Visualization and math

We are not all visual. I’m not strong in the visual department. Some people have a remarkable ability to visualize things. Some people remember colors vividly well and others just don’t have that ability. Math can be a very visual thing and I think visual people have a big advantage when it comes to learning math particularly in geometry, for example.

And textbooks aren’t effective instruction for everybody either and it doesn’t sound as if the textbook works for either your son or you. The language in textbooks is dry and stilted. Textbooks are not written the way we talk and to some children and to some adults as well, textbooks are incomprehensible. If textbooks don’t work for him, skip the textbook and just teach the skill. Or shop around a bit and find a textbook that works better. Go to any teachers’ store and look at the math instructional workbooks they have there.

That he doesn’t learn from textbooks doesn’t mean he can’t learn math but that he’s not visual does mean learning math may come a bit harder to him.

Good luck.

>I know that Des and others who have been trained or have been working with the various LMB programs may have a feel for this.

Ooh wish I were trained in it but am not. I think you are thinking of Janis?
However, I have used both OCN and V/V. I have also used LiPS (not that I’m recommending this).

>I am wondering if my son has difficulty with visualization. This is a relatively new question in my head because he was a very early reader and also he has a very good imagination and a good sense of humor. However, for some reason, his math facts (addition and subtraction) did not come easily. Funny enough, no real problems with mulitiplication, although he isn’t automatic on them all, but I think only due to lack of practice. He will still make mistakes or use his fingers quickly sometimes with simple addition.

Well I think that VV and OCN can help even IF the kid doesn’t appear to have difficulty in visualizing in other areas. First of all in math, kids are generally NOT taught to visualize. Good mathematicians do this instinctively practically, but people who are not good in math, don’t think about trying to visualize it for the most part.

The same goes for visualizing in reading. Someone may have good visualizing for other things but not do it in reading. I think it really is not particularly encouraged. Sometimes it just helps to give the kid permission to visualize. I was using V/V with one of my students. She has a delightful imagination and even sense of color and artistry, but her initial attempts at visualization in reading weren’t very good. She could not tell you anything outside the story line as it wasn’t in the book anywhere. As we worked on it she got much better very fast. It occured to me that all that was happening was that I gave her permission to do. She started spontaneously visualizing what she was reading (indicated by eye movements, etc.) during reading. And she started coming up with things like “I think that girl is jealous”, when the term was no where in the book.
I am also doing math with OCN with her. And she has responded by being quite enthusiastic about math and seeing relationships automatically.
I think this wouldn’t have happened without the encouragement and reinforcement for visualizing.

At the risk of being rather simple about it, I think the schools generally teach pretty “left brained”. Lots of auditory and the other senses get a little stuck and unused. They are still there though.

>I could see my son’s friend’s eyes look up like he was visualizing and he repeated them back. My son repeated the numbers under his breath as I said them which appeared to me to be total reliance on memory. Of course, I’m no doctor and I’m only speculating here, but am really curious.

Yes, eye movement is a sign of visualization. You can check this out by asking your child to try and see something in his head. The VV exercises start simply and become increasingly complex. VV talks about this quite extensively.

>Does the OCN manual tell you how to check this out if I were to buy it?

It will tell you exactly the above.

OCN is quite good and the most user friendly of the LMB books (also the last written). You do really have to do at least some of VV (also fairly user friendly)- basically get him to the sentence to sentence level. With your child it might not really take very long. There are few additional materials required. There is a $20 book containing stories for VV that is useful. And the only thing you really need to buy for OCN (outside the manual) is a plastic number line and unifix cubes. I made a number line that fits the size of the cubes. It isn’t very good and am thinking I will now buy the real thing. You don’t need the whole program in either case.

>Lori

—des

He probably does process things through the auditory channel as his “first preference” — most people ahve a preference, and fortunately it doesn’t mean there’s a disability in the other channels. However, if you have a strong preference for one (p’raps because you’re gifted in that area) and you don’t develop the other, and you use the strong one where most people are using the weaker one, it tends to widen the gap.
Often this happens in reverse — a visual learner, say, is able to read up to third/fourth grade on the strength of that visual memory — and then, oh dear, those multisyllable words come charging in and s/he hasn’t developed the auditory knowledge of the basics at all.
In either case it can go a long way to learn about those channels and using them.

