Attending to Student Ideas in order to Assist

In a previous post, I brought up an episode in which Stamatis observes a group of teachers discussing "electron repulsion" as a mechanism for Normal Force. Others in the group had suggested that perhaps normal force is something we just "made up" to balance gravity. In that post, I claimed that the teachers' conversation is what leads Stamatis to begin pursuing an instructional sequence consistent with many aspects of "Clement's Bridging Analogy".

Clement's Bridging Analogy

In Clement's Bridging Analogy paper, the instructional sequence for the Normal Force is outlined in the following way:

#1 The target question of whether the table exerts a force on book is introduced

#2 The anchoring situation of a hand pushing on a spring is introduced 

#3 Similarities and differences between the two situations are discussed

#4 Several bridging cases are introduced (book on foam, book on a flexible board)

#5 Discussion of similarities and differences continue

#6 The teacher introduces microscopic model of table as made up of atoms connected by spring

#7 Teacher demonstrates the bending of table using a laser and mirror.

In my mind, the bridging analogy provides two important things:

(1) It provides a plausible mechanism for how a table can possibly exert a force. Making sense of this mechanism involves reconceptualizing the table as being comprised of tiny stiff springs.
(2) That sense of mechanism has empirical consequences–we should be able to detect compression in the table. This provides support for the idea that the table exerts a force without relying on notions of balanced force.

Background for Episode

Nicole is the teacher who kept bringing up with her group the question of why there is a normal force on the book. In this case, the teachers already were in agreement that there is a normal force, and Sarah had even introduced an argument for why, which centered around an intuitive notion of balance:

"Just going back to the basic idea that the cup isn’t falling through the table. So we know there’s a force on the cup. So it’s almost like this is made up as like there has to be something countering it, so we’re gonna make it up."

Stamatis revoices Sarah's argument in the following way (although he doesn't attribute it to her):

"It seems to me that somebody says. So. One kind of reasoning, a logical reasoning, that says, Look I’m committed to the idea–for what reasons is a different story–that something that isn’t moving must have a balanced force. And so, if I have this force [pointing to gravitationally downward force drawn], and I believe that the force is there– the downward pulling of the earth–then I must invent a force that point upwards."

After revoicing the argument, Stamatis asks the teachers to set this reasoning aside for the moment, and asks if there might be any other lines of reasoning/evidence that would suggest there is should be a force exerted on the marker from the table.

I think to make sense of Stamatis' role in this group up until this point, we might think about Stamatis as an identifier of learners' needs. He has closely attended to their ideas and question concerning the normal force, and has identified within those ideas a need for a mechanistic account of normal force. He has been quietly attentive this whole time. When he joins in, he re-voices some of the ideas and question that they do have, and because he has identified specific needs, he begins pursuing a line of reasoning with them that will help them address that need. In that sense Stamatis is also in the role of being a provider. I suppose another way of conceptualizing Stamatis' role in this group is as diagnostician/prescriber. He has diagnosed that the teachers lack a mechanism or evidence for normal force; and he has prescribed the normal force bridging analogy.

A claim might be something like: Stamatis at first attends to student contributions in order to identify needs and/or diagnose issues. Some evidence that he attended to student thinking is that he re-voices Sarah's argument, and that asks teachers to set aside this reasoning and consider another line of reasoning. In the episode below, however, I want to claim that when Stamatis begins pursuing the Bridging Analogy, he shifts to a new way of attending to the teachers' contributions. Rather than listening in order to identify needs or diagnose, Stamatis attends to teachers contributions for the purpose of helping them through that sequence. This changes drastically both his role in the group and the way he responds to their contributions.

The Episode

So, here is about a 2 minute clip from a part of the larger episode. In this clip, I want to focus on the ways in which Stamatis responds to teacher contributions. There are three contributions that I'll draw our attention to:

• Dean suggesting they could try to create a scenario in which normal force exists without gravity
• Nicole and Dean suggesting you know your finger exerts a force when holding the marker because you (i) have to keep pushing and (ii) you are feeling the pressure
• Nicole suggesting that you know that the spring exerts a force because the marker has observable motion in response to force (rebounding)

In each of these cases, Stamatis doesn't seem to take up the their ideas; however, I think there is evidence that Stamatis is attending closely to their thinking. My claim is that he does not take up their ideas as contributions because he does not see their ideas as helping with the instructional sequence he is pursuing. The bridging analogy replaces the table with a spring; it does not get rid of gravity. The bridging analogy focuses on evidence of compression, not evidence of feeling. The bridging analogy focuses on evidence of displacement downward, not evidence of rebounding upward. Each time, Stamatis' response to their contributions is to redirect the teachers' attention to a new scenario, one that I think he hopes will get the instructional sequence moving forward in the way he understands its function.

