1st grader needs math help

As a graduate student undergoing training to become a SPED teacher, I have been fulfilling practicum requirements in a K-grade 4 school. Much of the support I currently offer is in math, and I have had the good fortune to have been exposed to a wonderful system known as “TouchMath”. “TouchMath” teaches its students to use touch points on the numbers 1-9 to help with addition, subtraction, and even multiplication math facts. The premise is simple. Each number is assigned a touchpoint or touchpoints to correspond to the numerical value. For example, the #1 has one dot placed at the top of the numeral. #2 has two, etc. up to #5. Numerals 7-9 have an apporpriate combination of dots and rings.

What is particularly appealing about “TouchMath” is its simplicity of usage. In simple additions, students are taught to put the larger number in their heads and use the touch points to count up. A similar process is used in subtractions, except that the students use the touchpoints to count down. This strategy eliminates the need for finger counting or use of unifix cubes, and when the touch points have become internalized, they may be used to help with multi-digit computations.

Another appealing component to “TouchMath” is that it is a very easy system to learn. I, for one, had never heard of this program prior to the start of the year, and now I find myself teaching it to anyone who will listen to me!

“TouchMath” is not an inexpensive program for the interested parent (you can check Amazon for prices). However, chances are the LD specialist at your elementary school will have heard of the program and may be able to procure some materials for you. If you can get your hands on a “TouchMath” manual and touchpoint number line, you will have everything you need to teach counting strategies.

I hope this missive has been of some help to you. Best of luck to you.

I agree with Chris. TouchMath has helped my LD daughter tremendously! She struggled with “counting on” with addition and any form of subtraction. TouchMath has been a wonderful help. Also, she had no problem changing from numbers with touchpoints to numbers without. Easy…easy…easy.

Yes, do a lot of work with concrete materials. I like a simple abacus frame with ten rows of ten beads; it works for counting, base 10, addition, subtraction, carrying, borrowing, and sums to 100. Get two and you can go to 200. Later good for multiplication and division too. Cheap and available at toy stores.

Avoid finger-counting — it leads to a lifelong nightmare of inaccuracy as for any sum over 5 you lose track of which finger is the pointer and which the pointee.

No, do not, never do repeated drills and filling out sheet after sheet. Usually the results even as far as simple memorization and retention are not worth the time; and this is a recipe for teaching her to hate and avoid math.

The Touchmath program recommended is a good method to transfer from concrete (such as beads on the abacus) to the symbolic nimbers on paper. But you’re too early to do it yet. At your present level, you’re not ready for abstractions at all. It will be useful in six months to a year when the foundation is built.

First make sure she can count accurately — most kids having trouble with any level in math actually have an original deficit one or two levels below that is preventing them from building the new skill; so a kid who can’t add at all is very likely to be unsure of counting. Also work on the base 10, ie for example 16 = one row of 10 plus six singles, 34 = 3 rows of 10 plus 4 singles. Once she is comfortable with counting to 20 or 30, then start addition by putting together. 2 + 3 means take two beads and then three beads, put them together and see how many you get. Work on that until solid, and them do addition of larger numbers. Don’t start sunbtraction until addition is very well learned and overlearned. Then do subtraction by taking away, first numbers under ten, then teens. THEN start something like Touchmath to do the work on paper without the abacus.

Victoria,

My son is in third grade and has CAPD. He was in resource room for two years for math both because of the way his language disability influence math (concepts like before, after) and visual-spatial problems. He now is doing B work in regular classroom, although he is in a group that moves slower. But I see some odd things with him and wondered if you had some ideas.

He is learning multiplication quite well using Math Fact the Fun Way. But when we went to learning the nines, he had a hard time using the “trick” it teaches where you start with the left had and and bend the figure down that you are multiplying the 9 by. He had trouble because he has a hard time looking at 7 fingers and knowing there are 7. He actually counts. (now he understand the concept of multiplication fine–I have seen him add on to whatever fact he knows). I notice other things with basic number sense. For example, he had trouble with figuring out what time it was when you know what time it is now, and how much time has elapsed. He had trouble knowing that if an hour had passed and it is now three o’clock, it was two o’clock when you started reading, for example.

He tests on standardized tests (both diagnostic and regular school ones) as average. But I am a bit puzzled and worried about these strange gaps.

Any ideas?

