How do I get my 6 y.o. to stop counting with her fingers? - Page 3 - Mothering Forums

Old 07-05-2010, 12:57 PM

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 Originally Posted by Carolinemaths The reason finger counting is discouraged is because it slows down the whole calculation process. Fast recall of of arithmetic facts are essential for questions from "There are 8 eggs in a basket and 3 are taken out. How many are left?" through to "Solve 7x + 3 = 52" and beyond. Yes there are calculation methods which use the fingers to work out calculations at super fast speed, which is great if you're going to train your child to do that but leaving your child to finger count while her classmates move ahead because they have memorised the arithmetic facts is just not fair. Try starting from the basics, memorising +1's first, then +2's , then +3's. I talk in more detail about this on my blog
Simple memorization may be faster for people who have good memories, but it both fails those poor memory and fails to give a child any degree of number sense.

The only reason I see that the OP's DD should not use her fingers is that she almost certainly has an already well developed number sense and was able to manipulate the numbers in her imagination. Being able to see math problems in ones imagination is one of the things that sets those who can really do higher (and I'm talking about beyond a very basic algebra problem like 7x + 3 = 52) math from those who just go through the motions. If the OP's DD in reality has simply memorized the addition, then I would actually encourage finger counting to help her develop number sense.

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Old 07-05-2010, 03:48 PM

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 Originally Posted by Geofizz Many people confuse arithmetic with mathematics. Remember that most of what is called "math" at this level is really just manipulating numbers, which is a different beast all together. I'm a great mathematician. My arithmetic is so-so. You don't hit what I call mathematics until algebra or so, unless you're really lucky and get a lot of logic mathematics earlier. It saddens me that so many people get turned off the number crunching so early they never see that math is just a series of logical statements.
Actually that was my point -- you can do multivariate calc and still count on your fingers. They're different skills.

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Old 07-05-2010, 06:23 PM

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I'm a big fan of using choc chips, raisins, biscuits etc to help children see (and taste) arithmetic connections and yes, formulating the equation 7x + 3 = 52 from a real life problem is real maths and solving it is higher arithmetic, however ideally we want our children to be confident in both skill sets.
Memorising number bonds need not be painful - 1 or 2 minutes a day is enough to increase a child's arithmetic confidence. I just don't want people to fall into the trap of thinking that just because one method of memorising number bonds hasn't worked, then it's better to finger count than to try other methods. Google "number bonds" and see ways of helping with those arithmetic connections. Whether or not arithmetic is real maths, a good grasp of it is needed in school and in real life.
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Old 07-06-2010, 05:06 PM

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Lets see, I was top of my grade in math all through high school, I have a degree in physics (a math heavy subject) and have been known to do complex equations in my head. I still count on my fingers for plenty of things. I like my fingers. They don't make mistakes as often and I don't misplace them.

I also think this need society seems to have for "fast math" is silly. Doing things faster increases the chance of a mistake. There are only a few situations outside of a test where math is required to be fast and no everyone is going to want to be a nurse, or work for shuttle launches or something like that where fast math can be life or death. Most people will only use their math for basic everyday situations where it doesn't matter if it takes 1 minute or 30 seconds or .5 seconds to get the answer.

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Old 07-06-2010, 08:21 PM

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 Originally Posted by MusicianDad I also think this need society seems to have for "fast math" is silly. Doing things faster increases the chance of a mistake. There are only a few situations outside of a test where math is required to be fast and no everyone is going to want to be a nurse, or work for shuttle launches or something like that where fast math can be life or death. Most people will only use their math for basic everyday situations where it doesn't matter if it takes 1 minute or 30 seconds or .5 seconds to get the answer.
Actually, even in a life or death emergency accuracy would seem more important than pure speed. I'd rather a nurse give me the correct dosage in 15 seconds than the incorrect one in 1 second.

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Old 07-06-2010, 08:43 PM

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 Originally Posted by LynnS6 Actually that was my point -- you can do multivariate calc and still count on your fingers. They're different skills.
I know you know, but I see a pervasive misunderstanding of that point throughout MDC and real life, so I thought I'd make the point. I hear a lot of "I'm no good at math" from my geophysics students when it really means that arithmetic was made unnecessarily hard/boring/confusing earlier in school.

