Modeling Instruction: A Pedagogy and A Program

Transcription

1 Modeling Instruction: A Pedagogy and A Program Empowering Teachers For rapid, deep and sustained STEM education reform I. Modeling Theory & Pedagogy (David Hestenes) II. Professional Development (Jane Jackson) III. American Modeling Teachers Association (AMTA) the engine to drive reform (Colleen Megowan) SCIENCE is the name MODELING is the game! APS APRIL, 2014

2 History of the Modeling Program still going! : PER to develop Modeling Pedagogy and curriculum design : NSF support for disseminating Modeling Instruction nationwide 2001: Creation of ASU Master of Natural Science program for teachers 2005-present: American Modeling Teachers Association (AMTA) created of, by, and for teachers to continue the Modeling Program expansion from physics to all STEM disciplines National Impact To date: > 3,000 physics teachers & > 6,000 STEM teachers have taken intensive 2-3 week summer Modeling Workshops In 2013, more than 50 Workshops for some 800 ASU, more than 1,000 took MNS courses; 31 from Singapore; 65 physics MNS degrees; ½-dozen PER doctorates Teacher buy-in: > 1,500 AMTA members University buy-in: ASU, FIU, BYU, ISU, PhysTec-AMTA partnership

3 Modeling Instruction in a nutshell! A centered on Scientific models as the content core of each science Modeling as the procedural core of science Cycling students through all phases of modeling Modeling phases experimental design & testing THEORY MODELS engineering design & testing EXPERIMENTS APPLICATIONS Models are basic units of coherently organized knowledge: tools for inference, predictions, explanations, plans and designs

4 Pedagogy versus content The most robust finding of science education research: You cannot separate pedagogy from content!! Modeling Instruction integrates curriculum and pedagogy: Curriculum is organized around a small number of conceptual models as the content core of each scientific domain. Pedagogy promotes scientific inquiry centered on making and using models as the procedural core of scientific knowledge Applicable to all STEM disciplines!! Example: abstract mathematical concepts such as variable, function and rate can be explored within the context of mathematical models with concrete applications in physics and deployed to other subjects (i.e. chemistry, biology, economics). Modeling Pedagogy flexible, evolving, research-based

5 Modeling integrates the STEM curriculum Modeling Instruction employs Unifying Themes recognized by National Science Education Standards (NRC 1996) National Council of Teachers of Mathematics (NCTM 2000) models and modeling quantitative methods structure of matter and energy **A Framework for K-12 Science Education (NRC 2011) recommends additional crosscutting concepts : 1. Patterns and Systems 2. Cause and effect: Mechanism and explanation 3. Structure and function 4. Stability and change but these have been incorporated in the broader themes

6 Physics First grade 9 grade 10 grade 11 grade 12 physics chemistry biology AP courses Why Physics must be central to STEM ed: It is essential for interpreting our most basic perceptions of matter, motion and light That is why it was the first science to develop historically It provides the foundation for quantitative methods & the first exemplar of scientific method Quantitative reasoning with number and unit goes hand-in-hand with modeling and measurement, which couples mathematics to science The divorce of mathematics from physics is one of the most serious deficiencies in current educational systems!

7 Elements of Modeling Pedagogy Impediments to learning physics: (a) Misconceptions about common physical phenomena. (b) Misconceptions about science & scientific method. Instructional objectives include: (a) a clear concept of "physical model, including both qualitative and quantitative aspects, (b) familiarity with a basic set of models as the core of introductory physics, (c) skills in the techniques of modeling, especially interplay between diagrammatic and symbolic representations, (d) experience in the deployment of models to understand the physical world--to interpret and analyze data, to explain, predict, plan & solve problems

8 Force Concept Inventory university physics post instruction Newtonian vs. Naive beliefs Results First Law < > Motion requires force ~ 60% (Impetus Principle) Second Law < > Force is action ~ 40% (No Passive forces) Third Law < > Force is war ~ 90% (Dominance Principle) Effects of conventional instruction (> 1,000 univ. students) small (< 15% improvement) independent of instructor & mode of instruction reproducible and universal (across the U. S.) persistence to graduate school Verified by Eric Mazur at Harvard! still maintain naïve view!!

9 Model: is a representation of structure (in a system/process) Four types of structure: (a) system structure (system schema): composition (internal parts of the system) environment (external agents linked to the system) connections (external and internal causal links) (b) geometric structure position with respect to a reference frame (external) configuration (geometric relations among the parts) (c) temporal structure specifies change in state variables descriptive models (explicit functions of time) causal models (dynamical equations) (d) interaction structure interactions (as functions of state variables) These four types suffice for modeling in all the sciences!! One needs examples to understand them

10 Content core: Basic Particle Models in Newtonian Mechanics Kinematical Models Causal Models Constant velocity Free Particle: Σ F i = 0 Constant acceleration Simple Harmonic Oscillator (SHO) Constant force: Σ F i = constant Linear binding force: Σ F i = - k r Uniform circular motion Central force (with constant r ) (UCM) Collision Δ p = I Impulsive force Instructional design: spend two weeks developing each of these models in an instructional cycle that emulates scientific modeling practice!