Beth

THe finger trick … it works for some kids, and for others it just doesn’t help much. THo’ if he’s bogged down with the “bigness” of seven, can he remember that the whole hand is 5? Just practice holding up 5,6,7,8, 9 and 10 fingers and see how fast he can say how many are there? And if 5 is too big (and it is for some)… that’s 3 & 2 (or you can be Spock, say “Live Long and PRosper” and hold it up as 2 2 and 1 :)). It might seem like a lot of messing around but it can really help with internalizing those basic number concepts.

There are other tricks for nines though — does he know how to add ten to any number ( another good thing just to practice)? That adding 10 to 38 is 48 — you only change the first digit?

Once that’s clear, then adding nine is as “simple” as adding ten and backing up one. So if he can remember that 9 x 5 is 45 (is that a problem?) then he can get to the next one by going up ten and back one.

Another trick for checking your guess — the digits to the nines will always add up to nine. 18 – 1 + 8 is 9. 63 – 6 + 3 is…

He can also practice *just* the nines, in order and then mixed up, on my site, I *think* (better go check…) — www.resourceroom.net and click on “math” and then teh times tables practice…

It’s ‘way too often abused… but practicing those facts — not guessing, but memorizing ‘em just like you’d memorize a poem (you don’t guess and mark half the words wrong, you break it into smaller bits) — means you’ve got them at your fingertips, quickly.

Some folks really struggle with any rote memorization — and I wouldn’t put them through trying to force it; and memorization is ‘way, ‘way, too often mistaken for knowledge, but it has its place IM(NS)HO.

I’m with you on that, Sue. During the Whole Language period, most memorization was thrown out the window. Out went spelling books, out went memorizing math facts. So what we have now are high schools with kids who can’t spell and sitting in Algebra counting on their fingers!!! Ugh!!!

Janis

Sue,

He is using the finger trick now pretty successfully. But I had to teach him to read my fingers first!! I think you are right about practicing knowing that your hand has five fingers. Seems so obvious to me that I am always amazed by what isn’t natural to him.

I tried the adding up to 9 trick but it was a total flop. He just isn’t good enough at adding for it.

I:’ll look at your site for other ideas. He has mostly passed this barrier but I see a real lack of number sense with him and that worries me.

Beth

Touch math is awesome. My son is good at math when he was in K he used to use his fingers on his chin going one way to 5 and then back to get to 10. He soon had the whole class doing his trick. The teacher didn’t show him how to do it.

When he got to 3rd grade the teacher taught touch math and now he does that he can add and subtract 4 colums of numbers and is starting multipication. With the touch math he rarley makes a mistake unless he is rushing.

However, I also do flash cards with him, lots of counting money, we play cards alot like black jack helps with adding.

I quote myself from above:

_______
Avoid finger-counting — it leads to a lifelong nightmare of inaccuracy as for any sum over 5 you lose track of which finger is the pointer and which the pointee.

No, do not, never do repeated drills and filling out sheet after sheet. Usually the results even as far as simple memorization and retention are not worth the time; and this is a recipe for teaching her to hate and avoid math
____________

Please note I am FOR memorization and retention — I’m just firmly of the opinion and experience that you don’t get successful learning, EVEN of those basics, by filling in blanks. Learning simply can’t be measured by poundage of papers filled in, usually quite the opposite; kids who spend hours filling in papers are learning very little, either of the topic supposedly being studied, or of anything else they could have done in that time.

I keep recommending oral recitation of math facts to a rhythm, with absolutely no other distractions (no cute songs, no stories, just the facts ma’am). Sure it’s old-fashioned. People did this for thousands of years and kept it up for generation after generation for one simple reason — it works. It takes a little time but in the end it sticks.

Most kids who fill in drill sheets put their minds elsewhere and daydream while doing the work on autopilot; you can see this by the number of extremely careless errors that occur. If any adult remembers back to their own studies, I’m sure almost all of you will agree that you simply were not involved with the work when it was presented in this way. And if you aren’t involved, you won’t remember and retain.

In this case I was writing particularly to a parent of a child in Grade 2 who hadn’t mastered the most basic concepts; in this particular situation, drill is a nightmare, because what are you drilling? If you don’t know the basic concepts, you can only do things wrong and drill failure.

OK, I’m not going to argue with what works. If he couldn’t do any math before and is managing now, that is a positive sign and changes should be made with caution. Take the following as suggestions for improvement, *not* as requirements to drop everything.

