Quick! 9x7=?
January 19, 2007 2:32 PM
100 multiplication problems in 5 minutes. Our 9yo needs help in speeding up his answers.
Each week the kids are tested on multiplication facts (#'s 1 - 12). And each week our A student fails. He knows the facts but can't seem to answer them quickly enough, averaging about 60 out of 100. He's getting very frustrated.
100 random written problems, 10 rows of 10, in 5 minutes.
To study he/we use a Multiplication Rap Video, Flash cards, home tests, and various on-line math games.
How can we speed things up? One thing we did was tell him to work across the paper, after noticing he was working down - this helped some. We're looking for more 'tricks' like this, or anything that can help speed up his thought process.
He can write the answers down quickly once he remembers the answer. Any ideas?
Thank you.
Each week the kids are tested on multiplication facts (#'s 1 - 12). And each week our A student fails. He knows the facts but can't seem to answer them quickly enough, averaging about 60 out of 100. He's getting very frustrated.
100 random written problems, 10 rows of 10, in 5 minutes.
To study he/we use a Multiplication Rap Video, Flash cards, home tests, and various on-line math games.
How can we speed things up? One thing we did was tell him to work across the paper, after noticing he was working down - this helped some. We're looking for more 'tricks' like this, or anything that can help speed up his thought process.
He can write the answers down quickly once he remembers the answer. Any ideas?
Thank you.
Ugh, I hated those tests so much. I'm a scientist and engineer, and I only recently completely memorized the multiplication tables.
Could he have a problem reading the questions? Have you gotten his eyes checked recently?
When you work with flash cards, does he do them faster, slower, or at the same rate (about 1 every 5 seconds)? While doing flash card work, try to time him (internally) - he needs to be able to answer 1 question every 3 seconds, so if you flash the card and it takes him longer than 1-one-thousand in your head, he's using some other method to come up with the answer, besides memorizing it.
Finally, I don't want to make any assumptions about this situation, but I do want to ask you not to put too much pressure on this little guy to do stupid tasks for a grade. My brother used to love math jokes and math tricks, until he had a crap teacher who would punish him for not being able to do long division quickly (she'd have people stand up when they finished, and he'd always be the last person sitting down). It demoralized him, and he really started to hate math with a passion around that time.
posted by muddgirl at 2:44 PM on January 19, 2007
Could he have a problem reading the questions? Have you gotten his eyes checked recently?
When you work with flash cards, does he do them faster, slower, or at the same rate (about 1 every 5 seconds)? While doing flash card work, try to time him (internally) - he needs to be able to answer 1 question every 3 seconds, so if you flash the card and it takes him longer than 1-one-thousand in your head, he's using some other method to come up with the answer, besides memorizing it.
Finally, I don't want to make any assumptions about this situation, but I do want to ask you not to put too much pressure on this little guy to do stupid tasks for a grade. My brother used to love math jokes and math tricks, until he had a crap teacher who would punish him for not being able to do long division quickly (she'd have people stand up when they finished, and he'd always be the last person sitting down). It demoralized him, and he really started to hate math with a passion around that time.
posted by muddgirl at 2:44 PM on January 19, 2007
It sounds like a dumb test of memorization, so I don't think there's any way to get better other than to memorize. I would practice drilling him orally — no writing to waste time on.
posted by raf at 2:45 PM on January 19, 2007
posted by raf at 2:45 PM on January 19, 2007
I am very, very bad at math. So, grain of salt.
Until I was a little older than your son, I learned math in the US, where I was taught largely with word problems and "games" and "solve this yourself and learn from your mistakes!"
After that, I was taught in a rote-based (Euro) system where I was drilled by rote and repetition.
I am STILL very bad at math. But I have noticed over and over that I am much better at arithmetic than my US peer group. (It is impossible to overstate how bad I am at math, so this is kind of shocking to me.)
This isn't a fun answer, but I think it's just endless drilling. You need to get to a point where it's automatic, and you don't actually think about the answer. If you have to pause to "do math" in your head, it's always going to slow you down.
Just my two cents. Good luck with your kidlet!
posted by thehmsbeagle at 2:48 PM on January 19, 2007
Until I was a little older than your son, I learned math in the US, where I was taught largely with word problems and "games" and "solve this yourself and learn from your mistakes!"
After that, I was taught in a rote-based (Euro) system where I was drilled by rote and repetition.
I am STILL very bad at math. But I have noticed over and over that I am much better at arithmetic than my US peer group. (It is impossible to overstate how bad I am at math, so this is kind of shocking to me.)
This isn't a fun answer, but I think it's just endless drilling. You need to get to a point where it's automatic, and you don't actually think about the answer. If you have to pause to "do math" in your head, it's always going to slow you down.
Just my two cents. Good luck with your kidlet!
posted by thehmsbeagle at 2:48 PM on January 19, 2007
This may or may not help, depending on how quickly he's remembering them already, but look up some of the common tricks or multiplication; 2's, 5's and 10's should be easy, 9's only slightly harder. Maybe some basic algebra (i.e., I know 5*7=35, so 6*7 must be 7 more = 42)?
Doesn't work for everyone, but it might be worth a try.
posted by spaceman_spiff at 2:49 PM on January 19, 2007
Doesn't work for everyone, but it might be worth a try.
posted by spaceman_spiff at 2:49 PM on January 19, 2007
You could teach him things that will help him correct answers, such as :
even # times any # = answer will end in even #
3 times anything = answer digits will add up to 3 or multiple of 3
5 times anything = answer will end in 5 or 0
and so on...so that he can have a higher confidence in the answers he's given with a few quick mental tricks. This assumes that the calculations he is missing have no specific pattern, other than the fact that he's rushing and that his teacher is evil for testing him this way.
posted by contessa at 2:50 PM on January 19, 2007
even # times any # = answer will end in even #
3 times anything = answer digits will add up to 3 or multiple of 3
5 times anything = answer will end in 5 or 0
and so on...so that he can have a higher confidence in the answers he's given with a few quick mental tricks. This assumes that the calculations he is missing have no specific pattern, other than the fact that he's rushing and that his teacher is evil for testing him this way.
posted by contessa at 2:50 PM on January 19, 2007
thehmsbeagle is right, btw. This is about drilling the tables in by rote. All the multiplication tricks we've learned are helpful generally, but in this situation the teacher is demanding strict memorization.
Let me say that I am good at "math", but I have a crap memory. When I think "8 times 7" I think "56", but then I think "Well, couldn't it be 54, then?" and then I have to calculate it or remember some mnemonic, which takes a lot of time. It's possible that your son may have the same problem as me - he's trying to memorize it but it gets all jumbled up in the other numbers he has to know.
posted by muddgirl at 2:52 PM on January 19, 2007
Let me say that I am good at "math", but I have a crap memory. When I think "8 times 7" I think "56", but then I think "Well, couldn't it be 54, then?" and then I have to calculate it or remember some mnemonic, which takes a lot of time. It's possible that your son may have the same problem as me - he's trying to memorize it but it gets all jumbled up in the other numbers he has to know.
posted by muddgirl at 2:52 PM on January 19, 2007
I wonder if he can't get the answers quickly enough because he's nervous and the teacher's ridiculous speed requirement makes his little brain shut down. I have to say that memorizing multiplication tables did absolutely nothing for me. I wish someone had bothered to teach me the theories behind mathematics -- and why numbers act the way they do. Memorization only teaches you to memorize. You don't LEARN anything by it. I agree with muddgirl and raf. You can memorize a poem, but if you can't divine its meaning and understand its subtleties, then what's the point?
posted by Lockjaw at 2:54 PM on January 19, 2007
posted by Lockjaw at 2:54 PM on January 19, 2007
There's a trick to the 9's also but it might be a bit too convoluted and it may just be better to memorize the dang things -
Example: 9 x 4 = ?
-- Subtract 1 from the number that 9 is being multiplied to
(4 - 1 = 3)
-- Subtract from 10 the number that 9 is being multiplied to
(10 - 4 = 6)
and that's the answer == 36.
posted by contessa at 2:55 PM on January 19, 2007
Example: 9 x 4 = ?
-- Subtract 1 from the number that 9 is being multiplied to
(4 - 1 = 3)
-- Subtract from 10 the number that 9 is being multiplied to
(10 - 4 = 6)
and that's the answer == 36.
posted by contessa at 2:55 PM on January 19, 2007
My god. I had the same problem as your son growing up. I distinctly remember being seven and having to do 100 easy addition/subtraction problems in 12 minutes. I could not do it. It wasn't the memorization but the pressure of being timed. 100 multiplication problems in 5 minutes? That's insane. I don't know if I could do that now.
