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Using the SD Process to Teach���STEM and Common Core ���
Math & Science
Diana Fisher Math/Modeling Teacher, Wilson High School
Portland, Oregon [email protected]
6/12/12
Agenda s STEM Education and STEM Benchmarks
s Common Core Mathematics and Science
s Why System Dynamics?
s Learning Theory
s Grades 9 - 12 s System dynamics models in algebra, physics, biology
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Integrative STEM Education ♦ “… ideas and practice of science, mathematics, and
technology are so closely intertwined that we do not see how education in any one of them can be undertaken well in isolation from the others.”
♦ grounded in the tenets of constructivism ♦ inherently learner-centered and knowledge-centered ♦ learn using context of real-world problems ♦ provides for the social interaction so critical to the
learning process
“STEM, STEM Education, STEMania,” by Mark Sanders, The Technology Teacher, Dec/Jan 2009
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STEM Benchmarks s Science
s Scientific Inquiry –physical science, life science, earth and space science
s Personal and social perspective – population, natural resources, environmental quality, natural and human- induced hazards, global challenges
s Technology s Enhance learning, increase productivity, collaborate
constructing technology-enhanced models s Solve problems, make informed decisions in the real
world
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STEM Benchmarks s Engineering
♦ Apply knowledge of mathematics, science, and engineering ♦ Design and conduct experiments – and analyze data
s Mathematics s Use mathematical models to represent and understand
quantitative relationships – analyze change s Apply and adapt a variety of appropriate strategies to solve
problems s Understand how mathematical ideas interconnect and
build on one another to produce a coherent whole s Use representations to model and interpret physical, social,
and mathematical phenomena
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Common Core Math s Construct Functions
♦ Model & compare linear, quadratic, exponential patterns ♦ Describe qualitatively the functional relationships between
two quantities. ♦ Interpret functions in terms of the situation they model.
s Modeling s Links classroom math to everyday life, work, and decision-
making. s Models can shed light on math structures. s Model cycle: identify variables, form model, analyze and
draw conclusions, interpret results, validate conclusions. s Making math models is a Standard for Math Practice.
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Common Core Science s Crosscutting Concepts (5 of 7)
♦ Patterns: guide organization & study factors in relationships
♦ Cause & effect: Mechanisms and explanations ♦ Structure and function ♦ Stability and change: rates of change of a system ♦ Systems and system models
♦ Defining a system under study ♦ Specifying boundaries ♦ Making an explicit model of the system ♦ Testing ideas/understanding ideas ♦ Feedback
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Why System Dynamics? s System Dynamics: focused on the study of the
internal behavior of systems in our lives and the world
s Based on feedback theory and circular causation analysis
s Uses computer simulation to test mental models of how a system works
s Eases the transfer of concepts/models across disciplines (due to generic structures and software)
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Learning Theory
s Student-centered lessons (active learning mode) s Test “what-if” scenarios s Extend the model to incorporate new ideas
s Uses visual representation s Useful with a broad audience of students
s Emphasizes conceptual understanding s Multi-disciplinary problems
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Theory of Finite Differences time Distance01234
47101316
1st Diff
3333
time Distance01234
1st Diff 2nd Diff
-9.8-9.8-9.8
2 52 92.2122.6143.2
5040.230.420.6
Linear
Quadratic
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My Sequence of Extra Lessons s Motion Detector s Theory of Finite Differences s STELLA Models
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My Sequence of Extra Lessons s Motion Detector s Theory of Finite Differences s STELLA Models
s Simple generic types – match traditional problems s Coordinate diagram and equation s Experiment with model structure
s Introducing feedback s Writing– explaining circular causation
s Extending problems to new situations
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The Software: STELLA s Stock!
! !!
s Flow! !
s Converter!!
s Connector!
!
Population
birth rate
births
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Linear Function Model
Constant Inflow or Constant Outflow
Money in Shoebox
depositsper month
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Quadratic Function Model Linear Inflow or Linear Outflow
Displacement
Velocity
vel
acceleration
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Exponential Model:���Reinforcing Feedback
Money in Bank
interest addedper month
monthlyinterest rate
months
Mon
ey
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Exponential Model:���Reinforcing Feedback
Money in Bank
interest addedper month
monthlyinterest rate
months
Mon
ey
Money inBank
interest addedper month
+
+
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Exponential Model���Balancing Feedback
Amount ofRadioactive Substance
amount lostper week
weeklydecay rate
weeks
Am
t.Sub
stanc
e
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Exponential Model���Balancing Feedback
Amount ofRadioactive Substance
amount lostper week
weeklydecay rate
weeks
Am
t.Sub
stanc
e
Amount ofRadioactiveSubstance
amount lost perweek
-
+
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Population Model Exponential Growth and Exponential Decay
Populationbirths deaths
birth rate death rate
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Two Population Model
RabbitsRabbit births Rabbit deaths
rabbit birthfraction
rabbit deathfraction
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Two Population Model
RabbitsRabbit births Rabbit deaths
WolvesWolf birthsWolf deaths
rabbit birthfraction
rabbit deathfraction
wolf birthfraction
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Two Population Model
RabbitsRabbit births Rabbit deaths
WolvesWolf birthsWolf deaths
Area
Rabbit densityRabbit kills per wolf
~
Wolf Death Rate~
rabbit birthfraction
rabbit deathfraction
wolf birthfraction
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Course Objectives s Prepare students to identify and analyze
problems in the world from which they can gain understanding by building and analyzing SD models. !
s Develop skill in model building, in analyzing model design and output/feedback, and in explaining what they learn.!
