arXiv:1303.1768v1[physics.ed-ph]7Mar2013 4th
Fermi Symposium : Monterey, CA : 28 Oct-2 Nov 2012 1
Using the Big Ideas in Cosmology to Teach College Students
McLin, K. M., Cominsky, L. R., Metevier, A. J.
Sonoma State University, 1801 East Cotati Ave, Rohnert Park, CA 94928, USA
Coble, K.
Chicago State University, Department of Chemistry and Physics, 9501 South King Dr., Chicago, IL, 60628,
USA
Bailey, J. M.
University of Nevada, Las Vegas, Department of Teaching and Learning, 4505 South Maryland Parkway,
Box 45305., Las Vegas, NV, 89154, USA
Recent advances in our understanding of the Universe have revolutionized our view of its structure, composition
and evolution. However, these new ideas have not necessarily been used to improve the teaching of introductory
astronomy students. In this project, we have conducted research into student understanding of cosmological
ideas so as to develop effective web-based tools to teach basic concepts important to modern cosmology. The
tools are intended for use at the introductory college level. Our research uses several instruments, including
open-ended and multiple choice surveys conducted at multiple institutions, as well as interviews and course
artifacts at one institution, to ascertain what students know regarding modern cosmological ideas, what common
misunderstandings and misconceptions they entertain, and what sorts of materials can most effectively overcome
students difficulty in learning this material. These data are being used to create a suite of interactive, webbased
tutorials that address the major ideas in cosmology. One common misconception that students in our
introductory courses possess is that scientific explanations are “made up,” and not supported by observational
data. Having students engage with real data is a powerful means to help students overcome this misconception.
For this reason, the tutorials we are developing include authentic student interaction with actual data where
possible. Students master the scientific concepts and reasoning processes that lead to our current understanding
of the universe through interactive tasks, prediction and reflection, experimentation, and model building. This
workshop will demonstrate the use of some of the modules we have created and will allow participants to test
the modules for themselves.
1. Introduction
The past several decades have seen a revolution in
our understanding of cosmology. Cosmological parameters
like the Hubble constant have been measured
to unprecedented precision [Freedman et al. 2001], as
has the geometry of the universe [Lange et al. 2001,
Spergel et al. 2003]. In addition, observations of distant
supernovae have shown that the cosmic expansion
rate is increasing with time [Riess et al. 1998,
Perlmutter et al. 1999], and surveys of galaxies have
revealed how cosmic structures have evolved over time
[Abazajian et al. 2003]. These observations and others,
along with powerful computer models, have given
us unprecedented insight into how the universe began
and how it has evolved and continues to evolve.
However, these new ideas have not necessarily been
used to improve our teaching of introductory astronomy
students. The disconnect is partly caused by the
fast pace at which cosmological discoveries have accumulated;
textbook publishers and course instructors
have been hard-pressed to keep up. A contributing
factor has been the low emphasis given to cosmological
topics in typical introductory textbooks [Bruning
2006a,b] and placement of cosmology in the last week
or two of the typical introductory course. The lack
of cosmological focus is unfortunate given what we
now about the origin and evolution of the Universe.
What’s more, cosmological topics are often of great
interest to students [Pasachoff 2002].
The Big Ideas in Cosmology project puts recent cosmological
advances at the fore, making them the primary
focus of a 15 week long course for general education
(GE) undergraduate students. The underlying
ideas behind the curriculum design are that interaction
with data is vital if students are going to fully understand
the material, and that preexisting concepts
held by the students can inhibit their learning and
must be addressed directly. The curriculum employs
computer interactive simulations that allow students
to “measure” spectra, brightness, and other relevant
properties of systems being studied, and then allow for
the students to formulate or test models to explain the
data. In addition, the interactives and text materials
are designed to address concepts with which research
shows students often have difficulty.
This article describes the research and curriculum
development project, as well as several of the interactive
materials that have been developed thus far.
The purpose of our workshop at the ASP was to have
participants learn about the curriculum and try out
some of the interactives. The remainder of the article
will describe the basic organization of the cosmology
curriculum, give an overview of the research program
behind it, and an idea of the remaining development
and evaluation methods we will use to complete it.
