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 Conference 2014 in the Best Zone Paper Competition held in Indianapolis, IN on June.

…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 2

think like a novice and not an expert! craft an experiment with careful scaffolding 3 Calculate %error List some possible causes Change the mindset of students about how to think about errors Propagation of error Students… Faculty…

Developed four experiments… Stacking cookies Nuts & Bolts of extrapolation Stacking nested Styrofoam cups Nuts & Bolts of let’s make an error 4 ruler balance Each has data collection, model development, and simulations with error analysis

…and what do students do? So let’s examine the stacking cookies experiment 5

Just add data and presto you get a model Enter data Model (by linear regression) Simulation to manipulate a variable Predictions 6 Best-fit line

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 589% no difficulty Fall 2007 (n = 10 students)3.4 out of 5100% no difficulty Fall 2008 (n = 15 students)3.6 out of 593% no difficulty Fall 2010 (n = 15 students)3.5 out of 580% 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 % noticed error Fall % noticed error Fall % noticed error Fall % noticed error If you did (circled yes in question 2), did you correct for it? Be honest! Yes No Fall % of total corrected error Fall % of total corrected error Fall % of total corrected error Fall % of total corrected error For the Stacking Cookies Experiment 7

…and what about ruler error? 8 Here we have induced a constant error

Nuts & Bolts of Extrapolation Mass of bolt by extrapolation M total = M nut * n + M bolt Determine mass of the bolt on a balance - % error Student data …and they whine over the finding the equation Verify model by just add data spreadsheet n M total 9 Enter data into Google form for discussion Mass bolt with from one thru five nuts on it

The extrapolated value of the bolt 10

The pedagogical approach… …so now we can extent concepts using simulations 11

Suppose we used magnesium nuts? 12

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 21 st -century technology in classroom (ISTE, Educause…) 13

…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, see 14

Questions and more info… Scott Sinex –See the paper in proceedings atlantic/spring-2013/Investigating-and-Visualizing- Measurement-Error-for-Novice-STEM-Learners.pdf atlantic/spring-2013/Investigating-and-Visualizing- Measurement-Error-for-Novice-STEM-Learners.pdf –Contact me - My thanks to the ASEE Zone 1 selection committee! This work was supported by the NSF Division of Materials Research Partnership for Research and Education in Materials (PREM) Grant Numbers DMR and DMR Thanks for coming today!!! 15