Counting on Fingers

From experience dealing with my own children, be concerned if he is still doing it after the 3rd month of school in 3rd grade (after they have finished reviewing 2nd grade). I have one who is ADHD/LD but gifted in math going into 4th who never used his fingers; one who is in the gifted program at school going into 3rd who still uses her fingers for some facts; and one going into 4th who is LD and still uses her fingers for even the simplest math facts.

Going into 2nd grade they are still teaching with manipulatives in our district so it is common to see kids still using their fingers. I would not worry about it until 3rd grade. Some people would argue against ever using fingers but many schools encourage it because manipulaitives get lost and fingers don’t. Try helping him come up with a system based on subtracting from the other digit to make the higher one 10 on the higher facts. 9+5=10+4=14; 8+5=10+3=13; etc. They will usually teach this system in 2nd grade.

Two answers, which aren’t exactly contradictory.

(a) At age 6-7, perfectly normal developmental stage. Don’t worry. He SHOULD be using concrete models — people why try to force kids into abstract verbalization of math actually work *against* real mathematical learning, whuch is very concrete. Go along with him using models to count and measure. Actively encourage using measures, such as rulers, as models — this is a good start both on measurement and fractions.

(b) Wean him off fingers and onto *less limited* models as soon as possible, starting today. Fingers are inaccurate for any sum over five and hopelessly inaccurate for sums over ten. And by the time you get to multiplication, with products up to 100, it’s a lost cause. You use one finger to point and another finger as the counter, and as soon as you go over five it’s total confusion as to which is the pointer and which the counter. Over ten and you lose place. Over twenty and you need a separate model for the tens anyway. Finger-counters get slower and slower and less and less accurate all through Grade 2, and they hit a brick wall in Grade 3. Unfortunately, as we all know, whatever habits you learn at the impressionable ages of 5 through 7 are pretty much stuck as habits for life. So when better methods are taught in Grade 3, many kids refuse to give up on finger-counting even though they are failing.

The argument that you lose models and not fingers is specious. Your models do *not* need to be expensive fancy boxes of blocks. I strongly recommend drawing dots. You can’t tell me it’s hard to find a pencil and paper or slate and chalk in the class, or a stick and some dirt outside. If you need to do 4 + 6, draw four dots and six dots and count the total. This works excellently for subtraction also; for 15 - 7, draw 15 dots and then cross out seven of them and you se that eight are left (This would be a nightmare on fingers, but is very very easy with a stick and some dirt, or a marker and some paper)

The simpler, more basic, and less distracting your models are, the better. With chalk dots on the board, you’re concentrating on the math facts, not other complications.

Andrea,

Have you tried the Touch Math system? It involves putting dots on the numbers. For example, a “1” has one dot on it at the top. A “2” has two dots on it - one at the beginning and one at the end. A “3” has three dots on it - top, middle, and end. When you get to “6” and above, dots within circles are used and the child counts one for each circle and dot.

Then when you will have to make up some problems for him with dots on the second number of the problem. For example, if you wrote 9+6=___, you would put three dots within three circles on the “stem” part of the six. He would continue to count from 9 using the dots and circles.

Subtraction works the same way. Some children do have difficulty counting backwards, especially in the teens.

My 8yo has started using this system with me this summer and seems to like it. She is entering the 3rd grade next week and does not know very many of her addition facts. I have also been researching to find out what type of LD she may have - right now I’m leaning towards dyslexia. I just finished a lengthy research paper for a graduate level class I took.

Also, you might want to look at symptoms for discalculia. If you look below these messages you’ll see some messages with some websites where you can search to see if you think your son has this LD. There are so many LD’s that have been identified in the last century that it might be worth your time to do some research that way.

Good Luck!

Laura

I went through some of the old messages below and found that you should do a search using the words Touch Math Concepts and you’ll find a better explanation.

Also, how old is your son? And, I have had a lot of people tell me it’s OK to use your fingers. With this Touch Math the idea is that the child will eventually be able to visualize the dots and circles and not need to put them on the numbers. I also made a Touch Math number line that I hope her 3d grade teacher will let her use in class.

