# Whats a Light Curve? Unexpected Reasoning Difficulties Learners Have Using Light Curves Tim Slater University of Wyoming Excellence in Higher Education.

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Whats 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

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

What is a variable star observers 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 planet 2. Kuiper Belt Object (KBO) 3. Frozen comet 4. 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 planet 2. Kuiper Belt Object (KBO) 3. Frozen comet 4. 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 1Graph 3 Graph 2Graph 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

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

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

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

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

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 DIFFICULTIES 1.Treating a graph as a picture – ICONIC INTERPRETATION 2.Confusing slope and height Slope is … – Rise over the Run – (y 2 -y 1 ) ÷ (x 2 -x 1 ) – y = m x + b – How fast the speed is changing

ICONIC INTERPRETATION WORKS SOMETIMES Treating a Graph as a Picture Whats 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? 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 10 20 30 40 50 DAYS 1 2

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 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")

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

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.

Whats 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

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