Counting on fingers

The Touch Math program uses a series of dots drawn right on the written numbers that the student uses for counting and calculating problems. They have a website www.touchmath.com. It looks like most of the material is geared for younger students, but the general idea may be helpful for your student.

Try an abacus with ten rows of ten beads each, and then replacing that with dot sketches. This is quick, especially if you use a pen so you can just tap once to make a dot, and more efficient than changing the counters each time.

Usually after a while the concrete stuff is just too much time and trouble and the student just drops it. Have you tried simply giving your student permission to count in her mind? I’m not joking here — many people take the rules they are taught in kindergarten and Grade 1 as the eleventh and twelfth commandments, and don’t realize that it’s OK to move on to different approaches (I have a personal battle against the incorrect but widely believed “Thou shalt write all numbers in pencil so that thou canst erase all thy work and end up with nothing but dirt.”) Students feel relieved but keep looking over their shoulders for a while after you give this kind of permission. You can see them waiting for the lighning to strike, and the relief and amazement when it doesn’t.

My son uses his fingers as well and is very accurate. Frankly, I don’t know how he does it but he has used it to compensate for his memory deficits. I can’t imagine taking this away from him. What is wrong with using your fingers? He is a hands-on learner. If it works for him I say leave him alone. Why would you try to switch him to a visual method, it would make him nuts. We have tried other methods which only leads to frustration and tears. He gets the correct answers so I say “don’t fix what aint broken.”

This is a judgement call. However, as an experienced teacher at all levels of education, I can tell you two big problems that are very common:

(1) accuracy and speed *how far*? It’s one thing to be accurate on small one-step fact problems in primary school. It’s quite another thing to be accurate on multi-step problems involving several operations. Or to look ahead and figure out what the next step should be. And even if you go to a calculator, the calculator won’t tell you *which* operation to use, or whether the results make sense. You need to develop what is called “number sense”. This is similar to reading fluency; once you know the basic skills (and those are vital, not to be skimmed over) the way to get better at reading is to read, and the way to get better with numbers is to work a lot with numbers. There is no quick trick or magic wand or royal road.
If you read the postings here, we see hundreds and hundreds of the same three: A. My kid can’t learn basic number facts; B. My kid knows number facts and simple rote calculation but cant do multi-step problems — “word” problems or fractions or long division — in middle school; C. My kid did OK in elementary but simply can’t understand algebra in high school.
I contend that problems B and C are made much worse by what happens earlier. If the child is encouraged from the very beginning to think things through and to apply math to the real world and to develop control and mastery of skills, then it’s possible to get over these bumps in the road. If the child has been encouraged to think of math as something totally divorced from reality, then there is a horrible crash. If the child has gotten into dead ends and blind alleys, there are a lot of tears of frustration, delays and failures as things have to be unlearned. Counting to learn addition and subtraction is a *good* thing, a connection to reality — as a learning tool. But there comes a point where counting is just too long and cumbersome and becomes a weight on the student’s backs instead of an assistance. And fingers are very limited by having to remember which is the pointer and which being pointed to. You can’t “take away” the fingers — but you can teach the child to use a more adult form of abstraction when (before) the time comes that it is needed.

2. You are happy because the answers are right. That’s OK for simple one-step rote calculations in primary school. That attitude is a killer in algebra. The entire goal in algebra is to teach *methods* of logical thinking and approach to problems. It is a very very common thing in my algebra classes to have a student who gets the “right answer”, i.e. the number in the back of the book, by just guessing, by estimate-and-check, by trial-and-error arithmetic, or by getting too much “help”. This student is very hurt and frustrated and angry to get a mark of F- or 20% on the algebra exam — he got all the right answers, didn’t he? Well, no, he didn’t. The “answers” in algebra are the *methods* of problem-solving and logic, and if you don’t use those, you aren’t doing algebra. Might as well say you should pass French because you can get your groceries by gestures without saying a word in the language.
What makes it worse is that, in order to help the student in a difficult new subject, we first give very very easy problems in which you can get the right number by just guessing; this allows you to double-check your work. But the student who focuses only on numerical answers and omits the methods because they are too much trouble gets a very nasty shock a few chapters down the road when it’s assumed he knows the easy stuff and he is expected to apply those skills to things that are not at all obvious. Some kids get tutoring and go back and learn what they should learn; far too many decide they are no good at math and give up for life.
As a teacher and tutor who goes back and forth from elementary kids with reading problems and basic arithmetic problems, to high school kids doing algebra, to college kids doing calculus, I keep seeing the same habits and attitude problems cropping up at all levels. Of course you have to adapt methods and approaches to the age of the child, but you can avoid teaching dead ends and mistakes.

I agree completely. When a student fails to internalize and genaralize the basic math skills they are stuck at that level of computation. More time needs to be spent on basic number sense and concepts. When I read an IEP that says the student knows his multiplication facts but cannot subtract with regrouping I know they do not understand the concept of numbers. go back and teach place value completely. You will never be able to do higher math if you do not understand this basic skill.

