Right now I have only one story written but more are to come.
Here is an entry, slightly edited, from a while back in my (fhs's) diary. At this point in the term, the students had used their calculators a bit and we'd done the difference between (20-8)/2 and 20-8/4 and the difference between 24/(2*3) and 24/2*3 and used factorials and square roots. The binomial distribution had been introduced the previous class and we were reviewing it this day.
Eleven people are on roll for my Elementary Statistics class (MATH 2670). Nine took the test on Tuesday. The scores are : 97, 91, 83, 63, 51, 47, 41, 40, 28. The 91 was made by a guy who has, I believe, attended only 2 of the previous seven classes; I don’t know what his story is. The 83 was made by a girl with about the same attendance but she’s sent me e-mail explaining that she’s caring for a sick grandmother and keeping up. The 97 was made by a girl who probably hasn’t missed a class. Only five showed up today. If I describe them by their grades, they were: 97, 51, 41, 40, 28. While attendance hasn’t been great, today’s was awful.
The grades and attendance are really preludes to a class interaction that I want to record. In my memory, nothing like this happen ten years ago and certainly not twenty. Perhaps ten years from now I can look back at his entry and say something similar to one of:
We were continuing with the binomial distribution and an approximate transcript, using the grades recorded above to indicate the speakers, is as follows:
fhs: In this problem, the probability of success, denoted by “p”, is .80. We denote the probability of failure by “q”. (fhs writes “q = 1 - p” on the board and is mentally weighing the pros and cons of doing the optional section on the Poisson distribution today. Just as an occasional reality check, he asks:) What is q?
fhs (after a period of silence making eye contact with each student allowing it): We have that the probability of success is .80 so q, which is the probability of failure, is one minus that. What is 1 - .80?
fhs (asking what appears to be an equivalent question but knowing that it more likely to get a response. While these students are not comfortable with percents, they like 80 percent a lot better than point eight zero. Also, the question is trimmed more to its essentials -- fewer steps are involved in answering): What is one minus eighty percent?
51 (brightly -- a light has just gone off in her head): seventy-nine (This is followed by a quick nervous shrug.)
fhs (I’m taken aback and think this a bizarre response. Right now, however, it is perfectly clear. While she did not solve the question that was asked, she did correctly compute, in her head, eighty percent minus one percent.) No; not 79 percent. (fhs looks around the room some more. He sees that 97 is wondering if she should answer. He rapidly looks away to say “no -- I know that you know this and the others need to learn it” and gives a small smile to say “I’m not ignoring you”. After a pause he repeats:) What is one minus eighty percent?
28 (very hesitantly): Thirty percent.
fhs (inwardly full of pride at his great patience and restraint answers in a perfectly calm manner and with a straight face): Nooo. Use your calculator. One minus eighty percent. (fhs is aware that the problem would be easier in terms of money -- most of the class could evaluate a dollar minus eighty cents but I want them to be able to evaluate "1-.80" also.)
28 (triumphantly announces -- after what seemed forever in punching in numbers): point two.
fhs (I allow myself white lies but this seems, in retrospect, out of control.): Good.
fhs: So we’ve read though the problem and picked out numbers and we’ve assigned the number .80 to the symbol “p” and we’ve computed the “q” that we need to plug in to the formula. We need the values for “n” and “k”. Assign them.
(With five people in attendance, I’m sure going to have them write in their notes -- which they ALL furiously take -- a few things that they might figure out on their own. I want to easedrop on their work and see what they are absorbing.)
fhs( speaking to 28 who is carefully straighting her stack of paper containing her class notes ): Your papers are straight enough. Do the problem.
(Mild chuckes in the class. The students know what is going on. I wait standing next to her but move on as she starts a new sheet -- carefully writting “continued” at the top. I move over to 41 to see how she’s comming. She indicates that she wants to quietly ask me a question and I lean over.)
41 (very quietly) : How did you get that answer. (She points to the board and I assume, correctly, that she is refering to “1-.80=.20”.)
fhs (quietly and thinking that 41 somehow overlooked that 28 took advantage of a technology boost): You can just do it on your calculator.
41: Yeah. But how?
Yes, I showed her how and ceased to wonder whether or not to cover the Poisson distribution today.
There is a bit more to add to the above diary entry. Yes, the students had an usually weak background but that is not why I'm sharing the diary entry. What I couldn't know when I made the entry is that 41, who didn't know how to do "1-.80" on the calculator, caught on and earned a B in the course. Also not recorded in the diary entry is that her desire to learn touched me somehow and I thought of my daughter who long ago was far away at college and, from time to time, needed a little extra help.