Math instruction generally does a horrible job at connecting the math symbols to the concrete ideas they represent. Teachers tend to assume a fluency that isn’t there — a kiddo who is imitating a procedure and getting right answers is assumed to also be processing what that operation does. Then you give ‘em the infamous story problems and … forget it. Figure out *which one* to do?
So he’s not likely to be visualizing at all because a: it’s not his natural path for remembering things and b: things are not being presented visually, or, if they are, it’s usually done separately from the “doing the arithmetic” and the connection isn’t well taught.

I suspect OCN would strengthen that visual channel (and at least teach him how to use it better :-)) and fill in some of the gaps and connections he’s missing.

One time a few years ago I was teaching college-level remedial, er … developmental basic algebra, and a student came up to me after class and *apologized* for having to visualize concepts. I scraped myself up off the floor and tried to stress to her that she was **supposed*** to be visualizing, and that was why I had spent the last month or so painfully teaching graphing in every class. I could tell that she didn’t really believe me.

Seriously, an awful lot of elementary teachers teach kids both directly and indirectly that visualization and concrete work are bad and memorizing verbal strings is good, exactly the opposite of what real mathematicians and most other creative people do. Teachers tell kids they are “too old” to draw pictures, they reward “neat” papers with only answers written in and no work on them, and they tell kids to hurry up and give the answer, don’t stop and think about it – all of which is exactly the opposite of what we try to teach in real math, anything above pre-algebra. It is very frustrating to try to teach a whole class of kids who are totally prejudiced, taught by their beloved kindergarten teachers in the most receptive learning period of their lives, to hate and despise everything they need to learn to do to pass math.

Des is right, the first step is just to give permission to visualize. The next is to model and teach directly methods that work. Also note methods, plural; teach that there are often several ways to a goal, although please avoid the trap of re-inventing the wheel with square axles i.e. inventing personal ways to do things that are very slow if not dead wrong.

By the way, I am both a math and a language person, both a visualizer and a verbalizer. When I double majored in math and foreign languages, the math department head said it was an unusual combination but she thought it was interesting and she’d work it out with me (Thank the Lord for old-fashioned intellectuals who do NOT look for excuses to avoid anything different.) She also noted that math people often do well in beginning Greek, because we already use the Greek letters all the time anyway … I memorize things by patterns — a visual pattern if there is one, a repeated rhythm chant if not. Both methods are good to teach.

Lori, your son sounds like a lot of kids I work with as a tutor. A few are moderately dyslexic but most are dysteachic. He is probably so confused and lost by what has been going on in school for the past few years that he either does not know how to use his thinking/learning skills or is actively afraid to use them, maybe even having been criticized and embarrassed for doing something “different”. You have to go into detail with him — not just give him a question, but ask him how he is going to try to solve it, and discuss those thinking skills in detail. You do this over and over until he regains more confidence in himself as a learner and problem-solver. This is time well invested.

Well, a lady I chatted wtih New Year’s Eve said that after the first few languages were figured out, the rest were “just like algebra.”
Since I”ve told students often that algebra is like a language, it didn’t seem too far a stretch.

Interesting that Virginia used the terms “visualizer and verbalizer” (after the manual Visualizing and Verbalizing :-)). This is EXACTLY what you want the kid to do. You have him talk his way thru a problem and if he can’t do that he doesn’t really understand it. It is also an excellent way of reinforcing knowledge.

Victoria’s concepts are right on target. I did not mean to imply that kid’s should not be taught how to visualize, but sometimes the fact that they are finally allowed to, is really enough, as they really have those skills in them.
Perhaps they need to be focused to do math with them though. Which your son isn’t doing.

I agree with her comments about schools trying to get the neat product and discouraging anything that might indicate that the kid can’t do the math in his head. Kids are taught “not to count on their fingers” but the kids aren’t always there yet. In order “not to count on your fingers” you have to have many many opportunites to count things. So they get the rug pulled out, they can’t count on their fingers but they can’t count anything else either! It would be best if they had much more time with manipulatives even into the more advanced mathematics. I think I could do algebra, if I knew what it was they were doing with it.
I have always wondered, given how much I like to teach math, that I don’t really have a math disability (I have a dyscalculia dx), but as Victoria says a dysteachia.