Laura

My almost-8-year-old daughter struggled with addition because she was using her fingers and eventually, of course, ran out of fingers and would inevitably get the wrong answer. She wouldn’t “count on” either, no matter how much I tried to teach her. She would insist on counting both digits that were being added with her fingers. We started with 2nd grade Touch Math about 3 weeks ago, and she is now doing double-digit addition WITHOUT the touch points with 100% accuracy. Thank goodness for Touch Math! I would highly recommend it.

In some schools I’ve worked in, this was a fairly common problem because the teachers were using a whole math approach that didn’t require the students to memorize math facts to automaticity (such as by using timed math sheets).

Everything I had heard about Touch Math, with the dots on the numbers, sounded like another good approach to the problem.

Then you start telling us about a system of dots within circles and a bunch of rules on how to use them . . Oh, oh.

I personally have a weird complex of NLD-type symptoms that make it very, very difficult for me to locate in space and time and to follow complex verbal instructions. Despite this, I have a number of university degrees including an Honours degree in math as well as MA in Education, and am working towards a graduate math degree.

My daughter also has a pattern of similar difficulties, and I have tutored a number of LD kids.

The one rule that can be generalized is KEEP IT SIMPLE. If your “simplified system” requires memorizing more or doing more steps than the “old” system, it’s part of the problem, not part of the solution.

One problem I run into with every one of my tutoring students and over 90% of my classroom students is this:

Somebody has taught them a “quick trick” to solve a certain class of problems. It’s quick and easy and they memorize how to do it; of course, since it’s a quick trick, the steps are not obviously logical and have to be taken on faith. The quick trick works great for a while.

Then they learn another quick trick for another kind of problem, and a third for a third kind, and a fourth, and a fifth …

Once your memory is overloaded with a thousand quick tricks, your system collapses totally. You don’t know which trick applies to which problem, you mix the steps from trick #45 with trick #236, and you have not the faintest clue why you’re doing any of them.

What really is a disaster is that kids who have been taught quick tricks have no big picture of math at all. To them, it’s a species of magic, where each day you memorize a new incantation. The purpose of said incantations is to please the teacher, and they certainly have no relation to the real world.

Somewhere in algebra this system becomes a nightmare. Logic and higher-order thinking skills are needed, and they have never been taught or learned.

I’ve actually turned my NLD pattern into an advantage; I *have* to break everything down one step at a time, visualize it and make it concrete, and relate it to the rest of the structure. I’m a lot slower than the verbal memorizers at getting started, and I’m difficult to the teacher who just wants to present a formula to memorize and fill in the worksheets, but I get a working structure that is solid and permanent, and I can do graduate school abstract math.

Be sure in teaching kids that you do keep it solid and concrete. Simple dots are good. A system where you have to add six rules to the dots is going to lose focus.

If you have NLD, please explain to me how to teach my daughter word problems where there are no “steps” or “processes” for her to learn. We are still struggling with multiplication tables. I am totally afraid of math for her next year.

Sorry, That Spencer message should ahve read Beverly-my son posted in For Kids.

OK, problem-solving comes under the “no easy answers, no quick tricks” department (which is why so many programs and teachers, who depend on rote and quick tricks, fail miserably at teaching it.)

A couple of points first:
The phrase “word problems” is redundant. When you’re out in the real world, how do you actually meet situations where you use math — measuring and planning and counting and money managing and crafts and science and statistics and so on? When was the last time you saw a bunch of frantic people in an office saying “We just have to get these worksheets filled in by the end of the month”? “Word problems” are the real stuff, real math, what you are going to use when you get out of the artificiality and deadly sterility of worksheets. Whenever I hear someone say “Well, I used to be good at math but I could never get ‘word problems’ ”. I cringe; that’s the same thing as saying “Well, I used to be good at reading as long as we were doing ‘normal’ stuff on worksheets, but I could never get the hang of those book things.” A person who can do worksheets but not read books can’t actually read; a person who can do worksheets but not solve problems can’t actually use math.

