Time of completion (Times Tables)

[physics girl phd]

We were told by my 4th grade stepson's teacher that he needs more practice to beef up his multiplication/division (up to the standard 12x12=144), since he seems to understand the concepts of higher math (they're starting more complex "long" division), but often goofs up the answer because he doesn't seem to know the basic facts. While we're going out to get the flashcards she recommended this weekend, I also set up the challenge of the basic "times-table grid"... you know where they set up a table with the numbers 1-12 across it and down, and he fills in the result of the multiplication? See http://en.wikipedia.org/wiki/Times_table" .

Right now it takes him 8 minutes to fill out the 12x12 ordered table accurately (down from 18 minutes with ~90% accuracy earlier this week). Of course he's still essentially adding to fill in the columns, but at least he's also getting better at our random inquiries (showing some recognition/recall).

My TWO questions:
How long do you think it should take him to fill an ordered 12x12 table?
How long do you think it should take for him to fill out a RANDOM 12x12 table (with the numbers randomized in order on both top and bottom)?

I set the goal of five minutes for the latter version (his handwriting is also miserably slow... so I think that would be a decent feat). Does this sound reasonable? I'd like to know what others think...

He's an odd character. (Note... not my genetics! ) He arrived to our house from a classic low-achieving/high-risk school (hence the bad writing and poor math), but he also soaks things up like a sieve (aka he memorized the Gettysburg address for his dad recently). Via his social-scientist dad, he knows a lot about history, politics, world affairs, etc. (was the one in his class to know what "guerrilla" meant versus "gorilla"). His teacher loves his "vast knowledge" and "mature sense of humor" (Blame his professorial dad and I for making continual fun of his "vast knowledge" at home before our conference with his teacher at which the "mature humor" comment came out). He also does well on standardized tests, so he was accepted into the gifted program (to start next term). So there's hope.

But darn it... it's my job to beef him up on math/science... at least until he dissects a frog in the gifted program!

So give me YOUR thoughts on the time it should take for the times table... for a fourth grader (no bragging!... I don't need to know YOUR time! ).

 

[Kurdt]

Soaks things like a sieve?

I have no more to add.

 

[physics girl phd]

Soaks things like a sieve?

I have no more to add.

Good catch Kurdt -- that's why I'm not teaching him language arts. I always mix my metaphors and stir up my analogies... I guess it's "sponge"... right?

 

[Kurdt]

I'd have have gone with sponge.

Unfortunately I have no idea how long it should take someone your step sons age to do a multiplication table. I learned them until I could recite them to the teacher and then promptly forgot them all.

 

[Evo]

As long as his mind isn't like a blotter - soaks it all up but gets it all backwards.

 

[Jimmy Snyder]

I've got a pretty soaky mind full of half vast knowledge myself. I'd go for accuracy over speed if I were in charge.

 

[wolram]

Robotic learning is fine if one wants to get on well in life, but where is the challenge in that?

 

[Art]

What age is 4th grade?

 

[Evo]

What age is 4th grade?

Usually 9-10 years old.

I would agree speed is not important, accuracy and retention are more important.

 

[physics girl phd]

Okay:
Yes: We Do want him to have higher learning skills, not just robotic learning. But let's also have a dose of reality, SOME robotic learning is needed, especially at early ages (he's nine). At this point in life most of his education is robotic learning... gee, he still needs to be taught more vocabulary, more about the parts of sentences and the parts of stories so that his garble to us about a variety of subjects keeps continuing to make more sense! Gee -- and he still even needs to form his letters correctly...)

Think: How would you like it if your students didn't know some basic facts and vocabulary of your subject, or couldn't form letters (or identify them on a typewriter)? Wouldn't that make it difficult/impossible for them to move onto those more desired thinking skills? Or communicate those skills intelligently? Higher skills obviously build on lower skills.

And YES: We DO want 100% accuracy above all (I don't care if he uses some to reasonably derive others). However, we AND his teacher do want him to have a fair amount reasonably memorized so he doesn't fail at class tests in things like long division and then eventually get tracked into lower math classes for the rest of his life. When he's in high school, it would be awesome if he reached some of the geometry, calculus, logic, and probability problems that I was doing (and really thinking about/enjoying)!

And note: While he likes to think, if it takes him too long, he's also prone to deciding to give up... based on the standards of his previous school and living environment (note -- he came to us from living in a low-income housing neighborhood, living in a communal living arrangement, and then a shelter... ). BUT: We need to save some of his thinking power and motivation for the actually more interesting part (the long division).

So: It just took me about 3.5-4.0 minutes to do a randomized 12x12 table with 100% accuracy. It's not like I'm asking him to do anything that the rest of you probably can't do. (I'm sure I can't do a 15x15 table well with speed.)