—des

I really think my son could benefit from a little VV and then OCN. What Sue said really hit home about him possibly having a strong preference for the auditory channel. It could be true that he hasn’t developed the other, especially since he’s of an impulsive nature (everything has to be quick, quick, quick). I would think the visual system needs you to slow down and focus, especially if it’s not channel #1. I often have to tell him to watch me when I’m showing him something, not just listen.

He approaches math in an impulsive way. He wants to get a quick answer and often makes silly mistakes. If you force him to slow down and think about it he will often get the right answer.

I took your advice today and talked to him about visualizing (that schools emphasis speed which doesn’t allow you to visualize) I’m looking for a math tutor, but in the meantime, I’m going to try to teach him fractions - I want him to be able to *visualize* them. At the same time, I’m just going to make sure he can do what they’re teaching at school in a rote way (decimals and fractions simulantaneously as discussed in another post).

I would love to find a tutor who is knows OCN. Would the local LMB people give out such info? I would love to homeschool my son for a while with the help of tutors, but am at odds with my husband. The school is really messing him up and stressing him out. Despite it all, his grades are good. Our parent conference last week focused almost exclusively on his disruptive behavior (turning around and talking to others, etc.). This is new behavior this year, not that he was a perfect student in the past. Somethings up. We’re trying to figure it out and plan to get a neuropsych eval soon.

Thanks for all your helpful feedback!

Kids with math problems need lots of time manipulating things and if you act like YOU are in no hurry they will enjoy it. I am absolutely blown away how much my student likes the practice with manipulatives. For example, we are doing adding (doubling, 9s, 8s, etc.). We do it in order once, then randomly once, then without the manipulatives in order and then out of order. She really likes this practice. The quick answer thing, I believe is taught, because you are required to get the answer quickly and not think about it. This is opposite everything Virginia has taught me. :-)
(Gosh but I’ve learned lots from you, Virginia).

I took your advice today and talked to him about visualizing (that schools emphasis speed which doesn’t allow you to visualize) I’m looking for a math tutor, but in the meantime, I’m going to try to teach him fractions - I want him to be able to *visualize* them.

You might try going backwards first. Make sure he really knows his stuff before you go on. Does he count on his fingers. If so, he has not really learned adding and requires the prop.

>I would love to find a tutor who is knows OCN. Would the local LMB people give out such info?

You’re not anywhere near Albuquerque?? :-)

I’m afraid they will not be. They will not give out names of people that have gone thru the training. You might be able to find someone but it would be purely random. I don’t think it is a particularly hard program though and you could tutor him if you have that kind of relationship. It is very user friendly. You must do at least some VV as it requires some knowledge of verbalizing and visualizing that you learn with that. I think you could get him there yourself if you have a good relationship.

>(turning around and talking to others, etc.). This is new behavior this year, not that he was a perfect student in the past. Somethings up. We’re trying to figure it out and plan to get a neuropsych eval soon.

Perhaps this is due to more frustration! As the learning demands get higher it is imperative that he have higher and higher skills and he may not have the lower ones yet. For example, if he doesn’t really understand multiplication and is required to do fractions he may get more and more frustrated.

I think homeschooling would be a great idea, too bad dad’s against it. I think you might be able to do some research showing that he will do just as well. Maybe better.

—des

My son is home from school today because I didn’t want to send him so stressed out. As a result, I am “homeschooling” him for the day. It’s wonderful in a way that he is being so compliant (because he’s thrilled to be home - he’d do anything - which I’m taking advantage of because he’s never had the patience to do much with me).

I told him that we were going to work on some basic skills today because that’s contributing to his difficulty. For example, he’s never had the patience to review his math facts over and over to get solid on them. So the fact that they are not all automatic hurts his performance. For the first time in forever, I pulled out addition flash cards and we went through them (we never even did that alot in earlier grades (he’s in 4th now) because of his impatience). He did great on most and employed good tactics, which I know because after he answered I asked him how he knew. An example was 9 + 6 - he said he took 1 away from 6 and made the 9 a 10 then added 10 + 5. I’m not a teacher, but this sounds pretty good to me. Am i right?

