AoPS recently interviewed me about my thoughts on math education and math contests. I shared a number of unconventional ideas around math education, including:
Math isn’t always fun. Learning often feels awkward and uncomfortable. If our mantra is “Learning is Fun!” what message do we send, when it clearly isn’t?
Using math creatively means students need to know why their algorithms work. Otherwise, it’s like telling a student how use red paint or blue paint, but never showing them how they combine to make purple.
Studying a math curriculum without participating in a contest is like going to soccer practice every day without ever playing a game.
Math contest rules are not the boss of you.
Normalize frustration. Did I mention that learning isn’t fun?
Call a three-term strictly increasing arithmetic sequence of integers special if the sum of the squares of the three terms equals the product of the middle term and the square of the common difference. Find the sum of the third terms of all special sequences.
Find the number of ways identical coins can be separated into three nonempty piles so that there are fewer coins in the first pile than in the second pile and fewer coins in the second pile than the third pile.
Circles and intersect at points and . Line is tangent to and at and , respectively, with line closer to point than to . Circle passes through and intersecting again at and intersecting again at . The three points and are collinear, and . Find .
Centered at each lattice point in the coordinate plane are a circle with radius 1/10 and a square with sides of length 1/5 whose sides are parallel to the coordinate axes. The line segment from (0,0) and (1001, 429) intersects m of the squares and n of the circles. Find m+n.