Using the SD Process to Teach STEM and Common Core Math &...

6/12/12

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

6/12/12

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

6/12/12

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

6/12/12

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

6/12/12

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.

6/12/12

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

6/12/12

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)

6/12/12

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

6/12/12

My Sequence of Extra Lessons s  Motion Detector

6/12/12

Motion Detector Linear

Parabolic

Vel

m/s

T(sec)

+

0

-

Vel

m/s

T(sec)

+

0

- ?

?

6/12/12

Motion Detector��

Linear and Quadratic relationships

6/12/12

My Sequence of Extra Lessons s  Motion Detector s  Theory of Finite Differences

6/12/12

Theory of Finite Differences time Distance01234

47101316

1st Diff

3333

Linear

6/12/12

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

6/12/12

My Sequence of Extra Lessons s  Motion Detector s  Theory of Finite Differences s  STELLA Models

6/12/12

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

6/12/12

The Software: STELLA s  Stock!

! !!

s  Flow! !

s  Converter!!

s  Connector!

!

Population

birth rate

births

6/12/12

Linear Function Model

Constant Inflow or Constant Outflow

Money in Shoebox

depositsper month

6/12/12

Quadratic Function Model Linear Inflow or Linear Outflow

Displacement

Velocity

vel

acceleration

6/12/12

Oscillatory Behavior��with the Motion Detector

6/12/12

Simple Oscillation Model��Harmonic Motion

Displacement

Velocity

vel

acceleration

6/12/12

Exponential Model:��Reinforcing Feedback

Money in Bank

interest addedper month

monthlyinterest rate

months

Mon

ey

6/12/12

Exponential Model:��Reinforcing Feedback

Money in Bank


monthlyinterest rate

months

Mon

ey

Money inBank


+

+

6/12/12

Exponential Model��Balancing Feedback

Amount ofRadioactive Substance

amount lostper week

weeklydecay rate

weeks

Am

t.Sub

stanc

e

6/12/12

Exponential Model��Balancing Feedback

Amount ofRadioactive Substance

amount lostper week

weeklydecay rate

weeks

Am

t.Sub

stanc

e

Amount ofRadioactiveSubstance

amount lost perweek

-

+

6/12/12

Population Model Exponential Growth and Exponential Decay

Populationbirths deaths

birth rate death rate

6/12/12

Two Population Model

RabbitsRabbit births Rabbit deaths

rabbit birthfraction

rabbit deathfraction

6/12/12



WolvesWolf birthsWolf deaths



wolf birthfraction

6/12/12



WolvesWolf birthsWolf deaths

Area

Rabbit densityRabbit kills per wolf

~

Wolf Death Rate~



wolf birthfraction

6/12/12


6/12/12

Teaching a Year-Long��System Dynamics Modeling ��

Course in High School

6/12/12

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.!

6/12/12

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

6/12/12

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



Init Car Commute time

Current Vs Init Traffic

~Effect of Commuting time on Percent that ride the bus

Init Percent Bus Riders


~Effect of Commuting time on percent that drive alone

INIT Car Poolers Percent


~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

6/12/12

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

6/12/12

Student Reflection Franklin High School (1999)

6/12/12

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

6/12/12

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

6/12/12

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

6/12/12

Thank You��

System Dynamics Modeling:��A Different Way to Think “We cannot solve our problems with the same thinking we used when we created them.”— Albert Einstein

Using the SD Process to Teach STEM and Common Core Math &...

Documents

Transcript of Using the SD Process to Teach STEM and Common Core Math &...