However, he still hesitates on some of his very simple facts like 4 + 3. He said 6, then quickly corrected himself. He wasn’t this way with all of them, just a few. Isn’t this strange? Any ideas for how to get him to internalize these so they are truly automatic? Is he not “seeing” them? I had him count some blocks this morning (i.e., all the combinations of 7). Actually, we had done some audiblox work over the summer (with great resistance on his part). We stopped when school went back because there was no way it was going to happen. I did see an improvement in his basic addition facts at the time we stopped right before school (we had done about 38 hours spread over a 8 month period with the most intensity being over the summer, but we were never able to get close to the intensity they recommend).

My son has always in the past gotten concepts quite easily in the past, but I am concerned that whatever this issue is, combined with his motor weakness, is going to really mess him up in math. He doesn’t think he’s any good at it and it really stresses him. It’s just such a shame because I know he has a good intelligence for it (he used to wow us with the basic concepts he figured out on his own when he was younger - not to be confused with a solid understanding, but nonetheless quite advanced for his age).

OCN may be an answer. It’s just hard to find time while he’s in school. What do you think the minimum amount of time allocated to it has to be for results for someone with a hopefully minimal deficit in this area?

Thanks so much!

Lori

Lori,

I think Lindamood Bell will not accept a child unless the parent can commit to at least an hour a day. The intensity of therapy is a real asset to progress.

On Cloud Nine has the strategies you want to teach math facts. I am sure he was taught the idea of adding one to the nine, etc. as I have seen that taught at schools, but what you want is for him to look at the 9+6 and simply say 15. That is “knowing” the math facts. But OCN wants the child to have some V/V first and then begin at the beginning of OCN. You begin by teaching them to visualize a number line and progress from there.

Kids like your son certainly can have increasing stress as they get into more difficult classwork while lacking basic skills. I think homeschooling would be an excellent idea if you can find the support you need and have a deal with him to cooperate.

Janis

Lori — the 9 + 6 = 9 + 1 + 5 = 10 + 5 = 15 system is a very very good method. This is exactly what “natural” math thinkers do.

BTW I would like to point out that a lot of people who are supposedly “naturally” good at something do NOT just pick it up out of thin air — they do an awful lot of work with it but since they do the work on their own it is never counted.

Youu can model addition on a abacus and then this “trading” is even more obvious.

Yes, it is absolutely normal to have uneven memory of math facts. Certain combinations seem to come out even, like the sums to ten, and things like doubles get used a lot and remembered more easily. Odd combinations like 4 + 3 seem to take longer to stick.

Keep working on the memorization. It’s a long slog for almost everyone. Your son is behind the eightball because he didn’t get this stuiff into memory when the other kids were doing it, but believe me, they worked over it too.

Try having him recite the tables in order, three plus one is four, three plus two is five, three plus three is six, and so on. Recite Question as well as answer — an answer isn’t much good until you know what question to answer to. Go over one set two or three times in the morning, two or three times in the evening. This is called spaced practice and is the best for memory. Just two or three minutes at a time. Keep practicing after he “knows” it — overlearning is necessary for permanent memory. If you do one set/line of the table every day and review every third day, in a couple of weeks he’ll have it down much better.

Janis is right about what LMB will allow. But if you did it, I don’t necessarily think you would need so much time for it. It is an ideal, and would no doubt get the best results but it is an ideal. We don’t all live in an ideal world.

Yes OCN requires some of the VV (at least to the sentence to sentence level). There is a common language and experience. Plus certain skills.

I like the sequenced practice— 1+1; 2+1, 3+1 for example. This gets the kids seeing patterns. I add to that going through manipulatives first in a sequence and then randomly. This is what OCN does. They also do this on a number line, though they *teach* the no. line, you can’t assume the kids will get this without instruction (as I remember Victoria pointing out).

Anyway you might buy the manual for OCN. This may give you some ideas and strategies you could use without actually going thru the program.

What’s your husband’s objections to homeschooling? (IF it’s any of our business. :-))
—des

Victoria - I think we were both surprised yesterday when we did the addition and subtraction flash cards. He did well on most. It was so weird that he did better on the more difficult ones than some of the simple ones. In a way it makes sense because he was so “not there” in Kindergarten and 1st Grade, and to a lesser degree, 2nd Grade. We were struggling to get his allergies under control and he had started getting therapy for mild sensory integration in 1st Grade. He never did the manipulative work near to the degree the other kids did for this reason and the fact that he had poor fine motor skills. I really think audiblox helped him with this, even though we didn’t get close to the recommended intensity.

