Taking steps in class

I mean this literally. I got a Fitbit last year, and during the spring semester, I tracked how many steps I took during an average of 5 class sessions of each of the 3 courses that I taught.

My classes were a content-based IEP class with 13 students, a mixed-skills intermediate-level credit community college ESL class with 21 students, and an advanced ESL writing class with 25 students.

Across 5 class sessions, the average number of steps total for each class was:

  • Content-based IEP: 236
  • Intermediate CC: 626
  • Adv. writing CC: 440

Of course, since the class sessions were of different lengths, it makes sense to divide the number of steps by the number of minutes in which I had to take them.

Steps per minute of class time, including breaks:

  • Content-based IEP: 2.63 steps per minute
  • Intermediate CC: 2.78 steps per minute
  • Adv. writing CC: 1.96 steps per minute

Last, because higher numbers of students might feasibly require the teacher to move more and farther around the classroom, here are the steps per minute further divided by the numbers of enrolled students:

  • Content-based IEP: 0.20 steps per minute per enrolled student
  • Intermediate CC: 0.13 steps per minute per enrolled student
  • Adv. writing CC: 0.08 steps per minute per enrolled student

What does this tell me?

I tended to walk around more, all other things being equal, in the content-based class. I attribute this to the type of work they typically did – small group discussions in which I would move from group to group and either guide the discussion, participate as an equal, or just listen. The other two classes, at community college, usually involved at least some “lecturing”, standing relatively still or sitting at the computer and typing notes projected onto a screen.

I think my classes could benefit from structuring more lessons around small group work rather than lectures to begin with. As it turns out, a further benefit might be that it helps me reach my fitness goals.

Image result for fitbit blaze
Lecture disincentivization tool. (source)

Unfactives

As with the same class last semester, and as happens to me often, I have been spurred to blog by an unusual utterance by a student, or should I say an utterance which in its non-target-likeness highlights an interesting linguistic phenomenon.

Some verbs, like “know”, say something about the mind of the subject of the sentence as well as the mind of the sentence’s speaker. That is, if Kim says, “Eva knows that 3 students will fail the class”, not only Eva but also Kim believes that the proposition “3 students will fail the class” is true. If Kim believes that Eva is wrong about those 3 students, she will probably choose a different verb, like “believe” or “think”, because if Kim says “Eva thinks that 3 students will fail the class”, she avoids giving the impression that she agrees with Eva.

(It’s an interesting question how many clauses deep these verbs have to be before the speaker is no longer presumed to agree with the proposition. For example, if Laura thinks that Kim believes that Eva knows that 3 students will fail the class, is it implied that Laura agrees? Does the factivity of “know” leap out of its clause and infect every person in the sentence, or does one non-factive verb break the chain? I tend to think that if Laura heard a sentence like “Eva knows that 3 students will fail”, but thinks she’s wrong, she’ll change the verb to a non-factive one in relaying that information to someone else.)

As you see from my aside, these verbs are called factive. In short, they imply that the content of noun clause that follows is factual. “Know” is one of these, as are “understand”, “realize”, “prove”, and “remember”.

The error that I saw that inspired this post was the opposite: a verb being used to imply that the content of the noun clause was false, as in “deny”, “disbelieve”, and “doubt”, which all mean that the subject believes or says that the proposition that follows is false. These words, unlike factive verbs, don’t presuppose that the speaker agrees. When the newspaper says, “Dems doubt that Trump will leave willingly”, the newspaper isn’t taking the position that they are right about him. The newspaper is simply relaying the Dems’ state of mind.

(Confusingly for Japanese learners of English, “doubt”, 疑う utagau in Japanese implies that the subject has a sneaking suspicion that the proposition is true, rather than false as it is in English. Another strike against grammar-translation.)

The error that I saw used a factive verb with a negative prefix and was followed by a noun clause that the writer intended to say was false. It was something like “Many people misunderstand that the earth is flat”. The writer, as I understood it, was trying to say that many people believe that the earth is flat, but they are wrong. This left me sitting and re-reading the sentence for a few minutes as I tried to figure out just what seemed so strange about it. I did my customary COCA search and found a relative lack of noun clauses after “misunderstand” compared to “understand”, validating some of my intuition, but it didn’t give me an answer as to why.

One factor that occurred to me is that “deny”, “disbelieve”, and “doubt” still leave the proposition standing on its own two feet epistemologically. They don’t bring up the proposition and in the same breath invalidate it – they just say that the subject disagrees with it. It is still free to exist as a proposition and be believed by other subjects. It seemed perverse to me that “misunderstand” would have a noun clause following it that was presupposed even by the speaker to be false.

As I was typing this though, I remembered “disprove”, which shares with “misunderstand” a factive root and a negative prefix. To my understanding, “disprove” is a true unfactive – if I say “Einstein disproved that matter and energy are distinct”, I am also stating my agreement with Einstein. If we accept the premise that some propositions are true and others are false, the above sentence can only be true if the proposition contained in it (“matter and energy are distinct”) is false. Therefore, the combination of negative suffix with factive verb to mean “the noun clause following this verb is definitely not true” cannot be the source of the strangeness of “misunderstand that…”

Another factor may be that unlike “deny”, “disbelieve”, and “doubt”, and even “disprove”, the speaker’s and the subject’s opinions of the truth of the proposition in “misunderstand” are different. When “Trump disbelieves that” his approval ratings are low, Trump believes that the proposition is false, and the speaker doesn’t take a position on it. When “Einstein disproves that” matter and energy are distinct, Einstein and the speaker agree. However, in my student’s usage of “misunderstand”, the speaker and the subject definitely disagree. “Trump misunderstands that millions of illegals voted”, in my student’s usage, means that Trump believes it, but he is wrong. In my limited exploration of this issue, this is the only case where the speaker uses a verb to imply both that the speaker believes the proposition and that the proposition is false.

Perhaps for an unfactive verb to make sense, as “disprove” does, it has to say not only that the proposition is false, but that the subject is right that the proposition is false. Anything else is uncromulent.