I do remember having to stay in during recess to try again, and I could do it then...perhaps it helped that the only people in the room were me, the teacher, and one or two other kids who also had trouble. There wasn't that frantic, stressed vibe created by 20-30 kids ferociously scribbling with pencils, trying to beat a clock.
I thought I was bad at math. I didn't find out until years later that I actually had really strong natural reasoning and math skills, but for whatever reason that style of teaching just didn't jive with them.
It's hard to implement to a little kid, but probably the best thing he can do is try to just relax and focus on answering the questions and try to forget about the timer. Easier said than done, I know.
posted by lampoil at 3:07 PM on January 19, 2007
I do remember having to stay in during recess to try again, and I could do it then...perhaps it helped that the only people in the room were me, the teacher, and one or two other kids who also had trouble. There wasn't that frantic, stressed vibe created by 20-30 kids ferociously scribbling with pencils, trying to beat a clock.
I thought I was bad at math. I didn't find out until years later that I actually had really strong natural reasoning and math skills, but for whatever reason that style of teaching just didn't jive with them.
It's hard to implement to a little kid, but probably the best thing he can do is try to just relax and focus on answering the questions and try to forget about the timer. Easier said than done, I know.
posted by lampoil at 3:07 PM on January 19, 2007
But those tricks won't help much in a timed test like this because there isn't enough time to apply the tricks to most of the problems.
This is, as someone pointed out, strictly a test of memorization rather than a test of mathematical ability. There is only so much you can do to speed that up. Might it help your son to stop thinking of it like problems to calculate the answer to and instead like memorizing lines in a play or something? The fact that these are numbers are almost irrelevant. The students aren't expected to think "what is the answer to 6 times 7? Hmm, it's 42. They are expected to recognize the pattern of "6x7" and have "42" pop into their head with no though, in the same way that we might have "that is the question" pop into our heads after we see "to be or not to be".
posted by Justinian at 3:09 PM on January 19, 2007
This is, as someone pointed out, strictly a test of memorization rather than a test of mathematical ability. There is only so much you can do to speed that up. Might it help your son to stop thinking of it like problems to calculate the answer to and instead like memorizing lines in a play or something? The fact that these are numbers are almost irrelevant. The students aren't expected to think "what is the answer to 6 times 7? Hmm, it's 42. They are expected to recognize the pattern of "6x7" and have "42" pop into their head with no though, in the same way that we might have "that is the question" pop into our heads after we see "to be or not to be".
posted by Justinian at 3:09 PM on January 19, 2007
Although I question the utility of the doing math in this way, if your main goal is to help him get faster, then repeated practice would seem to be the thing. A tech fix for this would be Brain Age for the Nintendo DS. It has a 100 simple math problem exercise in it (which also includes subtraction, addition, and division) that might help this. It'll time performance, and graph improvement over time.
And he can play Mario Kart when he's done with school work.
posted by mariokrat at 3:10 PM on January 19, 2007
And he can play Mario Kart when he's done with school work.
posted by mariokrat at 3:10 PM on January 19, 2007
If he is getting frustrated, maybe you should back off a little. It's really not important whether he can do 100 in five minutes. What is important (actually, it's not all that important, but it might prove helpful in future schooling) is that he knows the multiplication tables -- that is, when he sees each each question, he is actually remembering the answer, not 'figuring it out' in his head (by adding six sevens or something). For this you might want to back up a step -- instead of using flash cards or games that give him questions in a random sequence, work some more on drilling the basic tables in order, and in writing. Just make a grid on a page:
3x1 =
3x2 =
3x3 =
etc.
He might find it absurdly easy and repetitive, but that's the point.
Lastly, and I don't know how to say this in an entirely nice way -- your kid might not be an A student forever, at least when it comes to certain kinds of math taught in certain ways. There is no shame in coming to realize this, but he may start to feel that way if his parents continually stress this as something vitally important and he is unable to do it no matter how hard he tries.
That said, do you know how the rest of the class is doing on these tests? Maybe they are designed so that most people can't succeed, at least at first. (That would be a stupid pedagogical strategy for this age group and this material, but it is not out of the realm of possibility.)
posted by Urban Hermit at 3:10 PM on January 19, 2007
3x1 =
3x2 =
3x3 =
etc.
He might find it absurdly easy and repetitive, but that's the point.
Lastly, and I don't know how to say this in an entirely nice way -- your kid might not be an A student forever, at least when it comes to certain kinds of math taught in certain ways. There is no shame in coming to realize this, but he may start to feel that way if his parents continually stress this as something vitally important and he is unable to do it no matter how hard he tries.
That said, do you know how the rest of the class is doing on these tests? Maybe they are designed so that most people can't succeed, at least at first. (That would be a stupid pedagogical strategy for this age group and this material, but it is not out of the realm of possibility.)
posted by Urban Hermit at 3:10 PM on January 19, 2007
contessa's trick can best be demonstrated by holding up your (hopefully) 10 fingers. Counting left to right, hold down the finger you're multiplying by 9. For example 3x9, hold down your middle finger on the left hand. Count the number of fingers on the left of the folded finger. That's your first digit. Count the number of fingers on the right. That's your second digit. So 3x9 = 27.
posted by hindmost at 3:14 PM on January 19, 2007
posted by hindmost at 3:14 PM on January 19, 2007
I learned (memorized) my "times tables" as separate lists, one for each number, and that seemed to work: if you are not already doing so, maybe your son should focus on memorizing and practising one table at a time (i.e., 6 X 1, 6 X 2, 6 X 3, etc. to 12) until he has super confidence and speed on the one in question. If he can do some (and ever more) of the problems in the set really quickly, that should speed things up.
posted by sueinnyc at 3:26 PM on January 19, 2007
posted by sueinnyc at 3:26 PM on January 19, 2007
Oh, and as a member of one of the um, mathier cultures, it really does come down to memorization and practice. I had to recite multiplication tables all the time (on preview: exactly like sueinnyc did) and the nursery rhymes I learned were all math games in disguise. Example: A frog has 1 mouth 2 eyes and 4 legs. Two frogs have 2 mouths, 4 eyes and 8 legs. Three frogs have...
The only card game I knew was called 24. You deal 4 cards, Ace = 1, J= 11 Q=12 K=13, all other cards at face value. Using only basic arithmetic, try to form 24. So 3 5 Q A would be (5-3)x1x12 or (12-5+1)x3. We would play this all the time as a pasttime and I can still throw down at it.
In short, the more you surround yourself with numbers and use them the easier it becomes. The biggest trick is still familiarity. Many times learning a mnemonic like the one I posted above can be a crutch that actually slows you down because you're trying to figure out how it goes and which one works for what numbers.
posted by hindmost at 3:27 PM on January 19, 2007
The only card game I knew was called 24. You deal 4 cards, Ace = 1, J= 11 Q=12 K=13, all other cards at face value. Using only basic arithmetic, try to form 24. So 3 5 Q A would be (5-3)x1x12 or (12-5+1)x3. We would play this all the time as a pasttime and I can still throw down at it.
In short, the more you surround yourself with numbers and use them the easier it becomes. The biggest trick is still familiarity. Many times learning a mnemonic like the one I posted above can be a crutch that actually slows you down because you're trying to figure out how it goes and which one works for what numbers.
posted by hindmost at 3:27 PM on January 19, 2007
If you want to spoil the kid, get him a Nintendo DS and Brain Age. Granted, they also throw subtraction and addition into the mix, but one of their "games" is timing you and getting you to increase your speed at doing 20 or 100 simple math problems. If he practices with that enough, he'll breeze through his times tables like nobody's business soon enough.
posted by cgg at 3:35 PM on January 19, 2007
posted by cgg at 3:35 PM on January 19, 2007
This might be a little out there, but possible, given that you suggest he knows the facts when tested with flash cards and online games---Is he very careful/neat about handwriting? Sometimes young students who put importance on that (maybe because it's valued/emphasized for other school assignments) will continue with it even when it's not needed or slows them down during timed tests.
posted by PY at 3:45 PM on January 19, 2007
posted by PY at 3:45 PM on January 19, 2007
If you think he might be choking because he's intimidated, remind him that it's not really 144 things he has to memorize even though the way the table is written out might make it seem like that. Anything times 1 or 10 is trivial. And half the remaining is reflexive (x*y=y*x).
