Tuesday, May 26, 2009

Weird Math Problem Solving by Visual Spatial Learners

I have been told that visual spatial learners have a weird way of doing math, of their own design.

I can vouch this is the truth for my older son, who is eleven years old right now.

I have heard his explanations for how he could arrive at his solution (right or wrong) without doing written operations and it leaves my head spinning. He would do what I'd call wacky things, making this number rounded up then adding that then rounding down that one then getting a number then subtracting off that extra amount and adding in that other missing part.

When it works that is fine.

This year he is doing a computer based math curriculum (CDROM based). It is called Teaching Textbooks. There is an audio lecture on the screen and they watch the operations being done. Then they do practice problems (using paper and pencil supposedly). Then they input the solution and immediately says if it is right or wrong. If wrong, they get a second chance. They can also have a hint or if after a second wrong answer can see it done out in front of them. They don't go to the next problem until the last one was done and scored, thereby catching their errors quickly.

This is the first year I am not doing the teaching and I'm not sitting right by him. The downside to this is that I don't truly know what he knows or doesn't know. For example even for the wrong answers he says sometimes he slips on the keyboard and really did know the right answer, yet it is too late for the system to fix it.

Last week I was in the room when he was doing the lesson and he was getting erratic wrong answers. One was averaging out four numbers. I asked where his work was (in writing) so I could see where his struggle lay. He said he did it in his head. I asked how he could do all that in his head and he said he guess around at this number and rounded up that. The problem was he was doing it incorrectly so that didn't work out.

Today he was doing long division and asked for help. He clearly had forgotten how to do the operation out on paper. (How this is possible is mind boggling and all I can say is that from what I understand from reading the writings of Richard LaVoie in "The Motivation Breakthrough", erratic performance and forgetting things that seemed mastered the prior day or week is typical of kids with a learning disability.)

I asked him if the prior lessons covered this and how he got those right? He said it did cover it but the problems were either easy answers that he could do all mentally in his mind or else he had a different way of doing it.

I asked to please explain.

The problem was something like 532 divided by 5. He knew 5 went into 5 once so it was 1 + something. For the second part he needed to figure how many times 5 went into 32. He said he made a story of it (this was not a word problem by the way). He said he parceled out 5 to himself, and some was left over, so gave 5 to his brother, and some was left over so gave 5 to friend Mike, 5 to friend Thomas, 5 to friend Jack and then 5 to friend Ian. That makes 6 times he gave out 5's, and then after that there was two left over for a remainder of 2. So he came up with 106 with a remainder of 2.

The kid was right. That time at least.

However I said he needed to learn the order of operations for a good reason. I told him that sometime he'd have to figure out 569808 divided by 4039 and I asked how he'd do that one with a story. He balked. I gently explained that if he would learn the order of operations to compute this on paper with pencil then no matter how simple or complex the problem was, the answer could be found quickly.

For the record as with other "very visual spatial learners" this kid still does not have his math facts memorizes for multiplication. At the number 7 it gets murky and definately the upper numbers with 8x and 9x are not there and forget 11x or 12x.

I know some of you may think who cares, they will get it someday. Well this kid is almost 12 years old and still doesn't have all of the math facts down cold. I have spent hundreds of dollars on every known type of product ranging from simple flash cards to complex right brained learner flash cards to computer games like Timez Attack and Math Blaster to the (impressive) Flash Master. I have done multiplication songs, posted signs all over the house and used Wrap-Up's. He has done timed drills with Calc-U-Ladder and that doesn't work either, oh and the older program Quarter Mile Math that was much lauded by homeschoolers.

It gets to a point where goofing up on simple math facts either gives the wrong answer (7x9 does not equal 72 as he tried to tell me today) or it slows down the operations to the point where this child forgets his place in the 'order of operations' and puts numbers in the wrong spots.

Since this kid also has a diagnosis of (and is currently under treatment for) a visual processing disorder this further complicates matters. His sloppy handwriting which he swears is the best he can do, is sometimes so illegible that he can't read his own writing thereby getting a wrong answer when the original work was actually correct. Also the alignment of numbers in math operations like longer multiplication problems and long division goof up the final answer.

I am not stressing at this moment but am sitting her scratching my head at the challenges of teaching a very right brained learner math.


Clarification: We are presently using the FlashMaster for math fact drill ten minutes a day. Son says he is making progress and thinks he is learning but he still struggles with his math work due to not knowing all of the math facts.

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Latte Lady said...

I plan on using Teaching Textbooks next year for our 12/13 year old, too. (If we can afford it by then!)

So far, I like what I see with it but I am also worried about whether or not I will know what he is doing.


bakinchick said...

Another mom of a boy with very visual learning style here. He's only six, so I'm just now discovering the fun.

Boy also has these incredibly contorted "stories" for figuring out the problem. He does not yet show problems with remembering math facts. Our agreement is that he can try the first round in his head, but if it is wrong then he has to go back and "show his work" so we can figure out the problem.

Will be interesting to see how it goes as we progress in his schooling.

atara said...

