This is a 50-frame animation of an increasing iteration number for a scalloped convergence Mandelbrot set.

# Improving Fraction Teaching with a Game: FRAX!

This post is the second on the game *FRAX* and spends some time explaining how the game works and where it came from. The first post was on Occupy Math’s sister blog Dan and Andrew’s Game Place. FRAX seems, based on our initial testing, to be a fun game in addition to giving the players practice with fraction arithmetic. To get the rules to FRAX (and if you’re interested in testing the game), click the link! We are giving away FRAX sets to people who will help us with the play testing. FRAX is a card game, not a computer game, though we have some thoughts in that direction.

# Image of the Week #74

Another scalloped Mandelbrot set — this time with a more vigorous set of collors!

# Tricking Yourself into Being Bad at Math

Occupy Math has already written on the issue of thinking you’re not a math person and this week’s post examines the issue from another perspective: the value of hard work. If you want to be good at hockey or baseball, you go in knowing you’re going to have to practice. Contrast that with the way most people believe that either you can do math or you can’t. The academic tradition in Asia contains a strong belief that working on an academic subject makes you better at that subject. Americans — on average — *only* believe this about sports. This goes a long way to explaining why Chinese students are ranked top in math and Americans are in the bottom half.

# Image of the Week #73

This one is a scalloped convergence Mandelbrot set on a fairly deep zoom. Later I may move into the central sun and see what’s there. The black tentacles at the edge are a bit Lovecraftian?

# Why are we Requiring Teachers to do a Bad Job?

This week’s Occupy Math is on a familiar topic, the effective teaching of math, but it was sparked by a number of recent media reports on *why* students in Occupy Math’s part of Canada are doing worse into the teeth of increased spending and emphasis on math. The problem has two parts. The first is the elementary teachers are not required to learn math themselves and are often afraid of it. The second is they are being handed a teaching strategy that cannot work and then getting no help trying to make it work. This is a big multi-part problem and Occupy Math hopes we can all dive in and help.

# Image of the Week #72

This is a dual Julia set done with a palette that changes color fairly quickly.

# Occupy Math announces a book by Eun-Youn Kim

This week in Occupy Math, we proudly announce a book published by Dr. Eun-Youn Kim, *On the Design of Game-Playing Agents*. This book gathers, summarizes, and extends work on how much the way you choose to represent software agents in your code changes their behavior. This is a research project that has lasted a decade and is still going strong. The original publication suggested there are problems with thousands of published papers (they did not control for the factor “how were the agents coded?”) and, in the intervening decade, Dr. Kim, Occupy Math, and a dozen collaborators have drilled deeper into this discovery, finding many more factors that need control. Frankly, while this is high-impact work, its also a wonderful illustration of the way mathematicians end up cleaning up after other researchers and putting their work on a firmer foundation. To be clear — this is a huge clean-up and it addresses some serious problems.

Occupy Math will set some context by explaining the big story that Dr. Kim’s work covers. The original discovery was that experiments that were modeling cooperation completely changed their outcome when we changed the type of code learning to cooperate. One encoding, called a finite state machine, learned to cooperate quickly. Another, called an artificial neural net, almost never cooperated. A large number of published papers did not consider the choice of agent encoding at all — they just picked an encoding. Initial reaction to the work was somewhat extreme — denial and some attempts to ignore the work. After that the good researchers took Dr. Kim’s result on board and the smart ones noticed that it meant they got to publish their work again in a new, improved form. In the rest of the post, an interview with Dr. Kim and a few thoughts on the impact of the work.

# Image of the Week #71

This is an intriguing line of minibrots in the fourth-power Mandelbrot set. A little like butterflys, but not really.

# What Do Math Graduate Students Do?

This week’s post takes a look at the most usual way that you can become a professional mathematician: going to graduate school. The first university degree in mathematics gets you ready for a lot, working for a bank, starting up the ladder of the actuarial profession, or becoming a codebreaker for the military. Because the advanced reasoning skills are useful, you can usually find employment as a system administrator or as a manager of some sort. Someone who has been trained in mathematics gets an edge in many careers. This post is about moving on to the level where your job is to invent new mathematics.