I agree that mathematical ability builds on more than some one dimension of IQ. Same as IQ has many dimensions. I quite clearly see that in the different ways my sons are smart:
The oldest (11) has an enormous episodic and procedural memory—and uses it to solve complex tasks by combining methods.
The second enjoys operating with complex algebraic expressions mentally—he also has a very good memory for facts.
The third takes very long to deeply observe and then ultimately deeply grasp vague concepts. He also has a very good motor ability and spatial coordination.
The forth grasps symbolic concepts easily—negation at 2,5 years, reading number tables at 3 1⁄2. His language took some time but as to make up for it it is quite differentiated now.
For myself from introspection I notice that I can’t memorize iolated facts easily. Yes, presumably nobody likes rote, but I also struggle with mnemonic methods—I have difficulty forming mental mages—much less vivid and multi-aspected. Though my oldest can.
On the up-side I effortlessly absorb concepts that relate to other concepts that I possess.
Why do I tell you all these anecdotes? To illustrate the richness of the tool-box of the human brain. Not only do we come with different working memory sizes and speeds. And different types of memory. Different specialized brain areas (spatial, verbal, logical, social ‘coprocessors’). Different levels of interconnectedness of these areas. Different depth and width of pattern matching hardware. Also most of these are plastic and grow and adapt to what we encounter in life. Presumably some of these start to finally wire in late puberty or early adulthood (Giedd et al). Mathematical ability can come from lots of areas. And their combination. And training. Sure, great deep fast pattern matching goes a long way. But don’t be surprised if you are beat by some great coprocessor usage—at least in special domains.
And of course the self-image of your abilities can form before anything is decided. I used to believe that I was bad at languages in highschool. Turns out I’m above average—if I try.
I agree that mathematical ability builds on more than some one dimension of IQ. Same as IQ has many dimensions. I quite clearly see that in the different ways my sons are smart: The oldest (11) has an enormous episodic and procedural memory—and uses it to solve complex tasks by combining methods. The second enjoys operating with complex algebraic expressions mentally—he also has a very good memory for facts. The third takes very long to deeply observe and then ultimately deeply grasp vague concepts. He also has a very good motor ability and spatial coordination. The forth grasps symbolic concepts easily—negation at 2,5 years, reading number tables at 3 1⁄2. His language took some time but as to make up for it it is quite differentiated now. For myself from introspection I notice that I can’t memorize iolated facts easily. Yes, presumably nobody likes rote, but I also struggle with mnemonic methods—I have difficulty forming mental mages—much less vivid and multi-aspected. Though my oldest can. On the up-side I effortlessly absorb concepts that relate to other concepts that I possess.
Why do I tell you all these anecdotes? To illustrate the richness of the tool-box of the human brain. Not only do we come with different working memory sizes and speeds. And different types of memory. Different specialized brain areas (spatial, verbal, logical, social ‘coprocessors’). Different levels of interconnectedness of these areas. Different depth and width of pattern matching hardware. Also most of these are plastic and grow and adapt to what we encounter in life. Presumably some of these start to finally wire in late puberty or early adulthood (Giedd et al). Mathematical ability can come from lots of areas. And their combination. And training. Sure, great deep fast pattern matching goes a long way. But don’t be surprised if you are beat by some great coprocessor usage—at least in special domains.
And of course the self-image of your abilities can form before anything is decided. I used to believe that I was bad at languages in highschool. Turns out I’m above average—if I try.