What’s a Light Curve? Unexpected Difficulties Learners Have Using Graphs Tim Slater University of Wyoming Excellence in Higher Education Endowed Chair Stephanie Slater Center for Astronomy & Physics Education Research CAPER Team http://www.caperteam.com

I need someone well versed in the art of torture – do you know PowerPoint?

What is an amateur astronomer’s most important piece of equipment? http://shanghaiist.com/attachments/claudinekharris/napkins.jpg

http://wiki.vizthink.com/files/08n532/airport_napkin_500.jpg

Scientists use transcriptions everyday to explain ideas and make predictions http://thefastertimes.com/sexanddating/files/2010/04/lemondrop-graph1.jpg

No talking with your neighbor or searching Google We are going to look at some ideas and select which are the best ones for some given situations Considering its distance and size, Pluto is most likely a/an Terrestrial planet Kuiper Belt Object (KBO) Frozen comet Asteroid No talking with your neighbor or searching Google

Organic Voter Response System no hanging chads 

No talking with your neighbor or searching Google We are going to look at some ideas and select which are the best ones for some given situations Considering its distance and size, Pluto is most likely a/an Terrestrial planet Kuiper Belt Object (KBO) Frozen comet Asteroid No talking with your neighbor or searching Google

Consider the light source over there… Consider the light source over there…. Which of the following best represents a brightness versus time graph for it? Graph 1 Graph 3 Graph 2 Graph 4

Consider two stars, one bright and one dim… Consider two stars, one bright and one dim….Which of the following best represents a brightness versus time graph for them? Graph 1 Graph 3 Graph 2

Consider two stars, one bright and one dim… Consider two stars, one bright and one dim….Which of the following best represents a brightness versus time graph for them? Graph 1 Which is which? Explain your reasoning. Are their other interpretations?

Which of the following best represents the light curve of a variable star? Graph 1 Graph 3 Graph 2 Graph 4

SEEMINGLY UNRELATED: Sketch a graph speed versus time for a bicyclist riding over a hill

Sketch a graph speed versus time for a bicyclist riding over a hill REASONING DIFFICULTIES Treating a graph as a picture – ICONIC INTERPRETATION Confusing slope and height Slope is … Rise over the Run (y2-y1) ÷ (x2-x1) y = m x + b How fast the speed is changing Graph 1 Graph 2

ICONIC INTERPRETATION WORKS SOMETIMES Treating a Graph as a Picture What’s physically going on as this star changes its brightness? Getting larger & brighter Getting smaller & dimmer

ICONIC INTERPRETATION WORKS SOMETIMES Treating a Graph as a Picture Is this supernova shrinking?

At Day #40, which star, 1 or 2, is getting brighter faster? Most common answer is Star #1, because at Day #40, Star #1 is at a higher point. “highest must be greatest” Slope/Height Confusion is caused by students constructing graphs by plotting points from tables focusing students’ attention on points rather than shapes or trends. Star Brightening 2 1 10 20 30 40 50 DAYS

When is star 4 brighter than star 3? Most students answer with a particular point in time (e.g., d=30) rather than an interval. Demonstrates limited understanding of the story graphs are telling Point/Interval Confusion Star Brightening 3 4 10 20 30 40 50 DAYS

The end goal is interpretation….. http://www.aavso.org/images/terrellfig2.gif

Asteroid Rotation Rates http://www.dur.ac.uk/physics.astrolab/a_lightcurve/a_lightcurve.html

Asteroid Rotation Rates http://www.dur.ac.uk/physics.astrolab/a_lightcurve/a_lightcurve.html

http://www.astro.umd.edu/~miller/nstar.html

http://imagine.gsfc.nasa.gov/docs/science/know_l2/pulsars.html

http://www.nasa.gov/mission_pages/kepler/overview/index.html

http://www.nasa.gov/mission_pages/kepler/multimedia/images/aas_conference.html

The Light Curves of Different Types of Supernovae (adapted from Qing Zhang's "Introduction to Supernovae")

http://graphjam. files. wordpress http://graphjam.files.wordpress.com/2009/07/funny-graphs-respect-pluto.jpg graphJam.com

Key Take Away Messages Science often communicates using the mathematics of graphs (often on napkins) A graph is a visual representation exhibiting a relationship between two sets of numbers (written as vertical axis versus the horizontal axis) Astronomers often look at light curves (how brightness changes with respect to time) Learners struggle with (i) iconic representations, (ii) slope/height confusion, and (iii) point/interval confusion And public opinion about Pluto is still evolving

For More Reading Richwine, Pebble (2007). The impact of authentic science inquiry experiences studying variable stars on high school students' knowledge and attitudes about science and astronomy and beliefs regarding the nature of science. Ph.D. dissertation: The University of Arizona, AAT 3254711. Source: DAI-A 68/02 Leinhardt, G, Zaslavsky, O, and Stein M. (Spring 1990) Functions, Graphs and Graphing: Tasks, Learning and Teaching. Review of Educational Research , 60(1), 37-42. Bell, A and Janvier, C. (1981). The interpretation of graphs representing situations. For the Learning of Mathematics. 2(1), 34-42. Fagan, E.R., A summary of research on student graphing misconceptions and their roots, EDC: http://www2.edc.org/edc-research/curriki/ROLE/lc/sessions/session6/MisconOnGraphs.pdf Clement, J. (1989). The concept of variation and misconceptions in Cartesian graphing. Focus on Learning Problems in Mathematics, 11(1-2), 77-87.

But, it says so on the graph But, it says so on the graph! Reasoning Difficulties Learners Have Using Light Curves Tim Slater University of Wyoming Excellence in Higher Education Endowed Chair Stephanie Slater Center for Astronomy & Physics Education Research CAPER Team http://www.caperteam.com