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Screening for Tay-Sachs
Newborns
Carriers
Screened Carriers
Nonafflicted Afflicted
Nonafflicted Births
Carrier Births
Screening
Afflicted Births
Pregnancies
Birth Rate
∑
Total Population Minus Afflicted
Nonafflicted Nonafflicted
∑
Total Population Minus Afflicted
Nonafflicted Deaths
Carrier DeathsScreened Carrier Deaths
Afflicted Deaths
Afflicted Death Rate
Death Rate
Death Rate
Rate of Screening
Chance of Screening a Carrier
Carrier Carrier
New Carrier Mutations
∑
Non Nonafflicted Births
Nonafflicted CarrierCarrier Carrier Result
Nonafflicted Carrier Result
∑
Total Population
∑
Screened Population
Carrier Carrier
∑
Nonafflicted Population
∑
Total Carrier Population
Screened Nonafflicted
Non Screening
Proportion Carriers
New Afflicted Mutations
Scr Non Death
Rate of Screening
Chance of Screening a Carrier
How Does Genetic Screening Affect a Closed Community Afflicted with the Tay-Sachs Disease? !
by Charles Runckel and Ben Zimmerman �
Two students:Age 16 years
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Portland’s ���Traffic
Metro Population
Busses
East Side Light Rail Riders
Change in Riders
Percent that ride light rail
Init Percent ride light rail
Average Car Commuting Time
~Effect of Average Commuting Time
on Percent that ride Light Rail
Change in Metro Population
Metro Initial Growth Rate
~Effect of Metro Density on Metro Growth Rate
Metro Growth Rate
Number of Commuters
Land in Metro Growth Boundry
Initial Density
Current Density
Current Vs Initial Density
Bus RidersChange in Bus Riders
Percent Bus Riders
Drive Alone
Change in Drivers
Percent that drive alone
Car Poolers
Change in Car Poolers
Percent Car Poolers
Lane Miles in the Metro Area
Cars per Lane Mile
BussesRiders
per bus
Cars
Cars used for car pooling
People per car pool
Init vehicles per lane mile
Current Vs Init Traffic
Init Percent Drive Alone
Average Car Commuting Time
Average Car Commuting Time
Init Car Commute time
Current Vs Init Traffic
~Effect of Commuting time on Percent that ride the bus
Init Percent Bus Riders
Average Car Commuting Time
~Effect of Commuting time on percent that drive alone
INIT Car Poolers Percent
Average Car Commuting Time
~Effect of Average Commuting time on Percent that car pool
Percent Commuters
Current Density
Cars
Cars used for car pooling
Three students: ages 15 years
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Reforestation in Oregon
Seedlings
Saplings
Harvestable Trees
Regeneration
Seedling Survivors
Maturing Period
Matured Trees
Harvested Trees
Natural Deaths
Natural Lifespan
Trees Planted
Manual Regeneration
Animal Consumption
Harvesting Rate
Consumption Rate
Planted Tree Survival Rate
Seedling Lifespan
Two students age 16 and one age 17
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CC Modeling Systems s View Student Work
s model diagram, paper, video presentation s Link System Dynamics to National Education Standards s Resources and Research
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Why System Dynamics? s It gives us a chance to understand that
s Cause and effect are not closely related in time or space
s Low leverage policies are usually ineffective
s High leverage policies are usually difficult to apply correctly
s The cause of the problem is within the system
s There is conflict between short-term and long-term goals
s There is a tendency for goals to spiral downward
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Why System Dynamics? s It gives us a chance to understand that
s Cause and effect are not closely related in time or space
s Low leverage policies are usually ineffective
s High leverage policies are usually difficult to apply correctly
s The cause of the problem is within the system
s There is conflict between short-term and long-term goals
s There is a tendency for goals to spiral downward “Coming to an understanding of systems must be a
participative experience. Computer modeling allows an accelerated vicarious experience. …immersion in such
active learning can change mental models.” Jay Forrester
6/12/12
Resources s Diana Fisher
s [email protected] s www.ccmodelingsystems.com
s Creative Learning Exchange s www.clexchange.org
s Systems Thinking in Schools s www.watersfoundation.org