Also I'm an outlier to the "he won't have time for tricks;" I remember in 3rd grade, I consistently placed in the top 3 in the class to see how many we could do in 5 minutes and I was using plain addition the whole time (unless the one of the numbers was 1, 2, or 10 which I knew the tables for). The only "trick" I used was knowing the 2 times table so I could break bigger numbers up into a sum of smaller sums. I was just fast at adding, I think.
posted by juv3nal at 3:59 PM on January 19, 2007
Also I'm an outlier to the "he won't have time for tricks;" I remember in 3rd grade, I consistently placed in the top 3 in the class to see how many we could do in 5 minutes and I was using plain addition the whole time (unless the one of the numbers was 1, 2, or 10 which I knew the tables for). The only "trick" I used was knowing the 2 times table so I could break bigger numbers up into a sum of smaller sums. I was just fast at adding, I think.
posted by juv3nal at 3:59 PM on January 19, 2007
Seconding, thirding, fourthing the "please don't bother with tricks until you've got the tables locked down" view.
Anybody who has ever written speed-optimized code will tell you that the fastest way for a computer program to generate an output, given inputs from a restricted set, is to look up pre-canned answers in a lookup table. In this particular instance, the analogy between brain and computer is quite apt.
I would personally have no problem at all completing 100 multiplies of up to 12*12, given three seconds each. My lookup takes me less than a second. The bottleneck would be my writing speed.
The whole point of learning the multiplication table is so that you don't need to spend time working out what eight sevens are. You just know right away that eight sevens are fifty-six. And if you do have trouble with the 56 vs. 54 thing that trips up so many, the right thing to do is not to get in the habit of checking your table results; the right thing to do is spend a few minutes a day saying "eight sevens are fifty-six" to yourself until the doubt just goes away. Then do the same thing with "six nines are fifty-four".
Having the tables solidly locked in place means that when you're doing a multi-digit multiplication or a long division or somesuch where you need single-digit multiplication as a substep, you can just do the substep - you don't have to do a procedure to figure out the substep's result. This pays off bigtime, because you don't end up overloading your limited working memory by trying to keep track of where you're up to in both the substep and the overall problem.
Trying to do a long multiplication without a solidly locked-in digit-multiplication table feels like trying to type before your fingers have memorized the QWERTY layout, or trying to drive a stick-shift before your hands and clutch foot have made shifting something you don't have to think about. It's slow, frustrating, annoying, and likely to result in a belief that "I'm just no good at this".
Yes, it's good to have a feel for how numbers fit together, and it's good to know some tricks. But it's also good to have the multiplication table solidly locked in, and the most reliable way to do that is regular rounds of the old rote-learning chant - two sevens are fourteen, three sevens are twenty-one, four sevens are twenty-eight...
In fact you'll find that this literally mindless rote memorization actually promotes intuitive understanding of number relationships, because the results become something that's just there to be contemplated rather than something you have to regenerate laboriously every time you want to go looking for patterns.
Personally I think you'll get the most bang for your rote-learning buck by locking in the tables up to 9*9. I think the fact that the tables are traditionally taught to 12*12 is probably a remnant of the pounds, shillings and pence era in Britain. The elevens and twelves are actually not often of much use in a long multiplication.
You don't really need a one-times table or a ten-times table, because the rules for those are so trivial as to make applying them faster than a table lookup. That means that you really only need to rote-memorize sixty-four results (from 2*2 to 9*9) and you're golden. Do that to start with, and get those solid. Then, if your aim is to blitz speed tests that include elevens and twelves, just memorize the extra results later.
I was lucky enough to have had the multiplication table drilled into me in grade 3 by an old-school teacher. I got excellent maths results until I hit the next layer of required rote-memorizations in secondary school (trig and calculus identites). By that time I'd got so used to being able to work stuff out quickly from first principles - which I could do better than most people in my classes, largely because I could multiply fast - that I was completely baffled when all the trig and calculus stuff actually turned out to be hard.
Looking back on it now, the only reason it was hard was because I never did rote-learn all the stuff required to make it easy.
posted by flabdablet at 4:01 PM on January 19, 2007
Anybody who has ever written speed-optimized code will tell you that the fastest way for a computer program to generate an output, given inputs from a restricted set, is to look up pre-canned answers in a lookup table. In this particular instance, the analogy between brain and computer is quite apt.
I would personally have no problem at all completing 100 multiplies of up to 12*12, given three seconds each. My lookup takes me less than a second. The bottleneck would be my writing speed.
The whole point of learning the multiplication table is so that you don't need to spend time working out what eight sevens are. You just know right away that eight sevens are fifty-six. And if you do have trouble with the 56 vs. 54 thing that trips up so many, the right thing to do is not to get in the habit of checking your table results; the right thing to do is spend a few minutes a day saying "eight sevens are fifty-six" to yourself until the doubt just goes away. Then do the same thing with "six nines are fifty-four".
Having the tables solidly locked in place means that when you're doing a multi-digit multiplication or a long division or somesuch where you need single-digit multiplication as a substep, you can just do the substep - you don't have to do a procedure to figure out the substep's result. This pays off bigtime, because you don't end up overloading your limited working memory by trying to keep track of where you're up to in both the substep and the overall problem.
Trying to do a long multiplication without a solidly locked-in digit-multiplication table feels like trying to type before your fingers have memorized the QWERTY layout, or trying to drive a stick-shift before your hands and clutch foot have made shifting something you don't have to think about. It's slow, frustrating, annoying, and likely to result in a belief that "I'm just no good at this".
Yes, it's good to have a feel for how numbers fit together, and it's good to know some tricks. But it's also good to have the multiplication table solidly locked in, and the most reliable way to do that is regular rounds of the old rote-learning chant - two sevens are fourteen, three sevens are twenty-one, four sevens are twenty-eight...
In fact you'll find that this literally mindless rote memorization actually promotes intuitive understanding of number relationships, because the results become something that's just there to be contemplated rather than something you have to regenerate laboriously every time you want to go looking for patterns.
Personally I think you'll get the most bang for your rote-learning buck by locking in the tables up to 9*9. I think the fact that the tables are traditionally taught to 12*12 is probably a remnant of the pounds, shillings and pence era in Britain. The elevens and twelves are actually not often of much use in a long multiplication.
You don't really need a one-times table or a ten-times table, because the rules for those are so trivial as to make applying them faster than a table lookup. That means that you really only need to rote-memorize sixty-four results (from 2*2 to 9*9) and you're golden. Do that to start with, and get those solid. Then, if your aim is to blitz speed tests that include elevens and twelves, just memorize the extra results later.
I was lucky enough to have had the multiplication table drilled into me in grade 3 by an old-school teacher. I got excellent maths results until I hit the next layer of required rote-memorizations in secondary school (trig and calculus identites). By that time I'd got so used to being able to work stuff out quickly from first principles - which I could do better than most people in my classes, largely because I could multiply fast - that I was completely baffled when all the trig and calculus stuff actually turned out to be hard.
Looking back on it now, the only reason it was hard was because I never did rote-learn all the stuff required to make it easy.
posted by flabdablet at 4:01 PM on January 19, 2007
I was so good at multiplication tables in the 4th grade; beat everyone in the class at "Conductor" until they absolutely hated me. No tricks to it- I just knew them. Could you possibly review his tests, see which ones are causing most trouble, and study those first? (I feel like bigger, odd numbers would be hardest).
posted by ThePinkSuperhero at 4:03 PM on January 19, 2007
posted by ThePinkSuperhero at 4:03 PM on January 19, 2007
The other thing your A student may not realize is that in a speed based test, it's okay to be wrong or skip questions.
I was hellishly good at mad minutes (as those tests were called when I was in grade school) and one of the tricks of the trade is never to stop writing. If he sees a question and does not immediately know the answer to it, he should move on to the next question and not try to 'solve' the question he doesn't know. That's not the point of the test, and it will keep him from passing it.
Get his tests from him afterwards and drill him hardest on the ones he missed.
posted by jacquilynne at 4:15 PM on January 19, 2007
I was hellishly good at mad minutes (as those tests were called when I was in grade school) and one of the tricks of the trade is never to stop writing. If he sees a question and does not immediately know the answer to it, he should move on to the next question and not try to 'solve' the question he doesn't know. That's not the point of the test, and it will keep him from passing it.
Get his tests from him afterwards and drill him hardest on the ones he missed.
posted by jacquilynne at 4:15 PM on January 19, 2007
On lack of preview: juv3nal, it sounds like you had a pretty sound addition table locked in there. Many people don't. Quick, everybody - whats six plus seven? Don't think about it. OK, so what's sixteen minus nine?
The addition table from 1+1 to 9+9, subtraction tables from 2-1 to 19-9 and the factors table for numbers from 1 to 100 are also worth rote-learning, if you're seriously interested in being able to do quick and accurate arithmetic.
