How do I get my 6 y.o. to stop counting with her fingers? - Page 5

[MusicianDad]

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.

[treeoflife3]

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.

[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.

[eepster]

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.

[MusicianDad]

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.

[MusicianDad]

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).

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. )

[domesticidyll]

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

[MusicianDad]

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.

[anechka]

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.

[eepster]

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?

[MusicianDad]

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.

Sorry but I really do have to disagree with the bolded. Poor memory is not just an excuse. The person I know with the best memory, we are talking eidetic memory here, tried everything to "memorize" the multiplication tables and failed miserably. And to illustrate what we are talking about here, this is someone who can find a phrase or sentence in a 500 page book she read once, years ago. She memorizes poems, plays, conversations, anything and everything you can think of... Except numbers. There is something that prevents her from memorizing numbers, including her own phone number.

ETA: She is also much better at math than she thinks, because she was taught "if you can't memorize your times tables you can't do math."

[anechka]

Originally Posted by eepster

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?

. With all due respect, I am not saying here that one has to sacrifice their “number sense” in favor of memorization. All I was saying is that there is nothing wrong with memorizing multiplication table. I am not suggesting that one has to continue memorizing equations and formulas all throughout his school career. Obviously learning mathematics or any other subjects for that matter should not be concentrated on memorization alone. But learning does require certain degree of memorization. As I mentioned before, students often complain to me that they have poor memories and that it hinders their learning process a lot.

[eepster]

Originally Posted by anechka

. With all due respect, I am not saying here that one has to sacrifice their “number sense” in favor of memorization. All I was saying is that there is nothing wrong with memorizing multiplication table. I am not suggesting that one has to continue memorizing equations and formulas all throughout his school career. Obviously learning mathematics or any other subjects for that matter should not be concentrated on memorization alone. But learning does require certain degree of memorization. As I mentioned before, students often complain to me that they have poor memories and that it hinders their learning process a lot.

If one has relied on memorization to get through addition and multiplication, then why would they suddenly develop a real number sense, an ability to reason mathematically and the skills to use mental manipulations when it comes time to do more complicated math.

I know plenty of very smart people who did well enough in school in math by memorizing high school math. Instead of ever actually working out a geometric proof they simply read all the ones they thought might be on a test over and over till they memorized them. These people as adult completely lack a math sense. They were the people incapable of taking a mark down on the last piece of fabric on the bolt unless it was a full yard (and that is with a calculator available.) These are the people incapable of finding the upper levels in a parking garage (oh well, at least I can always find good spots up there.) These were the people incapable of applying a simple formula in order to determined what size to make a sheet of paper to be folded into the right size book with a certain number of pages. Never mind something as simple as figuring out what tip to leave at a restaurant. These are all situations that I have run into in my life, with multiple people.

[MattBronsil]

Memorization of math facts comes from doing them multiple times and a variety of different ways. Why do my kindergarten students know that 8+7 = 15? Because they have done 8+7 many times with many different materials. They just have seen it so much they know the answer, but they also understand why it is like that.

[Rosegin]

They teach them to use their fingers in school. Personally, I still use the method I was taught way back in first grade.

http://www.touchmath.com/

I wish they still used this method in schools.

[Carolinemaths]

MusicianDad,

I've shared the highlights of your pro finger counting arguments on my Maths Insider blog.

Now you're (even more) famous!

It was nice sparring with you!

[MusicianDad]

Originally Posted by Carolinemaths

MusicianDad,

I've shared the highlights of your pro finger counting arguments on my Maths Insider blog.

Now you're (even more) famous!

It was nice sparring with you!

Cool (not that it's a problem, but asking first is usually good form I still give permission though). ETA: Also you spelled "insider" wrong in your link.

I agree that lightening speed is not necessarily the main objective (but it’s cool!), especially if accuracy suffers. I’ve seen 10 year olds take 20 seconds to work out 13 + 9 because they’re counting out 13 fingers, then adding another 9. (very uncomfortable!)

Sounds like someone needs to teach addition in relation to place value. 13 + 9, huh? Well lets see 9 + 3 = 12, 12 + 10 = 22. 13 + 9 = 22... Hmm interesting.

If you have your fingers with you all the time, and use them all the time, there is no incentive to try to memorise and figuring out how to do more than basic arithmetic can be harder than using other visual or memory based techniques.

Memorizing and "figuring out how" are two different things, and not reliant on each other. Someone can memorize everything perfectly and still not know a single thing about how to figure out what needs to be done to get the right answer. On the other hand, someone could have no memorization done, still use their fingers or heck, even a calculator, and be able to figure out how to do a much more difficult problem simply because they have done so much work previously learning how to figure out what the answer is.

This can also be true if you ask a child to visualise counting their fingers or other objects in their head.

You could, but if they are most comfortable working with their fingers, why bother changing that?