Have any of you done it recently or have children that have had to done this recently so I can get an age 9 baseline? Or even remember from your own days? (I'm going on the vague recollection that for me, in 3rd grade, it was perhaps about 5 minutes... once my sole remaining pencil broke and I was devastated; I frantically sharpened it and had only a few remaining when my teacher called time!)

 

[ice109]

you need to be smarter about how you teach him this. it would be much more instructive to show him patterns in the table than to just force wrote memorization. things like n*11=nn and n*10 = n0 and n*5=m*5 where m=n-1 if odd and m=n/2 if n is even. those things will give him practice with the products and engage his curiosity.

things should never be memorized, education shouldn't be a task but a means to satisfaction of curiosity and one doesn't memorize things they're curious about - one relishes them. and if he's not curious then he's not curious and forcing him to fit in/do well/score high will supress his natural curiosity for other things.

 

[Proton Soup]

we learned our times tables in 2nd grade. and this was public school, mind you, but back in like '74-'75. rote is the way to go here. speed is important, but not necessarily at first, it'll come naturally in time. i understand the idea of the table, but think instantly knowing that 7x6=42 is important, not just counting fast by sixes or sevens. if you give him the table, then that's what he'll do. it may be an important concept to understand about how multiplication works, but I'm a bit leery of the idea of teaching him to do it the way a machine would.

 

[ice109]

you need to be smarter about how you teach him this. it would be much more instructive to show him patterns in the table than to just force wrote memorization. things like n*11=nn and n*10 = n0 and n*5=m*5 where m=n-1 if odd and m=n/2 if n is even. those things will give him practice with the products and engage his curiosity.

things should never be memorized, education shouldn't be a task but a means to satisfaction of curiosity and one doesn't memorize things they're curious about - one relishes them. and if he's not curious then he's not curious and forcing him to fit in/do well/score high will supress his natural curiosity for other things.

i'm quoting myself because i sincerely feel that this rote memorization idea is endemic of a huge education problem.

 

[Proton Soup]

i'm quoting myself because i sincerely feel that this rote memorization idea is endemic of a huge education problem.

in this case, you're wrong. you need both, of course. and most 4th graders are not ready for algebra, either.

 

[ice109]

in this case, you're wrong. you need both, of course. and most 4th graders are not ready for algebra, either.

there's a reason america's education is ranked one of the worst amongst first world countries and this is part of it.

 

[Proton Soup]

there's a reason america's education is ranked one of the worst amongst first world countries and this is part of it.

do you remember your numerals and alphabet by concepts? do you count out the result of 7x6 when muliplying 968x773?

 

[ice109]

do you remember your numerals and alphabet by concepts? do you count out the result of 7x6 when muliplying 968x773?

what's your point? i never said anything about learning solely concepts nor did i say it's not useful to have them memorized. i said that's not how they should be memorized.

anecdotal evidence for why you shouldn't do this to the kid:

"Never memorize what you can look up in books." Albert Einstein

 

[physics girl phd]

"Never memorize what you can look up in books." Albert Einstein

Does that mean that I shouldn't memorize pi to a small number of digits (say 3.14)... or the average gravitational acceleration at Earth's surface as g is about 9.8 m/s^2 (downwardly pointing of course)? I'd imagine Einstein had these things memorized, by some form of repetition / use ... as well as other things perhaps like the equation of motion for objects moving under constant acceleration under the limits of Newtonian mechanics: such as an object falling near the Earth's surface as y=-1/2 gt^2 + v0t + y0... until y = 0 (as referenced from ground level). I'd bet you know pi to about 3.14159. I do... heck, my fingers even have the instinct to type in it pretty fast on the keyboard. Granted, if I ever need to know it to more digits, I'll look it up. Chances are I won't, and my memorization of pi has allowed me to do a lot more interesting calculations with some reasonable rapidity.

For my stepson, who we have been told does not have some basic facts concerning multiplication memorized that will help him in his present math, our technique is going to be the routine completion of both ordered and randomized times tables, oral questioning, and the use of flash cards (as recommended and as we ourselves remember doing). We'd just like to have a reasonable goal for him on the times tables. He likes goals / challenges, and he's already shown improvement and rudimentary development of some higher thinking skills that will later link into algebraic methods... Note: By doing the ordered table he is also noticing patterns that are helping him easily come up with the trickier ones in the pinch situations when we call out problems orally (he's been noticing a problem like 9x8 is easier to quickly compute as 10*8-8). We DO discuss these thoughts in the process.

So in this thread, I'm not looking for your criticism (I'm an educator and I realize the values of many dimensions of education, especially, of course, the higher dimensions). I was simply looking to see if people had a reasonable time(s) for the goal of this relatively normal technique for someone of my stepson's age. If this continues to be a useless thread for the specific help I've requested I'm going to request a lock on the thread.

