I think this is due to the unique representation that is Energy Theater (or perhaps energy-tracking-representations, or ETRs). Sherin discusses different representations (programming v. algebra) and their effect on physics learning, and I think it might be just the ticket for explaining the teachers' 5 Laws. I'm using two items to better understand Sherin's work that I think may be most relevant:
(1) His dissertation, and
(2) "A comparison of programming languages and algebraic notation as expressive languages for physics" (International Journal of Computers for Mathematical Learning, 2001 vol. 6 (1) pp. 1-61)
The abstract from the second item is below...with emphasis added.
The purpose of the present work is to consider some of the implications of replacing, for the purposes of physics instruction, algebraic notation with a programming language... I begin with two informal conjectures: (1) Programming-based representations might be easier for students to understand than equation-based representations, and (2) programming-based representations might privilege a somewhat different “intuitive vocabulary.” If the second conjecture is correct, it means that the nature of the under- standing associated with programming-physics might be fundamentally different than the understanding associated with algebra-physics.He goes on to say: "I am interested in whether there are fundamental differences in learning and understanding that are traceable to features of the particular representational languages employed." In a way, I'm beginning from the opposite end: whether the differences between the 5 Laws and standard descriptions of the WE Theorem are a result of the representational languages.
Why programming may be different from algebra in significant ways (Sherin's initial conjectures):
- programs might be easier to understand or interpret than equations...programs can be mentally ‘run’ to generate motion phenomena... Thus, if programs are easier for students to interpret – if students are more likely to use them ‘with understanding’ – there would be important instructional implications.
- programming languages may be better suited for expressing causal intuitions...the very nature of the understanding engendered by programming-based physics might be different...in replacing equations with a programming language, we are not simply substituting one tool for another, we are changing the very nature of physics understanding.
Sherin then refines those ideas by proposing two theoretical constructs, interpretive devices and symbolic forms.
Interpretive devices: the natural language utterances that one can make concerning programs will have a certain structure.I don't have data on students discussing the work-energy theorem as it relates to algebraic representations - but I think the idea here is that, if I could compare the two conversations, I would see that there are certain kinds of utterances you'd see with algebra that you wouldn't see with energy theater and vice versa. This seems so undeniably true that I'd be excited to get a little data on this.
Symbolic forms. I will argue that students gradually learn to recognize a certain type of structure in symbolic expressions, and that these structures are associated with elements in a basic conceptual vocabulary. It is this association of symbol structure and meaning that I refer to as a ‘symbolic form.’ ...students learn to recognize a certain type of structure in symbolic equations, and this supports the interpretation and construction of equations. More specifically, each symbolic form involves an association between two components, a symbol template and a conceptual schema.Structures he notes are things like ☐ + ☐ ... here, I'll add the chart:
Programming and algebra have clear symbolic expressions that are static on a page/screen. ET is not this way - but there are nonetheless symbolic expressions, right? or no? So the way you express what kind of energy you are, the entering of an object, the leaving of an object, the number of people in a given object... er... is that all? Anyway, this will take some thinking through.
One point that Sherin notes that I want to keep in mind:
I am interested in episodes in which a student associates ‘meaning’ with an equationSo I'd like to look for instances in which teachers are interpreting - talking through - their energy theater representations. Not just setting it up but, as they run through, associate meaning with it. That seems like the place to compare to Sherin's own transcripts and interpretations. (As an aside, just looking at the kinds of algebra equations and interpretations... I wonder if differential equations are more causal? seems you'd read different kinds of things into these.)
it is in within-line structure that a great overlap between programming and algebra appears. And the locus of substantial divergence will be the line-spanning structure in programming... the arrangement of algebraic situations typically reflects the solution process, rather than an understanding of the physical circumstance.Oooh, and then looking at chunks of code...
In the physical system that this simulation purports to model, all of these parameters are constantly changing; they do not change one at a time as in this program. In essence, the act of programming requires the students to explode each instant of the motion into a series of actions that happen through what I will refer to as “pseudo-time” (deKleer and Brown, 1984).This definitely happens in energy theater - we "explode time" - person a walks in changes form then person B moves out so that the KE, say, won't change...
When writing simulations, students were often concerned with chains of dependent quantities, such as d depends on c, which depends on b, which depends on a. Within a program, these chains show up as the symbol pattern shown in Figure 12. In this programming symbol pattern, b is computed from a, c is computed from b, d is computed from c, etc. This sequencing of linked dependence relations, which students wrote into and read out of programs, is the meaningful pattern I call SERIAL DEPENDENCE.This makes me think of a goof I made in class when I set the force arrows for the ball underwater incorrectly, and switching one meant a whole cascading change... plus those arrows in the diagrams we draw show a similar chaining.
More quotes to keep in mind...
to some extent, the ease of interpretation of symbolic expressions depends on the existence of natur- ally available and useful interpretive devices. And there actually is some evidence that programming has an edge in this regard. The fact that the interpretation of a programming statement can be framed by the running program is an example of this sort of natural support. Because of the fact that programs can be run, there is a naturally available representational device – the TRACING device.and to consider causality:
programming forces students to engage with a unique set of issues-issues pertaining to which quantities change first and which quantities determine which other quantities ... when we write F = ma, we do not need to think about whether force or acceleration changes first. In fact, since these and other quantities are changing constantly, this question does not even make sense within algebra-physics. In contrast, programming forces you to take changes that happen simultaneously and break them up into ordered operations. And, in doing so, you have to decide which operation happens first. This is a step toward an ordered, causal world.He ends the paper with the question "Are Causal Intuitions Problematic for Physics Learning?" - and concludes "no" -
First, we must keep in mind that a concern with how someone understands physics is not the same thing as a concern with what is correct physics. Even the best physicists may sometimes think of forces as causing accelerations, even if they somehow know that this is not strictly correct.
although it may not be right to say that forces cause accelerations, it is not true that there is no asymmetry in the relation between the concepts of force and acceleration. At the least, there is an ontological asymmetry – forces and acceleration are two different sorts of entities.
there is an asymmetry here that causal intuitions could help students to keep straight: If you have in mind that forces cause accelerations, then you are less likely to misinterpret this equation. This is the sort of place that causal/dependence intuitions are useful.I'd rather there were strong claims from Science Studies showing that scientists think and work causally. Can I find those?
(Then there are also "representational devices" - taking this from the dissertation - "which function as a set of interpretive strategies."
.. "What determines, at any particular time, the forms that a student recognizes in an expression? The answer, I will attempt to show, is that initiates in physics possess a repertoire of interpretive strategies that I call “representational devices.” Roughly, representational devices set a stance within which symbolic forms are engaged. The term “device” here is intended to call to mind “literary devices,” for reasons that I hope to make apparent...")
As a final note: this is some really beautiful scholarship. I feel like a hack!
