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Do I have to be good at Spatial Reasoning to be good at Math?

October31

“There is much, much more to mathematics than “spatial reasoning“: I am a research mathematician with some kind of international reputation, but my inherent spatial reasoning abilities are no better than average.

I bought a bookcase a few months ago, but delayed assembling it and seem to have lost the instructions: without them, I think I would rather buy a new bookcase than worry about how to assemble the one I already have! When it comes to applying spatial reasoning to mathematics, I can see that I have to work harder than many of my peers but I can still do it: for instance, when I discuss finding volumes of revolution in calculus I can always identify a few students who can visualize the regions more easily than I can…but overall I am still better at these problems than almost any calculus student I have ever taught because (i) I have so much more experience with these problems than they do and (ii) there are aspects of solving these problems other than spatial reasoning. I think that if you want to work in certain aspects of low-dimensional topology then it is important to have strong spatial reasoning skills — sometimes I have seen talks or read papers in which proofs in these areas are done with the aid of pictures that look very confusing to me — but even here I think that other skills are just as important or more as naked spatial reasoning.” (read full discussion onĀ math.stackexchange.com)

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NCEA Level 2 Algebra Problem. Using the information given, the shaded area = 9, that is:
y(y-8) = 9 –> y.y – 8y – 9 =0
–> (y-9)(y+1) = 0, therefore y = 9 (can’t have a distance of – 1 for the other solution for y)
Using the top and bottom of the rectangle,
x = (y-8)(y+2) = (9-8)(9+2) = 11
but, the left side = (x-4) = 11-4 = 7, but rhs = y+? = 9+?, which is greater than the value of the opp. side??
[I think that the left had side was a mistake and should have read (x+4)?]

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