How do I get my 6 y.o. to stop counting with her fingers? - Page 4

[eepster]

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.

[LynnS6]

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.

[Carolinemaths]

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.

[MusicianDad]

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.

[eepster]

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.

[Geofizz]

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.

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.

[MusicianDad]

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.

[eepster]

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.

[Geofizz]

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.

[SustainablParentng]

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

http://www.youtube.com/watch?v=nYVp1B41nI8

[MusicianDad]

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.

[Carolinemaths]

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.

[eepster]

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.)

[eepster]

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.

[Ellien C]

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.

[emilysmama]

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.

[MusicianDad]

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."

[eepster]

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?

[BCFD]

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)

[Carolinemaths]

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!