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 Originally Posted by MusicianDad I also think this need society seems to have for "fast math" is silly. Doing things faster increases the chance of a mistake.
I mostly agree with you. I see a difference between memorization and being fast, though. I see a lot of value in generally memorizing the multiplication table because it's really useful when inverting it all (dividing) or working with the general properties of mathematics (algebra). Having this memorized makes things more efficient and more painless when doing a series of calculations. Take my reimbursements I filled out today -- I added everything up (~15 numbers) after having to calculate some of them (multiplying mileage and per diem). The whole task took me less than 5 minutes, and was likely as accurate as using my clumsy fingers on a calculator, and less likely for a mistake if using my fingers. That being said, I know my 6's and 8's and I add or subtract to get the 7's.

And to the point of the OP, the child in question is really young and will probably memorize most of the sums just through repeated exposure, and just knowing the result is a whole lot faster and less painless than totaling it up on ones figures. My DD did it towards the end of kindergarten but now just knows most of it cold, mostly just through repeated exposure, but some because she was so stinking bored in math last year she did a lot of writing out multiplication tables through repeated addition.
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Old 07-06-2010, 08:50 PM

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 Originally Posted by Geofizz I mostly agree with you. I see a difference between memorization and being fast, though. I see a lot of value in generally memorizing the multiplication table because it's really useful when inverting it all (dividing) or working with the general properties of mathematics (algebra). Having this memorized makes things more efficient and more painless when doing a series of calculations.
I don't think there is any importance to memorizing the multiplication tables at all. I think it's a product of the "fast math" mind set that we force kids to memorize a series of numbers instead of teaching them how to figure out how to get those numbers and it sets up a fairly intelligent portion of the population for stress in math class because they can't memorize a series of random equations.

What makes properties of math painless and more efficient is teaching students the way they learn best. For some, rote memorization may be the way to go, but for others it is nothing but a painful inefficient means of making them feel inadequate.

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Old 07-06-2010, 10:24 PM

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 Originally Posted by Geofizz That being said, I know my 6's and 8's and I add or subtract to get the 7's.
It seems more likely to me that you have a feel for the pattern of the 6s and 8s, than that you've simply rote memorized them. The pattern of the 6s and 8s give them a rhythm that the 7 lack. If you were going solely by rote memory, the less rhythmic 7s would be just as easy.

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Old 07-06-2010, 11:06 PM

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 Originally Posted by eepster It seems more likely to me that you have a feel for the pattern of the 6s and 8s, than that you've simply rote memorized them. The pattern of the 6s and 8s give them a rhythm that the 7 lack. If you were going solely by rote memory, the less rhythmic 7s would be just as easy.
No, I have them memorized. Honest. I was sick the week we had to memorize the 7s. Thankfully, I have solid number sense to use to fill in that gap.

MusicianDad, again, I mostly agree with you. Note that I put in enough weasel words in my post so that we mostly making the same point. I recognize that there are a variety of learning styles to approaching math. Also note I've emphasized number sense and the properties of math as distinct from arithmetic.

However, I dealt with a student every week in my office hours last quarter who could neither figure out when to add or multiply (mathematics) or do 201 / 3 using long division (arithmetic). I'm pretty sure that the process of long division would have been significantly easier if he'd actually known 3x6=18, which he did not. Using ones fingers would have made it just as painful and tedious. The OP should know that you don't hit this kind of problem until 3rd or 4th grade.

If there's another learning method you can tell me to help students like this, I'm all ears. It was a painful quarter for both of us.
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Old 07-07-2010, 12:43 AM

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When children learn how to use an abacus and become proficient they use their fingers and can solve problems remarkably fast - the use of fingers is an essential part of the process. I didn't spend much time searching for a good clip on youtube but I've seen competition footage before that is mindblowing and those kids rely on their fingers - I know its a different concept but the point remains that there is a connection between using our hands and mentally working out problems

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Old 07-07-2010, 01:30 AM

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 Originally Posted by Geofizz However, I dealt with a student every week in my office hours last quarter who could neither figure out when to add or multiply (mathematics) or do 201 / 3 using long division (arithmetic). I'm pretty sure that the process of long division would have been significantly easier if he'd actually known 3x6=18, which he did not. Using ones fingers would have made it just as painful and tedious. The OP should know that you don't hit this kind of problem until 3rd or 4th grade.
How about doing with out 3x6?