You’re right, I need to try to get him to overpractice his facts so it is sooo automatic. Knowing his math facts on flash cards when that’s all he’s thinking about is different than knowing them in the middle of a complicated problem, especially when his motor skills are being called on too. It’s like spelling..he does well when he’s spelling verbally, but it goes down the tubes when he’s writing.

I have an abacus, but have no idea how to use it properly. I’m sure I can find some instruction on the web…sounds like a good idea. Thanks, Victoria.

Des and Janis - Does OCN work on more than just math facts? Does it help with visualizing the whole math problem? If, in isolation, he can get his math facts automatic now with some practice, would the number line thing confuse things at this point?

As far as homeschooling, my husband and I had it out last night about it. He thinks it’s an extreme step. The reasons he’s against it is that his grades have been good (A’s and B’s), and for socialization reasons. He thinks we should just get him tutored. He doesn’t understand that my concerns go beyond specific instruction about specific things. I know that he needs to get more solid on foundational skills which require everyday practice. An example is phonics. I did the reading reflex test with him and he was not as automatic with segmenting and blending as he should be…he was a bit weak. He also didn’t know all of the code. Now I think it’s because he was such a natural reader that he didn’t need to learn it to read…but he sure needs it to spell. I also think it will help him with sounding out longer and longer words. He’s had so little experience sounding out, because his sight word vocab has always been so large. When he has to (which he likes to avoid) he can do a pretty good job figuring out a word because I think he gets close and then usually figures it out, but I don’t think that will carry him forever. He could really use work with lots of manipulatives in math and the practice on his facts that we talked about. I’d love to do some VV and OCN. The list goes on.

In addition, he has to go back to square one with writing composition. This is not going to be a quick thing that once or twice a week tutoring is going to help quickly enough.

The problem with just tutoring him is time and pressure on him. His school gets out at 3:15. He has homework. He has his NeuroNet exercises. He may have to do exercises for a spinal problem (that’s the medical thing…he’s having an mri and cat scan done). How can he handle anything else after school? He’s also one that needs to decompress. I temporarily took him out of karate which is very good for him and he wants to go back. He’s finally interested in a team sport (thanks to NeuroNet). He takes guitar lessons (another good thing). This is all before getting to the foundational skills I talked about.

I told him we need to reduce the stress on the kid, not increase it. My husband and I agreed to try a tutor and if it doesn’t work, we would talk.

Sorry this is so long..better go before I’m timed out!

Thanks, everyone, so much!

Lori

My issue is that

Just a clarification about the reading on my previous post. Although his reading skills are generally good, I do have some concerns about comprehension…I just don’t know if the culprit is attention or other issues. He has difficulty with textbook type material. I just want to make sure I don’t come across as concerned about just a more minor issue of possibly having a problem in the future sounding out words. Some other possible red flags are there and he has never had any reading instruction (because he was so ahead in earlier grades and because he “wasn’t there”, if you know what I mean). Also his writing skills were very poor so he didn’t get reinforcment with those either.

Lori

Lori,

He is beginning to have trouble with comprehension, because his decoding is not adequate. A sight word vocabulary will not take a child much farther than 3rd grade level. He must be taught to decode or your problems will multiply fast. It sounds like he has a lot of basic skills that need reinforcement.

I will have to say that the socialization argument in regard to homeschooling is a moot point, as far as I am concerned. I see as many or more negatives in public school socialization. This is where your son will hear all the bad language, have his first look at Playboy or worse, etc. This may or may not occur in elementary school, but you will not avoid it later. And I don’t need to mention the exposure to smoking and drugs.
He can socialize in scouts, sports, church activities, or whatever your family chooses to do. That way you have more control over the peer group, and he is not competing with them in academics. However, if his grades are A’s and B’s, perhaps a heavy dose of summer tutoring will be all he needs. You could certainly do PG in that amount of time.

On Cloud Nine covers all basic math concepts through fractions. It would not hurt any child to start at the beginning. You are teaching things in a new way, so it is not boring.

Janis