My exams are scheduled for this Thursday and Friday and suddenly—quite, quite suddenly—my office hours are filled with activity. In a hurry today.
Perhaps you, my dear readers, can help me. I have been approached by the leader of the math tutoring squad (for the second time) with the complaint that my introductory classes are so hard, that even the tutors cannot figure out what I am asking in my homework. Here is a question that was said to be the extremely difficult:
I teach a class called Statistics 101. There are 36 students signed up for this class. Before I come to class each day, I guess how many students will actually show up (I know you will be shocked, but some people actually miss class!). Obviously, I do not know for certain, the exact number. How do I express my uncertainty in this number? What is everything that can happen in this case? Which probability distribution would best represent my uncertainty?
Understand that this comes in a chapter which describes the binomial distribution and how to work it. It also comes after several lectures in which I describe—endlessly, to my mind—how to recognize a binomial, how to set it up, and how to calculate it.
The answers are, in this order: Using a probability distribution; 0 students show, 1 student shows, 2 students show, …, 36 students show; binomial distribution.
This question flummoxed many great minds, so perhaps it is I that am at fault. Can you suggest ways in which I might lighten the load of my students?
Before you answer, consider that one complaint about that question was that, “I couldn’t figure out how to calculate the answer.” It is so that there is nothing in this problem that needs calculating; but it is also true that I later offer questions solely for the enjoyment of those who like plugging numbers into binomial equations.
I told the tutoring chief that I ask questions like this because this question is just like the way problems come at you in real life: you do not know which distribution to use, you have to infer it. I admitted that this was more difficult that in other statistics classes.
For my Algebra Sans Algebra class, the most frequent complaint is that I do not allow calculators. But I also do not require exact calculations. If the answer works out to be, say, 2304/3208, then all the student need do is to write “2304/3208” and leave it like that.
Nearly every single time we do arrive at an answer like this, I get the questions, “But is that the way you want us to write it on the test?”, “If we don’t have calculators, how can we figure it out?”, and “Can we leave it like that?” Every time—and I am using the exact definition of the word every—I tell them, “Leave it like that. Or simplify if you can.”
I frequently tell them that anybody can plug that kind of number into a calculator, and that what is important is that they arrive at the right answer, or the right form of the answer. Understanding why the answer is what it is is vastly more important than figuring it out to the third decimal.
Now, I think I would be have been OK, except that I sometimes—for fun—offer methods that allow approximation of answers. These methods do not use calculators. They involve such things as writing numbers in scientific notation, using logarithms, finding answers to the nearest order of magnitude, and such forth. I say not only do you not need a calculator, but you are learning more math this way.
But this approach, I am told, is confusing. “Do they need a calculator or don’t they?” is what I was asked, yet again, today. Apparently, my explicit statement, in the syllabus and often in class, “No calculators are allowed” is insufficient.
Since this is not the first time this complaint has arisen, I am obviously at fault for not making my wishes clear. Can anybody suggest a way that I might let students know that calculators are not allowed, nor needed?
After the exams, I’ll post the questions I asked in Statistics so you all can see how difficult they are.
Update: I have taught the introductory statistics course many times, including three other times at this very university. I have not changed the course, but I have never had as much difficulty as I am having this time. One reason might be that the university where I am visiting has a record enrollment. They even ran out of room at the dormitories.