Josh's I-RISE presentation

This presentation was given on July 6, 2012.  It was about "representations as records of sense-making."  Representations -- including diagrams and energy theater -- can be records of student thought processes in at least two ways.  First, it may be that we can deduce student thought processes from the representations they produce.  Second, representations may record some aspects of student thinking but not others.  Rachel brought up the example of a frisbee game played in a muddy field.  The footprints are a record of the game, though not a very good record.  (They allow us to know, for instance, the location and spatial extent of the game, but we cannot reconstruct the identities of the players.)

I presented an outline of the talk.  I would begin by discussing my own background as a researcher.  Then I would show some diagrams constructed by the I-RISE teachers when they presented whiteboard depictions of energy theater.  Next, I would describe some mental models I use to explain how they constructed these representations.  (These models are highly speculative and a priori, although one of them -- the exposition model -- appears frequently in the data.)  Finally, I would show video of the teachers constructing the representations.

I have always been interested in physics and math, which ultimately led me to be interested in how students connect these two disciplines by constructing representations.  However, my PhD was not in PER.  I studied theoretical quantum computing and completed my PhD in radio astronomy.  (I worked with the SETI@home project.)

I have worked in PER as a postdoctoral researcher at Kansas State University.  At KSU, I have studied students use of Riemann sums (the "layers" framework) and infinitesimals in a physics context.  In order to better assess students' knowledge, I have often asked them to produce multiple representations, including graphical, diagrammatic, and symbolic representations.

Here is a picture of some teachers' representation of the energy transfers for a hand pushing a car.  They drew this whiteboard after performing the corresponding energy theater.

Here is a picture of some teachers' representation of the energy transfers for a cooling coffee cup. They drew this whiteboard after performing the corresponding energy theater.

Here is a picture of some other teachers' representation of the energy transfers for a cooling coffee cup.  (As part of the same exercise.)

How could we model the thought processes by which the teachers constructed these diagrams?  I claimed (somewhat tongue in cheek) that I knew the general model that describes students' construction of representations.  It looks like:

student =(?)=> representation

where "?" is some as-yet-unknown process.  The audience found various limitations even in this very generic claim.  (I don't remember what limitations they found, but they might have involved the possibility that a group of students would construct a representation, that the representation would in turn influence the student, etc.)

This "mimesis model" involves a student copying what an instructor presents.  (Possibly from a traditional lecture, though not necessarily.)  Suppose the instructor delivers a lecture.  In that lecture, the instructor presents a representation.  The student copies that representation to produce her/his own representation.

Perhaps instead of copying a representation precisely, this student sees representation #1 (in a book or lecture) and modifies it to produce a somewhat different representation #2.  For obvious reasons, I called this the "value-added model."  The value-added model explains why I was interested in student whiteboards that depict energy theater -- the energy theater is representation #1, and the whiteboard is representation #2.  By examining qualities of the whiteboard representation that were not present in the energy theater, I can investigate the students' contributions over and above their knowledge of the energy theater.  (I'm not sure any more how crucial this model was to my argument.)

This student does not simply copy the representation that s/he sees in lecture.  Instead, the student engages in sense-making in order to produce a new representation.  (This might be viewed as an elaboration of the value-added model.)

In this model, a group of students (along with possibly an instructor) negotiate with one another in order to generate a representation.

In the exposition model, a single student makes sense of the physical situation, then explains a representation to their group.  In other words, the creativity comes mostly from a single student.  This model will be relevant in most of the videos below.  It's possible that the most interesting claim I make in this presentation is that students often construct representations via the exposition model.  That is, (some) students develop their ideas on their own before selling them to the group.  (Might one therefore expect that students who are most capable of individual sense-making would benefit the most from group work, as the group work gives them an opportunity to articulate and consolidate their ideas?)

Having discussed a number of possible models, I asked whether a diagram is a record of sense-making?  In other words, do our teachers' representations correspond to an individual sense-making process, a group sense-making discussion, or something else?

Reminder: here is one of the cooling coffee diagrams.

I listed the conditions under which the table 7 cooling coffee diagram was created.  One of the students, Tim, has just show the group a diagram in his notebook.  He is about to convince the group to make use of this diagram in their whiteboard representation.  I will argue that this process fits the "exposition" model.

UE 2 / table 7 / Cooling coffee representation video:

Reminder about the exposition model.  Does the above video fit the exposition model?

Reminder: here is the other cooling coffee diagrams.

I showed the UE 2 table 2 cooling coffee video in two parts.  The first part shows how Wendy draws a diagram in a notebook on her own, and then uses this diagram to influence the group's diagram.  Again, this fits the exposition model.

Later in the same conversation, Wendy uses a pre-drawn diagram to explain to the group how to "show the T's moving away from the cup."

Finally, I discussed the UE 1 diagram of a hand pushing a cart.

In this video, the students discuss with the instructor whether they need to conserve energy in their diagram.

Does this fit the negotiation model?  (Albeit negotiation involving an instructor.)