I really like Willingham's take on this. I should note for the record that I refer to different ways of thinking about math when I teach my math classes (prealgebra and contest problem-solving for young elementary students), but I also assure my students that they can learn new ways of thinking from me and from one another, and end up with a larger toolkit for solving problems than they had before they started the class. I've always thought that learning styles are LEARNABLE, and that most actual human learners don't fit into one Procrustean bed or another consisting of just one learning style.

An example of a mathematics textbook series that appeals to multiple problem-solving approaches is the Singapore Primary Mathematics series

http://www.singaporemath.com/Primary_Mathematics_US_Ed_s/39....

and another is the Miquon Math series.

http://www.keypress.com/x6252.xml

Both encourage learners to look at problems from a variety of points of view.