Need help with 1st grader

I wouldn’t presume that this child is past the concrete level in understanding addition/subtraction. I would make sure to provide this kid with LOTS of opportunities to first do this on the concrete level (buttons, blocks, etc.) then on the semi-concrete level (pictures of objects on a page), and then the symbolic level (dots or squares on a page), before working on the abstract level.

The counting thing is not so serious. I am wondering if it indicates a memory problem though. Counting (1,2,3, etc) is not really necessary to math and may actually interfere with it. I would work more on counting actual objects, rather than worrying about rote counting.

—des

Lil,

I go to On Cloud Nine Math training by Lindamood Bell tomorrow! Ask me again then!

Janis

Hi again,

I’ve been really trying to think about this math thing for this child. Yesterday, we got a bunch of pennies, nickels and dimes. I had her use those for counting by 10s, 5s, and 2s. We also counted by twos with the odd numbers under our breath, and then we SHOUTED the even numbers. She liked that. :-) Maybe I should have her write the numbers in two columns - with odd in one, and then even in the other. Then she could see the even numbers visually while we count by twos.

Then I took the pennies, and we did some simple addition. I had addition facts written on index cards, and I did things like put two groups of three on the table in front of her, with the card that said “3 + 3 = .” I showed her how to count the pennies to get the correct answer, and then I had her repeat “Three plus three equals six.” She had to count the pennies a couple of times to get the right answer. Maybe they were too small for her to manipulate well.

It was interesting that when I asked her to add some number plus one, she always starting counting with the larger pile, and then added the last one. I need to get her to generalize that to the next number up, but don’t know how.

Do you think if I made some number lines and showed her how to add on a number line it would help? I have some graph paper I could do that with.

I’m trying to keep my costs down since I’m doing all this for free.

I’ve researched multiplication facts for my son (rising 5th grader) and know that different families are taught first, and then you move to the harder ones. Does any of that hold true for addition? So far we are only working on 1 + ?, 2 + ?, and 3 + ? with ? being 1 through 9. I thought I’d wait for her to mostly master those before I go any higher.

Thanks again. I’m having a really hard time trying to figure out the best way to help her.

Lil

I think that counting and adding *pennies* is good but you might be a bit careful counting dimes, etc. I think there might be some confusion when you are introducing the value of a dime, say, vs one dime, etc. Very confusing concept to some kids.

I think you are on the right track but I would have her add objects before actually using fact cards, etc. (And yes, I might use larger objects, as well as different kinds of objects— pennies, small blocks, buttons, spoons, pencils, etc.) Something like this: have a small group of things (ie 3) and then have her put two more in— count them. Have her make up her own problems. When she is doing really well at that—100% or close, then you can use no. cards (you know just 3*5 cards). Spread two of each out. (make sure she can identify). The still using the objects— start by having her place the no. card next to the objects. Then you can maybe use paper circles or something to put the objects in so it is clearer. This is a good way of introducing zero, nothing is in the circle. This is zero. And introduce the signs (like the + and =) to this. Then I’d do your facts cards. The point is to break this up a great deal. Make sure she understands before going on; etc. The other thing, is that the facts cards represent failure to her. So you want to make sure she sees herself succeeding before going to them. Not until she is this far, would I go maybe on to doing this would pictures on a page. I would NOT use the regular stuff they have in class. If you can’t draw the pictures, I’d go and put stickers on heavy paper and cut them out and lay them on the page. Then you can rearrange them. Or you can stick them on the page. Later you can introduce the actual addition problems on a page. And let her use counters or whatever she needs to use.

Also you should be careful when she is counting that she is counting not movements of her hand but actual objects. If she is counting hand movements you might teach her to place one object with another— you start with things that go together and work to something more or less meaningless, like a popsickle stick and a block.