However, I am always very very worried about quick tricks and gimmicks. The silly stories in Math Facts the Fun Way are a gimmick. They have nothing whatever to do with the mathematical functions involved.
The multiplying nines tricks suggested (at least three of them, not related and apparently self-contradictory) are quick tricks. They give the correct answer, or a check on the correct answer, but the logic behind why they work is incomprehensible to the child so they might as well involve chanting an incantation and waving a magic wand.

Why am I so against these things? They work, right? Well, that depends on your definition of “work”.
If you only want right answers today, they “work”. If you only care about reaching Grade 5 level, they “work”.

A problem starts to surface in upper elementary school and blossoms into a nightmare by high school algebra. And once you are already four years behind, it’s hard to go back and re-start those four lost years. The quick tricks and gimmicks are a dead end — they seem to get you close to where you are going, right next door, but there’s a big barrier ahead of you and the only way out is to back up, which most people resist doing.
Two difficulties arise: (1) memory overload. Sure the silly stories are memorable, and sure the quick tricks with the fingers are easy and fast. But when you get two hundred silly stories and three hundred quick tricks for three hundred different problems, retrieval becomes impossible. Was it the story about the dragon or the princess or the dog’s head? Am I supposed to fold my fingers over or stick my thumb out? Or maybe do I sort of remember something about making my hand into a dog’s ear? You start to retrieve the wrong story or trick, or to lose a few of them. (this is very closely related to the problem of reading without phonics skills)
(2) Logical background development. In the Grades 3 and 4 curricula, for just one example, there are all sorts of exercises in using models and graphs and number lines, measurement and rulers. Of course it takes time to draw these lines, and you can do an end run around them and “save time” by doing your quick tricks with numerical manipulation. Then in Grade 5 you are supposed to be learning about fractions. Much of the material makes sense best if presented as number lines and measurement. Of course, if you skipped all the previous number line exercises and did your quick tricks with computation, you aren’t easy and quick with number lines, so the new material goes over your head. The Grade 6 and 7 work gets farther and farther over your head, and after years of incantations and magic wands, the logical development of algebra might as well be a foreign language.

If your child is having trouble with the quick tricks because they don’t connect, and wanting to know why things work, this is a *good* thing, not bad. Try to get some math books that explain in terms of concrete, visual, real-world ideas and measures. Try to explain how numbers work, niot just how to play a finger game to get the answer. I have not seen them but many people have posted good reviews of the Singapore Math books.

“I keep recommending oral recitation of math facts to a rhythm”

Victoria,

I agree with what you are saying. It is awful to see high schoolers still counting on their fingers. My child is in first grade, and apparently the teacher has taught the children to count on their fingers. She is in Saxon math which is pretty good, though. Regarding oral recitation, what format would you use to say the facts? Use flash cards or not? If not, in what order do you recite them? 1+1=2, 1+2=3, 1+3=4, etc. and then 2+1=3, 2+2=4, 2+3=5?

This is going to be hard for her because of APD (I might have to at least use flash cards), but I agree with you, it does kids no favors to avoid teaching them to memorize math facts.

Janis

As far as recitation to memorize math facts:

Yes, absolutely, do them in order. Order and pattern are the foundations of math, and if you don’t teach them and leave the kids to guess, no wonder so many kids have weak upper stories.

Also, as you noted, be very very sure that the kid is reciting *both* the question and the answer, i.e. “Two plus three is five”.

Many teachers say the question “Two plus three” and leave the kid to say only the answer “five”. Well, if this is done in order, almost every kid will catch on fast that this just gives a counting pattern, and will proceed to ignore the question that is the point of the exercise. If it is done out of order, it doesn’t help build the pattern formation and is hard to stick in the memory.

Flash cards are fine; I like posters with nice large dots (please, no bunnies and leprechauns and other distractions) to visualize at the same time as memorization. You can also practice just verbally while walking or driving to school or stores or waiting for the bus, etc.

Constant concrete practice with abacus and dots on paper and several weeks of recitation will solidify math facts for almost all students. I very clearly remember my mother doing this with me for the multiplication tables, and they stuck. I have an ordering problem and reversals, so I speak of personal experience.

Victoria, I hate to ask this, but would you pair the dots with a numeral on the flash cards or put just the dots?

Janis

One more thing, I just happen to have an abacus because I bought one when we went to China to adopt our now 6 year old! I guess that’s a souvenier only a teacher would buy!!!

