1. 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

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

3. What is an amateur astronomer’s most important piece of equipment?

5. Scientists use transcriptions everyday to explain ideas and make predictions

6. 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

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

8. 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

9. 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

10. 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

11. 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?

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

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

14. 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

15. 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

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

17. 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
DAYS

18. 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
DAYS

19. The end goal is interpretation…..

20. Asteroid Rotation Rates

21. Asteroid Rotation Rates

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

27. http://graphjam. files. wordpress
graphJam.com

28. 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

29. 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 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),
Bell, A and Janvier, C. (1981). The interpretation of graphs representing situations. For the Learning of Mathematics. 2(1),
Fagan, E.R., A summary of research on student graphing misconceptions and their roots, EDC:
Clement, J. (1989). The concept of variation and misconceptions in Cartesian graphing. Focus on Learning Problems in Mathematics, 11(1-2),

30. 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