BTW, I think no. lines are great, but by the sounds of it she isn’t really ready. Wait til she can add objects easily and isnt’ threatened by the “problems”. You could teach her the no. line for checking her problems or assisting herself, instead of counting on fingers. BTW, the counting on fingers thing– this is NOT the problem. There is some theory that says we have a base ten system (10 digits), because we have ten fingers. The problem is she is just not ready for abstract math yet.

As for always having to start counting again, this is typical in kids without a firm sense of no. How do they know that the no. doesn’t change while they weren’t looking! They don’t because they don’t really realize no. is constant. They also can’t look at a group of objects and know it is “3” because they don’t have enough experience with nos. What you need to do is just give her more experiences. You could also have her do the following: get out say 4 objects, have her count them. Then you rearrange them, have her count. Rearrange again. Have her count. Spread them out a lot, close them in close, etc. each time have her count. I’d do this with a different quantity for a short time each time she sees you. At some point she will have a aha experience. OH this is the same number, I don’t have to keep counting it! I still remember doing this with a bunch of 4-5 year old special ed kids. It was such a cool thign when they realized this!

I don’t know about teaching families for addition. I would start with lower nos. first. In fact, maybe adding 1-3 initially. I wouldn’t work so much on having her consciously memorize addition facts, but have her have so much practice she will memorize them. I’m not sure this still goes for higher nos. But I sure don’t remember *memorizing* 2+2.

The above is quite a cheap way fo doing this. You have stuff to count around the house, lined and construction paper, pencils, no. line (homemade), and perhaps one pack of 3X5 cards ($1), 2-3 packs of stickers of objects ($2-3). Everything should cost between $5-10, maybe lower.

—des

Thanks a lot des -

What you say makes tons of sense, I just hadn’t broken it down into small enough pieces. I really like your insight re: counting things over and over until she understands the number doesn’t change. And having the individual numbers on cards rather than the equation makes sense, too. My son used to have blocks that did that - I wonder if they are still around somewhere. :-)

You’ve given me a lot of good ideas to move forward with. I really appreciate it.

Lil

Lil — the things you are doing definitely make sense. Des’s advice about concrete objects is really sound and I would recommend you go with it.

However, you are going at a rate of speed that makes my head reel. This is a first-grader!!. For this grade level, mastering counting to 100, understanding tens and ones in two-digit numbers, adding to 9+9, and subtracting by “undoing” addition are the major skills.

The next level of work (Grade 2) is understanding the hundreds place, counting numbers over 100, adding with carrying (quite difficult and will take a long time to get, needs that base ten understanding first), and subtracting with borrowing (extremely difficult and will take much of Grade 2 to get, and often need more work in Grades 3 and 4)

Counting by two’s and odds and evens are nice skills to get, but can wait until Grade 2.
Counting by fives and by threes are advanced skills that would usually be introduced end Grade 2 to Grade 3, and are the into to multilication. Take your time in getting to these. Make sure the basics are very very well-grounded first.

Number lines are OK but (a) I have students in middle and high school who still can’t use them right, and (b) I have had a number of students over-trained in using a number line mindlessly, and it actually worked against their understanding. A little too abstract for many kids at first; stick to counters or an abacus (I like it because the beads don’t roll all over and they’re already groupe din tens.)

Victoria has an excellent point here. I think her statement of the necessary first grade skills is very good. Of course, it’s possible she doesn’t have even first grade skills. (ie knowing 5 is always 5 or the concept of one to one coorespondence— one thing goes with one thing, makes real counting, vs rote counting possible.)

Counting by 2s and 5s, when she doesn’t really know what 5 is (perhaps), is just rote— what they call “teaching a splinter skill” at this stage, she won’t understand what she is doing. Even and odd, another meaningless concept at this stage. If she doesn’t know what a number is that it is constant, etc. then she can’t really manipulate it.

I would not fall in love too much with one manipulative at this stage. The blocks can be bought (about $17). But it is better that initially you count with all different things that you just have around. Some good ones: pennies, garden variety toy blocks, pencils, pens, crayons , plastic spoons, small identical toys (cowboys, space aliens, animals, etc.), safety pins (provided she isn’t hyperactive and wants to open everything). I’d get a container like a shoebox and some baggies and start a little collection. I’m sure you could go around the house and find lots of things. If not a dollar store or thrift store is a great place to buy lots of little odds and ends for little.

