From Maura
Reading Ethan’s post I was reminded of something a friend (poet/archivist) told me years ago. He said that the Japanese haiku writers would write their poems and then throw them into the river. The idea was that the act of writing the poem was itself sufficient, and whether any one read it or not didn’t matter. I’m not as “zen” as they must have been, for like Ethan I also wonder (and hope) that people out there are reading this. But if not, at least it is helping me to reflect on what I am learning as I teach.
In class I decided to start from the beginning and asked the students to tell me everything they could remember about linear functions. We eventually got to slope, intercept, y = mx + b and then we did a couple of examples. I asked them to graph the functions by hand (something like y = 2x+3) and was surprised at the difficulty they had with it. We talked a bit about the significance of the slope and the intercept and what they mean geometrically. Then I showed them how to use Excel to do most of the work, using the $ to fix the reference to slope. I think they found it to be a lot of work but in the end pretty cool. And it is cool that once we set it up, we can change the slope and the intercept and Excel updates everything immediately.
Then we looked at the Tamworth example and talked about how an electricity bill is an example of a linear function. Here the slope and intercept have concrete meanings and I highlighted that. I talked a bit about energy and power, but only to make the distinction between watt and watt-hour. As our last example, we worked through the cost of leaving a 60-watt light bulb on for a year with the assumption that electricity costs 20 cents per kiloWatt-hour. As a side note: I am fairly sure that these light bulbs will no longer be manufactured/sold in the US and that we are all supposed to use compact fluorescent or other bulbs. The wattage is unusual here – for example, I see many compact fluorescent bulbs listed as 13-watts; the packaging also talks about lumens. There are lots of claims about these bulbs and it would be a good QR project to try to validate some of them.
From Ethan
First class after break. It feels a little like starting from scratch. Homework 5 was due before break; most of it didn’t come in until today. Homework 6 was assigned before break, but few people started it. It’s due Thursday.
Nevertheless, I decided to move on – to linear models, via electricity bills. This time I made sure to make explicit the difference between energy and power. Or at least to try. It’s hard. But the attempt was worthwhile.
What’s energy? Something that’s used up doing work (note – no wish at all to define “work”. This isn’t a physics course) . Where does energy come from? There’s some in food – measured in calories. There’s some in gasoline, so that your car can go. Some comes over wires into your house to create light there (I needed that biblical phrase to avoid the confusing “power a light bulb” – power is something else again!)
How did the energy get into the gasoline? I was surprised that no one seemed to know, or if they knew, wouldn’t risk saying. One student suggested “made by the earth”. Another thought perhaps “made by fossils”. That’s because the phrase “fossil fuel” had some resonance. Many thought “fossil” meant simply “old”. So I did a little riff on decaying ancient organisms that had stored energy originally from the sun. I didn’t even begin to imagine describing how the sun produced energy!
Switch to something more practical. Where do you hear the word “watt”? 100 watt light bulb. How much energy does it use? None if it’s turned off, so the amount depends on how long it’s on for. It follows more or less convincingly (often less) that energy can be measured in watt-hours. We then computed how much energy it would take to keep a 100 watt bulb on for a year. To estimate the cost we used $0.10 per kilowatt hour.
Then we read the Tamworth bill, saw that the computations followed the same pattern for car rental and cell phone bills:
fixed cost + (amount used)*(rate)
and connected that to hated algebra:
y = b + x*m
(not, in this case, y = mx+b, even though they are mathematically the same). Worked on the meaning in each case of slope and intercept.
We studied the Tamworth electric bill spreadsheet – a scatterplot, not a line chart. Relearned using $ in a cell reference to prevent Excel autoincrement. Watched Excel automatically rescale the y axis, so that the graph looked the same when we doubled the slope. Interesting puzzle turned up when I tried to force Excel to extend the x axis by asking about the bill for 1000 kwh. The x axis didn’t change, so the big data point never appeared. Excel did change the y axis to accommodate the new large value, so the line was nearly flat, rising slowly to its proper height somewhere in the next room off to the right. I should have done an estimate about how far away that would be.
I think this was a class that I enjoyed much more than the students. Next time I shouldn’t talk so much.
I do wonder whether anyone reads this blog (other than Maura, who contributes half of it).
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