Thinking & Problem Solving

In pondering the possible relations between inventive thought in mathematics and bodily phenomena, the mathematician Jacques Hadamard (1865-1963) sounded a note of despair in his 1945 book The Psychology of Invention in the Mathematical Field. "While mathematicians have not sufficient...

Dr. William Newsome is sitting at his PC computer grumbling. "Do you know what IBM stands for?" Newsome asks in a slight Southern drawl. "It stands for 'I'm Building a Mac'," he quips, displaying quick-witted charm and ardent loyalty to...

A young woman sits in front of a computer, joystick in hand. On the screen in front of her is a large circular pool of water, which she "wades" through by moving the joystick. She is attempting to find a...

"Can you see in the still-life here on the table that the orange is in front of the vase?" "Yes," replied the student, "I see that." "Well," I said, "in your drawing, you have the orange and the vase occupying...

Educators often worry that some students just don't "get" math. In truth, some fundamental difficulties with math may be indicators of mild dyscalculia, or "number blindness." It's hard to imagine an aspect of daily life that is not touched by...