I agree that the abacus is probably better than a no. line at her age. I dont’ think she is ready yet. But if you keep up the practice with real things then she can move to this.

Go this way (i forgot the actual terminology):
“Real” concrete (real objects— balls, pens, toy blocks, toys); “artificial” concrete (math blocks, counters; cubical blocks; pocker chips; abacus beads); “semi-abstract” (pictures on page of real objects, might be drawings or stamps or stickers); “abstract” (boxes, dots, small circles) drawn on paper. True abstract stage, no drawings, all nos.

You want LOTS of practice at the real concrete stage without much pressure with actual numbers. Sorry about the terminology but I think I make my point clear anyway.

—des

Thanks Victoria and des -

My county does “curriculum mapping” and posts it on their website. I printed them off for first grade math to see what to target. They organize the skills by 6 week grading period - and these are some of the first skills taught in first grade. Not knowing any better, I just used the curriculum maps as a guideline. Silly me. Everything you both say makes tons more sense!

This child has already been through first grade once, and supposedly has been taught all this stuff. I was working from a review standpoint until I realized she didn’t know it.

I’ll back up and start small. I appreciate you setting me straight - and I’m sure my little tutoree does too! :-)

Lil

Hi des,

When I worked with this little girl yesterday, I had her tell me how many markers, styrofoam balls, popsickle sticks, etc. I placed in front of her. She would count correctly the first time, then I would re-arrange the objects but not change the number. She watched me do it - and then started guessing how many objects were in front of her. How interesting.

I suppose we’ll do this until she doesn’t guess anymore, and then move on to the next step.

Thanks again

Lil

I have just taken the Lindamood Bell Programs and one of the programs is called On Cloud Nine. How did your training go, Janis? :lol:

Anyway, it recommends that you start with the concrete (objects, blocks, manipulatives) and then ask the child to visualize it (ask her to close her eyes and have a picture of the number for ex. in her mind) and then go to computation (mentally and on paper). Obviously it’s hard to explain everything here, but if you would like to buy the book it’s $50 www.lblp.com. For me, the training was not necessary. The kit can also just be duplicated by using your own materials. Oh and the program uses a lot of the number line and the cubes.

The program uses a lot of “visualization”. To teach numerals for instance, you show the student cubes and you show a card that has the numeral for the number of cubes and you take the card away. The student then tells the number and writes it in the air. To teach the number facts, the student is shown the cards with the family and after a lot of discovery and manipulation, the child is taught to see them in her mind’s eye.

The book made sense to me (very easy to follow!) and I highly recommend buying it.

Hi, Maricel, I loved the OCN training, too! I have not read the whole manual yet, but I do believe the strategies are very, very good.

I did buy the Unifix numberline as I didn’t see it online, but I found flash cards (must have the problem with answer on one side) and triangle cards at a lower price at trendenterprises.com.

Incidentally, I thought Visualizing and Verbalizing was a brilliant program, too. I am going to take the rest of their training next year, hopefully. I think LMB is doing some unique things.

Janis

:) [b]
I don’t know how to teach for my child[/b]

I have a ten-year old boy, and he don’t know how to count. I tried to teaching him, but he isn’t interested in counting. Let me know good method.

I’d work with manipulatives. I’d get 49 + pennies and put pennies in front of her. (always smaller than 49)

After a few times of counting pennies, - or M&Ms - or Cheerios - actually I’d keep switching around to keep her interested - then I’d put 50 in front of her. When she got to 50, tell her - we call this many 50!

I wouldn’t work her up to 60 for a few more days after that.

And I wouldn’t get worked up if she doesn’t get it. She sounds as if she’s still thinking in a very concerete way and needs some more time with this.

