1. Models and Modeling in the High School Physics Classroom
Larry Dukerich
Modeling Instruction Program
Arizona State University Dobson HS - Mesa, AZ
We’re here to tell you about the Modeling Method of instruction: developed in a collaborative effort by Malcolm Wells, a HS teacher and David Hestenes, prof of physics at ASU. These are the folks who developed the FCI and MB test which appearedin Mar 92 TPT.
The MM, using results of physics education research attemprs to match instructional design to the way we believe students learn

2. The Problem with Traditional Instruction
It presumes two kinds of knowledge: facts and knowhow.
Facts and ideas are things that can be packaged into words and distributed to students.
Knowhow can be packaged as rules or procedures.
We come to understand the structure and behavior of real objects only by constructing models.
First some background on what is the problem with conventional instruction. p1
Leads to marketing model of education: researchers and university professors as producers , HS teachers as retailers, and students as consumers of knowledge. p2

3. “Teaching by Telling” is Ineffective
Students usually miss the point of what we tell them.
Key words or concepts do not elicit the same “schema” for students as they do for us.
Watching the teacher solve problems does not improve student problem-solving skills.
Our students don't share our background, so key words, which conjure up complex relationships between diagrams, strategies, mathematical models mean little to them. To us, the phrase inclined plane conjures up a complex set of pictures, diagrams, and problem-solving strategies. To the students, it's a board.
All my careful solutions of problems at the board simply made ME a better problem-solver.

4. Memorization vs Understanding
What does it mean when students can readily solve the quantitative problem at left, yet not answer the conceptual question at right?
For the circuit above, determine the current in the 4 W resistor and the potential difference between P and Q.
Bulbs A, B and C are identical. What happens to the brightness of bulbs A and B when switch S is closed?

5. Instructional Objectives
Construct and use scientific models to describe, to explain, to predict and to control physical phenomena.
Model physical objects and processes using diagrammatic, graphical and algebraic representations.
Small set of basic models as the content core of physics.
Evaluate scientific models through comparison with empirical data.
Modeling as the procedural core of scientific knowledge.
What should we teach?
Our students should learn to do the following:
They should see that physics involves learning to use a small set of models, rather than mastering an endless string of seemingly unrelated topics.

6. Why modeling?!
To make students’ classroom experience closer to the scientific practice of physicists.
To make the coherence of scientific knowledge more evident to students by making it more explicit.
Construction and testing of math models is a central activity of research physicists.
Models and Systems are explicitly recognized as major unifying ideas for all the sciences by the AAAS Project 2061 for the reform of US science education.
Robert Karplus made systems and models central to the SCIS elementary school science curriculum.
Emphasis on points 1 and 2.

7. Models vs Problems The problem with problem-solving
Students come to see problems and their answers as the units of knowledge.
Students fail to see common elements in novel problems.
“But we never did a problem like this!”
Models as basic units of knowledge
A few basic models are used again and again with only minor modifications.
Students identify or create a model and make inferences from the model to produce a solution.
We use the ability to solve problems as a means for evaluating our students’ understanding. But our students come to see problems and their answers as the essential units of knowledge. They call for us to show them as many examples as possible and pray that the test has problems like the ones they saw.
How do novices solve problems? They reach into their gunny sack of equation and find one with nearly the same variables.
How do experts solve problems? They start by drawing a diagram.

8. What Do We Mean by Model?
This word is used in many ways.
The physical system is objective; i.e., open to inspection by everyone. Each one of us attempts to make sense of it through the use of metaphors. Unfortunately, there is no way to peek into another’s mind to view their physical intuition. Instead, we are forced to make external symbolic representations; we can reach consensus on the way to do this, and judge the fidelity of one’s mental picture by the kinds of representations they make.
So the structure of a model is distributed over these various representations; later we’ll provide some specific examples.
with explicit statements of the relationships between these representations

9. Multiple Representations
Multiple representations. We all use them, but before I began to use this method, I didn't make the connection between the features of the various representation explicit.
with explicit statements describing relationships

10. constructivist vs transmissionist
How to Teach it?
constructivist vs transmissionist
cooperative inquiry vs lecture/demonstration
student-centered vs teacher-centered
active engagement vs passive reception
student activity vs teacher demonstration
student articulation vs teacher presentation
lab-based vs textbook-based
Here are the key ways in which the modeling method differs from conventional instruction.
Students present solutions to problems which they have to defend, rather than listen to clear presentations from the instructor. The instructor, by paying attention to student’s reasoning, can judge the level of student understanding.

11. I - Model Development Students in cooperative groups
design and perform experiments.
use computers to collect and analyze data.
formulate functional relationship between variables.
evaluate “fit” to data.
Instead of following a set of pre-determined instructions, students devise their own procedures. (collectively, with guidance?) Computers are used in the collection and analysis of data - a novel use when you consider what students ordinarily use computers for is word-processing or tutorial activities.
All of the kinematic equations we use in mechanics come from experimental results.

12. I - Model Development Post-lab analysis
whiteboard presentation of student findings
multiple representations
verbal
diagrammatic
graphical
algebraic
justification of conclusions
Students articulate their findings to their peers using white boards. We all know that the first time we really learned a topic was when we had to prepare to teach it. Giving our students the same opportunity allows them to work out the details clearly in their minds.

13. Preparing Whiteboard

14. Making Presentation

15. II - Model Deployment In post-lab extension, the instructor
brings closure to the experiment.
fleshes out details of the model, relating common features of various representations.
helps students to abstract the model from the context in which it was developed.
Instructor reinforces what students have learned in the lab, points out essential features of the model, and demonstrates appropriate modeling techniques.

16. II - Model Deployment In deployment activities, students
learn to apply model to variety of related situations.
identify system composition
accurately represent its structure
articulate their understanding in oral presentations.
Students get to apply model to a variety of situations. They develop confidence because they realize there is NOT a separate approach to each situation. Instructor elicits thorough explanation from presenters, encourages students to appeal to a model for justification of their claims, and brings students to confront their misconceptions.
Instructor is no longer the source of explanations or the final authority.
are guided by instructor's questions:
Why did you do that?
How do you know that?

17. II - Model Deployment Objectives: Ultimate Objective:
to improve the quality of scientific discourse.
move toward progressive deepening of student understanding of models and modeling with each pass through the modeling cycle.
get students to see models everywhere!
Ultimate Objective:
autonomous scientific thinkers fluent in all aspects of conceptual and mathematical modeling.