11 Quantitative methods require mathematical models to interpret data! Basic Mathematical Models are about RATE! 1. Constant rate (linear change): graphs and equations for straight lines (proportional reasoning, constant velocity, acceleration, force, momentum, energy, etc.) 2. Constant change in rate (quadratic change) graphs and equations for parabolas (constant acceleration, kinetic and elastic potential energy, etc.) 3. Rate proportional to amount: doubling time, graphs and equations of exponential growth and decay (monetary interest, population growth, radioactive decay, etc.) 4. Change in rate proportional to amount: graphs and equations of trigonometric functions (waves and vibrations, harmonic oscillators, etc.) 5. Sudden change: stepwise graphs and inflection points (Impulsive force, etc.) Ubiquitous: rich & unlimited applications to science and modern life! Skill in using these models in a variety of situations an essential component of math and science literacy. should be cultivated deliberately, systematically & repeatedly

12 Graphic Representations of Model Structure System Schema R System 2 C S 1 3 E Environment L E ~ R (A) (B) Situation Map m 2 m 1 m 3 µn Interaction Map N T T (m + m ) g 1 2 (C) (D) m 3 g

13 Distributed representations of structure in a conceptual model Situation Map m 1 System Schema P 1 S 2 Subsystem Schemas 1 S S 2 m 2 T E T E E Motion Map 0 x 1 v 1 x 2 v 2 f Interaction Maps N T 1 T 2 W 2 Interaction Laws T 2 = T 1 f = µn W 1 = m 1 g W 2 = m 2 g W 1 Geometric Structure x 2 = x 1 + L! v 2 = v 1 a 2 = a 1 Temporal Structure: (Eqns. of Motion)!! m 2 g m 1 g = (m 1 + m 2 )a 1 T 1 µn = m 1 a 1 m 2 g T 2 = m 2 a 2 N = m 1 g

14 Systematic use of system schemas as a modeling tool has the largest immediate impact on student performance of any teaching innovation I know!! It tells students how to start solving any given problem! Situation Map m 1 System Schema P 1 S 2 m 2 T E System schemas are not unique!!

15 Systematic mathematical modeling began with Galileo and Newton Newton s Modeling Cycle: Preface to the Principia From the motions infer the forces! motion force From the forces deduce the motions! Newtonian Theory specifies the rules for a modeling game: (research program): To find all the forces necessary and sufficient to account for all observed motions in the universe! Ref: Modeling Games in the Newtonian World (1992)

16 Instructional Modeling Cycle Stage I: Model development ( one week) m 1 A. Description Instructor sets context ( e.g. Modified Atwood machine) Guides students to identify the system of interest and relevant variables Discusses elements of experimental design (e.g., dependent and independent variables) B. Experimentation and Model Formation Organize student groups of 3 or 2 or 4 Design and perform own experiments Formulate functional relations among variables Evaluate fit to data m 2

17 C. Post-lab analysis: Formulate a conclusion. Defend it with evidence and argument; WhiteBoarding (shared responsibility) Presentations must address the questions: What is your model for the observed system? How good is its fit to the empirical data? What are the sources of error? limitations in experimental accuracy? limitations of the mathematical model?

18 Instructional Modeling Cycle (six cycles per semester) Stage II: Model deployment ( one week) Students are presented with diverse new situations or problems that require abstracting the model from the original context to describe, explain, predict, design or solve Results are summarized on white boards and defended orally in class discussion Objective: improving the quality of scientific discourse, and progressive deepening of student understanding of models and modeling with each pass through the modeling cycle. Problem Solving: The solution to every problem is a model! The S.I.M. approach (David Pritchard, MIT) S. Choose a system to consider I. Describe its interactions. M. Choose or construct a model to solve the problem.

19 Managing Classroom Discourse (talk is not enough!) " " Aim: raise level to scientific discourse Establishing the subject of discourse Demo Problems Issues, Questions }! }! Claims to be investigated " Communication requires shared meaning students get common access with whiteboards, etc. " Meaning (of words, equations, diagrams) is constructed from situated use must be negotiated " Quality of discourse depends on Representational tools and how they are used Structure of arguments Standards set by teacher " Scientific argumentation arises spontaneously when students have the discursive resources

20 To justify strong claims about teaching and learning science, we need a coherent theory of instruction with empirical support. Modeling Theory: a research program Scientific Research Cognitive Science Scientific Practice Modeling Theory of cognition and learning Modeling Theory of scientific knowledge Instructional Design If I didn t believe it, I wouldn t have seen it! Teaching Practice I won t believe the experiment until it is confirmed by theory!

21 A crucial distinction: Mental models vs. Conceptual models (World 2) MENTAL WORLD (World 3) CONCEPTUAL WORLD embodied in neural networks Mental Models (Subjective) Personal knowledge Understanding Creating Conceptual Models (Objective) Scientific knowledge encoded in symbolic forms Real Things & Processes Being and Becoming PHYSICAL WORLD (World 1) A Framework for K-12 Science Education (NRC 2011)

22 Students are not the only ones with naïve beliefs about physics! Clerk Maxwell addresses misconceptions of a pretentious colleague in his commentary on Herbert Spenser s appearance before Section A of the British association (Belfast 1874): Mr. Spenser in the course of his remarks regretted that so many members of the Section were in the habit of employing the word Force in a sense too limited and definite to be of any use in a complete theory of evolution. He had himself always been careful to preserve that largeness of meaning which was too often lost sight of in elementary works. This was best done by using the word sometimes in one sense and sometimes in another and in this way he trusted that he made the word occupy a sufficiently large field of thought.

23 The bottom line! It ain t what you don t know that hurts you, It s what you know that ain t so! Mark Twain

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