Pam posted Jun 16, 2013 1:14 AM : > > Visual thinking in mathematics, to my way of > > thinking, is not that my mind generates slick <snip> > > > I found that providing animations (which I did for > > several topics) for my student was a tremendous > > *aid* > > to understanding (not the whole story, but > >critical). <snip> > I believe that what Mike had been exploring is "how visual thinking could 'CONTRIBUTE TO' learning (in math; and probably in most other disciplines)". > > I teach students with learning disabilities, and my > mantra is "use the strengths, remediate the > weaknesses." > This 'mantra' is absolutely the most fruitful way to proceed in general with practically all learning. I know little or nothing about enabling children with learning disabilities - but I'm fairly sure that your claim below is entirely correct. > > If your student has difficulty > creating, using, and manipulating mental imagery, > then you must improve her ability to do so for her to > be successful in math. Math, more than most subjects > in school, requires the use and interconnection of > several areas of the brain. You may be interested in > the following articles: > I shall with keen interest read the articles you have linked to - thanks. > >And perhaps most surprising, > scientists have established that learning and > practicing certain skills can cause the corresponding > brain areas to morph and grow. IN OTHER WORDS, BY > HELPING A CHILD HONE HER ABILITIES, YOU CAN ACTUALLY > CHANGE HER BRAIN. [my emphasis] > I believe this may be entirely correct - though the 'direct physical exploration of the brain' is, in my opinion, probably not the most fruitful route to take to understand it.
Such studies will be fruitful (IMHO) only when we have learned a good deal more about the 'brain-mind' connection (i.e., just how the 'mind' [if such an entity exists, of course] is 'associated' with the 'brain', and what may be the nature of those associations. > **************** > > One disability that is associated with difficulties > in math is a Nonverbal Learning Disorder (NLD or > NVLD). "Nonverbal" in this case means they do not > exhibit general weaknesses with language-based tasks > (although they can have some specific language > deficits); some students with NLD have highly > developed language skills, scoring up to the 99th > percentile on tests of verbal intelligence, such as > verbal portions of the WISC or the SAT. They do > relatively poorly on tests of visual-spatial skills > and nonverbal forms of communication. There is a > similar discrepancy between verbal memory and > nonverbal memory tasks. Academically, they struggle > the most with math, although sometimes their > difficulties do not show up until middle or high > school, because they are able to do well in > elementary arithmetic by using their strong verbal > memories to compensate. > > Conversely, students with dyslexia, who typically > have strong visual-spatial skills, have trouble with > arithmetic, but often do well, even very well, in > higher levels of math. > > Correlative only, but the unique combination of > strengths and deficits of these learning differences > indicate that visual-spatial skills are vital to > success in math, therefore I would absolutely > recommend helping your student to develop these > skills. I find that students who have difficulty > with mental imagery fall into one of three > categories: > > 1) Those who can and do create mental imagery but on > a subconscious level. They are verbal thinkers with > mental imagery running in the background (like > watching a movie and listening only to dialogue, then > realizing there is a beautiful scene or music in the > background). This is easy to fix - you only need to > help the student to become more aware of the mental > imagery by discussing it. (Like you noticed, Mike, > when you wrote: "I wasn't aware of the extent to > which I have subtle mental imagery until I started > tutoring and paying more attention to what I'm doing > when I solve an equation, or a tough AMC problem. It > can be below the level of easy, direct awareness, but > it is there, and it is critical.") > > 2) Those who think primarily in pictures and have > difficulty with language (Einsteinesque), especially > "translating" between words and imagery. This is a > little more difficult to remediate but again simply > discussing imagery, actively moving back and forth > between images and language ("How would you describe > that picture in words?" or "Draw a picture based on > what you are reading" or "Describe your mental > imagery after reading that paragraph" along with > "This is what that passage made me visualize", etc.) > These students often have underlying language > e weaknesses, and an observant teacher might notice > how wording of a math problem can trip them up, even > though they understand the math. I have had the > experience of simply rewording a math problem - > syntactical changes - and the student says in an > exasperated tone, "Why didn't they say it that way in > the first place?!" then solves the problem without > difficulty. > > 3) Those who have a great deal of difficulty > creating mental imagery. This is the most difficult > to remediate with perhaps more limited success > possible. These are also the students who typically > struggle the most in math. You start small and work > in tiny steps. Have the student describe something > that is very familiar - a favorite pet, their house, > a character from a show, etc. Encourage them to add > more and more detail. Move onto reading a simple > sentence, such as "The book is on the chair," asking > the student to visualize and describe the color, > form, etc., of the book and chair. Then move onto > paragraphs, initially pausing at the end of each > sentence to form mental imagery. Ask questions to > prompt recall of visual details. > > I am purposely avoiding math problems in these > exercises - I think you work your way up to math, > then hone those visualization skills beginning with > pre-algebra story problems. Algebra introduces a > level of abstraction, so I wouldn't start there. > Fascinating ideas - I shall need to study these before I comment. (I shall of course be looking at them in regard to the learning process in general). Anyway, many thanks.