Lets see 3x10=30
30+30+30=90
90+90=180
3x60=180

(The 60 comes from counting by ten for every thirty, so 3 in the first and 3 in the second, and adding a 0)

201-180=21
3x5=15
180+15=195
3x65=195

201-195=6
3x2=6
3x67=201 ergo 201/3=67

(60+5+2=67 or [10x6]+5+2=67)

All you need to do is understand the pattern of 4 different multiplication tables 1, 2, 5, and 10 and you can figure out pretty much anything. That's all I have "memorized" (though not really, I have enough number sense that I can figure out all four of those without having them officially memorized) and I have managed to ace university level math courses.

The 6x table doesn't even need to be memorized to do multiplication of 6.

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Old 07-07-2010, 04:00 AM

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 Originally Posted by Geofizz However, I dealt with a student every week in my office hours last quarter who could neither figure out when to add or multiply (mathematics) or do 201 / 3 using long division (arithmetic). I'm pretty sure that the process of long division would have been significantly easier if he'd actually known 3x6=18, which he did not. Using ones fingers would have made it just as painful and tedious. If there's another learning method you can tell me to help students like this, I'm all ears. It was a painful quarter for both of us.
In that situation I would have taken that student right back to the basics. Start with 1 + 1 or 1 x 1 , memorise the 1's first, then the 2,s, then review the 1's and 2'sbefor moving on to the 3's, then review the 1's,2's and 3's before moving onto the 4's. At each stage make sure there is fluency before moving to the next.

It's not a quick fix, but even if you had limited time it would be better for that student to know some of the basics solidly which would likely increase his confidence as well.
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Old 07-07-2010, 01:04 PM

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 Originally Posted by MusicianDad The 6x table doesn't even need to be memorized to do multiplication of 6.
But the even 6 times make a lovely pattern that one can simply follow.

2x6=12 aka 1/2 the number in the tens column (1/2x2=1) and the number itself in the ones column (2.)
4x6=24 aka 1/2 the number in the tens column (1/2x4=2) and the number itself in the ones column (4.)
6x6=36 aka 1/2 the number in the tens column (1/2x6=3) and the number itself in the ones column (6.)
8x6=48 aka 1/2 the number in the tens column (1/2x8=4) and the number itself in the ones column (8.)
it's easier to follow the ten's pattern for 10x6=60
12x6=72aka 1/2 the number in the tens column (1/2x12=6) and the number itself in the ones column (12, just do a little carrying 6+1=7 so you have a 7 in the tens column and not a 6.)

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Old 07-07-2010, 01:29 PM

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 Originally Posted by Carolinemaths In that situation I would have taken that student right back to the basics. Start with 1 + 1 or 1 x 1 , memorise the 1's first, then the 2,s, then review the 1's and 2'sbefor moving on to the 3's, then review the 1's,2's and 3's before moving onto the 4's. At each stage make sure there is fluency before moving to the next. It's not a quick fix, but even if you had limited time it would be better for that student to know some of the basics solidly which would likely increase his confidence as well.
It seems pretty likely that a student that is faced with 201/3=? has already been told to memorize the addition and time tables. Said student probably did indeed memorize them well enough to pass the speed tests back in 1st and second grades, but then summer came and maybe s/he spent some time working on geometry in math. Obviously by the time s/he was faced with more complex arrhythmic, what simply had been memorized was now forgotten.

This is the problem of memorization, it relies on memory which for many is a faulty skill. Though there are many memory trainers out in the world, some people really just can't improve their memory. What has simply been memorized, can easily be forgotten.

A good number sense on the other hand, is not likely to be forgotten during a fun summer, and one rarely looses one's fingers.

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Old 07-14-2010, 06:07 PM

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This is all really interesting. I count on my hands. I figured out in grad school (when excel had come into fashion) that I was good at setting up equations but less good at that actual arithmetic part. I swap numbers around without realizing it. 8 x 6 = 84 looks quite right to me sometimes. I'm majored in science so I'm not hopeless, but it's not a strength. It's really the arithmetic that trips me up.

DH is VERY good at math and doing it in his. He thinks of it as his parlor trick. I was continually amazed that pre-school aged my daughter could do these simple addition and subtraction problems in her head. She just CAN. Like better than me even now. (She's 7) She'd start to ask me something and I start grabbing manipulatives or holding up fingers to help her work out, the problem, or grabbing a number line or tape measure, and before I could even get there, she'd be like - Never mind - it's 17.