Math is supposed to be fun. Really, it is. When we start putting all these rules down about "the right way to do math", when what is being forbidden works just as well though not the way some people would prefer, we start taking away the fun.

It reminds me of the book To Kill a Mockingbird. At one point Scout describes an event in her life, just after she started school. She enjoyed reading, and she learned early through her dad reading to her. At one point, her teacher started telling her "you're doing it wrong. You need to stop learning to read that way" (or something like that). The effect it had was she ended up not wanting her dad to read to her, and not wanting to read her self. Eventually the problem was mended, I believe, when Scout's dad had a talk with the teacher. Basically, the teacher took the fun out of reading but imposing arbitrary rules about it.

The best way to help the OP's child is to ignore any changes in how said child does math, as long as the answer is correct and as long as it's not imposed arbitrarily by the teach. I would only worry about a child finger counting, either from the start or after some previous work in math, if it became obvious that the child was not understanding the material or that the teacher was imposing her own restrictions on the children in regards to math.

AETA (Another Edited To Add): Maybe I could start a blog and we could have blog wars!

[Carolinemaths]

MusicianDad,

Yes, I'm sorry, I should have contacted you before I used your responses on my blog. No excuses. Thank you for handling the situation with good humour!

I'm sure you'd make an excellent blogger! I can see you've contributed extensively here on the mothering.com forums. I can't be the only person who's a fan of your writing style! The blogosphere would welcome you with open arms

(Also thanks for the broken link tip - it's fixed now )

One thing this debate has done is highlight the different learning styles and techniques in maths. My oldest 2 kids each have different approaches to maths problem solving and I'm sure my younger 2 will show me another few styles in the future. Future mathematicians come in all flavours!

Furthermore, to give your credit, I do agree that as parent and educators, it's more important to foster a love of this much maligned subject. A teacher commented on my blog that although she "aspires to (teach) good number skills" in her students, "There are bigger battles to fight, i.e. doing maths at all."

In the end, it's the love of (or at least comfort with) maths that should be our ultimate aim.

[anechka]

Originally Posted by eepster

If one has relied on memorization to get through addition and multiplication, then why would they suddenly develop a real number sense, an ability to reason mathematically and the skills to use mental manipulations when it comes time to do more complicated math.

I know plenty of very smart people who did well enough in school in math by memorizing high school math. Instead of ever actually working out a geometric proof they simply read all the ones they thought might be on a test over and over till they memorized them. These people as adult completely lack a math sense. They were the people incapable of taking a mark down on the last piece of fabric on the bolt unless it was a full yard (and that is with a calculator available.) These are the people incapable of finding the upper levels in a parking garage (oh well, at least I can always find good spots up there.) These were the people incapable of applying a simple formula in order to determined what size to make a sheet of paper to be folded into the right size book with a certain number of pages. Never mind something as simple as figuring out what tip to leave at a restaurant. These are all situations that I have run into in my life, with multiple people.

It was my understanding that the children learn how to add and subtract first, and then they move on to multiplication. So by the time they began learning the multiplication table, they should've practiced enough to understand how the adding of numbers work, right? Obviously they should not be going through school "memorizing math", as you have mentioned above. I mean, when do they learn the table, in second or third grade? And how many grades are there in the U.S. secondary school???
Look at the best math performing schools in the world - Singapore, Finland, Japan, China, Russia (in the good old "Cold War" days). The students in those countries, do in fact memorize the multiplication table to the best of their abilities. (I can testify to that because I am from one of those countries. In addition, I had students from Finland and Japan in my classroom who told me about their secondary school experience). But those students are also taught the beauty and the logic of math. Memorization is just one of the many elements of learning.

[MusicianDad]

Originally Posted by Carolinemaths

MusicianDad,

Yes, I'm sorry, I should have contacted you before I used your responses on my blog. No excuses. Thank you for handling the situation with good humour!

I'm sure you'd make an excellent blogger! I can see you've contributed extensively here on the mothering.com forums. I can't be the only person who's a fan of your writing style! The blogosphere would welcome you with open arms

(Also thanks for the broken link tip - it's fixed now )

One thing this debate has done is highlight the different learning styles and techniques in maths. My oldest 2 kids each have different approaches to maths problem solving and I'm sure my younger 2 will show me another few styles in the future. Future mathematicians come in all flavours!

Furthermore, to give your credit, I do agree that as parent and educators, it's more important to foster a love of this much maligned subject. A teacher commented on my blog that although she "aspires to (teach) good number skills" in her students, "There are bigger battles to fight, i.e. doing maths at all."

In the end, it's the love of (or at least comfort with) maths that should be our ultimate aim.

The goal I have with my kids is that they love math as much as I do, even if they don`t go as far with it.

Also I have had a couple of people suggest I start a blog, as well as a few have cyber crushes on me.

And for the record, do recognize how memorization can benefit certain types of learners.