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2. The Curriculum
The cosmology curriculum is being designed to address
student misconceptions whenever possible. Recent
publications from Wallace, Prather, and Duncan
[2012] and our own group [Bailey et al. 2012,
Coble et al. 2013, Trouille et al. 2012] have documented
some of these student misconceptions. The
curriculum includes traditional text, static imagery
and video, as well as computer-based interactive activities.
Emphasis is given to student experiences with
real datasets and measurements of the data. Because
most cosmological models are mathematical in nature,
we have introduced simple math exercises that use
graphing and proportions throughout, moving from
simpler to more complex treatments as the course progresses.
In addition, students are asked to reflect upon
the material they are learning. They must give feedback
to the computer learning system so that both
they and their instructor have a running tally of their
progress through the material.
2.1. Organization
The course is organized into three thematic modules,
and each module is divided into five chapters.
A chapter covers approximately one week in an introductory
course.
The first module is focused on basic ideas of size
and time scales of the Universe and its contents. The
purpose of this module is to bring students to a level of
comfort when thinking about relevant size scales, since
research and experience show that they often have difficulty
doing so. For instance, our own research shows
that students can have difficulty differentiating between
objects like the solar system, the galaxy and the
Universe, and between the relative sizes of each. Module
One also includes a chapter on the timescales relevant
to studying cosmology. Topics include the history
of Earth and the solar system, timescales of stars
and galaxies, etc. There is also a chapter in which
light and telescopes are explored - since this curriculum
is intended for an introductory course, we do not
assume that the students will have learned about the
electromagnetic spectrum previously. Finally, the last
chapter of the module introduces the modifications of
space and time inherent to special relativity, including
spacetime and invariance of the laws of physics.
This chapter is useful later when students learn about
general relativity, but much of it can be skipped if
instructors wish.
Module Two explores gravitation from a Newtonian
framework and from the curved spacetime perspective
of general relativity. This material is then applied to
learning about dark matter and the various lines of
evidence for it. The module introduces some of the
more involved treatments of data analysis and modeling,
albeit at a simple level. Module Two also includes
a chapter on black holes, as they are of general interest
to students, and they provide a good application
of ideas from general relativity. The treatment of relativity,
both special and general, goes beyond what is
typical for an introductory course. We try to avoid the
often confusing visuals used to discuss spacetime and
its curvature, and instead use a description more focused
on how curvature can be described by the effect
it has on distances between points in a space.
Module Three addresses most of the fundamental
concepts of cosmology. These include cosmic expansion,
conditions in the early Universe, the cosmic microwave
background and large scale structure, and
dark energy and the fate of the Universe. Each of
these topics is given its own chapter so that it can
be explored in some detail. In addition, many of the
tools developed in earlier modules are finally brought
to full flower in Module Three. Ideas from Newtonian
and Einsteinian gravity, electromagnetic radiation,
distance measurement techniques, and others,
are employed to understand the modern scientific conception
of how the Universe has been evolving since its
formation. In addition, we continue to use and build
upon mathematical tools like graphing and model fitting
that have been employed in previous chapters.
An overview of the three modules and the chapters
they contain can be seen in Table I.
2.2. Pedagogical Approach
Our goal is to approach this material in a more sophisticated
manner than is generally found in the typical
text. We chose an online format to enable the use
of interactive activities, which are integral to student
learning. The curriculum does include plain text and
static images, but we emphasize that the computer
exercises are not “supplementary.” They are a vital
part of the material and are built right into the flow
of the text.
Each chapter has the same format. It begins with a
short video intended to introduce the primary theme
of the chapter and get students thinking about it. The
chapter is then divided into sections that cover one
particular topic, and these sections are introduced using
fictional “dialogues” between archetypal students.
When possible, the dialogues use student-derived language
to discuss the topic of that particular section,
with phrases gleaned from our research. The dialogues
address commonly held misconceptions when appropriate.
