kitchen table math, the sequel: More Modeling Instruction: Techniques

Thursday, July 9, 2009

More Modeling Instruction: Techniques

Continuing the discussion of modeling instruction for physics education, we look to specific techniques to facilitate the model instruction. The modeling instruction method emphasizes that students must construct models and then infer results from those models. The idea is that the teacher need not appear to the student as the authority on what is true; the physics is the authority, and by investigating the physics (with carefully calibrated help from the teacher) the student will build his own intuition about that physical authority. At the same time, as the teacher purposefully falls back so the student can investigate and come to understand the model, the teacher is guiding the inquiry so that in the end, a model is clearly delineated and evaluated. "The modeling view is that students learn best from activities that engage them in actively constructing and using structured representations to make sense of their own experience and communicate with others. To optimize learning, the activities must be carefully planned and managed by the teacher. This requires considerable knowledge and skill on the part of the teacher which our Workshops are designed to cultivate."

Given the lab reports and worksheets shown in the prior post, this may not seem much different from a standard lab class, where the teacher directed the student-inquiry with the lab, and then received a lab report. But it is in several ways. First, the teacher himself is expected to have internalized that the students are generally operating on false premises, and his role is to uncover and replace those misconceptions. Second, the organization of the material into models may well lead teachers who held those same misconceptions to adjust their own teaching. Finally, the main difference comes from the use of interaction during and after the lab, in how the results of the lab work are turned into a model:using the Socratic Method and whiteboarding.

Consider a lab where the students designed the experiments themselves after using whiteboarding to generate a list of what variables they could investigate. Then after completing the lab, whiteboarding and teacher inquiry lead them to define and explain the system schema, for example. The system schema is a graphical representation of what elements of their lab were "in the system" and which were out of it. It should show a simple line drawing the interactions between the things in the system.

For the two blocks on the table, here's a system schema:

System schema drawings are extremely powerful representations, as they can lead directly to understanding when and where forces act on an element in the system.
"How does a system schema minimize the difficulties students have in constructing accurate free-body diagrams?
• By counting the number of interaction lines that end on the body of interest, the student will know the correct number of forces that act on that body.
• By looking at the body at the opposite end of an interaction line, the student can identify the body exerting a given force.

• Given a force on a body of interest, the student can identify its reaction force at the opposite end of its interaction line.
• Internal forces are associated with interaction lines that do not cross the system boundary.
• External forces are associated with interaction lines that cross the system boundary.
• Perhaps most important of all, a system schema provides the student with an easily understood process for creating accurate free-body diagrams.

There are additional benefits to having students constructing system schemas. The schema reinforces the idea that forces on one body are always caused by some other body. The schema also gives a visual reminder that any object also exerts a gravitational force on the entire Earth. With a system schema, the process of constructing a free-body diagram becomes an exercise in analysis instead of memory and/or educated guesswork. When mistakes do occur, good dialogues can occur between teacher and student because together they can examine the process for the source of the error. System schemas ultimately empower the students to select an appropriate system on their own.

The schema are the beginning of the modeling method, but not the end. The schema are expected to be arrived at using the techniques of Whiteboarding and the Socratic Method. The Socratic method of teacher inquiry is meant to direct them toward the correct answer while forcing them to justify their reasoning. Asking "why" they believe that, why they know that, may yield very different answers than expected, especially if the system graph seems right.

The Whiteboarding comes in when the students are asked to construct the model, and the components of it, such as the system schema, a motion map, an interaction map, the geometric or temporal structure, etc. Each of these details is supposed to be constructed by the group based on their data collection and work with each other. Basically, they are being asked to identify the properties of interest they discovered in their lab, and specify the variables that represent them. Students are expected to explain their solutions, and to justify these solutions. The whiteboards allow the teacher to see the students' reasoning in nearly-real-time, and allow the students to participate actively by questioning each other.

Is the model building all left up to student inquiry to drive it in the correct direction? No, absolutely not. Well, not at least in the best teacher's classrooms. Here's an excerpt from a paper on Whiteboarding listed in the Resource section of the Modeling website (italic emphasis his, bold emphasis mine):

The impression we instructors gave, unfortunately, was that the whiteboarding should be mainly student driven. This is unfortunate, because in attempting to make the WB sessions student centered, you lose much of its power and bring in irrelevant issues such as grading the white boards...The power of whiteboarding lies in its ability to allow the instructor to follow the learning process as it is happening, and to control that learning process in a way that optimizes learning. Whiteboarding should not become a report about the learning process to be scrutinized and evaluated by a group of peers. It is a process designed to let the professional guide and evaluate the learning process as it takes place...
This means that instead of standing in front of the group, a round table presentation showing everyone's work together is preferred. It means that mistakes should be correctable during the process; no one should have to parade their mistakes to the group after they realize that they are mistakes.

