Last week Occupy Math looked with deep skepticism at standardized tests. This week, a related problem: are our math tests — from in class to the scholastic aptitude tests (SATs) — testing math or something else like language proficiency? Occupy Math thanks Catherine Emerson for pointing to this topic and Peter Ashlock for serving as Occupy Math’s research staff on this one. The key point is this.
Math tests often test language proficiency and cultural norms, not math.
This week we return to the more general Newton’s method fractals. This one is gold and satin with a few other colors.
Occupy Math is writing this week as a break from grading the initial homework turned in by his first-year calculus students. These students are not stupid – this is a group that self-selected to take the much harder course that Occupy Math runs. In spite of this, Occupy Math had to grade nine papers to find a paper that gets a passing grade. This happens every year like clockwork. The problem is not the students; they are just the ones that are paying the price. What is going on?
- The students have not had much graded homework before, because their teachers are given too many classes to teach and not enough time for prep or grading.
- Most of the students have never had a math class. Instead they have been taught to look for a template and apply it, effectively math as ritual magic. No thinking about the problem, no asking if their answer makes sense, no practice with problem solving.
- The math curriculum the teachers are asked to present is badly designed and poorly presented because it is created by people that are both out of touch with mathematics and steeped, nay marinated in useless jargon. Here’s an example.
- The goal of the curriculum these students were subjected to was not the teaching of mathematics. It was Pavlovian conditioning to get better scores on (useless, more on that below) standardized tests.
Current math education in many high schools produces failing university students.
Another Newton biomorph. This one has lots of small daughter biomorphs.
Today’s edition of Occupy Math looks into cooperation and conflict – from a mathematical point of view. Occupy Math has published more than thirty scientific papers on a tool for modeling cooperation and conflict called the iterated prisoner’s dilemma. The big news in this edition of Occupy Math is that many published papers on the prisoner’s dilemma completely ignored a factor that controls their results. Let’s begin by understanding Prisoner’s Dilemma. It is based on the following story.
Two suspects are caught by a sheriff. She has them cold for trespassing, but she want to convict them of armed robbery — which she is pretty sure they committed. She puts the suspects in separate rooms and offers them a deal — leniency for testimony. Each suspect can cooperate with his partner (stay silent) or defect against his partner (squeal on him).
Another Newton’s method filigree fractal. Happy Monday!
A common complaint about math is that “it has nothing to do with my life”. In this week’s post we will look at the way math lets you understand what’s actually happening. Math not only has everything to do with your life, it can have a lot to do with your misery and death if you ignore it. Math can be used to build policy that might work, as opposed to policy that accomplishes the opposite of its goals.
Today in Occupy Math, climate change, teen pregnancy, and violent crime.
Going back to the Newton’s method fractals, but this time trying for a biomorph. These are fractals that look like they might be biological. Enjoy!
Occupy Math has raised the issue of mathematical humor from time to time. In this week’s blog, by request, there are nothing but jokes. There are 20 jokes here – keep track of how many you get and that is your Mathemagician Rating. Mathematicians use words a little differently from other people. That leads to the following sort of joke.
☆ Do you know what’s odd? Every other number.
☆ The obtuse triangle is upset because it’s never right.
Continuing with the Newton/Julia blend with stretched quadrant convergence pioneered by Mandy Saunders. Another botanical fractal.