The Benefits and Pitfalls of Memorizing Math Facts...a Discussion

[sweetpea3829]

So, DD7 is Dyscalculic and struggles quite handedly with math. I'm fairly certain that mental math (as Singapore presents it) will likely always be out of her reach. I'm cool with that. DS6 is gifted with math (go figure) and mental math is second nature to him. My question/discussion is really about both NT kids and LD kids. (Ok, not only did this post before I wanted it to, but I can't enter spaces between paragraphs for some reason.) Anyways...DS is at a point where he should probably begin memorizing math facts. DD on the other hand, is still learning how to add and subtract and is doing ok with it and will soon be at a point where she should also begin to memorize math facts. But I feel like that may actually be a detriment to both of them! For either one of them, memorizing math facts means they no longer have to think about the *math* behind the equation. They no longer have to think about WHY 7X6=42. I can see why this would be a benefit....it means quicker computations in later math when equations become longer and require more steps. So definite benefit there. But I can't seem to escape the feeling that perhaps this memorization is something we should really be waiting on. Am I making any sense here? I'm not sure it's good for them, at this point, to not be thinking about the why behind the equation. Anybody else feel this way?

[CookieMonster]

I see that this question posted for you several times in different formats. I'm am thinking this is the complete question?

 

I am not quite sure how to express my opinion on this. But, it seems to me that you've made an unecessary distinction between fact memorization and understanding mathematics. Memorizing math facts does not automatically mean that the child forgets the WHY behind the math facts. It CAN do that. But, I think that only happens when math facts are constantly placed in front of children to be memorized like some sentence in a foreign language.

 

My children memorized their math facts because they repeatedly worked out the problems using manipulatives, pictoral representations, and mental math. Their ability to recall the process behind the fact, and apply it to harder problems, was never diminished after they had successfully memorized the facts and recalled the answers "without thinking". I guess I never made the memorization part a separate activity, but trusted that through repeated use the facts would cement themselves. And that's how it worked out.

[geodob]

In regard to this, I would mention the traditional approach to learning math in Japan?

Where children learn to represent quantities and do math on a Japanese Abacus, called a Soroban.

 

But a crucial element, is that they avoid teaching children the name and symbols for numbers, until around 9 years of age.

Though 9 years old Japanese children, generally have the math abilities of 12 year old Western children.

But the way that 'mental math' is done in Japan is very different, where they don't think of numbers as words and symbols as they do the calculation?

Rather, they think of numbers as patterns, which having learned to represent on an abacus. They 'feel' with their hands.

So that they 'feel numbers', and feel a calculation.

In the same way that people who are born Deaf and learn sign language. Feel letters and words. Then when they are thinking, instead of hearing a word in their mind? They feel the words in their mind, without having to move their hands.

So that mental math in Japan is done without using number words and symbols.

These are only used to record and communicate an answer.

 

The difference in their approach, is highlighted by their common activity, of racing to do mental math quicker than a calculator.

[Heathermomster]

So, DD7 is Dyscalculic and struggles quite handedly with math. I'm fairly certain that mental math (as Singapore presents it) will likely always be out of her reach. I'm cool with that. DS6 is gifted with math (go figure) and mental math is second nature to him. My question/discussion is really about both NT kids and LD kids. (Ok, not only did this post before I wanted it to, but I can't enter spaces between paragraphs for some reason.) Anyways...DS is at a point where he should probably begin memorizing math facts. DD on the other hand, is still learning how to add and subtract and is doing ok with it and will soon be at a point where she should also begin to memorize math facts. But I feel like that may actually be a detriment to both of them! For either one of them, memorizing math facts means they no longer have to think about the *math* behind the equation. They no longer have to think about WHY 7X6=42. I can see why this would be a benefit....it means quicker computations in later math when equations become longer and require more steps. So definite benefit there. But I can't seem to escape the feeling that perhaps this memorization is something we should really be waiting on. Am I making any sense here? I'm not sure it's good for them, at this point, to not be thinking about the why behind the equation. Anybody else feel this way?

 

 

I don't understand this question.

 

The purpose and end goal of early math education is for students to know their math facts backwards and forwards, while establishing a firm conceptual base.