Janis

re pairing recitation to models and/or numerals:

With a kid who has other basic skills in line, I do as many interrelationships as possible:

Draw three red dots and two blue dots on a poster. Count the red (one two three) then the blue (one two) then the total (one two three four five)

Say “three plus two is five”

Write the numerals on the poster below the dots
3 + 2 = 5

Read again “Three plus two is five”

Make a set of ten of these posters from 3 + 0 up to 3 + 9, put them in order on the desk or the wall, and say each fact out loud while pointing to the poster.

After the idea is clear and the facts begun to be remembered, recite the facts without looking.

Note — this is also an excellent approach to multiplication, for example two rows of five dots to make ten.

If the child in question is having other difficulties; one example might be getting confused on reading symbols but counting orally OK — in that case, omit the symbols that are causing confusion *temporarily* (bring them back when the facts are learned) and just do oral counting and facts.

Flash cards are a fun self-test for mastery, *after* the facts are learned well enough that you have some mastery to test. Kids really enjoy flash cards used in this way. We used to play “If you get it right first try you keep the card, if not I keep the card” Then you re-do the failed cards over and get to review the weak spots.

A note on tables: it is a peculiar American tradition, dating from the 1800’s, to go up to twelve or higher in tables. If you’re frequently calculating dozens in your business this is useful; for the rest of us it’s a waste of time. Mathematically you need 0 to 9, and then our base ten system takes care of all the rest. Work hard on the base ten system and don’t waste the time on the twelve times tables.

Great advice, Victoria! I have been very concerned about my child using her fingers to solve her math homework problems. Hopefully the dots will give her some visual support for memorization without the use of fingers. I also agree completely about mastering 0-9 multiplication tables! Thanks!

Janis

Victoria,

My son has memory issues and the “quick tricks” seem to help him retain information. Interestingly enough, he has most of the multiplication facts down now without the benfit of the “quick tricks”. So, it seems to me, that “quick tricks” can be an intermediary step rather than a permanent one. If I am right (and this is only my observation of my son), then there is no danger of mixing up tricks by the time you get to highschool.

Really though we haven’t relied on “tricks” (except for multiplication which I see as a huge success for him) but still I see gaps in my son’s understanding. He does understand how multiplication well—he adds on when he can’t remember a math fact. He is in third grade and I am at a lost to see what exercises he should be doing with a number line. Can you help me here? It seems like they are doing a little bit of this and that (which I abs. hate).

Beth

Intermediate stages — yes, a reasonable idea. The reason I feel so strongly is that I have taught at literally every grade level and then worked in colleges. I see in colleges the disastrous results of poor decisions earlier. Many, many students have been taught something early that was supposed to be temporary but became permanent.

One that made my teeth grit: Teaching college, eighteen- to twenty-year-old “students”. Thay are discussing work together and I hear “Oh, that’s a take-away” “You have to times those together” OK, so the immature kindergarten-style vocabulary is not the end of the world. But it was easy to see from their work that as well as retaining kindergarten vocabulary, they had retained kindergarten thinking skills. How can you even think of teaching algebra to someone who doesn’t know the difference between addition and multiplication — calls them both “and” and waits for the teacher to say if this guess is right or wrong — someone who does not know which direction subtraction goes in — someone who doesn’t even recognize the division sign …
What I am saying here is yes, in kindergarten talk about taking away the markers, but be sure to introduce the words and the concepts “minus” and “subtract” in elementary school; yes, it’s OK to say “and” for addition, especially when learning, but by the time you learn to multiply you need to be able to distinguish two concepts and to use different words to mean different things.

Yes, if a few tricks help get multiplication facts into the memory at the beginning, OK, but make sure the meaning of multiplication is learned before high school and algebra (no more arithmetic will be taught); if the student hits college (as the majority of mine did) thinking that multiplication is a game where you slide digits from here to there, he is guaranteed (as the majority of all students in all the colleges I was in did) to flunk out.

Fact: if you consider success in college to be *either* getting a two-year diploma *or* getting a professional certificate *or* being accepted to transfer to a four-year school ( a reasonable definition) only about 40% of students entering American community colleges succeed; about 60%, or the large majority, fail or drop out. The two big stumbling blocks are inability to write and inability in math — below a Grade 8 level. So when people who have seen and worked with this in college see the same errors being commited and worse, being promoted as good ideas in elementary school, we tend to speak out strongly.