IMO, using the fact that eight sevens and seven eights are the same thing comes under "tricks". It's useful for generating correct results during the initial rote-learning chant, but shouldn't be used as a substitute for instantly-available table results that don't need their inputs pre-cooked. "Eight sevens are fifty-six" is a faster mental process than "eight sevens are shit is it fifty-four I dunno try seven eights are fifty-six got it" or "eight sevens are eight is bigger than seven are seven eights are fifty-six" or even "eight sevens are swap, seven eights are fifty-six".
posted by flabdablet at 4:15 PM on January 19, 2007
The addition table from 1+1 to 9+9, subtraction tables from 2-1 to 19-9 and the factors table for numbers from 1 to 100 are also worth rote-learning, if you're seriously interested in being able to do quick and accurate arithmetic.
IMO, using the fact that eight sevens and seven eights are the same thing comes under "tricks". It's useful for generating correct results during the initial rote-learning chant, but shouldn't be used as a substitute for instantly-available table results that don't need their inputs pre-cooked. "Eight sevens are fifty-six" is a faster mental process than "eight sevens are shit is it fifty-four I dunno try seven eights are fifty-six got it" or "eight sevens are eight is bigger than seven are seven eights are fifty-six" or even "eight sevens are swap, seven eights are fifty-six".
posted by flabdablet at 4:15 PM on January 19, 2007
If the test is 10 rows of 10, I'm guessing this is the numbers 1-10 written randomly horizontally and vertically, so that they're doing every combination between 1 to 100? If so, rather than complete the test either horizontally or vertically, how about starting with (for example) the column for #1, filling in those answers, going on to the column for #2, and so on? He probably memorizes the answers in that order, so he should be able to recall them more quickly in that order.
posted by Gortuk at 4:16 PM on January 19, 2007
posted by Gortuk at 4:16 PM on January 19, 2007
My answer won't please you if it doesn't match your parenting style, but I'll throw it out there anyways.
Memorizing times tables is silly and memorizing them to the degree that you can write answers out in 3 seconds repeatedly is even sillier. I don't know my times tables well enough to do that, nor have I ever (and I just finished a degree in physics).
I would reassure your child that it is fine not to be able to do as well as others in this sort of task and leave it at that. Explain to him that some people are better at rote memory tests than others but that this fact doesn't really matter. By the time he gets to the grade level were marks starts to actually count (i.e. for university admissions) he will be doing mathematics, not arithmetic. In my experience, many people who are good at mathematics are not very good at arithmetic, so I wouldn't worry about it.
Finally, it might be good for your A student son to not be at the top of the class once and a while. It might teach him not to overvalue marks.
posted by ssg at 4:19 PM on January 19, 2007
Memorizing times tables is silly and memorizing them to the degree that you can write answers out in 3 seconds repeatedly is even sillier. I don't know my times tables well enough to do that, nor have I ever (and I just finished a degree in physics).
I would reassure your child that it is fine not to be able to do as well as others in this sort of task and leave it at that. Explain to him that some people are better at rote memory tests than others but that this fact doesn't really matter. By the time he gets to the grade level were marks starts to actually count (i.e. for university admissions) he will be doing mathematics, not arithmetic. In my experience, many people who are good at mathematics are not very good at arithmetic, so I wouldn't worry about it.
Finally, it might be good for your A student son to not be at the top of the class once and a while. It might teach him not to overvalue marks.
posted by ssg at 4:19 PM on January 19, 2007
And on more lack of preview: phatkitten, you've been damaged by substandard educational methods :-)
Go and stand outside, take a deep breath, and spend the next five minutes singing "twelve eights are ninety-six" in a happy voice.
posted by flabdablet at 4:21 PM on January 19, 2007
Go and stand outside, take a deep breath, and spend the next five minutes singing "twelve eights are ninety-six" in a happy voice.
posted by flabdablet at 4:21 PM on January 19, 2007
Gortuk's cheat is the method employed on every homework sheet by Young Master Flabdablet. It doesn't help you learn times tables at all; it just helps lock in being able to count upward by threes, or fives, or eights.
What you're actually drilling in by doing things that way is a restricted set of addition tables that take no less time to learn than the standard multiplication table, but is nowhere near as useful.
Naturally, Young Master Flabdablet treats this opinion with absolute scorn, because he knows perfectly well that forty-nine plus seven is "easier to work out" than eight sevens. Sigh. Of course it is! He's just looking it up in a table.
posted by flabdablet at 4:26 PM on January 19, 2007
What you're actually drilling in by doing things that way is a restricted set of addition tables that take no less time to learn than the standard multiplication table, but is nowhere near as useful.
Naturally, Young Master Flabdablet treats this opinion with absolute scorn, because he knows perfectly well that forty-nine plus seven is "easier to work out" than eight sevens. Sigh. Of course it is! He's just looking it up in a table.
posted by flabdablet at 4:26 PM on January 19, 2007
Are you seeing significant slowness in his responses when you give him one problem at a time? If so, then it's probably a question of more, more, more practice. (I second Schoolhouse Rock for this!)
Otherwise, your son sounds just like me at that age. Just like me now, for that matter. I know the mathmatics perfectly well, but seeing so many numbers at once short-circuits my brain--all the digits swarm together until I can't focus on any one problem. Combine that mental dizziness with pressure from the time crunch and a heavy dose of frustration at not "being smart enough," and the result is a lot of failed quizzes. If you think this is the issue, absolutely speak to his teacher about it. A teacher worth her/his salt should be willing to make accomodations.
Also make sure that he's not getting stuck on the same difficult ones over and over. It always took me a few seconds to remember that 8x5=40, for instance, so I learned to skip over that one and come back to it at the end.
posted by hippugeek at 4:33 PM on January 19, 2007
Otherwise, your son sounds just like me at that age. Just like me now, for that matter. I know the mathmatics perfectly well, but seeing so many numbers at once short-circuits my brain--all the digits swarm together until I can't focus on any one problem. Combine that mental dizziness with pressure from the time crunch and a heavy dose of frustration at not "being smart enough," and the result is a lot of failed quizzes. If you think this is the issue, absolutely speak to his teacher about it. A teacher worth her/his salt should be willing to make accomodations.
Also make sure that he's not getting stuck on the same difficult ones over and over. It always took me a few seconds to remember that 8x5=40, for instance, so I learned to skip over that one and come back to it at the end.
posted by hippugeek at 4:33 PM on January 19, 2007
Instead of having your son do the problems across or down on the page, have your son do all the 1x's first, then the 2x's, then the fives and nines, and so on through all the numbers he's good at, until all that's left are the one's he has to think more about. His brain will have better mnemonic recall if he groups the patterns together and does them in bursts. He'll also be aware of what his "slow" numbers are (for me the sevens and eights) and can practice them more. If it helps his ego, you can tell him that this math major with a PhD can't remember the 7s and 8s and most of the 9s and 11s very fast either. Good luck.
posted by dness2 at 4:44 PM on January 19, 2007
posted by dness2 at 4:44 PM on January 19, 2007
so I learned to skip over that one and come back to it at the end.
Oh yes this is important! Let him know that he can take the test however he wants - he doesn't have to do every problem in order. Learning this sped up my test taking a lot, because I can do all the fast ones first and then go back to the harder ones.
posted by muddgirl at 4:47 PM on January 19, 2007
Oh yes this is important! Let him know that he can take the test however he wants - he doesn't have to do every problem in order. Learning this sped up my test taking a lot, because I can do all the fast ones first and then go back to the harder ones.
posted by muddgirl at 4:47 PM on January 19, 2007
I'm twenty, and I could never, ever have done what your nine-year-old is being asked to do.
I can barely add.
I am otherwise a very intelligent human being. Some have called me a genius, though I think that's kind of absurd. I figure without any math ability whatsoever, no one can be a genius :)
My inability to do math at a nine-year-old level... wow. I agree, however, that rote memorization is the only way I ever remembered some of them, like 6x6=36 (that and the fact that it rhymes)
posted by dmaterialized at 5:46 PM on January 19, 2007
I can barely add.
I am otherwise a very intelligent human being. Some have called me a genius, though I think that's kind of absurd. I figure without any math ability whatsoever, no one can be a genius :)
My inability to do math at a nine-year-old level... wow. I agree, however, that rote memorization is the only way I ever remembered some of them, like 6x6=36 (that and the fact that it rhymes)
posted by dmaterialized at 5:46 PM on January 19, 2007
Like others I hated doing times tables at school. I seem to recall I eventually flat-out refused to learn them. I was convinced by my mother I think to learn the squares and figure out differences from that, and I never looked back. It might not let him do 100 multiplications in 5 minutes, but these days that is a completely useless talent. He'll probably end up being able to work out things faster in his head, and more importantly than that, when he gets his hand on a calculator and works out 19x17 hits the wrong keys he'll likely spot it more quickly if it's a long way from 324.
If he's enjoying it all, and still wants to do particularly well at this test, then keep encouraging him to learn times tables, but if there's any risk he's not enjoying doing it any more you could put him off the maths, and that'd be much more of a shame. Getting him used to a more versatile and larger toolbox of skills and generally being more numerate, whilst enjoying it more, might be a better way to spend the time.
