Investigating and Visualizing
Measurement Error
for Novice “STEM” Learners
Scott A. Sinex
Department of Physical Sciences and Engineering
Prince George’s Community College
Largo, MD
Presented at ASEE Mid-Atlantic Spring Conference 2013 held at New York
City College of Technology, New York City, NY on 26-27 April.
…want students to be able to
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Know how good a measurement is
Graph and transform data
Derive mathematical models
Judge goodness-of-fit
Use simulations to explore multivariable models
Make predictions, interpret results, draw
conclusions
• Develop conceptual understanding
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"Sherman, set the WABAC machine to ..."
Sherman
Mr. Peabody
think like a novice and not an expert!
The Rocky & Bullwinkle Show
http://en.wikipedia.org/wiki/WABAC_machine
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Developed four experiments…
Stacking cookies
Nuts & Bolts of extrapolation
Stacking nested Styrofoam cups
Nuts & Bolts of let’s make an error
This is next!
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…and what do students do?
So let’s examine the stacking cookies experiment
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Just add data and presto you get a model
Enter data
Model by linear regression
Simulation to
manipulate a variable
Predictions
http://academic.pgcc.edu/~ssinex/excelets/NC/cookies_stack.xls
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For the Stacking Cookies Experiment
How would you characterize the use of the “just add data” interactive Excel
spreadsheet for this activity? Scale: very easy/easy/so, so /difficult/very difficult
Fall 2006 (n = 19 students)
3.5 out of 5
89% no difficulty
Fall 2007 (n = 10 students)
3.4 out of 5
100% no difficulty
Fall 2008 (n = 15 students)
3.6 out of 5
93% no difficulty
Fall 2010 (n = 15 students)
3.5 out of 5
80% no difficulty
Did you happen to notice that the rulers did not have the zero centimeter mark at the
end? (all rulers had the zero mark off from the end)
Yes
No
Fall 2006
53% noticed error
Fall 2007
40% noticed error
Fall 2008
33% noticed error
Fall 2010
67% noticed error
If you did (circled yes in question 2), did you correct for it? Be honest!
Fall 2006
37% of total corrected error
Fall 2007
20% of total corrected error
Fall 2008
27% of total corrected error
Fall 2010
27% of total corrected error
Yes
No
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…and what about ruler error?
http://academic.pgcc.edu/~ssinex/excelets/Ruler_error.xls
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Nuts & Bolts of Extrapolation
Mtotal
Mtotal = Mnut* n + Mbolt
Verify model by
just add data
spreadsheet
Enter data into
Google form
for discussion
Mass of bolt
by
extrapolation
Student data
…and they whine over
the finding the equation
Determine mass
of the bolt on a
balance - % error
n
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The extrapolated value of the bolt
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The pedagogical approach…
…so now we can extent concepts using simulations
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Suppose we used magnesium nuts?
http://epublications.bond.edu.au/ejsie/vol5/iss1/3/
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Why change?
• NRC Framework  Next Generation Science
Standards
• Common Core Standards in Mathematics
• AMATYC - The Right Stuff
• MAA CRAFTY College Algebra
• ASEE Innovation with Impact
• Enhance 21st-century technology in classroom
(ISTE, Educause…)
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…and students
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Are actively engaged
Are using accessible technology
Are involved in science process
Must think
Must develop an understanding of the model
See many multivariable systems
• More interactive Excel spreadsheets, see
http://academic.pgcc.edu/~ssinex/excelets/matsci_excelets.htm
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Questions and more info…
• Scott Sinex
– See the paper in proceedings
http://websupport1.citytech.cuny.edu/Faculty/hli/asee/proceedings.html
– Contact me - ssinex@pgcc.edu
– For papers - http://academic.pgcc.edu/~ssinex
• This work was supported by the NSF Division of
Materials Research Partnership for Research
and Education in Materials (PREM) Grant
Numbers DMR-0611595 and DMR-1205608.
Thanks for coming today!!!
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