A Road to Writing

As you may recall, the “mission statement” for the class is that each student will:

  • Learn to make effective and valid arguments using data
  • Become a critical consumer of data

Along about the beginning of November, we had been doing some problem sets from The Model Shop, and other activities from Data in Depth, and I had been getting laconic answers like “four” and “0.87%” and really wanted a little more meat. That is, getting the right answer is not the same as making an effective argument, or even telling a decent story. In a flash of d’oh! inspiration I realized that if I wanted it, I should assess it.

But there is a problem with that:  I have been constructing my standards (I’m calling then learning goals) as I go along, and had not figured out how to deal with the larger, mushier issues that are part of making valid and effective arguments using data.

This post is all about an at-least-partially-successful resolution.

Constructing learning Goals for Larger Pieces of Work

I love the kids in this class partly because they let me get away with, “this is a quiz and I want you to do your best but I really don’t know how to express the learning goals (a.k.a. standards) that go with it. So we’ll take the quiz first, OK? And figure out how to grade it later.” I explained to them what I was after in hand-wavey terms and off they went.

So they took the quiz (described later). Using their responses (and the pathologies therein),  I was able to construct learning goals for this kind of writing, in particular, for the final semester project I alluded to in the last couple of posts. And here they are, quoted, as if they were official or something (we start with Learning Goal 17):

17 Project: Clear and Concise

  • 17.1 Sentence-level good style. Crisp. Active.
  • 17.2 Good paragraph structure and length

18 Project: Organization

  • 18.1 Ideas presented in a good order
  • 18.2 Suitable introduction and conclusion
  • 18.3 Appropriate reinforcement without redundancy

19 Project: Logic and Reason

  • 19.1 Reason for the project makes sense
    • You set out reasons (probably in the first paragraph, or nearby) why we should care about the topic and the background. And the facts are right.
  • 19.2 Conclusions within the project make sense and follow from the data
  • 19.3 Suitable attention to alternative conclusions
    • If there is an alternative way to interpret a graph, one that stands your argument on its head, you better mention it
  • 19.4 Comparisons support the ongoing argument
    • example: if you’re arguing that Martians are taking over management jobs, it helps to show that the people who had the management jobs before are losing them.
  • 19.5 Care in assigning cause and effect
    • Don’t claim that you have proven that A causes B unless you really have. We have not yet covered the situations in which that’s possible!

20 Project: Mechanics

  • 20.1 Spelling
  • 20.2 Usage
  • 20.3 Headings support the project’s organization
  • 20.4 References to graphics work properly (in the graph below, …)

21 Project: Graphics and Analysis

  • 21.1 Graphs present where appropriate
  • 21.2 Mean what they claim to mean
  • 21.3 Good choice of graph types
  • 21.4 Good choice of sample size and use
  • 21.5 Correct calculations

22 Project: Data Wrangling

  • 22.1 Appropriate choice of data
  • 22.2 Cleaning data
  • 22.3 New attributes where necessary, correctly defined
  • 22.4 Appropriate filter & Baldocchi use
  • 22.5 Filters do what they say

23 Project: Dig Deeper

  • 23.1 Interesting and sensible extensions
  • 23.2 Asking and answering follow-up questions
  • 23.3 Asking questions for future investigation

Some of these terms will be mysterious if you weren’t there (for example: A forward Baldocchi is where you copy the data you want to study and paste it into a new dataset in order to work on it; a reverse Baldocchi is where you delete the data you don’t want to work on). And you may want other things than I do (my wife asked, “did you ask them to include a methods section?” No, I didn’t. But you might want one). And hooray, when they did the final projects, I was actually able to assess the projects based on these goals.

Furthermore, I can totally imagine somebody saying, next semester, “I got a two on mechanics; can I get a redo?” And have that make sense. I can ask what they’ve done to remediate, and find an upcoming task (including next semester’s project) in which they can demonstrate that they’ve fixed the spelling or usage or whatever problem gave them the two on LG20.

#19, Logic and Reason will be trickier, but we’ll see how I manage it.

The Quiz

Let’s look at the quiz that gave me the fodder I needed for those learning goals.

heating water graph
"Heating water" graph for the quiz

The data are about heating water. Students get a data set with temperature readings for a pot of water heating on my stove, with times. They plot temperature against time, add a line, make a residual plot, and interpret it. The graph appears at right.

Before the quiz, students had seen the underlying data twice before, first as in-class work, then as homework, as we learned about residuals. We also had a class discussion about boiling water. So there was as little confusion about the actual content as possible: it was all about writing it up.

Here is the quiz itself. If I did it right, you can click the link to see it full-sized.

And now, two examples of (redacted) student work that show both good thinking and enduring problems:

One tech thing that’s cool: everybody has learned to put the graphics in with the text. This seems such a small thing, but I think it makes a difference in how the kids see the work. It becomes more “like an article” than “like math,” and that supports the mission I mentioned 1000 words ago.

Also, you’ll see my comments in the PDFs. Now, fellow teachers, do the students actually read and process these comments? Not always. Maybe even “seldom.” I’m not sure what to do about that except to try really hard not to give up on writing them.

Final tech note: One aspect of the “best case” part of my job: yes, I really can now insist on pdf files when I need them. I insert the comments and email them back to the students. Now we both have copies of the original and the comments. It’s really important for me that I keep comments instead of handing back the only copy, because I find I need to refer back to the details of what I was thinking as I look back over a student’s body of work.



Published by

Tim Erickson

Math-science ed freelancer and sometime math teacher. In 2014–15, at Mills College in Oakland, California.

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