To get to be good at problem-solving, you have to do it, and make a habit of doing it. Math programs that relegate “word problems” to one chapter to be rushed over, or one section at the end of each chapter so they’re easier to omit, are the problem, not the solution. The first thing to do is to try to get the child working through a program where reading and thinking are normal everyday activities. If this can be done in school, all the better, but if it’s necessary to do it at home, look into materials available (I don’t have any modern ones on hand; I collect out-of-print books before 1955, many of which have excellent problem-solving).

As in reading, don’t try to skip over steps; a crack in the foundations means a collapse later. Start with the simple one-step problems that seem obvious to you and work through them until they’re obvious to your child. Practice multiple examples of each type, and overlearn massively.

The thing to do is to TALK over the problem, and (here’s the best technique I know) **Put yourself into the situation**.
Simple example: Jack has one apple. He gets two more apples. How many apples does Jack have now?
Tell the child: OK, you’re Jack (Let’s pretend). How many apples do you start with? Read and see. Right, one. Take one red chip to be one pretend apple. Now what happens? Read and see. Right, he gets two more. What should you do? Right, take two more chips for two more apples. Now, what was the question asked? How many Jack has now. Well, you’re Jack, and here are your apples. How many do you have now? Three. Right! The answer is three apples. Write it down.

Yes, this takes time. A lot of time. It would be so much quicker to just memorize a key word (very bad move, by the way — inaccurate and misleading) and tell the kid to write 1 + 2 = 3

Well, it would be so much easier to give her a speech synthesizer and not waste all that time teaching reading, and it would be so much quicker to just keep her in the stroller and not teach her to walk, but we have some idea in our minds that independent walking and independent reading are important, so we struggle and teach and patiently watch for years as our kids learn these skills. Same with problem-solving. Model, think through, take time, and do it over and over again just as you did with walking and reading, and if the child has motivation to get involved in it, it will slowly make sense (and will be one of the most valuable things you can do).

Unfortunately we are having problems with her undertanding how to translate into that math sentence. Very simple is Ok like Jill had 5, Pat had 6, how many do they have? But after that when it works to the harder problems with more steps she cannot get it. I guess it just is a matter of repitition to make it clearer??

I use TouchMath as a supplement to BJU math. This way, my daughter gets lots of practice with manipulatives and practical hands-on learning of math facts with BJU.

And allowing her to continue to support her growth with manipulatives until she looks ready to stop. Kids acquire conceptual knowledge and surety at varying rates- even within the realm of “normal”, and except for testing situations and some concern over efficiency, I would not be concerned. What you can do, is continue to scaffold her from the manipulative to the icon (picture). Let her build the problem- you draw the problem. She can solve from the drawing and check with the manipulative. Eventually, she draws. When she isn’t checking so much with manipulatives- then you write number sentences- she can draw or block or whatever. Flow the same sort of scaffold- a lot of input from you that gradually lessens to more independance from her. Have her verbalize what she does with the manipulatives too- Putting words to what you are doing helps an awful lot with retention. BTW, IMHO, manipulatives and touchmath are infinately preferable to fingers:)

Robin

Yes, that is the heart of the problem. Repetition? Yes and no. Lots and lots and lots of problems, a few every day, but not exactly the same ones (or else you just get memorization and get farther from understanding). Work with her step by step, modelling each step, until the problem that looks simple **to you** also seems manageable to her. Then move ahead one teensy tiny step to a problem only a little bit more complex. Again, **to you** it may seem easy, but to her it’s a strange world and one where she has been experiencing too much failure. Almost every math program I have seen leaves great gaping holes in problem-solving; you can do basic one-steps of particular limited types, so now let’s jump ahead to multi-step with no guidance. You can avoid this by making up tons of problems of similar types and printing them on your computer, making up her own math book.

I have also heard very positive things about Singapore math, although I haven’t seen it and don’t know if it would fit your particular needs; ask someone whpo has used it.

There aren’t six rules added to the dots.

