"I took statistics in high school," said one luminary, "And this course is below level."

So there I was, reading this stuff in Section 1 of Week 1 of Stat 2.1, knowing what lay ahead ... which was correlation and regression in Stat 2.1, and now Week 1 of Stat 2.2.

"My God that was hard" read a post today, joining a week-long chorus of "difficult," "very hard," and so on. Some of the students who say it's hard also say they did get the material in the end, but others remain all at sea.

Happens every time in intro stat on campus too, to some extent. Elementary probability theory, before the introduction of the binomial and other formulas, becomes a weapon of mass destruction.

The reason is clear: the combination of logic and the detailed attention to language and assumptions becomes too much for many people. That kind of use of the brain can be considerably harder than computation, which is minimal at this stage of 2.2X: there are only sums and products of a few fractions. But there's no "standard machine" into which you can throw things, crank a handle, and expect a correct answer. You have to develop your own little machine each time. I tried to say this in one of the lectures, and gave the closest thing I've got to a "step by step" approach to problem solving at this level. But then the students have to actually go through the process,

*slowly.*

And that's one of the two key difficulties with this material. The examples look easy: who can't add and multiply a couple of fractions? It should be quick, right? But it isn't. It takes a while to come up with the perfect little sum and product of fractions. Students don't expect it will take that kind of time to get to answers that look so simple.

The other problem is sloppiness in reading and in the use of language. That's disastrous with this material: whether two events must both happen, or you're already given that one of them has happened, or you want either to happen, or you want just one of them to happen ... the list of variations is endless and every word matters. A single wrongly read word, and you can be led far astray. Students don't expect that, either.

The problem with language is increasingly visible among students whose normal discourse relies on, "He was like, 'OMG!'" or "I was all, 'Whatever.'" But I don't see a large fraction of these in 2.2X. What we do have is an international community: lots of people who hardly use English at all outside of this class. For them, the persnicketiness of having to watch every small word can be a torment.

I've learned this the hard way. I was teaching an upper division (calculus prerequisite) probability class once; we were well into the semester and the class and I had a great rapport. I was doing a simple little thing with one card, the "2 of clubs," and getting mightily annoyed that the class was being dull about something so easy. The glazed fish-eye look stared back at me from a hundred people. Eventually, the problem was identified. The majority of the class consisted of students who were not native speakers of English. They didn't think the word "of" mattered; it was some little piece of decoration, in their minds, while the essence of the information was "2 clubs". So they were thinking about two cards, and I was thinking about one particular card, and thus there was discord and a gnashing of teeth.

I only use the jack of clubs, now.

2.2X will get more "machine"y. There will be more instantly recognizable techniques. It's already happening: a couple of people have written in saying they've aced Week 2 exercises. Weeks 3-5 will bring to mind Weeks 3-5 of 2.1X, with estimates, measures of error, and the normal curve. Students will be fine.

But I know I'll lose some students before then. I'm telling them to hang on, but students tend not to believe faculty when we say things like that. If Week 1 is hard, then Week 4 will be 4 times as hard. Isn't everything linear?

Maybe the next Exercise Set should include this test:

Henry the Eighth had six wives. How many wives did Henry the Fourth have?

He had 2 wives but then these were independent and mutually exclusive events (in relation to Henry the 8ths wives).

ReplyDeleteI love your insights about the topic of probability - how there is no single machine and how important language is. I identify greatly. Week 1 of stat2.2 was certainly harder than stat2.1, but I loved the challenge! And 2 submissions on a question allowed me to revisit the question, reexamine the language of it and figure out the answer. It was a greater challenge, and I aced it! :) Stuff like this makes statistics a lot more fun and a lot less dry, if I may say that!

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