Of course, now we're getting to the real meat. Can everyone make this model work? Here's another teacher (same paper as above) discussing the whiteboarding model:

I find that I am often dissatisfied with the "Wells" model of whiteboarding. The main problems are: 1. Ideally, the dialogue should be between students, with me (the teacher) offering occasional guidance. Instead, I ask most of (if not all of) the questions. As a result, students sometimes feel that they are being publicly grilled rather than engaged in a genuine public conversation. When I try keeping my mouth shut for long periods of time, the conversation quickly loses its focus. 2. I have difficulty keeping 20+ students engaged in a single conversation. As soon as someone says something really interesting, it stimulates a half-dozen small group conversations, rather than a single large-group conversation. I grow weary of constantly regrouping the class, particularly when the small-group discussions result from genuine curiosity. I would like to see a video of Wells or some other expert in this technique. I suspect that I am missing something. In the last two years, I have been experimenting with the following reforms in whiteboarding methods:

1. Using the "board meeting" ideas presented in this listserv, I have rearranged my classroom so that students can sit in a large circle while presenting. This helps somewhat with issue #2, but does not address issue #1.

2. I have been experimenting with a "whiteboard gallery." I ask the students to present conclusions, solutions, etc. on their whiteboards, along with three check-boxes across the top. One box is labeled "yes," one box is labeled "no," and one box is labeled, "maybe." The students prop their boards around the classroom. Then each student (or group of students) examines the other boards and places a tally mark in the "yes" box, the "no" box, or the "maybe" box of each whiteboard. Afterward, I go from board to board, asking for comment. This seems to improve the student-to-student dialogue, and also greatly
reduces the feeling of a public grilling.

Given the breadth of whiteboarding experience, what is the value of this presenting and discussion? It increases physical intuition in part by properly modeling how science is spoken and done. "Students learn to replace vague descriptive terms of ordinary language with precisely defined scientific terms like “system, interaction, velocity and force.” And to articulate reasons for doing so. They learn to coordinate these terms with increasing skill in generating coherent scientific descriptions, including the specification of system schema and escriptive variables. "

This means their mind is fertile ground for science in the future, since even if they know little, they know less that's just plain untrue. But what elements are the gains really due to?

It's clear from the writing that modeling instruction depends STRONGLY on the quality of teachers involved, and their ability to live up to the high standards that Hestenes et. al. are demanding. Is it possible? Under what circumstances? More on that later.


SteveH said...

"Consider a lab ..."

Is this just for the lab time, or is this method used for every class?

"In the Modeling Method, students work in small groups to explore and uncover physical relationships on their own with guidance from the teacher."

The link also starts out with a quote by Carol Ann Tomlinson, the queen of differentiated instruction, so my cynicism is set to high. In fact, "The Modeling Method of Physics Instruction" is not about physics models, but about teaching models.

I'm interested to know why system schema drawings are better than regular free-body diagrams, but why does it all have to be tied in with (as if it can't be separated from) a Socratic teaching method? My cynical conclusion is NSF money.

Is the added value the teaching method or the modeling method? I would like to evaluate the benefits of system schema drawings without the confusion of the teaching method. Why is it better than free body diagrams?

"It's clear from the writing that modeling instruction depends STRONGLY on the quality of teachers involved, and their ability to live up to the high standards that Hestenes et. al. are demanding."

So, this really isn't about better physics models? I know that Hestenes talks about things like "follow the energy", which sounds interesting, but why can't I study those those things independently from the teaching method? Is the teaching method somehow tied specifically to things like system schema models rather than free-body diagrams? It seems now like it's not the math; it's not the model; it's about the teaching method.

I feel a little like a victim of bait and switch.

RMD said...

Zig Engelmann had it right . . . the only way to get classroom instruction correct is to use scripts and test them before they go into the classroom.

There are just too many details that can go wrong in the course of instruction (ie., too much or too little information given, not enough reinforcement, bad examples) to leave it up to a lesson plan and a teacher's gut.

I know teacher's chafe at the idea, but the teachers I know who do it and get the hang of it (it requires a lot of training and expertise to get correct) eventually love it because they only have to focus on the classroom and not testing their own curriculum.

ChemProf said...

It still isn't clear to me how this method would compare to a lecture where you directly address student misconceptions, which are predictable according to this research, rather than just giving the correct answer.

As RMD says, that's one thing that a script can do for you. Honestly, having taught General Chemistry for a decade, I pretty much have a script, down to the same jokes at the same point in the sequence every year. If someone had written out a script, I'd be foolish not to use it!

It is interesting that almost all new college faculty members will borrow lecture notes from an experienced faculty member the first time they teach a course, then they modify the notes as they go and gain experience. This is true even though these folks are Ph.D.'s with tons of domain knowledge, and are only trying to prepare 3-5 hours of material each week. Why then do we expect that elementary school teachers with less domain knowledge can prepare a week's worth of material without a starting point?

Anonymous said...

So true about scripting.

I sometimes prepare a multimedia presentation with a synchronized audio script. It's not unusual to spend 2 to 3 hours to get 5 minutes of presentation. Most of that time is devoted to editing the script and ensuring that it ties in meaningful way to the visuals.

