Moving forward through math vs knowing math facts

[blondeviolin]

I've seen a general consensus here that kids' facts will cement themselves as they work through harder material. I agree, to a point. At what point, though, do you stop and make sure certain facts are down cold?

 

For example, what if your child understands place value and addition to the point of adding 3 and 4 digit numbers, but he's still not got his addition table memorized? It obviously takes a bit to calculate in such an instance. How do you require a child to divide large numbers before he can recall his multiplication tables?

 

At what point do you allow/encourage the accelerated child to slow down to facilitate automaticity of facts?

[regentrude]

My gifted DD resisted learning the multiplication tables - because for the first time, she had to memorize something as opposed to "just knowing" it automatically. She thought that must mean she is not smart. I did insist, and we found a way that worked for her visual learning style: she made a poster, hung it over her bed, glanced at it a few times each day, and learned the tables in a short time. But oh, before that, there were tantrums and resistance and "I can't do this".

What helped was to use color, to fill in just a triangle (the rest follows from the commutative property), to color the "trivial" ones (ones, twos, fives and tens) and thus to visualize that there really are only a handful of facts that require actual memorization.

I believe that, in order to do math efficiently and in order to become familiar with numbers, knowing the times tables is non-negotiable. So, for a child that does not have a learning disorder, I insist on memorizing before moving on to multi-digit division.

 

My kids are not allowed to use a calculator until absolutely necessary in precalculus.

 

I am not sure, however, what you mean by memorizing "addition table"- I never heard of such a thing.

[jennynd]

I agree with regentrude,

I didn't move my kid to multi-digit multiplication and division until he had the table solid down. I will do the same with my younger one. However, I will not force addition and sub. I never have to memorize add/sub

[Iucounu]

What I did was teach DS the framework of the basic math facts first. For example, all doubles, square numbers, etc. were memorized early on. In addition, I taught him, or he simply picked up, (re)construction techniques such as the following:

 

Ex.: DS has forgotten the math fact 6 X 8 = 48 .

DS realizes that he remembers 3 X 8, and that he can use this to (re)construct 6 X 8

DS adds 24 + 24 in his head (likely via 20 + 20 + 4 + 4)

 

... and so forth. Another thing that helped was printing out a multiplication table, with the square numbers picked out. He thought it was fun to look it over and note number patterns and relationships. He was learning during that time, but it didn't seem like drill to him.

 

This sort of thing seemed to work well for him for a few reasons: he had bought into memorizing the facts, because he was impatient with calculation slowness when working hard problems; reconstructing the number facts this way took longer than simply remembering them; and in doing reconstruction exercises, he would solidify other facts in the process (for example, he was never going to forget 3 X 8 after doing the above a couple of times, and he also practiced addition).

 

From this perspective I would not have naturally tended to delay DS's progress through new concepts or new calculation skills. If he hadn't gotten his times tables down by the time we hit long division, he would have really had to slow down, which would have created the pressure for him to start remembering, leading to improvement in short order. However, if he had gotten to the point where calculation slowness was impairing his ability to think clearly about problems, I might have put on the brakes; that just never happened. Elementary grade math is pretty basic stuff.

 

DS never was big on drill, and adding info on the structure of the numbers helped make it seem less boring, plus we never set aside big blocks of time to do boring drill; our time was focused on doing problems. This may have all worked so well for us because DS always had a good attitude about math, and if he encountered slowness in calculation, he was able to realize that this was because he hadn't finished internalizing math facts, and that the slowness was proof that that was a good thing to do. :)

 

I recommend Math Mammoth for useful memorization techniques for the basic math facts, based on a couple of Youtube videos by Maria Miller that I watched a while back. This math blog also has some useful techniques. You could probably get lots of ideas from such sources on how to build up a framework for the math facts in your little one, without having to do tons of drill.

Edited February 23, 2012 by Iucounu
Got rid of the light bulb icon; don't know how that got on there

[Dmmetler]

I do stealth memorization-lots of songs on the iPod, lots of games, lots of word problems and multistep problems and logic and algebra, while moving on. This is helped by Singapore being a soft spiral, because it allows time to work on the stealth stuff before we get back to computation, and the IP/CWP type problems do tend to mix up concepts a bit and provide practice. I imagine it would be harder in a program that spends longer on one topic. I've tutored kids doing Saxon, and I'm not sure either DD or I would have survived the grade 3 book with our sanity intact.

 

I've had in mind that I'll handle memorization like writing-make sure it's appropriate to her age/grade level, and so far, she's gotten there on or before schedule, even if it wasn't at the appropriate point in the math series.

[Crimson Wife]

When my DD had finished everything in Singapore 3 A/B with the exception of the chapters on multi-digit multiplication and long division is when we forced the issue. I wasn't going to get 4 A/B until she had finished 3A.