I did memorize the times tables, but they don't really stick with me. They get jumbled. For timed tests, I would quickly scribble down a multiplication grid (usually just 5-10) and I'd use it as a look-up feature for the answers. That was safer than relying on my memory and I didn't mix up 48 and 84. Hey - I could do it in the time frame so the teachers never said anything. I kind of knew it was "cheating," but it helped ensure I had the right answers.

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Old 07-15-2010, 12:48 AM - Thread Starter

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 Originally Posted by Geofizz However, I dealt with a student every week in my office hours last quarter who could neither figure out when to add or multiply (mathematics) or do 201 / 3 using long division (arithmetic). I'm pretty sure that the process of long division would have been significantly easier if he'd actually known 3x6=18, which he did not. Using ones fingers would have made it just as painful and tedious. The OP should know that you don't hit this kind of problem until 3rd or 4th grade.
I get quite a few students every semester like this. These are university students taking a science course. They are not students who aspire to technical careers. They want to teach ELEMENTARY SCHOOL.

The high school physics and math teachers that I talk to tell me the roots of the problem are in elementary school, so I feel overly sensitive about that.
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Old 07-15-2010, 01:14 AM

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 Originally Posted by emilysmama I get quite a few students every semester like this. These are university students taking a science course. They are not students who aspire to technical careers. They want to teach ELEMENTARY SCHOOL. The high school physics and math teachers that I talk to tell me the roots of the problem are in elementary school, so I feel overly sensitive about that.
I think the root of the problem is that we expect everyone to do math the same way, so when someone can't do it that one way we label them as "poorly taught" or "incapable" when in reality they are "not show a method that fits how their brain works."

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Old 07-15-2010, 02:30 AM

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 Originally Posted by MusicianDad I think the root of the problem is that we expect everyone to do math the same way, so when someone can't do it that one way we label them as "poorly taught" or "incapable" when in reality they are "not show a method that fits how their brain works."
Wouldn't "not shown a method that fits how their brain works" be synonymous with "poorly taught?" Shouldn't a teacher notice when a certain student's learning style is not fitting the teacher's preferred teaching style and make adjustments to reach said student? Isn't being flexible and not treating students like clones of each other teaching well? If a teacher can only teach math/arithmetic one way, then isn't that teaching poorly?

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Old 07-22-2010, 02:32 AM

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 Originally Posted by ramama I don't see finger-counting as a crutch at all. In fact, I kind of see it as a reflection of a true understanding of math and using all tools available. My DD1 is 6 and uses her fingers to count. She touches the finger to her lips to count each one and I think it's adorable!
I agree with that! And my 5 1/2 DD does the exact same thing! I love how she touches her little fingers to her lips. She will even say this, "5 + 2 =..." and then she will count, "1, 2, 3, 4, 5" on one hand (even knowing she has five fingers she STILL counts it out! Totally normal developmentally, btw) and then touches two fingers to her lips "6, 7. SEVEN!"

She attends a Montessori school and I talked to her teacher about this and the teacher said, "I will sometimes tell them to hold the bigger # in their head and then do the addition, but that is completely developmentally normal."

There are a lot of really great Montessori products for learning and understanding math. Check out www.montessorioutlet.com or www.alisonsmontessori.com under math. I love these:

Stamp game

Multiplication Bead Board (they also have these for division, long division, and square roots)

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Old 07-27-2010, 09:42 AM

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This thread inspired me to research further into the topic of finger counting. As you can see from my previous posts, I'm one of the few posters here who don't think finger counting a good thing. I've just published a blog post on my website titled

No! No! No! No! Don't Let Your Child Finger Count!

which lays out my argument, with some evidence. Enjoy!
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Old 07-28-2010, 02:12 AM

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1. Finger counting is visual period. Visual learners will not always be able to memorize from flash cards. For some, seeing numbers written doesn't help at all, they need to see numbers represented in some way. I know a couple of people like this, they did flash cards when in school and no it didn't help at all with memorization.

2. Finger counting does not discourage memorization. Working through a problem in a way that is effective for the student encourages memorization. Again, there are people, the more times they count on their fingers to figure out the equation puts the equation into the "I did it myself, so I have an easier time remembering next time" category. I have seen this happen too, it's how I memorized the equations I have memorized.

