I couldn't dream up a math problem for you.. I think that's hurting me explanation here. Let me try again.
X^2 - 25 = 0
<> chemistry/cookbook style learning... The Ti challenged would memorize that when we see a problem like this, we root the number and put it into (x + _ ) ( x - __) bubbles. Very visual style... But no real mathuition or logic is helping us really "learn math"
<> mathuition style ...root that number... Cancel the middle..
oof: ... answer!
<> logic based...
X^2 - 25 = 0
it must follow that if we add 25 to both sides, that we haven't changed the fundamental problem. It's analytically equivalent
x^2 = 25
It must follow that if we root both sides, that we haven't changed the fundamental problem. It's by definition still an equivalent problem
x = 5 and -5 there is no other possibility! No mathuition!
Have I butchered and shoehorned this example to fit my opinion? Absolutely. What do you expect from an F?
I really just wanted to communicate a potential way of seeing how some people get throu math, but never really learn it even with a normal IQ. Poor mathuition and no logic is a problem when cook book math stops being acceptable!