT THIS MOMENT).
So, I asked for permission to reproduce our text conversation in full. Perhaps it will help you if you find yourself in a similar situation.
MM: Cookie Monster does subtraction SO WEIRD that it makes me want to die. Took me over 30 minutes to figure out that he does the math in his head. He just uses the wrong terminology [when he explains to me what he is doing].
So he doesn’t think in terms of borrowing, etc. I was using manipulatives to do it and he was kinda getting it but not relating it to the way he does the problem.
And then he started pissing me off on purpose.
The problem was: 653 – 85 = ?
I asked him what he has to minus. He’s like, 2. No, 5. No, 4.
I’m like, LOOK AT THE FUCKING PROBLEM!! IT TELLS YOU!!
Then he finally decides he doesn’t want to use the manipulatives so he just stares a the problem and comes up with the wrong answer the first time (it was really close) and then the right answer the second time.
I make him explain to me how does it and somehow, he finally tells it to me in a way I understand.
He did: 653 – 5 = 648 then 648 – 80 = 568.
He got the right answer so clearly, that’s the way his brain works. But I don’t know what to do. Shouldn’t he know how to use borrowing? And carrying?
But his way is kinda faster?
I DON’T KNOW WHAT TO DO.
But he isn’t wrong.
Sorry to be blabbing. I’m just kinda at my wit’s end because I don’t want to change his brain – but there might be murder.
GR: Definitely don’t say borrowing. Use the word exchange. Because that’s what you’re doing concept-wise. You’re not borrowing anything.
MM: I think we use the word, 換 (huan4/exchange), like swapping.
GR: And hahaha on the not looking at problem. I swear they do it on purpose!
MM: (I just use the term borrowing because that’s the term I learned as a kid.)
GR: And no. He’s actually doing common core math the way he comes up with these answers. It is correct. That is how it’s taught in Montessori Math and I’m guessing Singapore Math.
MM: Singapore Math has them split up the 53 into 40 + 13.
I mean, obviously, there is more than one way to do math.
GR: What he’s doing is actually breaking the steps down when he does it, in his head. But that is exactly how you’re solving for the problem.
MM: So do I just let him stare at the problem and answer it? It seems to work ok when it’s a straight up question like 653 – 85 = ?
But doesn’t seem to work as well in word problems.
This explains why he doesn’t care if the problem is written vertically or horizontally.
GR: 53 into 40 + 13 IS borrowing. They’re telling him, “Exchange 10 in the 5 and now the 10 is added to the 3, hence 13. That’s Montessori Math.”
MM: Right, but he isn’t doing that. He’s splitting the thing that is being subtracted, which is how Hapa Papa does it, I think.
He’s splitting the 85 into 80 + 5. And subtracting the 5 first then the 80. So he’s doing two subtraction problems.
GR: But that IS what you do.
MM: Lol. Ok.
GR: 653 – 85 right? You said, he did 653 – 5 = 648 then 648 – 80.
So that’s right. He’s subtracting 5 from 3. But he’s learned to exchange so he did 13 – 5, which is how he got 648.
Then he subtracted 40 – 80, which then he has to exchange again.
You have to make the link between what he’s doing in his head and paper.
GR: From the math theory I’ve read, basically there is the concept of mathematical mind and constructivist math, which is that people arrive at answers multiple ways. And that’s fine.
And paper is just something we use to help us keep track of what our brain is thinking as it works it out. Because the equations get more complicated.
MM: Ok. So how do I teach him? Or help him if he gets the wrong answer?
GR: So he’s doing it right, but to write down what he’s doing in his head onto paper, he has to take note of what he did. This also helps him when he’s doing like 10 digit – 9 digit… and he gets it wrong. He can backtrack and see where he got it wrong.
I have to tell you though, this concept they’re not happy with. They just want to arrive at the answer and that’s that.
Took me a long time to convince Thumper that she needs to write out what she’s doing. Astroboy, on the other hand, had no problem. Shrug.
GR: So for your equation, 653 – 85, he did 3 – 5, but point out what he did was to make it 13 – 5, which meant he made the 5 into a 4 in his head. Then he should, in his first step, cross out the 5 and make that into a 4… for note taking purposes, to remind himself what he did.
MM: *thumbs up*
GR: Basically, Montessori Math has the kids do concrete, and then mapped the concrete to writing.
So now you have 648 – 80, which you again have to exchange so you should cross out the 6 and turn that into a 5. Now you have 140 – 80, which gives you 60, and you write down the 6.
And you just carry down the 5.
GR: So, I would say, if he’s giving you the right answers, don’t make him work it out. Because he sees no point.
That’s one option.
MM: Hahahahahah. Ok.
GR: But, when he starts getting them wrong – and he will as you add more digits – then point out this is WHY you write it down and note what you’re doing.
GR: Cuz that’s why we do math this way. That was an “Aha!” moment for me when I read that. We calculate on paper this way because it’s just note-taking. It isn’t the only way.
MM: I like this option because it requires me to do nothing until something happens.
GR: Cuz as an adult, I don’t calculate this way anymore. hahahahah.
MM: It’s true. BECAUSE I HAVE A CALCULATOR. Lol. Which really isn’t true, but you know what I mean.
GR: hahahah. I mean, in my head, I would do strange things like 653 – 85 is the same as 650 – 85 + 3.
MM: Yes. That is how Hapa Papa would do it. He is super fast at math. I usually ask him instead of using a calculator.
Maybe I should make Hapa Papa teach subtraction. Hahahahah.
And, because I really like to belabor a point, here’s part of my discussion with Irish Twins as I was discussing it with Guavarama.
IT: Wait, I actually looked a the problems you give him and that’s how I would do it. How do you do it???
MM: Hahahaha. I actually would’ve subtracted 80 first then the 5.
But that’s how I do math NOW. Not how I learned to do math, if that makes sense.
So, I’m not against the way he does math. I’m just not sure how to help him.
Guavarama suggested that I do nothing until he gets lots of things wrong which will happen when you add more and more numbers. And then explain why we take notes with the borrowing and carrying notations.
IT: Actually, weirdly enough, if you present it horizontally, I would probably take 53 off each side.
IT: I like nice, flat numbers.
Who knew I would have not one, but TWO conversations all on subtraction?
When I had this conversation again with Hapa Papa, I had him read my conversation with Guavarama vs tell him the same story. He mentioned that Cookie Monster does math the same way he does.
And then there was a TWIST.
Hapa Papa didn’t know what borrowing was.
I had to explain it to him and he was like, what? I was like, this is how they used to teach math. He said he had no idea what I was talking about.
He must have already figured out how to do math and ignored his teachers.
Is this what happens to homeschooling parents? We talk about theory and pedagogies?
How did this become my life?
Ah well. I do enjoy nerding out, even if I am clearly unworthy to do math around Cookie Monster.
Hope these conversational glimpses were helpful (or at the very least, not boring). Have a great day!