Investigating and Visualizing Measurement Error

for Novice “STEM” Learners

Scott A. SinexDepartment of Physical Sciences and Engineering

Prince George’s Community CollegeLargo, 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• 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 ..."

think like a novice and not an expert!

Mr. PeabodySherman

http://en.wikipedia.org/wiki/WABAC_machine

The Rocky & Bullwinkle Show 3

Developed four experiments…Stacking cookies

Nuts & Bolts of extrapolation

Stacking nested Styrofoam cups

Nuts & Bolts of let’s make an error

This is next!4

…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

6http://academic.pgcc.edu/~ssinex/excelets/NC/cookies_stack.xls

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! Yes No

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

For the Stacking Cookies Experiment

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…and what about ruler error?

8http://academic.pgcc.edu/~ssinex/excelets/Ruler_error.xls

Nuts & Bolts of Extrapolation

Mass of boltby

extrapolation

Mtotal = Mnut* n + Mbolt

Determine massof the bolt on abalance - % error

Student data…and they whine over

the finding the equation

Verify model by just add data spreadsheet

n

Mtotal

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Enter data into Google form for discussion

The extrapolated value of the bolt

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The pedagogical approach…

…so now we can extent concepts using simulations11

Suppose we used magnesium nuts?

12http://epublications.bond.edu.au/ejsie/vol5/iss1/3/

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

• 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, seehttp://academic.pgcc.edu/~ssinex/excelets/matsci_excelets.htm

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Questions and more info…

• Scott Sinex– See the paper in proceedingshttp://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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