The solution of mathematics problems of my students tend toward arithmetic representation and using formulas or other prescription. Mostly, the solution based on perception, so the conclusion is not logic. The main problem is that they are still not in higher order thinking, appearing when an item presented with 'not enough' information.
Perhaps you could say whether you think there is a way to tackle this issue, and what that way might be.
The answer to your question speaks of conscious perception and not just visual perception. Conscious perception relies on visual cortex, temporal lobes via prefrontal cortical processing. This is the epicenter of the mathematical brain.
Visual abilities in math concerns geometry and trigonometry. Numerous psychological studies related such abilities to spatial perception and cognition. For calculus and other advanced mathematical topics, such as quantum mechanics, spatial visualization may either be dominated or complemented by quasi-linguistic, logical processes. Higher-order thinking cannot simply rely on visualization, there are a lot of abstraction and mnemonics involved.
When mathematics problems presented visually, mostly the solutions compelled algebraically. But, what I want to explore in my research is an ability to solve the problems by 'ignoring' algebra viewpoint. That is what I calls visual manipulation to get a new one. Regarding to the Higher Order Thinking, the visual ability means considering the activity based on the smallest information and construct the others on visual representations.
Hello Mohamad,
I do not know if it would be an example of what you are talking about, but I found these very helpful for some of my own analysis. I did not watch the lecture (which I am posting), but I went through the pdfs. The idea that Dr. Simoncelli has is understanding the math you are using from a geometric perspective, which is helpful to those of us who are not mathematicians.
Sorry if this does not contribute to the discussion more.
http://www.cns.nyu.edu/~eero/math-tools17/Videos/lecture-05sep2017.html
Ted
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