I’ve seen too many of my junior college kiddos who look at the numbers in a word problem and take a wild guess at what operation to use, based on what the numbers are (if they have *that*much number sense) and what operation was needed in the previous problem.

I”ve had others with all kinds of number sense, who can figure out the problems really well… and still need those fingers. HOwever, it’s a good 10:1 ratio. The former is much more common.

Yes, this is a point that came up in a truly wonderful math education class — High School Students Misconceptions in Math, taught at University of Maryland — I had to take an incomplete due to illness, but a great class if you can take it; many articles from there are on some web sites which I’ll try to track down if anyone is interested.

One researcher discovered that given a problem that looked like a division, most weaker students automatically assumed you divide the smaller number into the larger; in fact many say (as they have been mistaught) that it is “impossible” to divide a larger number into a smaller. They completely ignore the presentation of the problem and divide in the order that they think makes sense. This of course means disaster in fractions, but hey, the teacher throws out the lowest test grade so you can ignore that chapter (a well-meaning approach that sets the kids up for immense trouble later) so many kids get A’s through elementary and then hit that brick wall in high school algebra where you can no longer pretend that fractions aren’t there or that division is just little number into big. Anyway, the researcher looked for the sources of this misconception, and discovered that even in the higher grade levels where fractional answers could be possible, the leading texts presented division problems from 85% to 95% with little into big, so this misconception could be highly successful, until that brick wall came up.

Hi Lisa , My son almost 7 uses his fingers and so we switched to touch math which he learned quickly and which does give him a faster way to calculate however I found out that he uses his fingers not to count but to rememberthe names of numbers. Has trouble remembering eight esp. He will calculate the right value then not be able to remember what that no is called until he counts on fingers. Could your son’s prob be similar? this is more word recall, I think and related to his reading probs.

Well I am just a parent (snicker) but I have watched as my childs teacher has tried to cure him of using his fingers and understanding the 100s chart. Problem his HE ISN”T PROGRAMED THAT WAY. He can’t us a numbers chart because of his visual learning deficit.
He can do multistep math problems in his head sometimes referring to his fingers for back up, but when you throw in visual cues such as that damn numbers chart it completely throws him off. Oh and please don’t get me started on regrouping. I think the concept so bores him he gets it wrong because he rushes right through it. He is a auditory and kinesthic learner. His fingers are helpful so let him use them. He loves math. He thinks it is fun and frequently asks mom and dad for complex problems to solve. Why would anyone want to destroy that by insisting there is only one way to do it?
I am (as you probably noted already) annoyed with the concept that children must learn skills the “right” way. As if there is one “right” way for all children.

PS. He does algebra problems, math and some division and is only in second grade.

I’d like to say this without sounding like I’m trying to start an argument — I’m really not.

OK, if your child isn’t a visual learner, and your teacher’s 100 chart isn’t helping, fine.

But a lot of us speak from a “been there, done that” perspective. Not only have I raised a visually-disabled verbally-gifted child of my own, but I’ve been teaching and tutoring for over twenty-five years.

I wish I had a dollar for every time I heard “But he’s so good at math — he was doing algebra in Grade 2 — why is he failing everything now?” “But she’s so good at reading and she used to love it — she wrote her own little books in Grade 2 — why is she failing now?” I’d be rich.

I’ve seen and heard this over and over with school students, college students, tutoring students, and two young relatives who got cheated out of a decent education, plus my own daughter who hit a needless stop to her math career. Kids who pass on and get the right answers in the right blanks but miss some fundamental skills and worse yet some fundamental concepts, and five years later hit a brick wall with a dreadful crash.

One problem is that education, and child-rearing, is a really long-term job. The Grade12 graduate and the college graduate are not products of one year of teaching in their senior years, or even of a four-year program, but rather of thirteen years of school or seventeen years of school plus college, not to mention the most important five years of foundations before they entered formal education. Anything you do now in education will only show its true value twelve to twenty years down the road, and more, as the children grow up and enter their careers.

In Grade 2, doing algebra and publishing books are gravy. OK to have as a topping, but not necessary, and not to be used to hide the lack of meat and potatoes. The solid nutrition that has to be there is understanding and controlling the system of written English and the number system.

Getting the right numbers/words in the blanks is OK and a start, but the thinking skills that get those correct numbers/words are the actual subject matter, and it is important to work on those thinking skills. No, there is no single “right” way, but there are several ways that have been demonstrated to be dead ends. Any “quick trick” that gets the number/word in the blank while avoiding *thinking* about numbers or words is usually counterproductive.

I thought of a quick snappy answer to your comment, but if I just posted it alone it would sound nasty and sarcastic, and that is not my intention. Please take this as a serious comment and suggestion: come back and talk to me (us, the board) in a couple of years and tell me/us how he’s doing then.