And like phatkitten says, if he does keep doing actual mental arithmetic rather than memorising things he's likely to pick up the multiplication tables along the way, and he'll be in a position to put them to much better use.
If however he's still actually enjoying the learning of the tables, then that's cool. Go with the suggestions from those answers that are aimed at improving the memorisation.
posted by edd at 6:03 PM on January 19, 2007
If he's enjoying it all, and still wants to do particularly well at this test, then keep encouraging him to learn times tables, but if there's any risk he's not enjoying doing it any more you could put him off the maths, and that'd be much more of a shame. Getting him used to a more versatile and larger toolbox of skills and generally being more numerate, whilst enjoying it more, might be a better way to spend the time.
And like phatkitten says, if he does keep doing actual mental arithmetic rather than memorising things he's likely to pick up the multiplication tables along the way, and he'll be in a position to put them to much better use.
If however he's still actually enjoying the learning of the tables, then that's cool. Go with the suggestions from those answers that are aimed at improving the memorisation.
posted by edd at 6:03 PM on January 19, 2007
Hmm...I guess I'm the opposite of Lockjaw. I learned (and am ridiculously good) at the times table because of memorization. And yes, I knew then (and now) how it "worked." To each his/her own though. (And I will admit that my experience was very good thanks to great parents/tutors).
I did these from 4th grade until 6th grade, and I always found them to be a pretty lame part of the curriculum, even at that age. I will be honest and say that I come from an "immigrant" family who still believes in raising their kids from the methods "back home," so by the time I started 3rd grade I had the multiplication table inside and out thanks to countless drills & hours of memorization. HOWEVER, (like another mefi user said above), the US (or California at least) tends to teach math via silly games. (I distinctly remember "learning" multiplication in 4th grade via rubber bands and beans. "GROUP THE BEANS" the teacher would say. What...?). Needless to say, my peers couldn't group beans fast enough to do very well on these drills, even in sixth grade.
So basically: in my humble opinion, he just needs to memorize the multiplication table. Well. Very very well. I didn't use flashcards. I kind of just stared at the times table for a bit, and then covered the "answers" for each "set." I will admit that I learned it in another language so it was easier to "chant" (translated: 3 3 9, 3 4 12, 3 5 15, etc), but I imagine it can't be THAT bad in English (just don't say "equals"). The trick is to not think about it in terms of 3 groups of 4, but rather to know instinctively that 3 x 4 is 12.
In terms of "little tricks" (that have nothing to do with math), I'd say:
1. Don't bother erasing. Just cross it out and write it below. The point is to be fast, and erasing carefully will just slow him down. Of course this is useless if neatness counts (which it usually does at that age, if I remember correctly).
2. Answer them in a "zig zagged" path. This is similar to your horizontal tip. I know you're going to say that this couldn't possibly make a difference, but I swear it does! (Through experience).
3. This is going to be difficult to teach, but after a while, I got to the point where I could physically write the answer to #1 while thinking about the answer to #2. Saves lots of time.
We used to do these problems in 60 seconds, and I come from a pretty competitive community/school district (for lack of a better label). So, the tricks above are tried & true. (Not that we ever shared them till AFTER the fact!)
5 minutes is significantly longer than 1, though, so I think at this point he might just need to familiarize himself with the times table in non-bean counting ways.
(On preview, it almost sounds as if I'm being a cocky arrogant bitch who's implying that your son doesn't know his times table... That's NOT what I meant though! I just think that to truly be good at it...and honestly, I was always top 5 out of a group of 60 or so...rote memorization is the way to go. I'm too wordy to just put that as my answer though, so you get this essay instead. Sorry!)
posted by mittenedsex at 6:41 PM on January 19, 2007
I did these from 4th grade until 6th grade, and I always found them to be a pretty lame part of the curriculum, even at that age. I will be honest and say that I come from an "immigrant" family who still believes in raising their kids from the methods "back home," so by the time I started 3rd grade I had the multiplication table inside and out thanks to countless drills & hours of memorization. HOWEVER, (like another mefi user said above), the US (or California at least) tends to teach math via silly games. (I distinctly remember "learning" multiplication in 4th grade via rubber bands and beans. "GROUP THE BEANS" the teacher would say. What...?). Needless to say, my peers couldn't group beans fast enough to do very well on these drills, even in sixth grade.
So basically: in my humble opinion, he just needs to memorize the multiplication table. Well. Very very well. I didn't use flashcards. I kind of just stared at the times table for a bit, and then covered the "answers" for each "set." I will admit that I learned it in another language so it was easier to "chant" (translated: 3 3 9, 3 4 12, 3 5 15, etc), but I imagine it can't be THAT bad in English (just don't say "equals"). The trick is to not think about it in terms of 3 groups of 4, but rather to know instinctively that 3 x 4 is 12.
In terms of "little tricks" (that have nothing to do with math), I'd say:
1. Don't bother erasing. Just cross it out and write it below. The point is to be fast, and erasing carefully will just slow him down. Of course this is useless if neatness counts (which it usually does at that age, if I remember correctly).
2. Answer them in a "zig zagged" path. This is similar to your horizontal tip. I know you're going to say that this couldn't possibly make a difference, but I swear it does! (Through experience).
3. This is going to be difficult to teach, but after a while, I got to the point where I could physically write the answer to #1 while thinking about the answer to #2. Saves lots of time.
We used to do these problems in 60 seconds, and I come from a pretty competitive community/school district (for lack of a better label). So, the tricks above are tried & true. (Not that we ever shared them till AFTER the fact!)
5 minutes is significantly longer than 1, though, so I think at this point he might just need to familiarize himself with the times table in non-bean counting ways.
(On preview, it almost sounds as if I'm being a cocky arrogant bitch who's implying that your son doesn't know his times table... That's NOT what I meant though! I just think that to truly be good at it...and honestly, I was always top 5 out of a group of 60 or so...rote memorization is the way to go. I'm too wordy to just put that as my answer though, so you get this essay instead. Sorry!)
posted by mittenedsex at 6:41 PM on January 19, 2007
(and oh my god i'm sorry my answer is so long...)
posted by mittenedsex at 6:41 PM on January 19, 2007
posted by mittenedsex at 6:41 PM on January 19, 2007
OKAY final "answer." Try to let him know that he can be brilliant without exceling at this drill. Like others have said, it really is rather pointless. (Though knowing the times table is very useful...)
posted by mittenedsex at 6:43 PM on January 19, 2007
posted by mittenedsex at 6:43 PM on January 19, 2007
Urban Hermit has it right. He just has to learn them. Yeah it is a stupid memorization test, but the multiplication tables should be memorized or known. He will need them all his life. My son just did this unit too. You can teach your son basic test taking skills also. My son knew that anything time 1 was that number and anything times zero is zero. So, when the 30 second warning came, he would quickly find those two types of questions in the unfinished ones and answer them. Then if there was time he would go back to the others. If he know the 10's he could do those first too.
posted by JohnnyGunn at 8:18 PM on January 19, 2007
posted by JohnnyGunn at 8:18 PM on January 19, 2007
The speed requirement isn't that ridiculous. Just practice a lot, and make sure they know all the short-cuts to get a few easy ones.
Three seconds per answer isn't nearly as tough as everyone is making it out to be, but it provides a stress and intimidation that could be a bit tough.
posted by Tacos Are Pretty Great at 8:32 PM on January 19, 2007
Three seconds per answer isn't nearly as tough as everyone is making it out to be, but it provides a stress and intimidation that could be a bit tough.
posted by Tacos Are Pretty Great at 8:32 PM on January 19, 2007
It's not terrible - as I recall, we used to get mad minutes in the 60 questions / 60 seconds range - but it's still not really time to calculate the answer. He's going to need to know the answers.
posted by jacquilynne at 8:46 PM on January 19, 2007
posted by jacquilynne at 8:46 PM on January 19, 2007
Can your child get a pass without it?
I never could manage it when I was young. Probably still couldn't do it now and I worked for a year writing software to teach math tables to young children. Traumatic when you're young. I missed a lot of recess frustrated because I knew exactly how to do the math, but the speed failed me. Didn't endear me to math.
If the kid knows how to do the math and apply it, forget the memorization. It's a version of the old fishing metaphor. If you know how to fish, you don't need to keep a lot of fish around stinking up the joint.
(Note that many years later in university I was finally tested for learning disabilities where I was found (not to my surprise) really crappy rote memorization skills. If it's a true difficulty for your child, talk to his school about it.)
posted by Ookseer at 8:59 PM on January 19, 2007
I never could manage it when I was young. Probably still couldn't do it now and I worked for a year writing software to teach math tables to young children. Traumatic when you're young. I missed a lot of recess frustrated because I knew exactly how to do the math, but the speed failed me. Didn't endear me to math.
