Model Thinking When All Models are Wrong

In the late 1970s, statistician George Box created the famous wisdom, “All models are wrong, but some are useful.” The earliest version of the sentiment comes from Box’s 1976 article, “Science and Statistics“: Since all models are wrong the scientist cannot obtain a “correct” one by excessive elaboration. On the contrary following William of Occam he should seek an economical description of natural phenomena. Just as the ability to devise simple but evocative models is the signature of the great scientist so overelaboration and overparameterization is often the mark of mediocrity. While often used to explain that statistical, and especially

Crossing the Bridge

There’s a myth that goes around that math exists in a bubble and this is just something you have to do graduate, like some sort of perverse challenge. But math does not exist in a bubble, and math professors are not trolls under the bridge taking a toll on the way to commencement. Math is a tool to analyze and understand the real world. Image by Holly Victoria Norval / Flickr.

Gelman’s Candy Weighing Demonstration

We did Andrew Gelman’s candy weighing demonstration in class on Friday. This was the first time I’ve had a chance to teach sampling in some time and really wanted to do it. These were not traditional statistics students, however. We did this in research methods. So these are students interested in management and getting drug through a statistics course. And that might be putting it nicely. Nevertheless, they were good about the experiment. We also had some slight modifications to Gelman’s procedure. First, we used the measurements (in grams) printed right on the side of the packaging. And everyone did

Syllabus for Intermediate Algebra

I am teaching intermediate algebra this spring and I wanted to post the syllabus and give a bit of a comment here. You can find the syllabus on my math education page. The course catalog gives a description: A study of problem-solving techniques in intermediate-level algebra. The goal is to demonstrate number sense and estimation skills; interpret mathematical ideas using appropriate terminology; manipulate, evaluate, and simplify real-number and algebraic expressions; and translate, solve, and interpret applied problems. Emphasis is on numbers and algebraic properties, graphing skills, and applications drawn from a variety of areas (such as finance, science, and the

Say “Yes” to the Dress

One thing I am sure my students hate is that I don’t give extra credit. I’ve talked about this before, and there is no reason to rehash them. But I do like to add something when I can use extra credit to push their boundaries, or something neat. Last semester, while teaching precalculus, Nina decided to make a dress for Ducky. She made a small math error when she first did the calculations and the results were clearly incorrect at the end. Fortunately, we caught that before she started working from them, and we got it together on round two.