When I'm recording and playing it back I find better and better ways to be very precise in my language. I have lots of ELL students and every single word has to be scrutinized. There's no way to do that on the fly in front of 25 jumpy kids.

What is incredibly sad today is that every day thousands of teachers get up and do virtually the same work to prepare for classes. This, in a world where we have incredible tools for communicating the BEST teacher's output to every kid in the country.

Sometimes I feel that teaching is a 16th century guild system operating in the cargo hold of the Starship Enterprise, or maybe it's that hologram room where they've dialed things back a few dozen centuries to see how the locals behave.

Anonymous said...

First, system schema:

Free body diagrams are difficult. They require already comprehending clearly what the system is, what forces act on it, and what force it creates, etc.

Large fractions of students will tell you that the free body diagram for that ball being thrown straight up has TWO arrows: one for g down, and one for "the force of the hand" that threw the ball up.

Before you get there, a way to help students is to just isolate the system. What are the elements of the system. Which are in contact with which. What's outside the boundary, what's inside. Getting good facility with free body diagrams is difficult because the student wants to draw all sorts of lines for forces that don't exist. This is easier if you concentrate on where forces come from, and what generates them. The simplicity of the system schema as a first step is helpful.

Second, re: the nsf/etc:

It's impossible to tell to what extent the ASU modeling group actually buys into the ed school ideas of constructivism, differentiated instruction, etc. It's only possible to see that in certain contexts, they use the lingo and not in others; that they certainly don't mean student centered instruction is preferable to teacher guided inquiry in all cases; that they strongly believe in teacher professional development in content and classroom management rather than just in ed school theories.

They got NSF funding. That means that some of their pieces will be written in the language the NSF wants. That really doesn't tell you anything but that they are college academics who know how to get funded.

to my comment about teacher knowledge and skill, you said,
--So, this really isn't about better physics models?

I think it's STRONGLY about better physics models, and one of the most important ways those models get used is in educating the high school science teachers themselves, who have been perhaps strongly functioning with the wrong models in their heads the whole time, and certainly haven't thought about these models enough to notice that their students have been functioning with the wrong models the whole time.

I too would like to see some separation of the "what we're teaching in modeling" from the "how we're teaching modeling", but I have a sneaking suspicion the reason it's extremely difficult to separate them is because a) the state of knowledge of hs physics teachers is so poor, and b) their actual pedagogy toward (intellectual) empathy with their students is so poor that you can't get them to change WHAT they teach unless you get them to teach HOW they teach.

It's a "break them down to build them up" situation, like the military, perhaps.

What if the hs phys teachers just teach the wrong physics, over and over again, unknowingly? Looking at their FCI scores, most are poor--below 50 as well. You can't raise your students above your own number. but even if they know some physics, they seem to be locked into assuming their students are properly comprehending things the way they are--despite all evidence to the contrary.

You can't get a teacher to recognize their own errors and misconceptions, and definitely can't get them to admit that their teaching is doing NOTHING to fix their students' misconceptions until you get them to SHUT UP and LISTEN to their students "think out loud" and think WRONG.

So to just start lecturing about system schema isn't enough. To just start lecture about the "right" model isn't enough. You've got to be forcibly probing the wrong model and ACTIVELY CORRECTING THE ERROR. how are you going to do that from a lecture?

Anonymous said...


I wanted more to hear what you thought about their whiteboarding...

my biggest concern is how you stop these classes from becoming utterly humiliating. The whiteboarding looks easily to degenerate into that, even if the teacher didn't intend it.

Anonymous said...

They use the whiteboards more formally than I do. After reading the white paper I think I will change my ways. I have to use mine under the radar as my technique is not pooh bah approved. One day I had a VP roar into my room, blowing her fight whistle. She thought there was a fight. The kids were chanting at me to go faster and most were out of their seats, jumping and thumping their chests on correct answers.

Your concern about humiliation is misplaced, in my experience. Quite the opposite occurs. Kids that NEVER participate orally do so with whiteboards. Not only that, they don't shut down after wrong answers. Their persistence seems to spike up.

I think two things happen. Because it is a 'silent' choral response, kids see that they're not the only one that gets things wrong so they don't feel singled out (which is very humiliating). The other thing that happens is the white board is very easy to erase. Your mistakes are not etched in stone so it seems more permissible to make them. It's not unusual on 'paper work' to have kids erase all of their work after they get an answer. It's like they don't want you to see their messy thinking processes. The white boards eliminate that concern.

At times, I'm the one that gets humiliated because it is very hard to come up with meaningful questions at a fast enough clip to satisfy the room. That's when the chanting starts. I guess "more, more, more" sounds like "fight, fight, fight" through my closed door. I'll have to model the pressure waves to see how that happens :>{.

I don't plan my sessions because I want to be able to go wherever the misconceptions take us. But after reading the paper I think I should have a better idea about what I want to achieve. For example, I could include a model as a first step instead of jumping into the middle of a process.

I would add that it is an exhausting process so I only use it sparingly as a 'wrap' for short periods of time, 10 to 15 minutes tops. It sounds like the paper describes a more dignified approach than mine.