If the kid knows how to do the math and apply it, forget the memorization. It's a version of the old fishing metaphor. If you know how to fish, you don't need to keep a lot of fish around stinking up the joint.
(Note that many years later in university I was finally tested for learning disabilities where I was found (not to my surprise) really crappy rote memorization skills. If it's a true difficulty for your child, talk to his school about it.)
posted by Ookseer at 8:59 PM on January 19, 2007
phatkitten: in fact, I've never heard of Schoolhouse Rock, but the very fact that you recommended it as a way to teach the "trickier" times tables, and quoting "12 times 8 is the same as 10 times 8 plus 2 times 8 (80 + 16 = 96)" as an example of what you've learned from it, is what gave me the impression that it's defective.
There are no "trickier" times tables, and anybody who thinks there are has simply not spent sufficient time getting them memorized. There are only times-table results you know without thinking, and times-table results you don't; the latter are the ones you have to "work out". The whole point of learning the times tables is to avoid the need to work them out! Working things out is slowed than just knowing them.
The most reliable way I know to lock in the ones you don't already instantly know is just endless repetition (e.g. "twelve eights are ninety-six, twelve eights are ninety-six, twelve eights are ninety-six" for minutes on end). I'm recommending that method, and if I've understood you correctly, it's not what Schoolhouse Rock does.
Endless repetition works well for the advertising industry, and it can work for you :-)
posted by flabdablet at 9:33 PM on January 19, 2007
There are no "trickier" times tables, and anybody who thinks there are has simply not spent sufficient time getting them memorized. There are only times-table results you know without thinking, and times-table results you don't; the latter are the ones you have to "work out". The whole point of learning the times tables is to avoid the need to work them out! Working things out is slowed than just knowing them.
The most reliable way I know to lock in the ones you don't already instantly know is just endless repetition (e.g. "twelve eights are ninety-six, twelve eights are ninety-six, twelve eights are ninety-six" for minutes on end). I'm recommending that method, and if I've understood you correctly, it's not what Schoolhouse Rock does.
Endless repetition works well for the advertising industry, and it can work for you :-)
posted by flabdablet at 9:33 PM on January 19, 2007
First off, if his 100-question exams look like mine did, there's no rows and columns, it's 100 randomly placed questions, so column and row tricks don't apply. I remember going horizontally, and I was the fastest in my school at filling those out, I don't think it makes a difference.
I - Break it up into pieces. Test him on the individual tables (1 x, 2x, etc...) and see where he's slow. It shouldn't be very difficult to time him on each of the different numbers to find out which ones are giving him the most trouble. Make sure he knows 7 x 2 is the same as 2 x 7 (Important!).
II - Invent mnemonics/tricks for every problem he doesn't know how to do quickly. To this day I still remember '5-6-7-8' for 7*8, and to multiply 11 by anything you just added the two numbers and put the sum between them.
III - Statistics! Keep records of how he does, show him that he's improving with practice.
IV - Don't let it bother you, or him, that he's not the best right now. He's a little behind in a very long race. The gazelles right now will all eventually hit their walls. If he learns to be a trooper now, this attitude will serve him for the rest of his life.
Practice, practice, practice. Do this the way you would any other important and difficult job. I did these math quizzes every single day. You could try looking into a Kumon center in your area. They focus on exactly this sort of speed work.
posted by onalark at 12:02 AM on January 20, 2007
I - Break it up into pieces. Test him on the individual tables (1 x, 2x, etc...) and see where he's slow. It shouldn't be very difficult to time him on each of the different numbers to find out which ones are giving him the most trouble. Make sure he knows 7 x 2 is the same as 2 x 7 (Important!).
II - Invent mnemonics/tricks for every problem he doesn't know how to do quickly. To this day I still remember '5-6-7-8' for 7*8, and to multiply 11 by anything you just added the two numbers and put the sum between them.
III - Statistics! Keep records of how he does, show him that he's improving with practice.
IV - Don't let it bother you, or him, that he's not the best right now. He's a little behind in a very long race. The gazelles right now will all eventually hit their walls. If he learns to be a trooper now, this attitude will serve him for the rest of his life.
Practice, practice, practice. Do this the way you would any other important and difficult job. I did these math quizzes every single day. You could try looking into a Kumon center in your area. They focus on exactly this sort of speed work.
posted by onalark at 12:02 AM on January 20, 2007
I remember doing this in school, and kicking butt at it, but his teacher missed a very important step. This exercise is supposed to be called Mad Minutes. You start with smaller quantities to do in 60 seconds (thus the minutes part), starting at the lower end of the multiplication tables, and then add more and more to increase your speed (really, your recall ability) as you begin to ace the smaller quizzes. A quick Google search shows several web-based versions of this. If I were you, I would find some worksheets, and do them at home with your son. I remember that when we did it in school, the big blowout 100 questions worksheet came after you passed 10 or 12 levels, which everyone got to at his or her own pace. Building up to the big game instead of trying to tackle it all at once builds the confidence and speed needed to get those multiplication tables down.
posted by messylissa at 1:31 AM on January 20, 2007
posted by messylissa at 1:31 AM on January 20, 2007
Yep. Don't focus on tricks. When I went through this it was AGONIZING, but the only thing that really helped me (after failing the multiplication test four times) was spending time with my mother and some flash cards. Lots of impromptu shouting of "9X6?" and quick-fire sessions with the cards. Worked like a charm and eventually set me on a path to studying with my mother that got me into a few of those universities with lots of greenery.
I'll also suggest you take mariokrat's advice and grab BrainAge. It helped my neighbor's 4th grade son through the same tests (and he was miserable at them). Anecdotal, but it's another data point.
posted by LGCNo6 at 2:55 AM on January 20, 2007
I'll also suggest you take mariokrat's advice and grab BrainAge. It helped my neighbor's 4th grade son through the same tests (and he was miserable at them). Anecdotal, but it's another data point.
posted by LGCNo6 at 2:55 AM on January 20, 2007
I would reassure your child that it is fine not to be able to do as well as others in this sort of task and leave it at that. Explain to him that some people are better at rote memory tests than others but that this fact doesn't really matter. By the time he gets to the grade level were marks starts to actually count (i.e. for university admissions) he will be doing mathematics, not arithmetic. In my experience, many people who are good at mathematics are not very good at arithmetic, so I wouldn't worry about it.
Seconded. I failed every memorization timed test given to me in the second and third grade. I still studied through calculus in high school and tested out of my college math requirements. Reassure your kid that it does not matter if he does not ace this portion of school. It does not mean that he is stupid or bad at math.
posted by donajo at 6:58 AM on January 20, 2007
Seconded. I failed every memorization timed test given to me in the second and third grade. I still studied through calculus in high school and tested out of my college math requirements. Reassure your kid that it does not matter if he does not ace this portion of school. It does not mean that he is stupid or bad at math.
posted by donajo at 6:58 AM on January 20, 2007
I'd be really interested to find out, from people who claim to be bad at rote memorization tests, just how much time they actually spent on the rote memorization process itself, and what methods they used to get it done.
My present belief is that people who consider themselves "bad at" rote memorization are really only "bad at" passing rote memorization tests, and that the reason for this is that these people have simply not put in the hours and hours of tedious and repetitious work required to stamp the stuff into their brains. It really does take a long time, and if you start from a belief that you can't remember stuff by rote, or that doing so is pointless, you're just not going to bother.
It's funny that nobody would expect to be able to bench press massive weights without having done hours and hours of training, but people quite commonly appear to believe that they just have inherently bad memories when they simply haven't done the hours and hours of memorization exercises required in order to test well. I can assure you that I had to spend many, many hours in Grade 3 just chanting multiplication tables before they became second nature.
It seems to me that the main problem with doing this kind of thing in second and third grade is that unless a kid understands why they're doing it, and cares about the results of doing it, they're not going to be paying much attention to actually doing it. It's a motivation thing. I was lucky enough to have a Grade 3 teacher who was capable of motivating me to ignore the fact that drilling in the tables was boring.
posted by flabdablet at 7:38 AM on January 20, 2007
My present belief is that people who consider themselves "bad at" rote memorization are really only "bad at" passing rote memorization tests, and that the reason for this is that these people have simply not put in the hours and hours of tedious and repetitious work required to stamp the stuff into their brains. It really does take a long time, and if you start from a belief that you can't remember stuff by rote, or that doing so is pointless, you're just not going to bother.
It's funny that nobody would expect to be able to bench press massive weights without having done hours and hours of training, but people quite commonly appear to believe that they just have inherently bad memories when they simply haven't done the hours and hours of memorization exercises required in order to test well. I can assure you that I had to spend many, many hours in Grade 3 just chanting multiplication tables before they became second nature.