Good luck.

Buy the book Teaching numbes by John Wright. He has numerous activities to teach these skills. Rote counting is a very necessary skill. Don’t disregard it.

I just bought almost all the manuals for LMB and am feeling a bit poor. Can you ‘splain why he says rote counting is so important. I can understand that it is a normal skill that kids aquire (usually without difficulty). I also understand that it is useful to know what no. comes after or before another no. So you want to know what one and another one equals you would need to know two follows. But others say that rote counting in and of itself may even interfere with math skills. The rationale goes like this: real counting involves counting things; to aquire math skills you must first learn them concretely; when counting objects a lot of kids fall back on rote counting, so they are counting five things they don’t actually count them, they go back to rote counting and count maybe five touches vs counting the objects.

As I recall the kid that was being worked with has limited concrete math skills, no addition skills, and perhaps questionable one to one correspondence. She also doesn’t rote count very high, but I think for her if she can rote count to 10, she is doing as much as she needs to at this stage. I would think later she is going to need to count higher, but I question the need to drill her in rote counting when she is not really quite able to count objects.

I know it usually goes the other way, but only because preschools, kindergarten and tv drill rote counting.

—des

Lil,

I am an area representative for Math-U-See and have only recently found this site. In reading through your post I thought I might be able to help.

If you are looking for some excellent hands-on manipulatives look at the Math-U-See blocks. The blocks have units, twos through nines, tens and hundreds blocks. They are designed to demonstrate both positive and negative (addition and subtraction) numbers. They are clearly delineated to tell the student how many units are in each block. No guess work like with some blocks. They are also based on a half inch per unit so they are larger than other blocks too.

Also, the program has some strong instruction on teaching number concepts, especially since our english language makes ten, eleven, twelve, thirteen through nineteen difficult for students to understand in an auditory manner. Also, there is a strong focus on place value.

I would also be careful not to place too much emphasis on counting. I have seen too many programs (especially in the LD area) that start teaching counting and never actually teach addition. Addition is the act of fast counting so 3 + 3 = 6 is not 1,2,3 + 4,5,6 = 6. Being able to do addition is a crucial step to being able to do multiplication, which is fast adding of the same number. (I understand that for some students counting will be the only method they can use, unfortunately, many of student that could move on don’t)

Later, the tool for teaching fractions is incredible. You can contact you local representative for a free demo video at www.mathusee.com

>When I worked with this little girl yesterday, I had her tell me how many markers, styrofoam balls, popsickle sticks, etc. I placed in front of her. She would count correctly the first time, then I would re-arrange the objects but not change the number. She watched me do it - and then >started guessing how many objects were in front of her. How interesting.

Bingo?
I missed this somehow (dated July 17th). I hope you insisted that she count it. It really sounds like she does not have the concept of no. strongly enough to really manipulate it. You can do some fo the early adding stuff (might actually help her) but until she really grasps this I don’t know that you can go on much. If she insists on guessing, I would insist on her counting. She WILL get this.

I would bet there might be some gaps in one to one correspondence as well. So here are some recommendations:
1. have things that naturally go together- cup and spoon, napkin and fork, pen and pencil, etc. you have her match a no. of these together.
2. A no. of similar real things— stones, spoons, pencils, etc. And some popsickle sticks. Just lay them out and have her match one stick with one object. (change objects)
3. Then you might do the same with 2 sticks for one object. (change your objects here)
Make sure you get to each step.

>I suppose we’ll do this until she doesn’t guess anymore, and then move on to the next step.

If she starts saying things like ” ‘3’, it would be three because you just mixed them around”— I mean she says essentially that, that’s when you stop that exercise.

How is she doing now btw? If she has not grasped it I would do lower nos first. You might find she can do this with 2 or 3 for example, but not with 8-9. I wouldn’t go higher than that, at this point.