 

[hypatia]

Math, to me, was better when I learned it as a game. I was really slow at learning math and flash cards made me really made me feel stupid. Then I had a teacher that made it all fun.

Try some internet sites like
http://blackdog.net/games/math/multiply/index.html and

http://www.multiplication.com/interactive_games.htm {look at knights of math}

 

[BobG]

what's your point? i never said anything about learning solely concepts nor did i say it's not useful to have them memorized. i said that's not how they should be memorized.

anecdotal evidence for why you shouldn't do this to the kid:

"Never memorize what you can look up in books." Albert Einstein

And never memorize what you can punch into a calculator?

I think you're comparing two vastly different levels of knowledge. A person has to memorize the basic math facts at least up to 10 the same as they have to memorize the alphabet.

I think it is a good idea to understand how to quickly fill out an ordered multiplication table first, since the patterns quickly fill in any gaps that the kid is slow to remember and the overall functionality is more important than how fast he can remember them. I wouldn't worry about the speed for the random table as much as I'd make sure he has an ongoing experience with the multiplication facts. The speed kind of comes on its own after he's actually gotten to the point of really remembering each fact instead of having to figure some of them out.

The computer games hypatia mentioned are a great way to do that.

(Why would I want to remember the digits of pi? It's just a special mark on my slide rule with the letter pi above it to me. And, on a modern calculator, it's a special key with the letter pi on it or above it. About 3.14 is good enough unless you're figuring it out with pencil and paper - in fact, maybe I like the idea of going beyond 3.14 even less if I'm figuring it out with pencil and paper. It happens that I do know the first 6 digits of pi, but I can't really remember why I had to remember that many digits.)

 

[Gokul43201]

i'm quoting myself because i sincerely feel that this rote memorization idea is endemic of a huge education problem.

there's a reason america's education is ranked one of the worst amongst first world countries and this is part of it.

Have you checked out the rote memorization children go through in China, Japan, Singapore and India?

 

[Evo]

I memorized my multiplication tables, and it worked for me. When you get the simple things down, it makes it easier to move onto other things. To this day any simple multiplication is automatic for me and I don't like math. I love biology and scored 110% on a test naming all of the bones, muscles etc... in the human body and I'll bet that the next day most of it was gone. It was too much information memorized too fast just to pass a test. I think that kind of thing is useless in learning. If we had actually spent time learning about the parts it would have had meaning, but no, we just had to name them. Take the test, move on.

I would just pay attention to the type of learning that he responds to best. I would not be concerned at all about how fast he does anything, but more to your concern that he might get distracted. I don't see speed tests as the answer though. Just try to figure out how to keep him interested. Of course you are asking people that don't know him and don't know his strengths or failings.

 

[dol88]

Hi,

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All along the race the pilot faces different kinds of arithmetic problems under the form of panels. Without stopping his progression he has to determine the correct answer and to drive towards it.

For even more fun, a double players mode allows to compete simultaneously against another pilot. The level of difficulty can be tuned independently for each player so it is possible to get fair races with players having different arithmetic skills.


Regards

$88

 

[Chi Meson]

Education in America is currently going through an "Anti-memorization" fad. It sucks. Seems as though I can't expect any of my students to remember anything. I tell them to be sure to know the meaning of all the key terms listed in the back of the chapter, and they say "How are we supposed to know all of them?" (there are about 12 words and phrases, such as "wavelength" "period" "frequency") I tell them "Just memorize them."

No clue.Regarding multiple tables, when I think of the product of 6 times 7, I do not retrace my steps through the "concepts" of multiples of 3 or the multiples of primes, I just bring up 42. There is no need to wait for, or "prove" the result. Some things should just simply be memorized. After which, there is a lifetime of opportunity for discovering the patterns within numbers.

 

[Proton Soup]

i recently met up with some old alumni at my former high school, which is about to be razed. the subject of the deterioration of the music program came up. apparently, the flute players don't know how to form a proper embouchure, or how to roll it back and forth. none of the trumpet players can reach the upper registers. by all accounts, they are playing on a junior high level. and one anecdote tells me that our old geometry teacher is just disgusted with her pupils. it's a bit scary to think what this means to the rest of the program. the new school will have all the latest technology, including lcd projectors in the classrooms and such. and the football team were state champs. yet the future of these children seems far from certain as best i can tell.

 

[Unknot]

It's now a big trend in Asia to teach kids who are in somewhere like 3rd grade 1x1 through 19x19.

 

[Proton Soup]

good for them. we learned 12x12 in grade 2. but why 19?

 

[Unknot]

I have no idea. It apparently originated in India as far as I know, and parents in East Asia felt that it will make their children smarter.