It seems to me that the main problem with doing this kind of thing in second and third grade is that unless a kid understands why they're doing it, and cares about the results of doing it, they're not going to be paying much attention to actually doing it. It's a motivation thing. I was lucky enough to have a Grade 3 teacher who was capable of motivating me to ignore the fact that drilling in the tables was boring.
posted by flabdablet at 7:38 AM on January 20, 2007
sperose: I think you're perfectly right; tricks and flashcards are pretty much useless. What works is lookup tables, just like the one you've written down for the nines. Tricks can at least help you write down a lookup table to use and/or study, but all flashcards are is nasty little anxiety-producing mini-tests. I hate them.
The easiest way to do rote-learning is to avoid trying to do any working-out or recall while you're drilling the stuff in. Sucking and blowing at the same time is too hard.
I'm an audio/kinesthetic learner, so chanting works for me. Visual learners would probably be better off just doing loads and loads of randomly-ordered written single-digit multiplications with something simple and orderly like this
Naturally, whether or not you consider this to be time well invested depends entirely on you.
posted by flabdablet at 8:11 AM on January 20, 2007
The easiest way to do rote-learning is to avoid trying to do any working-out or recall while you're drilling the stuff in. Sucking and blowing at the same time is too hard.
I'm an audio/kinesthetic learner, so chanting works for me. Visual learners would probably be better off just doing loads and loads of randomly-ordered written single-digit multiplications with something simple and orderly like this
1 2 3 4 5 6 7 8 9 2 4 6 8 10 12 14 16 18 3 6 9 12 15 18 21 24 27 4 8 12 16 20 24 28 32 36 5 10 15 20 25 30 25 40 45 6 12 18 24 30 36 42 48 54 7 14 21 28 35 42 49 56 63 8 16 24 32 40 48 56 64 72 9 18 27 36 45 54 63 72 81right there on the desk next to the work. Note that there is no working out involved in this process - it's all done by straight table lookup. Do three thousand of these spread over two weeks and you will know your times tables to 9x9; a hundred every couple of weeks after that (with the chart always available, if not always referred to) should be enough to keep them stable.
Naturally, whether or not you consider this to be time well invested depends entirely on you.
posted by flabdablet at 8:11 AM on January 20, 2007
Of course you should fax the deliferate mistale befire ysing that chert. Stupid keyboard fingers :-)
Seven fives are thirty-five, not twenty-five.
posted by flabdablet at 8:15 AM on January 20, 2007
Seven fives are thirty-five, not twenty-five.
posted by flabdablet at 8:15 AM on January 20, 2007
Another thing that was actually useful was to realize that 7 x 8 is the same as 8 x 7. I learned to always mentally read the question with the small number first and then the big number. That cut in half the amount of information I actually had to memorize.
So:
When I started doing that it was hard to do mentally, so I did a couple of tests where I'd do all the ones that had the small number first first, and then return to the ones that had the big number first and mentally flip them as I did them. I did badly on those couple of tests, but better after that.
posted by jacquilynne at 8:44 AM on January 20, 2007
So:
9 6 x 6 x 9 ----- -----were both read to myself as 6 x 9 = 54
When I started doing that it was hard to do mentally, so I did a couple of tests where I'd do all the ones that had the small number first first, and then return to the ones that had the big number first and mentally flip them as I did them. I did badly on those couple of tests, but better after that.
posted by jacquilynne at 8:44 AM on January 20, 2007
If he is answering the questions correctly, but just cannot finish the table in a specific time period, and is otherwise an A student - what the hell is the problem? Talk to the teacher. The time constraint is in my mind completely dumb. The most important thing is knowing how to answer the questions, not how long it takes to get the answer the way the teacher wants it. Being able to answer questions quickly is great but is NOT a measure of how well the student actually knows the material.
I had an algebra teacher who insisted we answer percentage problems including some stupid overlapping circle diagram that the book used as a visual example. I quite quickly realized that percentage problems could be solved by a simple fraction ratio (ie, X% of Y is solved by Z/100 = X/Y). I could get the correct answer in seconds. It took me several minutes to draw the damn diagrams. My teacher repeatedly marked questions wrong if the diagram was not included, even if I obtained the correct answer. As a result it took me hours to finish my homework, if I expected to get credit for having done the work, and I rarely finished tests in time. I was also an A student, I have good math and logic skills, etc., etc. - much like your child, to hazard a guess.
In short, the teacher's stupid insistence on including an unreasonable constraint on the learning process is the real issue here. Make sure your child knows this. Having my mother (a K-12 teacher) and my father (a K-12 principle) tell me that my problem was with the teacher's method and not with my math abilities really helped me, and was a big boost to my confidence. Prior to that, I was just frustrated and it made the problem worse.
posted by caution live frogs at 10:59 AM on January 20, 2007
I had an algebra teacher who insisted we answer percentage problems including some stupid overlapping circle diagram that the book used as a visual example. I quite quickly realized that percentage problems could be solved by a simple fraction ratio (ie, X% of Y is solved by Z/100 = X/Y). I could get the correct answer in seconds. It took me several minutes to draw the damn diagrams. My teacher repeatedly marked questions wrong if the diagram was not included, even if I obtained the correct answer. As a result it took me hours to finish my homework, if I expected to get credit for having done the work, and I rarely finished tests in time. I was also an A student, I have good math and logic skills, etc., etc. - much like your child, to hazard a guess.
In short, the teacher's stupid insistence on including an unreasonable constraint on the learning process is the real issue here. Make sure your child knows this. Having my mother (a K-12 teacher) and my father (a K-12 principle) tell me that my problem was with the teacher's method and not with my math abilities really helped me, and was a big boost to my confidence. Prior to that, I was just frustrated and it made the problem worse.
posted by caution live frogs at 10:59 AM on January 20, 2007
These are great suggestions. I love all the different perspectives. I memorized the tables--crying and flunking, then having to pass them and studying the damn charts. I began working with my son in 2nd grade and he is now in 6th and has been unable to completely memorize them. I wish he could and we have certainly put in enough hours. I felt that worksheets I downloaded from the internet were the best practice for tests, but some people will never completely memorize the tables. Your son may or may not be one of those. We talk about how each of us have "special abilities" and "challenges" in school. You can help him practice the tables, help him with testing strategies, and help him understand that some people do better on certain tests than others do. Good luck!
posted by aliksd at 2:19 PM on January 20, 2007
posted by aliksd at 2:19 PM on January 20, 2007
Today my son took his first test since I asked this question one week ago.
He made a 97% !!!!!!!!!!!!!!!!!!!!!!!
Everyone who posted has my heart felt thanks. I marked as best answers those 'tips and tricks' that we actually used, but everyone had something valuable to say and in the future we will be using a lot more of the suggestions.
Again, THANK YOU! I'm amazed at how a few little changes made such a drastic difference. We didn't expect this at all. Amazing!
(and sorry for the late reply, we had bad weather and our internet service was down for 3 days)
posted by LadyBonita at 3:32 PM on January 26, 2007
He made a 97% !!!!!!!!!!!!!!!!!!!!!!!
Everyone who posted has my heart felt thanks. I marked as best answers those 'tips and tricks' that we actually used, but everyone had something valuable to say and in the future we will be using a lot more of the suggestions.
Again, THANK YOU! I'm amazed at how a few little changes made such a drastic difference. We didn't expect this at all. Amazing!
(and sorry for the late reply, we had bad weather and our internet service was down for 3 days)
posted by LadyBonita at 3:32 PM on January 26, 2007
Congratulations LadyBonita, I hope your son learned a valuable lesson through this about overcoming adversity.
posted by onalark at 3:57 PM on January 26, 2007
posted by onalark at 3:57 PM on January 26, 2007
A bit more -
My son said, "You should have asked those people a long time ago!" And he's right.
We didn't practice any more than usual, but we did use the following 'tips & tricks' to speed up his test taking and enable him to answer all 100 questions within the time limit.
We used flabdablet's "eight sevens are fifty-six" phrase suggestion during our regular rote memorization drills. Previously our son would have said "eight times seven equals fifty-six" during drills. Great time saver, and flabdablet gives an even greater explanation as to why rote learning is valuable!
PY pointed out the importance of not taking too much time for neat handwriting, so we told our son to write the answers quickly instead of neatly. This caused him to miss only one test question today, 2x4 - his correct answer 8 sort of looks like a 6 (I could argue that he actually made a 98% today ;)
ThePinkSuperhero suggested that we review his tests in order to see which problems were consistently causing the most trouble. There were no consistently troubling problems, BUT we did notice that on the home practice test he was able to finish the last two rows very quickly. So we instructed our son to complete those two rows first, and then move back to the beginning of the test. Previously our son hadn't the time to even make it to the last two rows of questions. Not exactly what ThePinkSuperhero intended, but s/he did give us the idea to review the test results.