Have you looked into mathusee? I think they use a lot of manipulatives. This site also looks cool for learning math facts: http://rightbrainmath.com/

Amy said...

I recently started reading your blog when I started thinking about homeschooling my own children. At any rate, your description of your son sounds very much like me. I am very right brained and very visual/spatial. We spent FOREVER on math facts!!! One of the things that I found most helpful and that I have used when I used to work at Sylvan was stories for math facts.

For example, the 2 most challenging facts for most children it seems are 7x8 and 8x8. 56=7x8 so all you think is 5, 6, 7, 8 (like counting off a song or something). 8x8 I think of the Beatles. They had a song called When I am 64. There were 4 guys in the group, and there are 4 holes in the two eights, so 8x8=64. Of course with the 9's you can number down the paper 0-9 and back up 0-9 and you will have the answers:
9x2=18 and so on.

It seems like a rather backwards way of doing it....but once I learned them that way I never forgot them and got rather quick at it.

Elisheva Hannah Levin said...

Hi, Christine.

Since kids who are very visual usually have problems with auditory short term memory, they may not ever have the basic math facts down.

Calculators are very good for such kids, and by teaching the use of the calculator you can make sure that the kid has an idea of why they do what they do with it.

There is also a simple technique using the hands for remembering the times tables that works for some kids.

Elaborate story, that, and my guess is your kid could see it all! I love it. It also sounds like he is beginning to translate what he sees into language. As he does that, his sequencing will get better.

Definitely stress the order of operations! And don't stress about the fact that it might take a while for him to 'see' the value of it.

livnletlrn said...

Easy way to do nine times tables for visual kids:

Times Tales picture stories for the few multiplication facts that were stumpers otherwise.

My son is making his way through Math-U-See. Still sometimes with struggle (and much of this personality-based, not learning style-based), but less so than other things we've tried.

For a long time, we turned lined paper sideways for long multiplication and division problems. He has been diagnosed with dysgraphia and the columns helped him keep his numbers lined up.

Grace 77x7 said...

Hi! One of my kids had a very difficult time learning her math facts & did not learn them solidly until around 12 either.

For learning addition & subtraction facts, initially it helped to use counting manipulatives &/or cuisennaire rods moving one over at a time as we went up each addition group.

Then it was a matter of practice, practice, practice (for repetition, repetition, repetition)

She loves music so the Schoolhouse Rock multiplication songs were a big help & we followed that with skip counting each day.

We didn't move up to the next set of multiples until she could easily skip count the one she was on backwards & forwards several days in a row.

Yes, she hated it - some days she whined & cried like a 2 yr old - but I gave her no choice in getting the practice done in some fashion, while doing what I could to make it a little less blah (jumping on the mini-trampoline aka rebounder or something that allowed her to set a rhythm for herself).

I see it as the beginning of teaching them how to learn what they need to even when they don't want to since they will need that ability in life (think choosing an insurance plan, for example)

I have 5 kids, 4 of whom I am homeschooling & who all have their own learning issues. Some days I think I am going to lose my mind completely, lol! But the gift of homeschooling is that I am able to help them where they need help rather than having them suffer some govt. minimum standard that doesn't even apply to them forced on them by a teacher who is yoked by the bureaucratic system and could never love & care about them as I do!

Hang in there!

P.S. Oh and I have a friend whose daughter struggled with math until she started taking violin lessons. Google it - turns out that learning music helps the brain with learning & especially math concepts!

Jennifer Fink said...

I don't know the answer to your problem, but I just wanted to say that your son sounds a lot like my oldest son! My oldest son is 11 too, and like your son, has his own system of solving math problems in his head, doing operations I don't even understand. And like your son, that's great -- when it works.

He doesn't have the multiplication facts down yet either, and, like you, I know it's a stumbling block for him, 'cause he ends up putting a lot of time and energy into figuring the higher ones out from scratch every time -- and when it's incorrect, he gets so frustrated that he can't even think.

We're trying. I just keep telling myself that's a continual process.

All the best,

Kanisha said...

I chanced upon your blog looking for info on visual spatial learners I so identify with your son and his method. If only I had had a parent or teacher willing to help me with a less conventional method of learning; I have been IQ tested at 155 so why am I so dumb! I never did crack it and use a calulator.take heart and well done for trying;

Blank said...

Hey! I read this post just now. I've seen partially completed long division worksheets. These provide a lot of hand-holding and are very useful help master the process.

Jennifer said...


I have the same problem and only recently I was finally diagnosed with dyscalculia. Most people have never heard of this LD, even though it may be more common than dyslexia. I think a lot like your son and can totally relate.

Good luck and Best wishes to your son! Oh, and here is a great pdf on learning multiplication for visual spacial learners that I just stumbled on while looking for math strategies for myself. I bet it would really help him.


Jonathan said...

