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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