 

[NeoDevin]

Education in America is currently going through an "Anti-memorization" fad. It sucks. Seems as though I can't expect any of my students to remember anything. I tell them to be sure to know the meaning of all the key terms listed in the back of the chapter, and they say "How are we supposed to know all of them?" (there are about 12 words and phrases, such as "wavelength" "period" "frequency") I tell them "Just memorize them."

Give them enough assignments that they should have them memorized from use.

 

[Astronuc]

Education in America is currently going through an "Anti-memorization" fad. It sucks. Seems as though I can't expect any of my students to remember anything. I tell them to be sure to know the meaning of all the key terms listed in the back of the chapter, and they say "How are we supposed to know all of them?" (there are about 12 words and phrases, such as "wavelength" "period" "frequency") I tell them "Just memorize them."

No clue.


Regarding multiple tables, when I think of the product of 6 times 7, I do not retrace my steps through the "concepts" of multiples of 3 or the multiples of primes, I just bring up 42. There is no need to wait for, or "prove" the result. Some things should just simply be memorized. After which, there is a lifetime of opportunity for discovering the patterns within numbers.

There is a place for memorization, but one must be educated beyond simple memorization in order to achieve an understanding of process and method.

I memorize a lot small details (and facts) which are relevant to my work, primarily in order to save time.

 

[Moonbear]

If he can figure out how to multiply by applying the concept that it's addition, does he really need to be able to quickly regurgitate the times tables? I don't think I ever learned my times tables (to this day, I have to stop and think about things like 8X7). Between being moved from one math class to another as they realized I was smarter than they expected for whatever reason, and then being moved to a different school when we were redistricted, I skipped some of those more tedious lessons. While I was always very slow with my math problems, I would still score 100% on tests regularly. I wouldn't worry so much about how fast he can recite a times table, but instead focus on accuracy. I think if he can figure out the answers without memorization, it will set him up for much better lifelong learning. Maybe he'll prefer the frog dissection anyway.

 

[Integral]

I taught my step son the multiplication tables while driving him to school. We had about a 15 min drive and I just kept quizzing him as I drove. I went through the tables pretty much in order until he learned the patterns, then began to mix it up so he had to know the answer. I am with Chi, I think there is a lot of value in being able to spit out such facts without having to figure it out from scratch each time. Such exercises are good for brain function and as confidence builders. It is distressing to me at how low our expectations are of American students. Higher expectations cannot do anything but cause higher performance.

Why shouldn't some 4th graders be learning Algebra? Not clear that ALL 4th graders are ready but there are some that are. Currently elementary school teachers are to a high percentage math phobes themselves, to have then teaching math is criminal.

 

[moose]

Have you taught him methods like when multiplying by 5 you can just half and multiply by 10, etc?

EDIT: I just remembered when I learned these. We were quizzed extensively on multiplication tables in 3rd grade. My teacher placed huge emphasis on being able to pass her timed trials, so every now and then I would memorize the tables/find patterns and such worried that I'd be the only one in the class who didn't pass them. Turns out I was the only one to pass her timed test of it and that's how she plans it out, making it "impossible" to make us do the best we can. It was a good confidence booster because I moved to the US in 3rd grade and knew 0 english at first.

Also, I know a few people who would take 5 seconds to tell you that 6x7 is 42. That's just weird.

EDIT2: This, somehow, reminds me of my roommates friend who is in Calc 2 at the local community college, and wasn't able to tell us what a derivative at a point looked like graphically. Somehow he passed Calc 1 with a B though. So yes, memorizing things is definitely stupid unless you actually understand what you're memorizing as well.

 

[Chi Meson]

Have you taught him methods like when multiplying by 5 you can just half and multiply by 10, etc?

That's the basic stuff. I'm still fascinated by multiples of 9. Take any multiple of nine, and add the digits. THey add up to nine. If the sum is more than 1 digit, then add the digits of the sum, and that adds up to nine.

 

[rootX]

That's the basic stuff. I'm still fascinated by multiples of 9. Take any multiple of nine, and add the digits. THey add up to nine. If the sum is more than 1 digit, then add the digits of the sum, and that adds up to nine.

I loved the tables of 1,2, 5, 9,10, and 11..
(for 11 also discovered that:
11*12 = 11+22
11*13 = 11+33
)
9 has always fascinated me too :)

Other reason for loving 9:
Start from 0 to 9 .. and then write 9 to 0 in reverse next to each digit

09
18
27
3.
4.
5.
6.
7.
8.
90

As for memorization or learning, I think there's no match for experience and practice with one thing. I see many people expecting to understand things without any practice...

And Personally, I think learning is one of the easiest job in the world - you need only one thing: time! And, there's no risk. You input your effort and you learn.