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.