3. I have mentioned before, the only time anyone will actually need to calculate fast is when taking a timed test. I personally do not agree with timed tests for many reasons, not the least of which is they inhibit many people from showing their true potential. Someone who can figure out a complex math problem using their fingers can still figure out a complex math problem. Failing them because they can't do it fast enough is just plain dumb.

4. Finger counting does not disadvantage anyone unless it is strictly forbidden in the class. I finger count at times, I have friends that finger count at times. Many of us have excelled in math intensive studies in spite of (or maybe because of?) this.

Using a different set of items is still using a visual representation of numbers, the only difference is you have your fingers with you at all times. You can't misplace them, and taught properly, you can do larger number equations as well. You won't need a whole bag of them to do 233 + 432.

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Old 07-28-2010, 02:50 AM

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speaking of memorization... I have very very little memorized. I never could memorize it. for multiplication, I can do the 1's and the 2's and the 5's and the 10's fine as well as the doubles (6x6, 7x7) but the 3s I often need to count through same with 4s. I do the hand trick for 9's. For 6's 7's and 8's I usually do something different and add or subtract whatever I need to... 7x7 is 49 minus 7 is 42 which is 7x6. 6x6 is 36 and 6x2 is 12 so 36-12 is 24 which is 6x4.

I also still often count on my fingers. I even count on my fingers IN MY HEAD. yes, I can do it in my head.. if I visualize my fingers. That is how I do my 9's on my hands... in my head. I also visualize dots. Counting through for 3's and 4's is literally me going 3 6 9 12 15 18 21 24... 3x8! while yes, counting on my fingers til I've added that 3 eight times.

Yes, I am slow but I just couldn't remember all of the combinations I needed to memorize. In fact, stressing out about not being able to do it when my classmates could is exactly what turned me off to math class.. and I've always been GOOD. I get nervous though when I can't do something 'right' and generally give up. Worse when I was a kid.

I still managed to be slightly advanced for most of my school days, but I definitely didn't enjoy it and was usually very embarrassed about my 'in'abilities. I just never could memorize everything. The numbers all just blur together in my head.
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Old 07-30-2010, 09:25 AM

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Musiciandad, your arguments are both reasoned and persuasive, but if we return to the OP's question, her child only recently started finger counting and was previously able to recall number facts to 10. What I want to draw attention to is the unspoken idea that not only is it ok not to be able to recall number facts with ease but that as a parent, the OP shouldn't try to help her child memorise these facts.

Yes, I'm sure her child could still become a great mathematician even if she continued finger counting, but let me support the OP in her attempt to help her child.
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Old 07-30-2010, 01:47 PM

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 Originally Posted by Carolinemaths Musiciandad, your arguments are both reasoned and persuasive, but if we return to the OP's question, her child only recently started finger counting and was previously able to recall number facts to 10. What I want to draw attention to is the unspoken idea that not only is it ok not to be able to recall number facts with ease but that as a parent, the OP shouldn't try to help her child memorise these facts. Yes, I'm sure her child could still become a great mathematician even if she continued finger counting, but let me support the OP in her attempt to help her child.
Why do you believe the OP's DD memorized basic arithmetic?

The OP had never shown her DD "math fact" flash cards, or had her do work book pages, or shown her tables, or any other thing that would tend to lead towards memorization. What the OP did with her DD was kitchen math. OP's DD picked up addition from shelling pea pods. This is a manipulative, just like fingers. She was able to internalize these manipulatives. Possibly she formed a mental picture of them, or she could feel imaginary ones.

The ability to use mental manipulation is a good one. It is much more valuable in mathematics than rote memorization.

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Old 08-02-2010, 12:44 AM

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Quote:
 Originally Posted by Carolinemaths Musiciandad, your arguments are both reasoned and persuasive, but if we return to the OP's question, her child only recently started finger counting and was previously able to recall number facts to 10. What I want to draw attention to is the unspoken idea that not only is it ok not to be able to recall number facts with ease but that as a parent, the OP shouldn't try to help her child memorise these facts. Yes, I'm sure her child could still become a great mathematician even if she continued finger counting, but let me support the OP in her attempt to help her child.
Humans rarely stick to doing something the same way their entire life. Why is it a bad thing that she has suddenly decided to start finger counting? Maybe she has started understanding the actual number relations and finger counting is helping her to fully understand why the answer is what it is. Or maybe, as eepster said, she just had a different way of representing numbers before and has now stumbled across a more portable method.

