Day 3: STEM Integration
MSTA Region 11 Teacher Center

Goals
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2.

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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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You have implemented a lesson now.
◦ Prepare for a gallery walk of your posters
Keep a record of ideas you have heard from others in terms of what you might be able to use in your classroom.

Lesh & Doerr (2003)

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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
◦ Can you hit the target?
◦ Can you make the plane “float” toward the target?

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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?

Individually:
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Read the newspaper article and answer the readiness questions.
In your teams:
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Read the problem statement and answer the team questions together.
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Create a procedure for the judges of the paper airplane contest
Be prepared to share your solutions in a
2 minute presentation.

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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?

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

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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?

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 target 2 + angle from the target 2 = accuracy 2 , 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.

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.

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 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
◦ 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

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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

Nature of MEAs:
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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

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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

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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?

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◦ 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?

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◦ 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?

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◦ 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?

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◦ 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?

What can student documentation tell us?
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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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◦ 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

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◦ 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?

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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?

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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.
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.
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

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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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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.
◦ Launch, Explore, Share/Summarize, Apply
◦ Engage, Explore, Explain, Elaborate, Evaluate
Include ideas for extensions to this problem.

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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.