 

How exactly were you planning to get your son to memorize his math facts? If he can already perform mental math, fun math practice directed to his learning style, will solidify his math understanding so that the math facts become automatic. Fun math practice takes a short amount of time and includes manipulatives, movement, songs with clapping, flash cards...whatever helps him learn.

 

Sousa's book How the Brain Learns Mathematics would really benefit you.

[sweetpea3829]

First, let me apologize for the multiple postings. I'm not sure what in the world is going on, but when I tried posting that topic, it acted all weird. In fact, I didn't think anybody had even seen the postings, and I tried deleting the duplicates, but they wouldn't delete. Now, I can't seem to get it to stop underlining while I write. So weird! And it won't let me hit enter for a paragraph break. Am I the only one having these difficulties? Maybe it's because I upgraded to IE9 (or whatever IE they're on now....I didn't actually want to upgrade, they forced me to...lol). Anyways, back to the question at hand. DS pretty much has his addition facts memorized within 20. When I say he's doing mental math, I mean he's rapidly making tens in his head (or fives) so as to more easily add and subtract. But now that he's learning multiplication and division, he can do the mathematics quite easily...but he still does need to actually calculate by skip counting. He's not memorized any multiplication or division facts as of yet. And for sure, he's only JUST learned these computations, so I'm not exactly expecting him to have the facts memorized. But I see a lot of mention of having kids memorize these facts and it occurred to me that perhaps I should be spending some time with him, using flashcards, or whatever, to memorize multiplication facts. And THEN it occurred to me that I'm not really sure that I WANT him to have those facts memorized, because if he were to memorize them NOW, at this point in his mathematics, I can't say for sure he'd ever really internalize the mathematics BEHIND multiplication. Sure, he would be able to spit the facts out...but would he actually KNOW the computations. (pretend there's a paragraph break here) And then I started thinking about DD. Now, I don't know exactly how far she will be able to go with mathematics. Right now, while she continues to struggle with remembering what number comes before a given number, I'm more inclined to say she will not likely be doing any sort of mental math and may always need manipulatives, or a calculator, or her fingers, or to write it down, or whatever works for her. Perhaps she will surprise me, and as her brain matures, mathematics will come more readily for her. But as I sit here now, and I see her working addition and subtraction problems (simple ones...with numbers up to 20), and again, I am hearing a lot of parents talk about their kiddos memorizing their math facts...well anyways, I'm wondering if this would be something that would benefit her. At this point...should I go ahead and take time and have her memorize addition facts. And then subtraction facts. Or will I be doing her a disservice in giving her a memorized fact, instead of a conceptual understanding of WHY the computation works the way it does. Or am I completely missing the point that it doesn't have to be one or the other...they can memorize the math facts, but still maintain an understanding of the conceptual process. I guess I'm just concerned that if I spend much time with them on memorizing the facts, than I may end up undermining that conceptual understanding. Anyways, I'm not really sure where I'm going with all of this...it just had occurred to me that perhaps explicit memorization of math facts may not necessarily be the best path for my kiddos. But it seems like a common thread, especially on some of the LD boards I'm a part of...talk about how so and so's LD kiddo really struggled with memorizing their math facts. And I was just thinking about how I hadn't even considered the necessity of memorizing math facts. Especially for DS, who more or less picked up those addition and subtraction facts on his own through, as Cookiemonster stated, repeated practice and exposure.

[sweetpea3829]

And Heather, you've mentioned that book to me before. I need to get a copy of it and give it a good read-through. Sounds like an interesting read. (and hey, look...no underline this time...still can't hit enter for a paragraph break though).

[FLDebbie]

As a previous poster said, memorization of the facts doesn't preclude understanding of the concepts. And whether the child memorizes 6 x 8 = 48 before they've learned the concept of multiplication shouldn't matter either, as long as they get that conceptual understanding when they're developmentally ready for it. 6 and 7 is young for lelarning multuiplication, they have time still.

 

Thinking of it in a different way, would you stop your child from memorizing a beautiful poem simply because he or she doesn't understand the literary allusions or structure of poetry? They'll learn that later, when they're ready. And will they then not be able to apply those advanced ideas to the poem they learned when they were younger? Of course not. In fact, they won't have to work on memorization at that point and can apply the advanced concepts to information already in their heads.