I know this may come after your child has learned his multiplication facts, however you might try this problem solving approach. Every multiplication series (2x's, 3x's, etc.) has a repeating pattern. These patterns may be as long as 10 number-groups (7, 14, 21, etc.) before repeating. Try this on paper: Make ten columns of four rows. Allow enough space to the left of each row to give it a name. At the top of this matrix call it : "Finding the pattern for the 7 x's facts". In the first row number each column 1 through 10. Name the second row "Ones". Now have your son (without your help) fill in the first column with "7" (7x1), the second with "14" (7x2), and so on through to the last column which will be "70" (7x10). It is fine for him to finger count as long as he figures it out himself. If he gives an incorrect product have him try again until the answer is correct. Now label the next row "Tens" and have him repeat the process. Encouragement is important as you remind him that this is a type of puzzle where he must find the repeating pattern. You will notice that the last number in each column ends in the same last number as the row above. You will also notice that the number before the last number will or will not increase to the next "Tens" (21, 28, 35) in the same pattern as the row above. Lead your son to this discovery with as little input as possible, but not at the expense of his interest. It's best if you try this yourself first to become familiar. The 7x's repeating pattern is one of the patterns that will take the full 1-10 series to identify so when your son completes the second row he will have completed the longest type of repeating pattern. I use three different colored highliters, one to identify the last number (the core repeating pattern series),one to identify the first number(s) (the secondary pattern series), and a third color to draw a line through the 1-10 numbers at the top to indicate the numbers in the series before it repeats. Remember that the 7x's goes all the way to 10 before repeating. One of the students I tutor added another interesting element. He used his pencil to draw a line from, number-to-number, above the numbers in the top row (1-10) and when the secondary numbers in each column "Jumped" up to the next tens (28, 35) he drew a hump instead of a straight line. It does make it a more visual indicator.

I know this sounds complex when you read it but give it a try for yourself. It works because visual-spatial learners can be overwhelmed by the endless possibilities of numbers in multiplication. As holistic learners, they need to understand new information as a whole and not in sequence. This experience takes multiplication, which seems too big for them, and gives them a system of no more than ten steps to remember in order to master the facts. It also works well because it engages their curiosity for puzzles and games.

Once your son gets the hang of this (usually within 10-15 minutes) don't be surprised if he brings his paper to you in a few more minutes with his 7x's facts all the way up to 50. Take advantage of his excitement and practice the repeating pattern. In multiplication facts that go up to 10 such as the 7x's brake it into the first five and the second five. Making a musical lyric out of the helps too. This will show your son that math is reasonable and knowable when you realize it is a set of patterns. Skip-counting (7, 14, 21, 28, etc.) will come naturally.

you can email me if you have any questions. honneyman@mac.com

Carmi said...

I'm not sure if anyone mentioned it since I didn't read all of the comments but my math professor showed us a strange method that one of her previous students brought in as a project. It's for your times table from 6-10 and I barely glanced at it but it might help your son, it is called Chisenbop or Chisanbop. You can copy and paste some of these links for more info.




My prof. also taught us an easy way to multiply big numbers called Lattice Multiplication.

Hope this helps!

Jesse Garcia said...

I don't know if this helps, but when you think in pictures and you're doing math it actually helps to picture the numbers. I find it easier to multiply larger numbers in my head from left to right (as opposed to right to left like you do on paper) by breaking them into more easily computable numbers and then adding or subtracting. For example, if I were asked to multiply 47 x 51 I would think half of 47 with a zero + 47 or 23.5 with a 0 + 47 = 2350 + 47= 2397. (It is much simpler then that when you just see the numbers in your mind) I know it sounds harder, but if you can picture the numbers and you learn a few tricks it makes math pretty simple.

hangin in by a thread downunder said...

I have 2 visual spatial learners(both with auditory processing disorder, visual processing disorder and Irlens Syndrome) the youngest, now 13 has always struggled with basic maths facts and times tables. We downloaded an app that he uses on an ipod touch called Times Yable clock (available on itunes - $1.99) @ http://www.timestableclock.com/ designed by a lady named Robyn Sorensen. Half an hour playing this and he has mastered (and I mean totally) a set of times tables....the look on his precious face was priceless. He also found another online game called maths lines at http://www.basic-mathematics.com/adding-integers-calculator.html(centre of the page). This game had him memorised his basic addition and subtraction for his number 1-10 and doesn't use his fingers any more. Hope these give you some help :-)

classical said...

Hi Cristine,
As a 29 year old visual spatial learner I can tell you I had great difficulty in math at school. The teachers did not understand where I was coming from and I often asked if they could explain it a different way. I still do not know the basic math fact and am pretty much horrified when I have to do anything math related. The reason I am unable to grasp the basic facts is because I have nowhere to store, or place it if you will, the basic facts in a global environment. Also, the so called visual aids with these 'new' programs are not that effective because all they do is add pictures to what is essentially a sequential process. As a vsl I need to see the whole picture first, how things relate to one another and from there I can add the details. I found your blog while searching for any new developments on this front that might aid me in learning math. I just thought a few words from one who is vsl might help and give some further understanding to how we learn. One more thing, once I have something assigned in a global visual context I never forget it.