Our intent is to introduce new science topics
in the students’ own language, and to address misconceptions
that we and others have found are common
to the target audience of GE students. Research
has shown that students learn better when new concepts
are based upon their existing ideas about the
world [Bransford et al. 2006], and so we incorporate
their ideas from the outset. The students are asked
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Table I Organization of the Curriculum
Module Chapter
1. Our Place in the Universe: 1. The Size and Scope of Space
Space and Time 2. Observing the Universe: Light and Telescopes
3. Motion and Time
4. Measuring Distances
5. Special Relativity
2. The Dark Side of 6. Classical Physics: Gravity and Energy
the Universe: Gravity, 7. Dark Matter
Black Holes and 8. General Relativity
Dark Matter 9. Black Holes
10. Gravitational Lensing
3. Our Evolving Universe: 11. Cosmic Expansion and the Hubble Flow
Past, Present and 12. The Early Universe
Future 13. The CMB and Large Scale Structure
14. Dark Energy
15. Cosmic Concordance and the Fate of the Universe
Warm-up Dialog:
elicit student
idea
Text: including
Figures and
visualizations
Short
Interactive
Task
Activity with
real data
Figure 1: Flow chart of the pedagogical design for each section. Chapters typically contain several sections, each of
which explores a single topic related to the subject of the chapter.
to think about each dialogue and choose one of the
fictional speakers with whom they most agree and explain
why. A sample dialogue is given below:
Some students are looking through a telescope
at a star.
Alicia says, “How many light years away
do you think this star is? Do you think we
could measure the distance to it?”
Bill replies, “No way; its physically impossible
because we can’t go there.”
“I dont think we have to go there if we use
the correct method,” Corey says, “like in
geometry class when we learned how to triangulate
distances on construction sites.”
“But I thought that would only work on
Earth because we are there,” Alicia says.
Corey says, “I think it will work everywhere;
its just a different scale.”
Which student(s) do you agree with, and
why?
a. Alicia
b. Bill
c. Corey
d. None
The dialogues are followed by a text passage, with
illustrations or visualizations as needed, and then an
exercise of some sort. The exercises can be ranking
tasks, simple numerical exercises or a short interactive
computer activity. Throughout the lesson students
are asked to record their thoughts and answers
to questions for later review. Students are given automatic
feedback about the acceptability of their answers,
and their responses are recorded so that they
and the instructor have a running record of how their
thinking evolves over time.
Each chapter will generally have several sections as
described above. When all the important topics for
a chapter have been explored, the chapter closes with
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a longer summary “Wrapping it Up” activity, and an
exercise called a “Mission Report.” The Wrapping It
Up generally involves the students working with actual
datasets and integrating the important topics in
the chapter. The Mission Report is graded for accuracy
and is an easy way for the instructor to assess
whether or not the student has mastered the most
important learning objectives in the chapter. It also
provides an opportunity for the student to provide
feedback about the learning efficacy of the chapter
materials. A schematic overview of the pedagogical
flow is shown in Figure 1.
2.3. Sample Interactives
An integral part of each chapter is a set of computer
interactive exercises. In this section we describe
one of these in order to give a flavor for how they
are used in the curriculum. The example described is
part of Chapter 4, on the cosmic distance scale. We
cite the main sequence (MS) fitting method, which is
a standard candle distance method. In this method,
the MS of a cluster is compared to a fiducial one with
known distance. The offset in brightness on a colormagnitude
diagram between the observed cluster and
the fiducial gives their relative distance. The computer
exercise allows the student to slide the observed
cluster’s MS up and down until it overlays the fiducial.
The interactive tool gives a running display of the offset
in magnitudes and converts it to a distance for the
observed cluster. No attempt is made to get a “best
fit” in this exercise, nor do we worry about complications
like extinction. The goal is that students will
understand that the difference in brightness between
objects is related to their distance from us. Similar
interactive exercises are used to teach the other rungs
on the cosmic distance ladder. A detail from the MS
fitting exercise is shown in Figure 2.
3. Research Overview
This curriculum is strongly based upon results from
research into the understanding that undergraduate
students bring to their GE astronomy classes. We
have conducted open-ended surveys at multiple institutions
as well as in-depth studies at a single institution.
