I’m going to do that again: Day 4 of the Blogging Challenge
Amazingly, given my current schedule, I have made it to Day 4 of the 20-day blogging challenge. This was the brain child of Kelly Hines as a way to get herself to blog more regularly. Today’s prompt was :
Share a topic/ idea from class this week. What’s one thing you did with students this week that you will (or will not) do again. Why?
I’m not teaching a course right now but I am revising the curriculum for the biostatistics course. The topics students had the most trouble with was hypothesis testing. Even though all of them had a previous course in statistics, many had it back when they were undergraduates, and let’s be honest, how much do you remember from any class you took five or six years ago?
One thing I would do differently is go back to an idea I had when I very first started teaching statistics. I noticed that some students only had a vague idea what an exponent was. A few times I got asked why I wrote that V thing next to numbers (students who had never heard of a square root). I could go on, but you get my point. Students in a GRADUATE program. It turns out you can get a degree in some fields with very, very, very little mathematics. I was teaching the first course in the statistics sequence and I started each term with a 20-item algebra test on the first day of class. It was not part of the course grade, but I told students if they did not get over 85% they were going to have great difficulty in the course. The questions were things like find A when A² = 9 or identify the coordinates of a given point on a plot.
Usually, I would have one or two students who scored below 60%. Almost always, those students dropped the class, which was, I think, for the best. HOWEVER, important point coming up here …. I did not tell them they couldn’t pass the class. I told them that it would be very much to their benefit to take a course in algebra and come back the following term. I would show them some of the problems later in the course and emphasize that they would be able to do this much, much easier later on if they went and took another math class first. Most students saw my point, dropped the class and took a prerequisite course. Even though it wasn’t an official university prerequisite, it was prerequisite information. The few students who did not knew what they were getting themselves into and planned to meet with me during office hours every single week, and allocated their time for a LOT of extra studying.
The course I am teaching now is not as basic as that one, but I do think the students could benefit by having some assessment of their understanding of basic concepts. Do you know what a z-score is? A normal curve? Percentile? Yes, I give quizzes, but I don’t mean exactly that. I mean a test of basic concepts, like what does a probability of .45 mean .
So, that is what I am ruminating on tonight. What are the absolute basics of statistics that you need to comprehend before forging ahead?
Definitions for basic words like “statistic” and “mathematics”.
Here is a wager: at least half of a given class can’t give a reasonable definition for the subject they are studying, i.e. they don’t know what they are studying.
And I don’t mean a fancy definition, I mean something as simple as “the science of using numbers to represent a situation”. They know all kinds of details about it, but they don’t know what the subject is.
(It’s just a bet, I have never been involved in teaching stats, but I have done a similar survey for Maths and found that to be the case, people unable to explain what the subject was).
@Sylvain: Funny question, more a philosophical one, don’t you think? I studied lots of mathematics, algebra, topology, geometry, mathematical physics but never numbers, they remain – at least to me – among the most mysterious (almost scary) objects. Your definition might describe engeneering and the part of physics where it is close to engeneering: but e.g. a Schrödinger-type PDE on a Hilbert space is not about numbers. Nor is the result, that a certain phenomenen carries, say, a beta-inverse distribution. Numbers in common sense (aside from their number-theoretical weirdities) are merely a bridge between observation and thought.