From Maura:

One the challenges of teaching is the issue of keeping up with the syllabus. For some courses it’s very important to keep on track (students will be taking a common final, or they will be moving on to the next course in the sequence).  And in those situations it’s not easy to move on to new material when you know that some students are being left behind.  The best you can do is suggest tutoring or extra work (or, possibly, trying the course again later). In the QR class the “next course” in the sequence is life.  I don’t know what from this course my students will end up using after this course is over, but I’d like them to have as many tools as possible.  What this means is that I don’t worry as much if I get off track.  But I do know that there is great material in the last few chapters (on probability) and that I do want to get to that. Something else may be sacrificed along the way.

Another challenge of teaching is that sometimes you assign (or create) problems that don’t work out as you had planned.  That happened in today’s homework, where we asked students to verify the calculation of the Obamas’ 2008 income tax.  It turned out that we didn’t have enough information. When we tried the graduated tax approach, our calculation was too high.  But there are lessons here too.  One is that some problems may be too hard, even with good quantitative reasoning skills.  Another is that we don’t always have enough information to solve the problems.  But we don’t give up.  If I had looked hard enough I’m sure I could have found the actual tax return and figured out which deductions were applied.

We talked a bit about the tax problem in class, then talked about the upcoming exam.  I asked the students to tell me what they thought should be on the exam and I got a list of topics that we’ve recently covered.  I asked them how they could get insight into what Ethan and I think should be on the exam.  Some suggested the homework, or the examples in class.  Both good ideas.  I then told them that they could get real insight into what we think by reading this blog.  One students said she has been reading it lately, others pulled it up.  We’ll see if anyone comments (which would be a new way for Ethan and me to see what our students are thinking).

As for actual class work, I knew that they needed to review building linear models in Excel, graphing the models, and interpreting the information.  We spent a good 45 minutes on problem 7.7 in the book, in which they need to model three different monthly costs for cell phones.  I wanted the students to print (to see the challenges of printing and the importance of print preview when using Excel) and to use Excel to do the work.  I learned a lot by walking around and working with students.  Some converted 7.5 cents to $0.75 (but I think they all realized that 10 cents is $0.10); some did the arithmetic themselves instead of having Excel do it; some didn’t extend the data far enough to see where the lines intersected; some had trouble graphing; most had trouble printing.  It didn’t help that the print server froze several times and that we ran out of paper.

Was it worth it to slow down and review the information that I hoped they had already learned?  Absolutely.  I think they could still work on this material and could still learn more from it (although I really can’t take any more class time for it).

From Ethan:

I second Maura’s views. I knew from her class that I needed to spend more time helping the students develop Excel skills, so I did the CFL vs incandescent bulb homework exercise from scratch – starting with the observation that it was much harder than I had realized when I assigned it. I warned them that book exercises flagged [U] (for untested) might well be like that, but that life itself was [U] and more complex than it might appear …

That said, we started without Excel and without numbers and without detailed reference to the questions, looking at what the answer to the problem might look like. The basic issue is that CFLs cost more to buy but less to run, so that for little use they are more expensive but for long use they are cheaper. We could also see that as use time increased the total cost would increase a constant rate depending on the cost of a kWh of electricity. So we drew a qualitative graph like this – a picture of the kind of thing we expected Excel to draw for us.

     |                   * slope ($/hour) cost of electricity
 c   |             *
 o   |      *
 s   |* intercept ($) - cost of bulb
 t   |
     +--------------------------
                 hours

Then we built the spreadsheet, step by step, always documenting before we put in any numbers.

In particular, we worked out the entry for the CFL running for 100 hours by hand as

    $4 + 100 hours * 25 watts * 0.15 ($ / kilo watt hour)

physically replacing the “kilo” by 1000. Then we knew what to expect when we created the formula in Excel for that cell. Which we did. When it came time to copy that formula to other cells we thought through which row and column references should stay fixed, and inserted $ as needed.

We just had time for some what-if questions. Not enough time to demonstrate how recalcitrant the printer could be, but I did show them print preview so you could know after moving the chart (so that it didn’t cover the data) it would fit on the page.

Although the students were in principle following along as I built the spreadsheet from the front of the room I didn’t have a good sense that they were trying to anticipate next steps, or follow the reasons for mine. I was trying to model a process for them rather than just the solution to this problem. I don’t know how well I succeeded.

Exam next time. One student asked “how many Excel questions?” – with legitimate fright since they are time consuming. I suggested two – one like the one we just worked on, on dealing with averages and histograms.

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