Here is the Transcript

SV:     What I’m saying is that this is based on the idea that I must invent a second force–

N:        Right

D:        Right

M:        Mm-hmm

SV:      And what I’m saying is, can I have an independent line of reasoning that does not depend on the, “There has to be a second force.”

N:        Yeah, I don’t know.

SV:      So… let’s think about this… from another perspective

D:        Create a scenario where you don’t have this [gravity], but this [normal] somehow shows up.  [Laughs]

S:        Yeah.

SV:      So that could be the case, OR, I could actually start from a scenario where I know that there is a force.

D:        Which one? This one here?

SV:      No, no.

D:        I’m sorry. I’m sorry. I’m sorry. [Hands up, “my bad” gesture]

SV:      I start with a scenario with a marker that I know there is a force exerted on the marker, and then I can actually make modification [gesturing] of that scenario until I get to the table,

D:        Mmmmmmm

SV:      And if I believe that so… [pointing to Nicole who is holding a marker] Do you, in that situation, do you believe that you, your skin, is exerting a force?

N:        Yes.

SV:      OK. What evidence do you have for that?

N:        Cause I have to–I have to push to keep [gesture] the marker from moving.

D:        Also, there’s a sense in which you can feel [gesture] the pressure

M:        Yeah, that’s what I was going to say

N:        Well wouldn’t that be evidence that it’s pushing on me?

[silence]

N:        or No?

D:        [unintelligible]

SV:       [Takes marker from Nicole] So here is a situation. Suppose that I do not start from that scenario, but I start from a scenario where I take the marker and I put it on a spring.

N:        Oh.

SV:      So I put it on the spring [pantomime], and it goes… “boing!”, right?

Many:  Right

SV:      So do I have any evidence that the spring is exerting a force on the marker, in that case?

N:        When it comes back up, it pushes on it and makes it move.

D:        Right.

SV:      If I substitute the marker with my finger, will I have any evidence that the spring is pushing on my finger?

Digesting the Episode

A few things stand out:

First, Dean suggests that they might look for a scenario in which normal force exists and gravity does not. This seems reasonable in the sense that Stamatis has told them to pursue a line of reasoning that won't involve the balanced forces argument. The bridging analogy doesn't have this as the next step, so if Stamatis is pursuing the bridging analogy script, he is unlikely to take up this contribution. Stamatis responds by saying, "So that could be the case, OR, we could start from a scenario..."

Second, Stamatis asks the group what evidence they have they their skin is exerting a force. Dean and Nicole offer different contributions–both about how they know there is a force based on *feeling*. Nicole seems to suggest you having to exert yourself, and Dean says you can feel the pressure. The bridging analogy I think involves pursuing evidence from visible compression, not feeling. In response to these contributions, Stamatis takes the marker from Nicole in order to introduce another situation.

Third, now with the scenario of the marker on the spring, Stamatis asks about evidence. Nicole doesn't offer up the evidence based on compression. Instead, she offers up the idea that the spring will cause visible motion (rebounding). In response, Stamatis again changes the situation. Stamatis replaces the marker (which might rebound), with your finger, which you can hold still while having the spring compressed. Stamatis now asks the question again, "what evidence?"

In that sense, Stamatis has moved the group from Step#1 in the bridging analogy to Step #2.

Attending to Student Ideas–For what Purpose?

I think there is pretty good evidence here that Stamatis is attending to student contributions and using those contributions in order to make improvised instructional moves. Let me be clear: one kind of way that teachers might attend to student contributions is to evaluate those ideas in terms of correctness. That is not what Stamatis I think is doing here. I think Stamatis is attending to student contributions in terms of their propensity to keep them moving along a particular instructional sequence–the Normal Force Bridging Analogy. This instructional sequence requires that certains ideas and argument come into being, and certain kind of scenarios be considered. Within that instructional sequence, Stamatis is monitoring and adjusting in order to keep the conversation "on track." This kind of attending to student thinking was preceded by a period of time in which Stamatis was attending to student ideas for the purposes of "identify needs and then providing for those needs" or "diagnosing issues and prescribing." (Neither of these metaphors feels quite right to me; the first one doesn't convey my sense of Stamatis's expertise, and the second one doesn't convey his caring. Maybe together they give you some sense of how I see it.)