Transcript STEM_Day3_PPT - Region 11 Math And Science Teacher

Modeling in STEM
Day 3: STEM Integration
MSTA Region 11 Teacher Center
Modeling in STEM
Goals
1.Teachers
helping students develop
connections among STEM disciplines
through representation and translation.
2.Teachers helping students elicit their
mathematical, scientific, and engineering
thinking through modeling.
Sequence of the Day
Understanding Paper Airplanes
 Paper Airplane Contest Model-Eliciting
Activity
 Understanding MEAs and their Design
 Choices of MEA Participation
 Plans for implementation
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Review
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You have implemented a lesson now.
◦ Prepare for a gallery walk of your posters
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Keep a record of ideas you have heard
from others in terms of what you might
be able to use in your classroom.
Engineering Thinking
Review Lesh Translation Model
Lesh & Doerr (2003)
Let’s play with Paper Airplanes
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Get in teams of 3-4
◦ Each person in your team choose a different
paper airplane to build.
Make a target somewhere in the room
with a starting point of about 10 paces.
 Fly your plane and the other planes in
your group
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◦ Can you hit the target?
◦ Can you make the plane “float” toward the
target?
Let’s play with Paper Airplanes
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Record your observations about:
◦ What contributed to the differences in the
plane flights? Pilot? Construction? Plane
properties? What else?
◦ Which plane was the most accurate?
◦ Which plane was the best floater?
Paper Airplane Contest
Individually:
 Read the newspaper article and answer
the readiness questions.
In your teams:
 Read the problem statement and answer
the team questions together.
 Create a procedure for the judges of the
paper airplane contest
 Be prepared to share your solutions in a
2 minute presentation.
Representations Revisited
In your groups, jot down your ideas about
what representations were elicited in this
problem.
 How can you as a teacher foster multiple
representations on this problem?
Translations between representations?
 What are the “big” conceptual ideas that
are elicited in this problem?
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Ideas from the Field
Practical Advice for Implementing MEAs
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DON’T
Expect an MEA to be an
“easy fix”
Fixate on a “right” solution
Give students “hints”
Isolate teams from one
another
Just have students hand in
work
Move on to next unit
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DO
Prepare by KNOWING the
MEA content
Let students explore/fail
Ask students questions
Build in time for teams to
share partial solutions
Spend time critiquing each
others’ work
Connect MEA content to
formal principles
Ideas from the Field
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Student work from the Paper Airplane MEA
◦ You have been provided with 2 student team
samples of work.
◦ What do you see in these responses?
◦ What are some of the good STEM ideas
represented?
◦ What are some of the misconceptions?
◦ How well did they communicate their
understandings?
Samples of student work
In response to your need for an adequate equation to judge the paper plane
entrees in the categories of the most accurate flyer and the best floater, we
have created and tested equations for each. Each equation went through a
period of trial and error and thus proved to be the most fair for the required
criterion.
For the first category of the most accurate flyer, we determined that
the distance and the angle from the target should be factored into the equation
and we realized that if those two factors went into a shape, a triangle, the
hypotenuse was missing. Because of this missing component, we determined
that the equation for a hypotenuse in a triangle would be most effective for
finding accuracy. The equation: distance from the target2 + angle from the
target2 = accuracy2, was tested against sample data and it proved to be most
effective. The equation proved that the Golden Flyer with the plane Hornet
would be the most accurate overall.
For the second category of the best floater, we determined that the
average time in the air for each plane would work as the equation needed. The
equation: (a+b+c)/3 was tested and proved to work because the time in the air
is the only component needed for floating. The equation proved that Hornet
was the best floater and Pacific Blue was the best pilot.
Thank you for considering our equations to help better the judging
and fairness of this prestigious competition.
Samples of student work
We believe that certain measurements obtained during this competition should be
brought into account in the judging, however, we believe some areas hold more
value than others. Since we are looking to find the best floater and the most
accurate plane, we have divided the measurements to suit the requirements of the
category. For the floating competition the planes will be judged based on time in
flight and the distance from the start. For the accuracy competition the planes will
be judged based on the distance from the target and the angle from the target. We
will take the averages of all the measurements to keep the planes from winning
from one good toss.
For the floating competition, we feel that the planes should be mainly
judged on the time spent in the air. For this research we have decided on the
equation (Average Time)2 x (Average Distance) = Score. We incorporated
distance to avoid people making planes that launch straight up, and we feel that a
floater should travel a distance and not dive straight down. It should resemble the
path of a glider. We decided to square the average time to put more emphasis on
the time in the air. In this competition, the highest score wins.
For the accuracy competition, we decided the planes should be judged
on the distance from the target and the angle. For this reason we have developed
the formula 2(Average Distance from Target) + |Average Angle from Target| =
Score. We will take the absolute value of the angle so the score will not be
affected by a negative angle and the distance will be doubled to make it more
important than the angle. For this competition the lowest score wins.
