Models and Modeling in the High School Physics Classroom

Presentation Objectives The problem with conventional instruction Key features of Modeling Instruction The Modeling Cycle sample pre-lab activity evaluation of data post-lab extension - development of kinematic equations deployment exercises

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.

“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.

Consequences of One Semester of Conventional University Physics Instruction figures courtesy of Alan Van Heuvelen Belief Beginning 1st Semester (100 students) Beginning 2nd Semester (60 students) 40 Try again later or change majors? Other Understand Newton’s 2nd Law 37 Did NOT understand Newton’s 2nd Law

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.

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.

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.

What Do We Mean by Model? with explicit statements of the relationships between these representations

Multiple Representations with explicit statements describing relationships

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 How to Teach it?

The Modeling Process Making Models 1) Construction Identify system and relevant properties; represent properties with appropriate variables; depict variables and their associations mathematically. 2) Analysis Investigate structure or implications of model. 3) Validation (reality check ! ) Compare model to real system it describes; adequacy depends on fidelity to structure and behavior.

The Modeling Process Using Models 4) Deployment (or application) Use of a given model to achieve some goal. Describe, explain, predict, control or even design new physical situation related to original. Infer conclusions from the outcomes of the model. Extrapolate model for studying situations outside original domain. Examine and refine one’s own knowledge in terms of the new modeling experience.

Modeling Cycle Development begins with paradigm experiment. Experiment itself is not remarkable. Instructor sets the context. Instructor guides students to identify system of interest and relevant variables. discuss essential elements of experimental design.

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.

slope related to angle of incline

I - Model Development Post-lab analysis whiteboard presentation of student findings multiple representations » verbal » diagrammatic » graphical » algebraic justification of conclusions

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.

Post-Lab Extension Recall Constant Velocity Lab  Contrast shapes of curves from exp 2 and exp 3.

Post-Lab Extension Instantaneous velocity Use graphing calculator to draw tangents to curve at given points. Slope of tangent is the instantaneous velocity.

Post-Lab Extension Instantaneous Velocity Exercise  use Graphical Analysis™ to plot velocity vs time  define acceleration as slope of velocity - time graph

Post-Lab Extension Derivation of Kinematic Equations  from equation of line of v vs t graph  from area under curve of v vs t graph ∆v

 when there is an initial velocity, the area under the curve is computed by summing areas of the rectangle and triangle Post-Lab Extension Derivation of Kinematic Equations

II - Model Deployment In deployment activities, students articulate their understanding in oral presentations. are guided by instructor's questions: » Why did you do that? » How do you know that? learn to apply model to variety of related situations. » identify system composition » accurately represent its structure

Model Deployment Exercises Stacks of kinematic curves Motion maps

Newtonian concepts developed distinction between instantaneous and average velocity acceleration as rate of change in velocity Emphasis on physical interpretation of graphs slope of tangent to curve in x vs t graph slope of v vs t graph area under curve in a vs t graph Descriptive Particle Models: Kinematics- Uniform Acceleration

Model Deployment Exercises Patrolman and speeder Multiple solutions (algebraic, diagrammatic, graphical) Graphical Analysis™ to produce x vs t graph

Model Deployment Exercises Patrolman and speeder Area under v vs t graph yields displacement.

Objectives: 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! II - Model Deployment Ultimate Objective: autonomous scientific thinkers fluent in all aspects of conceptual and mathematical modeling.

Effectiveness of Modeling Method FCI Scores

Effectiveness of Modeling Instruction Gains by Group

Modeling Instruction Program Coordinates professional development opportunities nationwide for further information, contact  Dr. Jane Jackson Box Dept. of Physics & Astronomy Arizona State University Tempe, AZ  voice (480)   check out our home page