If you go to a Touch Math website, you will see how simple it is. And, at this point, I am willing to try something that other teachers I have visited with know has worked for their students. Granted, the same things don’t work for every child. But what doesn’t work for my 8yo may be helpful down the road for my 4yo or my 2yo.

I don’t feel Touch Math is a “quick trick” to help my child learn her addition facts. Once they’re memorized she won’t need the dots. Or, she can choose to visualize them on a number without actually putting them on. This system presents addition in a specific sequence with a definite series of steps in each section. And, as we all know, structured learning is very necessary when teaching students with any sort of learning disability.

For example, when my daughter was in a very structured phonics program and reading aloud to the teacher nearly every day she was a much better reader than she is now. This whole last school year she did very little reading aloud, and, consequently, when she reads aloud now she’s not nearly as fluent and expressive. She has also developed a bad habit of substituting words (“while” for “white”, “it” for “is” or “in”, etc.) and adding small, nonessential words (such as “an”, “of”, “the”, etc.) Someone told me not to be concerned with her difficulties with reading aloud. But she says that she gets confused about what she’s reading when she does it, so I see a need to help her with that. And I know she doesn’t want to be embarrassed by these problems when reading aloud this year in class, which her teacher says they do. We are tentatively planning to pre-read at home to help this problem. And, she does really like to read.

Victoria, I can see how what you recommend would work for a child with decent reading skills. But what if a child with dyslexia isn’t able to read the problems, yet has normal ability in learning math concepts? How would you teach that child problem-solving? Would you read the problems to him, or what?

Yours truly,
Kathy G.

I just worry when somebody presents something they say is “simple” — it’s simple to them, but it’s a lost cause to me. I keep stressing KEEP IT SIMPLE on math, because so much of what I see out there isn’t math at all.

You’re right on with your daughter’s reading. Accuracy is absolutely vital!! If we didn’t need all those little words, if we could change them or add them or delete them or re-order them at will, why are they still part of the language? Answer, they’re there because they give information. “on the table” is clearly different in meaning from “off the table” and “in the table” (ie in the drawer), but people who teach guessing instead of reading say and accept all three. Ignore the teacher, have your daughter read aloud to you every day and stress accutracy. In two or three years, he classmates will hit a brick wall and she’ll be able to keep moving ahead.

As I was suggesting in my post, I work *with* the child. If possible, the child would read the problem to me independently, one sentence at a time; if the reading is still a battle, then the child reads word-by-word and I help with the unfamiliar words and re-state the sentence after we’ve plowed through it. If the child can’t even do that, I work really hard on the reading skills, but I would also read the problem out loud, slowly, pointing to the words as I go in order to add some reading teaching (every little bit helps). Yes, you could do problem-solving reading all the problems aloud in this way. It is important to go slowly and one piece at a time; a new student can’t grasp a whole batch of new information at once. That may be part of your child’s difficulty with the topic; most of the kids I have worked with in math also have an underlying reading weakness, and they are lost and overwhelmed.

LOL! Not being a mother, I don’t have a child with that problem or without it. I was simply very interested in learning how that kind of obstacle would be overcome. Thanks, Victoria. What you explained makes perfect sense.

Yours truly,
Kathy G.

victoria wrote:> > As I was suggesting in my post, I work *with* the child. If> possible, the child would read the problem to me> independently, one sentence at a time; if the reading is> still a battle, then the child reads word-by-word and I help> with the unfamiliar words and re-state the sentence after> we’ve plowed through it. If the child can’t even do that, I> work really hard on the reading skills, but I would also read> the problem out loud, slowly, pointing to the words as I go> in order to add some reading teaching (every little bit> helps). Yes, you could do problem-solving reading all the> problems aloud in this way. It is important to go slowly and> one piece at a time; a new student can’t grasp a whole batch> of new information at once. That may be part of your child’s> difficulty with the topic; most of the kids I have worked> with in math also have an underlying reading weakness, and> they are lost and overwhelmed.

Thank-you………..

