I loved drawing as a kid. A recent "aha!" was realizing how similar the process of good drawing is to good learning -- they depend on recognizing and mastering underlying structures. My philosophy in 3 words:
Pencil, then ink.… Read article
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Does .999… = 1? The question invites the curiosity of students and the ire of pedants. A famous joke illustrates my point:
A man is lost at sea in a hot air balloon. He sees a lighthouse approaching in the … Read article
So many math courses jump into limits, infinitesimals and Very Small Numbers (TM) without any context. But why do we care?
Math helps us model the world. We can break a complex idea (a wiggly curve) into simpler parts (rectangles):… Read article
I’ve struggled with how to write about calculus. The standard techniques seem to be:
Puzzles can help develop your intuition -- figuring how to navigate a grid helped me understand combinations and permutations.
Suppose you're on a 4 × 6 grid, and want to go from the bottom left to the top right. How… Read article
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Frustrated with rote definitions?… Read article I was too -- until I started looking for the intuition behind each concept.
Math, BetterExplained condenses a dozen math concepts into clear, The Monty Hall problem is a counter-intuitive statistics puzzle:
Integrals are often described as finding the “area under the curve”. This description is misleading, like saying multiplication is for finding “the area of a rectangle”. Finding area is a useful application… Read article, but not the purpose. Integrals help us
Counting isn’t easy. Suppose your boss wants you to work from 8am to 11am, and mop floors 8 to 11. Simple – it’s one floor per hour, right?
Nope! There are 4 floors to mop (8, 9, 10 and 11)… Read article