[LittleIzumi]

We are going wider while working on her facts. Facts: games daily. Math: Single-digit and tens multiplication, negative numbers, learning basic division, basic algebra, inequalities (using MEP problems), doing more complicated single-digit addition through Miquon (4-1+7=___-10 sort of problems), etc.

[Iucounu]

What I take away from this thread so far is that some view multi-digit multiplication and long division as the point by which the times tables must be mastered. That's not an unreasonable pausing point, although I tend to disagree slightly, only because I think that that's the point at which most non-disabled students, who fully appreciated that going on was a privilege and wanted that privilege, would memorize the facts if they weren't memorized already. Really, the only thing sacrificed by going on is extra time to do the work, and it's going to get boring eventually for the student, especially a gifted one.

 

I'm always in favor of being flexible and trying to suit the learning to the student. I find it works best if the student understands that it's in their best interest to do something, and that you're trying to help them. Maybe I have a luxury in having a child who's been bored silly in public school so far, so he knows how bad it can get for him. He loves our time together, because it's a huge intellectual relief.

 

This is an interesting thread for me personally, since I have tended to view mastery in math as the ability to get the right answer in a good way, based on the right understanding, but with "good" not including calculation speed. I always figured that would improve on its own (which has been true in our specific case). I would have in the past seen memorization of math facts as an efficiency aid, the lack of which would never by nature halt forward progress at all, just slow it down, a problem that would fix itself due to student impatience.

 

From the perspective of this thread, I am starting to see going on more as a wait-and-see approach: you advance to new concepts while you wait and see if the facts gel without drill; if not, you resort to drill at a pausing point. Up to this point I was thinking about it from an almost unschooling perspective, that the student would acquire the facts as necessary, but without any pausing point if that didn't happen, just faith that it would. I can see, though, that different kids would show different aptitude and interest for memorizing such things, whether through drill or on the fly, and they do have to learn them eventually.

 

I don't know if I would skip earlier parts of a curriculum, though. I tend to like latching onto some curriculum like Singapore Math with a clear scope and sequence, and then going through it. I wouldn't personally tend to skip around, so I wouldn't skip earlier calculation-heavy sections to get on to later more conceptual ones. Instead, I'd not outright skip any sections (because the only reason IMHO to do so is when a student pretests out); if a student showed a lack of mastery on a calculation-heavy section, I'd have him do it; but I'd let him take as long as he needed to do it. If the student failed the end-of-unit test, I'd do extra work then.

 

I would also probably not ever suspend other privileges in an attempt to force memorization of math facts, as was mentioned in another thread IIRC. This is for a few reasons, including that I have highly stubborn children, who would probably view that as a chance to have fun showing me how stubborn they can be; and that in the end I want the motivation for learning to be internal whenever possible, and I think it's important to nurture that. External motivation is the thing I worry about most when I read about Tiger Mom style education, as I worry that it would tend to create children without an innate love of learning, who don't have a true work ethic though they can work hard when forced to do so. This is probably the wanna-be unschooler in me coming out again. :D

Edited February 23, 2012 by Iucounu

[coffeegal]

I've seen a general consensus here that kids' facts will cement themselves as they work through harder material. I agree, to a point. At what point, though, do you stop and make sure certain facts are down cold?

 

In my experience, kids who are gifted at math either become superfast at calculating the math fact or memorize the facts easily. If you're worried about your child learning the math facts, I'd suggest getting some math games to drill the facts in a fun way. There's Quartermile math for the computer, Math-it as a board game, and my kids enjoyed a mythology card game that drilled multiplication facts. When we were at our height of fact memorization, I required the kids to spend a certain amount of time drilling in addition to their math lesson... their choice of methods. :D

[jennynd]

 

 

I would also probably not ever suspend other privileges in an attempt to force memorization of math facts, as was mentioned in another thread IIRC. This is for a few reasons, including that I have highly stubborn children, who would probably view that as a chance to have fun showing me how stubborn they can be; and that in the end I want the motivation for learning to be internal whenever possible, and I think it's important to nurture that. External motivation is the thing I worry about most when I read about Tiger Mom style education, as I worry that it would tend to create children without an innate love of learning, who don't have a true work ethic though they can work hard when forced to do so. This is probably the wanna-be unschooler in me coming out again. :D

 

 

I do agree it partly depends on the kid. I have a extreme perfectionist and have him not master the table, He probably will get very frustrated working on multi-digit multiplication/long division. and that probably gonna lead him to not wanting to do math altogether. He also have the strength that he has almost photographic memory, so, memorize facts really was not too much a task.