One thing to start with is that some words translate directly. “Of” is times, “is” means equals… that got me over a few dozen multiplication and percentage problems. (so “A box of yongas costs 34.00. How much would three of these cost?” translates to ?? = 3 x these.. oh, these are $34.00).

Great idea, thanks. I’m going to go through some and work with her on some translations. As long as she can set up the equation, she can do it, though the computations take awhile. Even that is getting better since we got the diagnosis because we have been using math songs-Multiplication Rock and some others have really helped. She memorizes songs very quickly, it’sjust a matter of her singing them silently to herself in school while doing the computations!!!!

When you try to analyze problems by “key words” you run into a number of difficulties. Even in your own example, you say “of” means “times” and then you say “A box *of* yongas”. The confused student stops there and tries to see what has to be multiplied. Well, of course that isn’t the point in the problem where the “of” means “times”, but the student started out confused and is just trying to follow directions.

Similarly, people tell students that “less” means subtract; well, sometimes it does, but sometimes you may have to add.
Examples:
Subtract — James weighs five pounds less than Helen. Helen weighs ninety pounds. How much does James weigh?
Add — James weighs five pounds less than Helen. James weighs eighty-five pounds. How much does Helen weigh?

Any single word in isolation is not enough to tell you what to do in a problem. It is important to analyze patterns, not just single words.

Any other ideas??? I’m open to anything. She is still having problems knowing when she is supposed to regroup in subtraction-she knows the rule but overapplies it, for example she will use regrouping to subtract 17-9 and does not grasp that it is still the same problem whether regrouped or not. The fact that she has been unable to memorize the addition/subtraction facts makes it worse. We managed to get her to memorize songs to learn multiplication but she cannot reverse the multiplication to get division. Add word problems into that and it is a recipe for disaster. Any ideas, anyone??

Get an abacus (sold as kid’s toys) with ten rows of ten beads. Do 17 - 9 by taking 17 beads (one full row and 7 more on the next) and counting nine off them. Have her do hundreds and hundreds of these until she visualizes addition and subtraction and tens automatically. Also good for multiplication and division, especially if you get two more abacuses so you can go up to 300. It doesn’t come as fast as we adults might think (Rule 1 of teaching — **anything is easy if you already know how**. It wasn’t so easy the first time you did it, either) but it does come.

Recite the addition/subtraction/multiplication tables in order, in rhythm. In general, omit the songs and tunes, which are often distractors — the kid focuses on the tune or the joke and omits the math. Be very very sure to recite the question as well as the answer, and be sure she recites the whole thing too: three plus one is four, three plus two is five, three plus three is six, three plus four is seven, … This is a long term project, maybe a year each for addition, subtraction, and multiplication; but if you don’t do it, where will she be in three years? Tables can be put on tape too, if she will listen, but it’s more fun to interact with another person.

Make up cards with dots (no bunnies, no leprechauns, no distractors) and illustrate each math fact — large poster-size cards for the wall, large 1 inch circles and 1 to 2-inch numbers for visibility.
Example: 3 red dots and 2 blue dots; write underneath
3 + 2 = 5 2 + 3 = 5
5 - 2 = 3 5 - 3 = 2
Example: 12 purple dots, arranged in 3 rows of 4; write underneath
3 x 4 = 12 4 x 3 = 12
12/4 = 3 12/3 = 4 (or use the divide by sign; I just can’t print it here on this system)
Go over and over with her how to count the dots and use them to find the math facts, and have her refer to the card as she does problems. Again, after a year or two, she can leave the concrete, but get it fixed in the mind first.

Thanks for the ideas. I welcome any help in this area. She starts school Wednesday and I am very concerned about 4th grade math for her. The last half of last year was a CHALLENGE. The fact that her same age brother is in accelerated math so is one year ahead doesn’t always help her self esteem. Any other good ideas, feel free to email me directly.

i specialize in helping children with learning difficulties reading,writing,math etc
with this method he won’t have any problems with remembering, becasue he will have the number pattern memorized, for more info. contact me and i will send you more info on this method i’m the only one in the states who offer this method, as a dyslexic and founder of dyslexiaworld i know it’s a success..email your address and phone