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

Graphs

Tim SlaterUniversity 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?

Scientists use transcriptions everyday to explain ideas and make predictions

http://thefastertimes.com/sexanddating/files/2010/04/lemondrop-graph1.jpg

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 1. Terrestrial planet2. Kuiper Belt Object (KBO)3. Frozen comet4. Asteroid

No talking with your neighbor or searching Google

Organic Voter Response System

no hanging chads

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 1. Terrestrial planet2. Kuiper Belt Object (KBO)3. Frozen comet4. Asteroid

No talking with your neighbor or searching Google

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….Which of the following best represents a brightness

versus time graph for them?

Graph 1

Graph 2

Graph 3

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 2

Graph 3

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

Graph 1

Graph 2

REASONING DIFFICULTIES1. Treating a graph as a picture –

ICONIC INTERPRETATION

2. Confusing slope and height• Slope is …

1. Rise over the Run2. (y2-y1) ÷ (x2-x1)

3. y = m x + b4. How fast the speed is

changing

ICONIC INTERPRETATION WORKS SOMETIMESTreating 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 SOMETIMESTreating 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

10 20 30 40 50 DAYS

1 2

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

10 20 30 40 50 DAYS

3

4

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://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")

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!Reasoning Difficulties Learners Have Using

Light Curves

Tim SlaterUniversity of Wyoming

Excellence in Higher Education Endowed Chair Stephanie Slater

Center for Astronomy & Physics Education Research CAPER Team

http://www.caperteam.com