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Old 08-02-2010, 01:07 AM

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As for encouraging vs. discouraging memorization. I'll quote myself because I am just that vain (or maybe I can't explain it better if need be).

Quote:
 2. Finger counting does not discourage memorization. Working through a problem in a way that is effective for the student encourages memorization. Again, there are people, the more times they count on their fingers to figure out the equation puts the equation into the "I did it myself, so I have an easier time remembering next time" category. I have seen this happen too, it's how I memorized the equations I have memorized.
Now I am going to tell you a story (not trying to be sarcastic if thats what you think, stories sometimes explain things better). A long time ago (maybe about 20 years or so?) there was a young math prodigy (by his standards anyway). In class they always worked on simple things, like adding and subtracting, and while he enjoyed this he also found this very tedious. You see he could do the math they were working on. Not the way the teacher asked him too, but it worked none the less and he was able to add and subtract in his head.

So at home, he began to examine multiplication, but it was harder. Now there were groups and a certain number of items in a group and the object was to figure out how many items in total. As he started on this new endeavor, he found himself "going backwards" in his ability to do math. He couldn't do these new, unseen equations in his head and he had to write out each group and count how many items there were in them. One day, while working on multiplying by two, he thought to himself "You know, I can count by two but if I just do that I loose track and can't figure out what 2 x 6 is. Maybe if I keep track some other way it will help." So he start counting by two on his fingers until he reached the sixth finger and a count of 12. He kept at it, finding ways to multiply on his fingers, and giving himself little tests to see if he could get the right answer.

One day while out with his dad, who knew he was working on multiplication, his dad asked him a question.

"Son," the dad said, "can you tell me what 2 x 6 is?"

Without even looking at his hands the boy announced "It's twelve, right?"

"That's right," the dad replied. "You are very good at math, aren't you."

"I guess, but mostly I just figured it out on my fingers so many times that I had no trouble remembering it now." The boy told him. And it's true, he had counted by twos on his fingers so often that by that time he just knew what the answer was.

(O.K. truth be told I just wanted to write a story and you gave me a chance, feel free to disregard this post. )

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Old 08-04-2010, 03:50 AM

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Why is it a bad thing that she has suddenly decided to start finger counting? Maybe she has started understanding the actual number relations and finger counting is helping her to fully understand why the answer is what it is. Or maybe, as eepster said, she just had a different way of representing numbers before and has now stumbled across a more portable method.

I am not the OP; I am an earlier poster who also had a child who suddenly, bafflingly, started finger-counting. And in his case, I do see it as a bad thing. In his case, it wasn't a spontaneous switch that accompanied a developmental leap, or even a guided switch that let him progress into more interesting or deeper math knowledge. For him, it seemed like a regression--something like a child who reads fluently being required to point to every word on the page.

For DS, it started right when his (non-differentiated) class was introduced to baby addition. Suddenly, he was dawdling over problems that had been easy for him, insisting on counting each problem out, even things he had easily grasped and moved beyond. I remember him helping a friend with adding 9 + 9 and saying, look, you know 9 + 10 is 19, so it must be 18, or playing around in the car with all the different strategies he could do for adding 36 and 36 (thirty plus thirty plus six plus six, forty plus forty minus four minus four...), playing around with and enjoying different strategies, and suddenly he is very serious and irritable and insistent on counting out 5 plus 6. (Although, interestingly, if we gave him harder problems of a kind the teacher hadn't talked about, he was happy to play around. So we fiddled around with fractions and prime numbers and let the addition slide.)

Not saying I can't picture a situation in which it might be positive, but it absolutely did not feel so in our case.

Heather
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Old 08-04-2010, 04:53 AM

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My guess is, in your case the teacher is probably requiring him to do the equations the way it was taught in class. And if that is the case, then yeah it is a problem because it's not how he works out math problems, but it's not his problem.

