I started with this informal anonymous survey about the course so far, and percentage computations in particular (results shown):
1 — Knew it all before
4 — Learned something new
3 — Now it makes sense
3 — Still confused
0 — Lost
So most of the class is pretty much on track. (Perhaps the few students who came in late were ones who would have put themselves in one of the last two categories. )
Before class I revised the on line syllabus, moving the discussion of Chapters 4 and 5 into the vacant places I’d left for the next week or two – I am behind where I optimistically hoped to be, but not surprised, and glad I anticipated the slowdown.
I spent almost all of the rest of the class working Exercise 2.12 on Goldman Sachs bonuses (I promised that on Tuesday). I knew that the difficulty was in reading the words around the numbers more than in the manipulations themselves. I was surprised at how important just plain vocabulary problems were. In particular, some students thought “consistent” meant “the same from year to year” (which Goldman Sachs’ data aren’t) and not (when applied to numbers) something like “fit together the way they should”. Later some people didn’t quite grasp that “salaries plus bonuses”, “compensation” and “what GS paid employees” were all referring to the same quantity.
The same kind of problem came up in a previous class about the meaning of “wholesale.” Since I can’t anticipate all the words students might not know (both in the course and after they leave) I hope I’ve convinced them that they can’t make sense of paragraphs with numbers in them unless they check out the meanings of words they’re unsure of. That said, I will try not to use fancy ones too often.
One student called the need to think about both the words and the numbers a perfect storm. I hope not.
Reading the newspaper extract carefully, we could construct a table for four numbers: revenue and compensation for each of 2008 and 2009. We filled it in with two numbers we were told, and noted three percentages that expressed relationships between pairs of those numbers.
The first was between two known entries, so we could check it (That was the first question, on “consistency”.) Then we used the other two percentages to fill in the other two places in the table. One computation called for dividing by 1+(percent change), the other for dividing by (percent). We figured that out by thinking about the meanings, not by trying to remember.
All along I was loudly philosophical about the worthlessness of teaching them to solve carefully constructed problems – a skill they’d never need after the course was over. Perhaps too loudly. Maybe I’d be more convincing if I just let the problems speak for themselves.
In the four minutes remaining I started on unit computations – just rate X time = distance.
So far one student has commented on this blog. The comment appears on the feedback page. When I get a little spare time (hah!) I will figure out how to make them appear here.
Notes later. When I described today’s class to my highly educated wife at dinner time, she said she’d have had the same trouble as some of the students with the meaning I attached to “consistent”. She did agree after we looked it up in our (hard copy) dictionary that I’d used it correctly – but that it was unreasonable of me to assume the class would have been able to. She suggested I bring a dictionary to class, and a thesaurus too. I pointed out that we already have a dictionary in class – on line -and that we should have used it right then and there. At dictionary.com the first meaning is
- agreeing or accordant; compatible; not self-contradictory: His views and actions are consistent.
which would have cleared things up right away – particularly “not self-contradictory”.
Tomorrow I will add this discussion to the instructor’s manual for Common Sense.
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