BTW, I think the On cloud Nine assumes that the kid has a basic concept of no. As for the MUS, well I think there is a kindergarten level, but as I remember Lil here is pretty poor, and doing this volunteer. I think she can do a pretty good very basic bunch of activities without spending more than $10 or so.

>Lil

—des

[quote=”Samsuk Lee”]I have a ten-year old boy, and he don’t know how to count. I tried to teaching him, but he isn’t interested in counting. Let me know good method.[/quote]

Are you talking about counting—1, 2, 3, 4 ,5 etc.??
Or are you talking about counting OBJECTS.
Work on counting objects, and use lower numbers. If he really is very unmotivated someone recommended food and that would be great.
(ie counts 5 M&Ms and then gets to eat them).

Another thing you should do is make sure he knows what 3 say is?
Have him count 3 objects– pennies, stones, M&Ms, chetos, etc.
Spread them around, have him do again. He should know that how
you that whether you spread them around or make them tight together, it is still 3 or whatever no.

–des

Des — you say that you read somewhere that counting can actually interfere with learning math processes. Well, yes and no.

A student who has an ingrained habit of counting may continue to count even if he knows the answer by addition; this is obviously slow and counter-productive. One problem I see all the way from kindergarten through to university is bad teaching of rote methods; the student has been so firmly drilled that he thinks there is only one God-given “right” way to do things, and it would take a bolt from the sky to make him change. Obviously a student in this case is stalled and cannot possbibly learn anything new. It is important to teach flexibility.

On the other hand, there is something called “number sense”. You have to have some kind of image in your mind of how much a number means before you can get a meaningful or useful answer out of it.
One bad example: I was correcting science papers from correspondence students. These students all had the rigididty problem described above. Every single one of them, when faced with a division problem, automatically rewrote it to divide the small number into the big number, whatever the real sense of the problem. In one case they were supposed to divide 1 by 10 to get .1 meter or 10 centimeters. Every single student (well separated, correspondence, no collusion) divided 10 over 1 and happily claimed 10 meters. This was supposed to be the focal length of a camera, the distance from lens to film. .1 meter makes sense, about 4 inches; 10 meters is ludicrous, over 33 feet. A person who had a “feel” for the meaning of these numbers and measures would look at that, say “Gee, that can’t be right” and would correct themselves.
Another bad example: in the same district, I worked with a boy who had Kelinfelter’s Syndrome, a genetic disorder one of whose symptoms is a problem with verbal ordering (He could order things physically just fine; just couldn’t verbalize or abstract order.) Well, the school system claimed he could add and that he was working on multiplication and had mastered the three times table. I spent several months working back and back and back until I found out how little he actually knew. The poor kid could “add” only if he had two free hands and a ruler. His comprehension of the process was on the level of a trained chimp - put this hand here, count out these spaces here, and copy this symbol here. What a waste! And an insult to a reasonably intelligent person. Multiplication was even sillier, and he could not retain any of it. Finally I discovered that he couldn’t count accurately past six. Which sounded too much like “sex” to him, and he had been punished for using that because it was a dirty word. Six years of very hard work, time, and money put into “teaching” this kid, and nothing to show for it but emotional disturbance. He could never progress until he knew what these numbers meant.

The point here is that you have to have some number sense, or all the years of teaching arithmetic will go for nothing, because you are manipulating meaningless symbols.

>On the other hand, there is something called “number sense”. You have to have some kind of image in your mind of how much a number means before you can get a meaningful or useful answer out of it.

Your stories are wonderful (or horrendous) depending on how you look at it. But “number sense” isn’t just from rote counting. It has to be also an understanding of what the number means, take your student with Kleinfelters!

I do feel you have to know what no. comes after what. At some point you have to rote count, just like abcs. The names of the alphabet are very much unimportant and might interfere with learning to read. You can see this when the child sticks to “A” says “ae”, one reason why systems like Phonographix works.

BUT at some point, the abc thing will need to be learned. For example putting things in alphabetical order. It is quite helpful to be able to say them in order, and maybe essential.

