Have you ever seen a movie for the 2nd time and wondered how in the world you missed all of "those things" the first time? That's kind of what I feel like today. My poor students! If any of them get a 3 it will only be by the grace of God. Before this week I was thinking that it was possible for a few of them to do well. Now, I only hope for 1 because she scoured 5 steps to a 5 and really worked. She may be one of those that could get credit by just studying on her own. Anyway, I digress. I'm dreading Sunday but looking forward to the improvement that my students next year are SURE to make!
Today's take-aways are:
1) "The lottery is a tax on people who can't do math" Michael Legacy. I LOVE this quote! I was so entertained by it.
2) Begin to lay the ground work for hypothesis testing all year long with vocabulary but especially in probability. Ask, "How likely is it, given _______, that we will see _______________".
3) Use different ways to randomize, the hat method, a random number generator, a random number table, so that the students are familiar with them all.
4) Use this applet from Rice University to demonstrate the Central Limit Theorem. The population is in black and the sampling distribution is in blue. You can refer back to the "black" and "blue" distributions when teaching Inferencing and the students will know what you are talking about.
5) ML did a great job of explaining degrees of freedom, which I have personally struggled with learning - much less teaching. I have basically just said, do it because it's a rule. He explained that if you use a grade analogy you can build understanding. It's not the statistical definition of degrees of freedom but it does make me say, Oh! He started by listing 6 week grades on a report card. Suppose the first 6 weeks a student makes an 80 in the course and the next 6 weeks he tanks thinking that he doesn't have to study because he did so well during the 1st 6 weeks and makes a 60. The third 6 weeks rolls around and he rebounds to a 65. If he wants to keep his parents off his back, the question he wants to know is, what does he need to make on the semester exam to pass? ML assumed that all 4 grades are equally weighted for simplicity. He said that once the mean is set, the exam grade is not free to be anything except the number that would average with the others to yield a 70. I thought it was a great explanation of why degrees of freedom is always n-1 for 1 variable. Of course when you start inferencing for regressions you have to account for 2 variables so the degrees of freedom is n-2.
6) After that ah-ha moment, we spent the rest of the day covering details that I didn't know to tell my students to avoid. For example, students must be sure to use the future tense when referring to a population because using past tense refers to the sample. I also didn't know that a graph was necessary when checking for normality on a small sample means problem.
At any rate, I'm hoping for more 2's than 1's this year and for someone to pass next. Baby steps! I really love teaching this class and I know I've said it before but I'm REALLY thankful that I found more Stats teachers to ask questions! One more day to go...