We investigated the reasoning and conceptual difficulties non-STEM majors have with cosmology in introductory astronomy courses (hereafter Astro 101). To probe students' ideas about cosmological topics, we administered four different surveys. Each survey form focuses on a different aspect of cosmology: Form A: Interpreting Hubble plots Form B: Expansion and the Big Bang Form C: How expansion affects the evolution of the universe Form D: Evidence for dark matter in spiral galaxies.We are developed a new suite of Lecture-Tutorials to help students overcome their most common difficulties. Each tutorial is a two to six page worksheet activity filled with Socratic dialogue-driven questions that a group of two to three students can complete in approximately fifteen minutes. We have written and evaluated the following five tutorials: Dark Matter: Helps students understand why flat rotation curves are evidence for dark matter. Hubble's Law: Helps students understand how Hubble's law results from an expanding universe. Making Sense of the Universe and Expansion: Helps students understand how an expanding universe can have no center and no edge. Expansion, Lookback Times, and Distances: Helps students realize the effects of expansion on the lookback times and distances to far away objects. The Big Bang: Helps students overcome the idea that the Big Bang was an explosion of pre-existing matter into empty space.This poster contains a sample of our results from ~2300 students enrolled in Astro 101, of which approximately 1700 used the new lecture-tutorials.The map below shows the locations of colleges and universities whose Astro 101 students have participated or are participating in this study.

Final results on a 2300 student study on Astro 101 students' difficulties with cosmology: A lecture-tutorial approach

Colin S. Wallace1, Edward E. Prather2, Doug Duncan1, and CATS21University of Colorado at Boulder, Boulder, Colorado, 2Center for Astronomy Education (CAE), Steward Observatory, University of Arizona

Introduction Normalized gains Sample results

This material is based upon work supported by the National Science Foundation under Grants Nos. 0833364 and 0715517, a CCLI Phase III Grant for the Collaboration of Astronomy Teaching Scholars (CATS). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

Figure 1: Normalized learning gains for classes that do and do not use the cosmology lecture-tutorials (blue and orange bars, respectively).

Sample results

Table 1: For each form, the pre- and post-test results for each class were compared using the Mann-Whitney test. P-values are shown below. Statistically significant P-values (P < 0.05) are highlighted.

Group Form A Form B Form C Form D

LT Fall 2009 0.2005 <0.0001 <0.0001 <0.0001

No LT Fall 2009 0.5029 0.1676 0.3843 0.2460

LT Spring 2010 <0.0001 <0.0001 <0.0001 <0.0001

No LT Spring 2010 0.0033 <0.0001 <0.0001 0.0549

LT Fall 2010 0.0262 <0.0001 <0.0001 <0.0001

No LT Fall 2010 0.1762 <0.0001 0.0001 0.0150

Figure 2: Percent of students who said the universe's temperature decreased over time pre- and post-instruction (blue and orange bars, respectively).

Figure 4: Percent of students who selected the correct rotation curve for a spiral galaxy (graph 2 on the left). Blue bars represent pre-instruction responses and orange bars represent post-instruction responses.

F09 LT

S10 LT

F10 LT

F09 N

LT

S10 N

LT

F10 N

LT0

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S10 LT

F10 LT

F09 N

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F10 LT

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Table 2: Common student responses to the following question: Explain, in as much detail as possible, what astronomers mean by the “Big Bang Theory.”Common Responses LT F09 No LT F09 LT S10 No LT S10 LT F10 No LT F10

It was the beginning of the universe.

34% pre21% post

32% pre21% post

44% pre47% post

52% pre56% post

43% pre46% post

50% pre73% post

It was the beginning of expansion.

12% pre50% post

9% pre29% post

10% pre68% post

9% pre15% post

33% pre51% post

13% pre27% post

It was the beginning of something smaller than the universe.

20% pre3% post

0% pre0% post

23% pre3% post

19% pre8% post

9% pre1% post

11% pre4% post

It was an event that happened to something smaller than the universe.

10% pre1% post

0% pre0% post

12% pre0% post

2% pre0% post

3% pre0% post

0% pre2% post

It was an explosion. 51% pre23% post

59% pre50% post

50% pre12% post

59% pre58% post

55% pre23% post

57% pre35% post

There was matter before the Big Bang.

29% pre15% post

45% pre43% post

27% pre6% post

33% pre25% post

33% pre26% post

48% pre25% post

F09 LT S10 LT F10 LT F09 NLT S10 NLT F10 NLT0

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Figure 3: Normalized gains on the question about the temperature of the universe for both lecture-tutorial (blue bars) and non-lecture-tutorial (orange bars) students.

F09 LT S10 LT F10 LT F09 NLT S10 NLT F10 NLT0

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