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Old 08-04-2010, 11:26 PM

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 Originally Posted by MusicianDad I don't think there is any importance to memorizing the multiplication tables at all. I think it's a product of the "fast math" mind set that we force kids to memorize a series of numbers instead of teaching them how to figure out how to get those numbers and it sets up a fairly intelligent portion of the population for stress in math class because they can't memorize a series of random equations. What makes properties of math painless and more efficient is teaching students the way they learn best. For some, rote memorization may be the way to go, but for others it is nothing but a painful inefficient means of making them feel inadequate.
In my opinion this is precisely the problem we have with our secondary education. Every few years or so, the schools here in U.S. follow certain educational fads that talk a lot about how all students learn differently and how teachers must create and utilize various teaching styles to fit each student's abilities (imagine that in the classroom of 30-40 students!!!), and how knowledge of the subject matter is no longer important, and that students must learn the "concepts" rather than actual subject matter, and on and on.... The reality is that the students must learn the substance before they can apply the “concepts” . They need to memorize the multiplication table because this will make their life MUCH easier down the road. Poor memory is just an excuse for not doing the "boring" memorization. Memory must be developed and improved through sets of simple exercises. For example, a child should read poetry as often as he/she can; this is the best and easiest way to improve one’s memory. This is what we all did in elementary school, by the way; we read poetry A LOT and we had to recite poems on the weekly basis. Also, the multiplication table hung on the wall in my bedroom and I looked at it every time when I went to bed or when I got up. As I recall, no one in my class had problems with memorizing multiplication tables; and there were 20 students in my class in elementary school. Hell, wake me up at night, and I can give you the whole table within five minutes. And I am eternally grateful to my teachers that they made me do that. Memorization is a part of learning process and while it is could be boring, it is absolutely necessary. My students often complain to me that they have poor memories and this makes their learning experience much more difficult that it should’ve been. They tell me that they never were asked to memorize and recite poetry, to remember important historical dates, and yes, they were not required to memorize the multiplication table as well. And I see them failing my and other professor’s classes, getting frustrated and dropping out.
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Old 08-05-2010, 04:43 AM

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Quote:
 Originally Posted by anechka In my opinion this is precisely the problem we have with our secondary education. Every few years or so, the schools here in U.S. follow certain educational fads that talk a lot about how all students learn differently and how teachers must create and utilize various teaching styles to fit each student's abilities (imagine that in the classroom of 30-40 students!!!), and how knowledge of the subject matter is no longer important, and that students must learn the "concepts" rather than actual subject matter, and on and on.... The reality is that the students must learn the substance before they can apply the “concepts” . They need to memorize the multiplication table because this will make their life MUCH easier down the road. Poor memory is just an excuse for not doing the "boring" memorization. Memory must be developed and improved through sets of simple exercises. For example, a child should read poetry as often as he/she can; this is the best and easiest way to improve one’s memory. This is what we all did in elementary school, by the way; we read poetry A LOT and we had to recite poems on the weekly basis. Also, the multiplication table hung on the wall in my bedroom and I looked at it every time when I went to bed or when I got up. As I recall, no one in my class had problems with memorizing multiplication tables; and there were 20 students in my class in elementary school. Hell, wake me up at night, and I can give you the whole table within five minutes. And I am eternally grateful to my teachers that they made me do that. Memorization is a part of learning process and while it is could be boring, it is absolutely necessary. My students often complain to me that they have poor memories and this makes their learning experience much more difficult that it should’ve been. They tell me that they never were asked to memorize and recite poetry, to remember important historical dates, and yes, they were not required to memorize the multiplication table as well. And I see them failing my and other professor’s classes, getting frustrated and dropping out.
Why should number sense be sacrificed to improve the memory? Admittedly, a good memory is a useful thing, but amongst the various academic disciplines higher math is the one least likely to be mentioned when ranking those that require a good memory. Every other subject I can think of has more need for recall than math; history, literature, science, art, music, psychology, etc. So why use a young child's first exposure to arithmetic as an opportunity to exercise something that has little relevance to the true subject at hand?

Socrates (see I do use my memory to recall useful information) was concerned that learning to read would lead to laziness in memory. Before the written word, most knowledge had to be memorized (though math was done on fingers or an abacus.) Yet, we don't sacrifice really learning to read in order to improve a child's memory. We encourage them to sound out the words in Hop On Pop and not to simply memorize the entire library. If after they have deciphered The Cat in The Hat for the 6th time we suspect they have memorized it, we deliberately go and get The Cat in The Hat Comes Back, so that their decoding skills will continue to be challenged. This is b/c we see the true value of real reading. Why is the value of mathematical thinking beyond what can easily be memorized so readily discarded?

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