(We also noticed that the teacher gives the exact same test each week, and it's also the same one she gave us for at home practice, but we didn't use this knowledge or let our son know - we want him to memorize the multiplication tables, not the test answers)
jacquilynne pointed out that it's okay to skip questions that he doesn't immediately know the answer to - we pointed this out to our son, and also told him to go back and answer the missed questions if he had time left.
We also used mittenedsex "little tricks" #1 (don't erase a wrong answer, just cross it out and write below). She wrote more good advice, but that's the one trick we used for now. This was a little difficult for him at first but he's getting the hang of it - although one of the questions he missed was because he answered 3x5=25, realized the mistake and crossed over the #2 with a #1. The teacher counted that as a wrong answer. (I could argue that he actually now scored a 99% - just to point out how effective these 'tips & tricks' really are;)
The one remaining problem that he missed? 11x10. He answered 120.
posted by LadyBonita at 4:28 PM on January 26, 2007
My son said, "You should have asked those people a long time ago!" And he's right.
We didn't practice any more than usual, but we did use the following 'tips & tricks' to speed up his test taking and enable him to answer all 100 questions within the time limit.
We used flabdablet's "eight sevens are fifty-six" phrase suggestion during our regular rote memorization drills. Previously our son would have said "eight times seven equals fifty-six" during drills. Great time saver, and flabdablet gives an even greater explanation as to why rote learning is valuable!
PY pointed out the importance of not taking too much time for neat handwriting, so we told our son to write the answers quickly instead of neatly. This caused him to miss only one test question today, 2x4 - his correct answer 8 sort of looks like a 6 (I could argue that he actually made a 98% today ;)
ThePinkSuperhero suggested that we review his tests in order to see which problems were consistently causing the most trouble. There were no consistently troubling problems, BUT we did notice that on the home practice test he was able to finish the last two rows very quickly. So we instructed our son to complete those two rows first, and then move back to the beginning of the test. Previously our son hadn't the time to even make it to the last two rows of questions. Not exactly what ThePinkSuperhero intended, but s/he did give us the idea to review the test results.
(We also noticed that the teacher gives the exact same test each week, and it's also the same one she gave us for at home practice, but we didn't use this knowledge or let our son know - we want him to memorize the multiplication tables, not the test answers)
jacquilynne pointed out that it's okay to skip questions that he doesn't immediately know the answer to - we pointed this out to our son, and also told him to go back and answer the missed questions if he had time left.
We also used mittenedsex "little tricks" #1 (don't erase a wrong answer, just cross it out and write below). She wrote more good advice, but that's the one trick we used for now. This was a little difficult for him at first but he's getting the hang of it - although one of the questions he missed was because he answered 3x5=25, realized the mistake and crossed over the #2 with a #1. The teacher counted that as a wrong answer. (I could argue that he actually now scored a 99% - just to point out how effective these 'tips & tricks' really are;)
The one remaining problem that he missed? 11x10. He answered 120.
posted by LadyBonita at 4:28 PM on January 26, 2007
LadyBonita: please pass my congratulations on to your A student, and give both of you a gold star and an elephant stamp! Nice work!
I'd also like to pass on something else I wish I'd understood in school: speed matters, the only way to build speed is practice, and if you approach practice as an opportunity to build speed rather than as a way to demonstrate that you can get the right answers even if students around you are struggling, you'll be much much much less bored when they give you long lists of problems you've known how to do since forever.
Nobody told me that at the time, which is why I went from being an A maths student in Grade 6 to an E student in Form 1. I couldn't understand why, having gone from primary school to secondary school, they were bothering trying to teach me stuff again that I'd already been competent in for years, and I simply went on strike and refused to do the endless sheets of what I perceived as Grade 3 and Grade 4 problems.
The reason that speed matters is that mathematics is built in layers, and the less you have to think about the layers underneath the problem you're trying to solve right now, the easier it will be.
If you're bright, there's a tendency to get into the habit of working everything out from first principles, because doing so saves a lot of tedious memorization. But at some level of conceptual complexity, regardless of how bright you are, your native cunning will become unequal to this task and that's as far as you'll advance. Meanwhile people you know are not as bright as you just seem to be able to keep on making progress - the whole tortoise and hare thing.
Nobody actually explained to me what practice was for, all the time I was in school. I mean, everybody said it was good and necessary and that I had to do it, but I never understood why; it seemed to me that practice was something you did in order to learn something, and that once you'd learned it, there was no point practising any more.
The fact that practice matters because it builds speed, and that speed matters because it lets you learn more things, is something I didn't understand until I was thirty years old and learning to play drums.
If you manage to convince your A student that this is true, he'll go far, and he'll enjoy the trip!
Something else your boy may find useful: the lattice method for long multiplication is way, way easier to get correct answers with than the standard method I was taught in school. My sixth grade teacher showed it to the class once, as a curiosity. It should have been the only method taught, IMHO.
phatkitten: I learned through the course of working them out.
I'd got the idea from what you wrote that the cumbersome procedure you quoted was what you'd actually ended up retaining.
And now I know them and no longer need to work them out.
I withdraw my "damaged by substandard educational methods" remark, but not the smiley that followed it :-)
posted by flabdablet at 5:14 PM on January 26, 2007
I'd also like to pass on something else I wish I'd understood in school: speed matters, the only way to build speed is practice, and if you approach practice as an opportunity to build speed rather than as a way to demonstrate that you can get the right answers even if students around you are struggling, you'll be much much much less bored when they give you long lists of problems you've known how to do since forever.
Nobody told me that at the time, which is why I went from being an A maths student in Grade 6 to an E student in Form 1. I couldn't understand why, having gone from primary school to secondary school, they were bothering trying to teach me stuff again that I'd already been competent in for years, and I simply went on strike and refused to do the endless sheets of what I perceived as Grade 3 and Grade 4 problems.
The reason that speed matters is that mathematics is built in layers, and the less you have to think about the layers underneath the problem you're trying to solve right now, the easier it will be.
If you're bright, there's a tendency to get into the habit of working everything out from first principles, because doing so saves a lot of tedious memorization. But at some level of conceptual complexity, regardless of how bright you are, your native cunning will become unequal to this task and that's as far as you'll advance. Meanwhile people you know are not as bright as you just seem to be able to keep on making progress - the whole tortoise and hare thing.
Nobody actually explained to me what practice was for, all the time I was in school. I mean, everybody said it was good and necessary and that I had to do it, but I never understood why; it seemed to me that practice was something you did in order to learn something, and that once you'd learned it, there was no point practising any more.
The fact that practice matters because it builds speed, and that speed matters because it lets you learn more things, is something I didn't understand until I was thirty years old and learning to play drums.
If you manage to convince your A student that this is true, he'll go far, and he'll enjoy the trip!
Something else your boy may find useful: the lattice method for long multiplication is way, way easier to get correct answers with than the standard method I was taught in school. My sixth grade teacher showed it to the class once, as a curiosity. It should have been the only method taught, IMHO.
phatkitten: I learned through the course of working them out.
I'd got the idea from what you wrote that the cumbersome procedure you quoted was what you'd actually ended up retaining.
And now I know them and no longer need to work them out.
I withdraw my "damaged by substandard educational methods" remark, but not the smiley that followed it :-)
posted by flabdablet at 5:14 PM on January 26, 2007
11x10 = 120 says to me that he's using table lookup for elevens or tens or both, which is fine as long as his tables are correctly locked in. But using the "trick" for tens - just stick a zero on the end of the other number - really is as quick as using a table, and habitual use of that trick pays off later because it works for any number, not just small ones. In that specific case, I'd recommend using the rule instead of the table.
If your boy is into collecting handy tricks, and is motivated to do extracurricular study, and you reckon he's capable of learning several methods in parallel without getting them all hosed up, have a look at the Trachtenberg Speed System. This involves loads of rote-memorization of rules, instead of rote-memorization of tables. As a kid, I found it interesting but no more useful than the methods I was taught in school.
posted by flabdablet at 5:28 PM on January 26, 2007
If your boy is into collecting handy tricks, and is motivated to do extracurricular study, and you reckon he's capable of learning several methods in parallel without getting them all hosed up, have a look at the Trachtenberg Speed System. This involves loads of rote-memorization of rules, instead of rote-memorization of tables. As a kid, I found it interesting but no more useful than the methods I was taught in school.
posted by flabdablet at 5:28 PM on January 26, 2007
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posted by Loto at 2:41 PM on January 19, 2007