What is a model?
a system that explains, describes, or represents
another system
 contains elements, operations, and relations
that allow for logical relationships to emerge
 sometimes not sufficient to completely
describe the system it represents
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◦ if it is a useful model, it closely approximates the
system in a manner that people can use when
working with the system without being
unnecessarily complex
Nature of
Model-Eliciting Activities
Model-Eliciting Activities (MEAs) are clientdriven, open-ended, realistic problems that
involve the development or design of
mathematical/scientific/engineering models
 These are broadening classroom experiences
that tap the diversity of learning styles and
strengths that students bring to the classroom
 Intended to make advanced STEM content and
substantive problem-solving experiences
accessible to a diversity of students
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Model-Eliciting Activities
Nature of MEAs:
 Realistic problems with a client
 Require team of problem solvers
 Product is the process for solving the
problem
◦ End product is a model that the client can
use
Motivation for Using MEAs
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How MEAs Have Helped
◦ Framework for constructing highly openended realistic problems
 Require model development
 Support development of teaming and
communication skills
◦ Meaningful contexts for students
◦ Increase student engagement: addressing
diversity and under-represented
populations
Paper Airplane Contest MEA
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Who was the client?
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What did the client need?
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How did your team go about meeting that
need?
MEA Design Principles
 Model-Construction
◦ Description: Ensures the activity requires the
construction of an explicit description, explanation, or
procedure for a mathematically significant situation
◦ What is a model?
 Elements
 Relationships among elements
 Operations that describe how elements interact
What models are the students developing when they solve
this MEA?
MEA Design Principles
 Reality
◦ Description: Requires the activity be posed in a
realistic engineering context and be designed so that
the students can interpret the activity meaningfully
from their different levels of ability and general
knowledge.
◦ Realistic contexts are constructed by:
 Gathering information from actual sources
 Making simplifying assumptions when information is
conflicting, missing, or difficult for students to use
What knowledge do students bring to this problem?
MEA Design Principles
 Self-Assessment
◦ Description: Ensures that the activity contains criteria
students can identify and use to test and revise their
current ways of thinking
 Students recognize the need for model
 Students use the client’s criteria to inform
refinements to their model
 Students must judge for themselves when they have
met the client’s needs
What is provided in this MEA that students can use to test
their ways of thinking?
MEA Design Principles
 Model-Documentation
◦ Description: Ensures that the students are
required to create some form of
documentation that will reveal explicitly how
they are thinking about the problem situation
What documentation are the students being asked
to produce in this MEA?
“Thought-Revealing”
What can student documentation tell us?
What information, relationships, and
patterns does the solution (model) take
into account?
 Were appropriate ideas and procedures
chosen for dealing with this information?
 Were any technical errors made in using
the preceding ideas and procedures?
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MEA Design Principles
 Model
Share-Ability and Re-Usability
◦ Description: Requires students produce solutions
that are shareable with others and modifiable for
other engineering situations
◦ Biggest challenge for students
 Tendency is to create a solution only for the
situation as given and only readable by the creators
 We are looking for the students to construct a
model that:
 Someone else can pick up and use
 Could be used to solve similar problems
 Extent to which students can achieve this can be
used in feedback and assessment strategies
MEA Design Principles
 Effective
Prototype
◦ Description: Ensures that the solution generated
must provide a useful learning prototype for
interpreting other situations
 Want the situations or concepts used in creating the
model to be useful in future coursework & practice
What are the “big” conceptual ideas?
Connections to Standards
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To which standards does this MEA connect?
◦ Consider math, science, and engineering
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Are there standards to which all MEAs
connect? Which ones?
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How can this help you as a teacher trying
to integrate STEM?
Choose an MEA
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Aluminum Bats
◦ Students use micrographs to measure average grain size in
aluminum (strength of materials) so the coach can choose
better bats.
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Ancient Crocodile
◦ Students compare the modern day animals with their
prehistoric cousins to help the camper decide the size of
the ancient beaver whose teeth he discovered.
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Departing on Time
◦ Students use airline departure times to compare airlines for
the Spanish Club so they don’t miss their connecting flight.
You might want to have at least one representative at each MEA
MEA Discussion
What standards were addressed in this
MEA?
 What were the big ideas elicited in this
MEA?
 What are possible follow-up activities that
could be done after this MEA?
 Did you go through the express-testrevise cycle?
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Plan for MEA Use
Read over the teacher materials that come
with one of the MEAs we did today.
 Make an implementation plan with your
team. This plan should include all parts of
the LESA model or the 5E model.
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◦ Launch, Explore, Share/Summarize, Apply
◦ Engage, Explore, Explain, Elaborate, Evaluate
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Include ideas for extensions to this
problem.
Exit Slip
On a separate piece of paper, reflect on
how modeling is represented in your
discipline and how it could be used to
help integrate STEM in your classroom.
 Hand your exit slip to one of the
facilitators as you leave the session.
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