What’s a Light Curve? Unexpected Reasoning Difficulties Learners Have Using Light Curves

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

2. I need someone well versed in the art of torture. Do you know PowerPoint?

3. What is a variable star observers most important piece of equipment?

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

6. 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

7. Organic Voter Response System no hanging chads 

8. 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

9. 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

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

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

12. Brightness vs. time graph for bright & dim starsWhat do students say?? Graph 1 Graph 2 Graph 3 16% 42% 42%

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

14. Which are variable star graphs? What do students say?? Graph 1 Graph 2 Graph 3 Graph 4 77 % say all

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

16. 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

17. ICONIC INTERPRETATION WORKS SOMETIMESTreating a Graph as a PictureWhat’s physically going on as this star changes its brightness? Getting larger & brighter Getting smaller & dimmer

18. ICONIC INTERPRETATION WORKS SOMETIMESTreating a Graph as a PictureIs this supernova shrinking?

19. At Day #40, which star, 1 or 2, is getting brighter faster? • Only 50% say Star #2 • 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

20. When is star 4 brighter than star 3? • Only 18% give range • 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 3 Star Brightening 4 10 20 30 40 50 DAYS

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

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

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

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

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

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

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

29. Imagine you have four bottles half filled with water. Draw a line across each bottle showing where the water level would be.

30. graphJam.com

31. 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

32. 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.

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