Investigating undergraduate students’ ideas about the curvature of the Universe

[This paper is part of the Focused Collection on Astronomy Education Research.] As part of a larger project studying undergraduate students’ understanding of cosmology, we explored students’ ideas about the curvature of the Universe. We investigated preinstruction ideas held by introductory astronomy (ASTRO 101) students at three participating universities and postinstruction ideas at one. Through thematic analysis of responses to questions on three survey forms and preinstruction interviews, we found that prior to instruction a significant fraction of students said the Universe is round. Students’ reasoning for this included that the Universe contains round objects, therefore it must also be round, or an incorrect idea that the big bang theory describes an explosion from a central point. We also found that a majority of students think that astronomers use the term curvature to describe properties, such as dimensions, angles, or size, of the Universe or objects in the Universe, or that astronomers use the term curvature to describe the bending of space due to gravity. Students are skeptical that the curvature of the Universe can be measured, to a greater or lesser degree depending on question framing. Postinstruction responses to a multiple-choice exam question and interviews at one university indicate that students are more likely to correctly respond that the Universe as a whole is not curved postinstruction, though the idea that the Universe is round still persists for some students. While we see no evidence that priming with an elliptical or rectangular map of the cosmic microwave background on a postinstruction exam affects responses, students do cite visualizations such as diagrams among the reasons for their responses in preinstruction surveys.

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Figure 1

Maps of the CMB will have a different characteristic angular scale depending on the curvature of space. In a spherical space (positive curvature, bottom left), the typical size of the hot and cold spots in the CMB will be larger than in a “flat” space (zero curvature, bottom middle) and will be smaller in a hyperbolic space (negative curvature, bottom right). By comparing models to data (top panel), the BOOMERANG team determined that the Universe as a whole is not curved. From the BOOMERANG Team.

Figure 2

(Left) An elliptical map of the CMB. Credit: WMAP. (Right) A rectangular map of the CMB. From BOOMERANG.

Figure 3

ASTRO 101 preinstruction survey responses for What is the shape or geometry of the Universe? ($N=16$).

Figure 4

ASTRO 101 preinstruction survey responses for Which of the following best describes the “geometry” or “curvature” of space (the Universe)? (a) Round, (b) flat, (c) hyperbolic, (d) some other, (e) no way to know ($N=265$).

Figure 5

Heat map highlighting relationships between ASTRO 101 students’ ideas on the shape or geometry with their responses to How do we know? ($N=16$) Each cell specifies the number of responses coded with a particular combination of shape and reasoning.

Figure 6

Heat map highlighting the relationships between ASTRO 101 students’ selection of the geometry or curvature of space with their responses to Why did you select the answer you chose? ($N=265$). Each cell specifies the number of responses coded with a particular combination of curvature and reasoning.

Figure 7

ASTRO 101 Preinstruction survey responses for What do astronomers mean when they talk about the “shape” or “curvature” of space (the Universe)?

Figure 8

ASTRO 101 Preinstruction survey responses for How do they measure this trait?

Figure 9

ASTRO 101 Preinstruction survey responses for What does the cosmic microwave background tell us about the overall curvature of the Universe? ($N=75$).

Figure 10

Students’ responses to the question of the curvature of space were examined to determine if they were influenced by an elliptical ($N=53$) or rectangular ($N=22$) map of the CMB on a postinstruction exam.

Figure 11

Shape of the Universe as described by students in interviews.