Bits and pieces curriculum: the major fault in American math programs, and something to keep speaking against. Look at the Third International Math and Science Study and other international studies for detailed and informed condemnation.

Number lines: not a huge deal in Grade 3, but there should be measurement exercises and addition problems using a ruler as a number line. Thermometers are good too. So are simple graphs, for example graphing the temperature every day. Then when fractions and mixed numbers are presented, they should be used as actual measures, finding 2 1/2 inches on a ruler, measuring an eraser to be 1 3/4 inches long, and so on.

Victoria,

I see where you are coming from. I will make sure we do all the number line stuff well. He is doing some measuring and temperature stuff and frankly I haven’t take it as seriously as other things (plus he seems to be better at it–a relief). He does seem to forget things he has learned which is a continual challenge. The latest is he has forgotton how to regroup in subtraction. I guess I will have to reteach him. Sigh.

Beth

OK, if the child really is LD, I can see how he might forget.

For most students “forgetting” translates as they never knew the work to begin with.

I spend so much time with so many kids (most *not* LD) who have learned a sort of trick — teacher moves this number from here to there and sticks that number on top and erases this other one, and the kid does the same mystical magical moves. In the short run, it *looks* like the child has learned math. On any investigation, you find the child has learned the opposite of math: leave logic at the door, ignore common sense, and memorize, don’t think.

There is a wonderful article called “Benny” (a case study or similarother subtitle) which details an interview with a kid who had “succeeded” for two years in a self-study programmed math curriculum. It turns out when anyone actually asked questions that he was just playing guessing games with the tests and had totally erroneous ideas about what he had been supposed to be learning. Not his fault, nobody asked him to do anything different.

If “math” to you means totally meaningless minipulations and long recipes and magical chants, of course you’ll forget it. You can copy the moves for a few days and pass the test this week, but if you see exactly the same questions two weeks later, you’ll score zero.

If you see this pattern in your students, it means they need fundamental re-training in how they approach math. They need to develop number sense — an idea of the size of numbers and how they relate to each other and what makes sense in the real world. They need to develop confidence that numbers are meaningful and informative and behave logically. It can be long and difficult, but it takes less time in the long run than failing math for the rest of your school career and limiting your life choices.

This list is so long, I can’t remember if anyone commented on the Learning Wrap-ups for math facts. Any opinions?

Janis

I would also suggest touch math. It is great because it is visual. Also Linda Mood Bell (if you can afford it) has a program for kids with math delays. They specialize in children with learning delays. Check out their website
www.lindamoodbell.com

I started using touch math with my 10 year old dyslexic son who is advanced in math but could not memorize addition and subtraction facts. I homeschool him and could not afford the whole Touch Math program. I made up my own worksheets and number cards using the touch math concept. I have also made cards up using fabric paint—I use puff fabric paint for the touch points. He is learning his facts now. It seemed to give him a visual picture of the facts that he can recall from memory. It worked for multiplication as well. My son could skip count well, but was not committing the facts to memory. Touch math is helping him form the pictures in his mind for recall later. The funny thing is I have used touch math all my life but didn’t realize it. I tap my pencil when I add something I don’t know. Of course, that way is harder and my son wasn’t able to do it. He needed the visual that TouchMath gave him. Val

I agree memoization is important. It make life so much easier later on. A little everyday is the way to go. I also have my son trace the numbers with his fingers. He is severely dyslexic and this tactile method helps the facts stick. I agreed that your child has to say the whole problem. I make my son trace the plus, minus, or multiplication sign as well because they tend to move around in his mind. It helps to trace the signs as well. Val

I use simple arrays and graph paper for multiplication tables. We play the great array game. We roll dice to make multiplication problems, make an array on graph paper, color it in, cut it out, and put each colored array on an oversized graph paper board. The first one to fill in the whole board wins! We right the math fact on each array to be used later for other games. It aids memorization and it is fun!

I agree that using the right language is important. I tell my son to “times it” but I also tell him to “multiply it by” and to “find the product of.” He has learned to understand the different ways of saying the same thing—a task that many dyslexics find difficult. In the end, what works for your child is the best!

I didn’t understand at first what these math “tricks” were that everyone was talking about. After reading Victoria’s reply, I now understand. I have never experienced this with my son. He is dyslexic and has to “see” the concept. There is no way he would be able to learn a math trick. He has to really know it, in order to do it or even have a desire to do it. Once he can visualize the concept, he’s got it down. I quess I’m lucky that his brain is wired the way it is.