The research is ongoing, and we have recently
published the first of our results. The first publication
[Bailey et al. 2012] describes the findings from a
set of open-ended questionnaires that explore student
understanding of the size, structure, composition and
evolution of the Universe. These surveys were done
prior to instruction, with a total of 1270 students participating;
more than 200 responded to any of three
surveys. The research uncovered many areas of difficulty
for students. For instance, more than a quarter
ApparentVisualMagnitude
8
12
0
4
K MGAB F
Stellar Spectral Type
Figure 2: Detail of the main sequence fitting tool that
allows students to slide the MS of one star cluster up and
down until it overlies that of a fiducial cluster of known
distance.
of students had difficulty explaining the differences between
the solar system, the Galaxy and the Universe.
They also were unsure of the hierarchal relationships
between them. Fewer than a third of the students
thought that the age of the Universe was measured in
billions of years, and more than a quarter did not even
attempt an answer for this item. In addition, some
students did not even believe that there was or even
could be scientific evidence for some of the subjects
queried; fewer than 20% thought that it was possible
to know anything about the age of the Universe. One
important finding, consistent with earlier studies, was
that many students have trouble with the specialized
language of science. For instance, terms like light-year
or Big Bang can be confusing when students attempt
to interpret their meaning in the context of everyday
usage. Care must be taken by instructors to ensure
that their students appreciate the special meanings
these terms have in a scientific context.
Another two papers are forthcoming: [Coble et al.
2013, Trouille et al. 2012]. The first of these focuses
on distance and size scales. The second looks at student
understanding of relevant timescales in cosmology
and the Big Bang Theory. These studies are based
on results covering several semesters of an introductory
course in astronomy at an urban minority-serving
institution. Research instruments included: essays
given as homework, open-ended surveys given after
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lecture but before lab, exam questions (essay, MC,
TF, FIB) and interviews. Data was collected over
five semesters and spans the entire course, from preinstruction
through the final exam. Depending on the
instrument and question, N ∼60 for courses artifacts.
A subset of 15 students was interviewed in order to
delve more deeply into their thoughts about cosmology.
In general, the results from these studies corroborate
those from Bailey et al. [2012]. Unsurprisingly,
students do not know a lot about cosmology at the
start of the term. However, student understanding
can increase through the semester and is greatly enhanced
if the students are given relevant and engaging
exercises; lecture alone was not seen to improve
student understanding significantly. Students’ poor
math skills are a hinderance to mastering new cosmological
concepts, but continued practice with activities
that involve making and interpreting graphs,
and working with proportional relationships, can improve
these skills over the semester. Disturbingly, it is
found that students have difficulty letting go of some
of their preconceived ideas about the size of the Universe.
Working with real data seems to help students
understand the evidence behind scientific world views,
and also to discard some of their mistaken preconceptions.
Since basic math skills are needed for most
data-driven activities, helping students attain these,
especially in terms of working with graphical data and
using simple proportional relationships to guide their
reasoning, can pay large dividends over the course of
the semester.
Space here does not allow for more than a short
synopsis of some of our research results. Readers who
are interested in the details of these studies and their
findings are urged to read the papers referenced.
Acknowledgments
This three-year project is being funded by the Education
and Public Outreach program for NASA’s
Fermi Gamma-ray Space Telescope, grant NNX-
10AC89G from NASA’s EPOESS program, and from
the Illinois Space Grant Consortium. Background research
was also funded in part by the National Science
Foundation CCLI Grant #0632563 at Chicago State
University. We gratefully acknowledge the artistic
and technical expertise of the Educational and Public
Outreach Group at Sonoma State University, especially
Aurore Simonnet and Kevin John, and the help
of our current and former research students on the
project: Melissa Nickerson, Carmen Camarillo, Virginia
Hayes, Donna Larrieu, K’Maja Bell at Chicago
State University; Roxanne Sanchez at UNLV; and
Geraldine Cochran at Florida International University.
We thank Ted Britton and his staff at WestEd
for developing and analyzing the evaluation. KendallHunt
will be publishing the curriculum modules for
national distribution.
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