Transcript Models and Modeling in the High School Physics Classroom

A Modeling Approach
to Science Teaching
Nicholas Park
Greenhill School
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A Private Universe
• We go through life collecting memories,
and organizing them into mental
models, or schema.
• Our memory depends on connections;
new inputs which do not fit in an existing
schema tend to be “forgotten.”
• It takes a very discrepant phenomenon
to motivate a change in existing
schemata.
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Science and Modeling
• Scientists construct and use shared
models to describe, explain, predict
and control physical sytems.
 By making this process explicit, we help
students to
• Revise their mental schemata (models) in
the light of experimental evidence and
collaborative discourse
• Understand the scientific process
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What Do We Mean by Model?
Symbolic Representations
Verbal
Physical
System
Algebraic
Mental
Model
Diagrammatic
Graphical
 Essential and non-essential elements of a physical
system or process are identified
 Models are used to represent the structure
underlying the essential elements
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Why Models?
 Models are basic units of knowledge
 A few basic models are used again and
again with only minor modifications.
 Students DO work from mental models
– the question is which model it will be:
 A shared, rigorous model with explicit
experimental support?
 An inconsistently applied, private model
based on miscellaneous experiences.
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What about problem solving?
 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 doesn’t work
 Presentation of facts and skills, with the
assumption that students will see the
underlying structure in the content.
 They systematically miss the point of what
we tell them.
 They do not have the same “schema”
associated with key ideas/words that we
have.
 Students passively listen while T works
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What works
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Interactive engagement
Student discourse & articulation
Cognitive scaffolding
Multiple representational tools
Consensus-based model building
Explicit hierarchal organization of
ideas and concepts into models
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The Modeling Method
 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.
 Recognize a small set of models as the
content core.
 Evaluate scientific models through
comparison with empirical data.
 View modeling as the procedural core of
scientific knowledge
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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
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THE MODELING CYCLE
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I - Model Development
 Students in cooperative groups
 design and perform experiments.
 formulate functional relationship between
variables.
 evaluate “fit” to data.
 Post-lab analysis
 whiteboard presentation of student findings
 multiple representations
 justification of conclusions
II - Model Deployment
 In post-lab discussion, 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.
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.
•
are guided by instructor's questions:
»
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Why did you do that?
How do you know that?
Modeling in a Nutshell
 Through carefully guided discourse,
students construct shared models,
using various representations, to
describe shared experiences with
physical systems and processes.
 Let the students do the talking
 Ask, “How do you know that?”
 Require diagrams and representations
whenever possible
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A Closer Look:
CHEMISTRY
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Algorithms vs Understanding
What does it mean when students can
solve stoichiometry problems, but
cannot answer the following?
Nitrogen gas and hydrogen gas react to form
ammonia gas by the reaction
N2 + 3 H2  2 NH3
The box at right shows a mixture of nitrogen and
hydrogen molecules before the reaction begins.
Which of the boxes below correctly shows what the
reaction mixture would look like after the reaction
was complete?
A
B
C
D
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How Do You Know?
 All students know the
formula for water is H2O.
 Very few are able to cite
any evidence for why we
believe this to be the case.
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Do They Really Have an
Atomic View of Matter?
Before we investigate the inner workings of
the atom, let’s make sure they really believe
in atoms.
 Students can state the Law of Conservation of
Mass, but they will claim that mass is “lost” in
some reactions.
 When asked to represent matter at submicroscopic level, many sketch matter using a
continuous model.
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Where’s the Evidence?
Why teach a model of the inner workings of
the atom without examining any of the
evidence?
 Students “know” the atom has a nucleus
surrounded by electrons, but cannot use this
model to account for electrical interactions.
 Why disconnect the Bohr model of the atom from
the effort to understand the hydrogen line
spectrum?
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Uncovering Chemistry
Examine matter from outside-in instead
of from inside-out
 Observable Phenomena  Model
 Students learn to trust scientific thinking,
not just teacher/textbook authority
 Organize content around a meaningful
‘Story of Matter’
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Sample Cycle: Density
 Prerequisite activities
 Define volume by “counting cubes,” and
validate the formulas learned in math.
 Define mass as amount of matter,
measured using a balance.
 Develop law of conservation of mass –
through a lab with physical and chemical
changes
Sample Cycle: Density
 Density Lab and Follow-up
 Question: What is the relationship
between the mass of a solid and its
volume?
“Even if students correctly say ‘mass per unit volume’
rather than ‘mass per volume’ in interpreting M/V,
there is no conclusive assurance that they really
understand the meaning. Some do, but others have
merely memorized the locution. It is important to lead
all students into giving simple interpretation in
everyday language before accepting a regular use of
‘per.’ Many students do not know what the word
‘ratio’ means. Those having difficulty with reasoning
and interpretation should always be asked, at an
early stage, for the meaning of the word if they, the
text, or the teacher invoke it.”
A Arons, Teaching Introductory Physics, John Wiley &
Sons, 1997.
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 In worksheet 3 students make comparisons of the
mass, volume and density of pairs of objects based
on particle representations.
 Worksheet 4 further reinforces the notion that the
slope of a graph has physical meaning.
 The first quiz requires students to determine the
slope and perform standard calculations involving
density.
 In next activity: Density of a gas, students determine
the density of carbon dioxide. The fact that the value
is 3 orders of magnitude smaller than that of liquids
and solids sets the stage for the discussion of an
atomic model of matter that accounts for this
difference.
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Recap: What works
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Interactive engagement
Student discourse & articulation
Cognitive scaffolding
Multiple representational tools
Consensus-based model building
Explicit hierarchal organization of
ideas and concepts into models
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For more information
• Local workshops next summer (hopefully!)
in physics, chemistry, and physical
science.
• Modeling curricula do an excellent job
sequencing the curriculum to provide a
good storyline and to facilitate model
construction and deployment.
• Elements of the modeling approach can be
adapted to any curriculum.
• I am happy to provide advice, resources,
or assistance.