But like the thing with rote counting, rote alphabet is just something kids are taught on tv and in kindergarten with little thought to why they are taught or in what order. It’s also always been done that way.

—des

Oh my gosh, I am glad I found this thread. The things you describe with the 1st grader sound just like my daughter who will be starting 2nd grade in 2 weeks. She can count to 100 most of the time but cant count like…39,40,41,42,43,44etc… Also when asked to add a group of objects and then you add one to it, she will start with the big group and count it before adding one. if asked to add 9+5 she will count out loud to nine and then add the five on her fingers… She is Add with a suspicion of math LD, but the test were inconclusive. The school feels she will catch up at her own pace, but when i spoke with the 2nd grade teacher she said the kids should be solid on math facts at the beginning of the year. She is definitely not close to that. So here as always is the dilemma….How long do you wait for a kid to catch up and how do you battle the negative feelings she gets from feeling that she is not smart….She asks me daily why everyone else can do math and she cant….This kid has developed some pretty strong defense mechanisms for anything that has anything to do with math…..Mary

Hi des -

Now it’s my turn to play catch up. :-)

I had L do the “counting” thing until she understood that the number didn’t change.

Then I grouped similar objects by 2 and 3, or 1 and 2, etc. and had her tell me how many. Then I had her place an index card with the correct number below each group. Then I told her we were going to add the groups together, and had her place a plus sign between the numbers and an equal sign after them. Then I checked to see if she could tell me how many, and then had her place the correct number after the equal sign.

We didn’t go over 3+3, but she seemed to be internalizing the number/addition concept. We didn’t have time to get to subtraction.

I’m finished with tutoring her over the summer because I am taking my son to a reading clinic in Florida next week and we’ll be home just before school starts. Then I’ll have his homework/schoolwork remediation/therapy to do in the afternoons after school. I don’t know if I can get to L, too. :-( I will see her at soccer practice (her older sister plays with my son), so maybe we can play “games” at practice to continue helping her move her skills forward. I hope so.

I’d love to be able to go into her school and work with her one on one when they have math and language arts, but I think my school system is too backwards for that concept.

But, she did make progress, and I did see some lights turn on. Thanks for all your insights. I was way over her head when I started, and she would never have gotten as far as she did without your help. :-)

Lil

>Oh my gosh, I am glad I found this thread. The things you describe with the 1st grader sound just like my daughter who will be starting 2nd grade in 2 weeks. She can count to 100 most of the time but cant count >like…39,40,41,42,43,44etc… Also when asked to add a group of objects

I think at this stage I would be more concerned that she really understand numbers (the way I discussed it) and you might try some of the things that I suggested for the other kid.

>and then you add one to it, she will start with the big group and count it >
before adding one. if asked to add 9+5 she will count out loud to nine and

It sounds to me like she is very unsure of the numbers— just like the other kid (maybe a bit more advanced), and as I said I wouldn’t be so sure that she has an abstract concept of all those things. I’d go back to the concrete objects and start there.

>but the test were inconclusive. The school feels she will catch up at her own pace, but when i spoke with the 2nd grade teacher she said the kids should be solid on math facts at the beginning of the year. She is

Well she may or may not. I don’t know about the math ld either, you know she just may need more concrete experiences than she got.

>definitely not close to that. So here as always is the dilemma….How long do you wait for a kid to catch up and how do you battle the negative feelings she gets from feeling that she is not smart….She asks me daily why everyone else can do math and she cant….This kid has developed

You might look into a couple things. On Cloud Nine (though I think that it assumes a basic understanding of number (ie that 5 is always 5 how ever I move it around— might try that with her!)

Another one is Math U See. Very nice concrete program and not terribly expensive, as some of them are.

—des

>But, she did make progress, and I did see some lights turn on. Thanks for all your insights. I was way over her head when I started, and she would never have gotten as far as she did without your help. :-)

Lil[/quote]

I’m glad I could help, Lil. Sounds like she did make some good progress that she can build on.

—des