For my DD, I might agree with you that your approach might work better for her. She is stubborn as a cow (Chinese expression). Trying to force her to memorize something might have neg affect

[Dmmetler]

I don't skip around-but I've found that Singapore really does that for me-usually there's computation fairly heavily in A, and B does other things, which gives time for DD to get the facts/concepts that we spent time on in A to mastery before computation comes around again in the next A book, in ways that don't seem quite so repetitive to her. I used to tutor math for a school that used Saxon, and I think the explicit repetition of Saxon and focus on memorization would very literally drive either DD or I insane because she'd dig in her heels and refuse to memorize, but by playing math games, doing multi-step problems, especially word problems, playing with Hands on Equations where the same skills are dressed up with algebra, and so on, she really had gotten one set of multiplication facts fairly solid by the time she needed to add the next set.

[vito]

How do you require a child to divide large numbers before he can recall his multiplication tables?

 

"Memorizing = bad" is just trendy these days, possibly in light of problems with teaching in schools.

IMO, memorizing and understanding are equally important.

Where are those days when kids were memorizing poems, and it was considered one of the key points in education?

 

There is no way to do long division without strong multiplication skills including quick estimations of say 2-digit number multiplying by 1-digit number.

 

Example: do long division 234/27.

You will need to estimate 27*8. For this you will need to do some of 27*7 and 27*9 and 27*6 depending on your skill.

[blondeviolin]

In my experience, kids who are gifted at math either become superfast at calculating the math fact or memorize the facts easily. If you're worried about your child learning the math facts, I'd suggest getting some math games to drill the facts in a fun way. There's Quartermile math for the computer, Math-it as a board game, and my kids enjoyed a mythology card game that drilled multiplication facts. When we were at our height of fact memorization, I required the kids to spend a certain amount of time drilling in addition to their math lesson... their choice of methods. :D

 

Oh, I'm not worried about memorizing facts. My oldest is very good at memorization and knows nearly all of her sums to 20. The ones she's not sure on, she has a quick way of figuring.

 

I just am interested in these schools of thoughts. :D I was raised to memorize my math facts until I could move on. As a linear and mathy person, this was of no detriment to me. The Husband was also required to memorize facts and he still counts on his fingers (especially if it is a subtraction problem).

[boscopup]

I didn't have to worry about add/sub facts for DS1. He picked them up by time we started working on multiplication, where addition was also used.

 

I did have to work on multiplication tables, but not a ton. I basically had decided that he needed to know them before we got to long division. We were successful. He does still have to think about them sometimes, but he has never had any trouble doing long division fairly quickly. I actually need to review the 6's, 7's, and 8's with him, as he has done a couple funky things this week. :tongue_smilie: But if I see one that he did wrong and I ask him that fact again, he'll correct himself. He does know them.

 

DS2 is figuring out his addition facts on his own right now (in K math), so I think he'll also be fine with add/sub facts by time we need them memorized. It will be a while before he gets to multiplication, so who knows what we'll need to do there. I guess we can pull out the whole bucket of C-rods. :D

 

ETA: So far, I haven't ever had to skip a topic and move on. We've just done everything per the sequence of the curriculum being used, and the facts knowledge caught up while we were moving on because the new topics used the facts knowledge and thus gave us more practice without having to be mired in boring add/sub practice forevermore.

[Embassy]

I move my kids forward while they are still learning their facts. I do math on three levels. Math facts is the lowest level, a standard program, and additional supplements at a higher level. I will probably make sure all math facts are secure before we start pre-algebra. I've found that my oldest has learned most of his math facts through repeated use.

[Crimson Wife]

The trick is finding a privilege that the child will be super-motivated to earn back. I had spent months trying a bunch of different things- different games, Times Tables the Easy Way, flashcards, Multiplication Mosaics, oral drilling, etc. without much success. Yet when DH finally stepped in to play "bad cop" and took away the computer, Wii, and DVD's, all of a sudden she got her backside in gear and had them down pat within a week. All it took was the proper incentive.

[3Blessings]

I am also interested in this thread . . . .

 

I have always thought that addition and subtraction should be memorized first. We've worked steadily with addition and are plugging away on subtraction. In the meantime, we do other concepts (measurement, etc). I just recently discovered, however, he has managed to memorize all his multiplication tables with no help from me, dad, etc.

 

My first thought was to drop memorizing add/subtract, but then I second guessed myself.

 

I guess I just keep coming back to "ease of recall" for add/subtract. I don't want counting on fingers when the math gets more complex. Does anyone else think that, too?

 

So I guess I'm not adding much to this conversation, but rather still :confused: about the memorizing!!

[Beth in SW WA]

Older dc did drill & kill via Saxon 1-5 w/ daily timed tests at private school.

 

Younger dds have never taken a timed test and they are buzzing through math and learning their facts on the fly by just using them day after day...