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Investigating Student Ideas about Cosmology I: Distances and Structure
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Figures

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Figure 3.1.

Precourse homework essays: Space travel.  = 55 essays were collected and analyzed for themes. It is possible for an essay to be coded with more than one theme. Since essays were free-form, the number shown for each category reflects a lower limit on the number of students who hold a particular concept.

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Figure 3.2.

Precourse homework essays: Speed of light and the light-year.  = 55 essays were collected and analyzed for themes. It is possible for an essay to be coded with more than one theme. Since essays were free-form, the number shown for each category reflects a lower limit on the number of students who hold a particular concept.

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Figure 3.3.

Interviews: Light-years.  9 students used the term light-year in interviews. Students were either asked specifically, or it came up during the course of the interview.

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Figure 3.4.

Precourse homework essay: sizes and distances.  55 essays were collected and analyzed for themes. It is possible for an essay to be coded with more than one theme. Since essays were free-response, the number shown for each category reflects a lower limit on the number of students who hold a particular concept. Many students described sizes and distances in their homework essays, but responses were often nonspecific relative terms.

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Figure 3.5.

Exam 1: Matching absolute scales, thematic coding. The correct answer is highlighted in pink. Here,  = 64 because one student did not respond to the question.

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Figure 3.6.

Interviews:  14 students were asked to discuss size and distance scales. Since responses were free-form, thematic codes can add up to more than 100%. All interviews were conducted after the initial unit on size and distance scales.

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Figure 3.7.

Precourse homework essay: size and distance measurement.  55 essays were collected and analyzed for themes. Since essays were free-response, the number shown for each category reflects a lower limit on the number of students who hold a particular concept.

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Figure 3.8.

Figure used in the Laboratory 9 pretest question on parallax. Students were informed that the two pictures were taken six months apart and were asked which star is farther away, A or B? They were also asked to explain their reasoning. Similar illustrations were shown in FIB questions on the midterm and final exams (see Tables ??? , tA3.16 ).

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Figure 3.9.

Laboratory 9 Pretest: Parallax measurements, reasoning, thematic frequencies.  = 36. Responses in purple are Correct, in blue are Incomplete, in green are Partial, and in red are Wrong. The correct answer and reasoning incorporated the elements: Star B is farther away because it shifted less.

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Figure 3.10.

Exams: Difficulties with the inverse square law, thematic coding. It is possible for a response to be coded with more than one theme.

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Figure 4.1.

Precourse homework essay: Types of astronomical objects listed.  55 essays were collected and analyzed for themes. It is possible for an essay to be coded with more than one theme. Since essays were free-response, the number shown for each category reflects a lower limit on the number of students who hold a particular concept. We classified the objects that students listed into Solar System, Galactic (other than stars), and extra-galactic. Objects in quotes were ones that students specifically listed by name.

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Figure 4.2.

Final Exam: Difficulties with Solar System size and structure.  = 48 essays were analyzed for themes. It is possible for a response to be coded with more than one theme.

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Figure 4.3.

Examples of student drawings of the Solar System from the Final Exam. (a) This student drew only the Sun and named planets. (b) This student gives a much more detailed picture of the components in our Solar System.

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Figure 4.4.

Interviews: Solar System.  14. Students were asked to describe the term “solar system.” All of these students were interviewed after the introductory material on structure and distance as well as after in-depth instruction on the Solar System. The two students who listed incorrect components (noncentral stars, galaxies) had not yet been instructed in-depth on galaxies.

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Figure 4.5.

Exams: Difficulties with Galactic size and structure, thematic coding. It is possible for a response to be coded with more than one theme.

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Figure 4.6.

Examples of student drawings of the Galaxy from the Final Exam. (a) Like many, this student is unclear about the halo. (b) This student gives a correct picture of our Galaxy.

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Figure 4.7.

Interviews: Galaxy.  15. Students were asked to describe the term ‘galaxy.’ All of these students were interviewed after the introductory material on structure and distance as well as after in-depth instruction on the Solar System; 13 had received in-depth instruction on the Milky Way Galaxy and 12 had received in-depth instruction on the types and properties of galaxies in general.

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Figure 4.8.

Precourse homework essay: Descriptions of the universe as a whole.  55 essays were collected and analyzed for themes. It is possible for an essay to be coded with more than one theme. Since essays were free-response, the number shown for each category reflects a lower limit on the number of students who hold a particular concept. These descriptions are of the universe as a whole and are in addition to any objects or “stuff” in the universe that the students might have listed.

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Figure 4.9.

Precourse homework essay: Whether the universe has an edge or is endless.  55 essays were collected and analyzed for themes. It is possible for an essay to be coded with more than one theme. Since essays were free-response, the number shown for each category reflects a lower limit on the number of students who hold a particular concept.

Image of Figure 4.10.

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Figure 4.10.

Interviews: Descriptions of the universe as a whole.  = 13. Students were asked to describe the term ‘universe.’ All of these students were interviewed after the introductory material on structure and distance as well as after in-depth instruction on the Solar System; 10 had received in-depth instruction on the types and properties of galaxies and 7 had received in-depth instruction on Big Bang cosmology. These descriptions are of the universe as a whole and are in addition to any objects or “stuff” in the universe that the students might have listed.

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Figure 4.11.

Pre-course homework essay: How objects are arranged.  55 essays were collected and analyzed for themes. It is possible for an essay to be coded with more than one theme. Since essays were free-response, the number shown for each category reflects a lower limit on the number of students who hold a particular concept.

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Figure 4.12.

Interviews: Relationships. Students were asked to describe the relationships between the terms solar system, galaxy, and universe.  = 7. All of these students were interviewed after the introductory material on structure and distance as well as after in-depth instruction about the Solar System. Furthermore, five had received in-depth instruction on the Milky Way Galaxy, four on galaxies, and two on large-scale structure. Additionally, there were four unsolicited correct statements with regard to hierarchy, all made by students after instruction on large-scale structure.

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Figure 4.13.

This student gives a correct relative ranking and explanation for solar system, galaxy and universe, but does not give absolute scales consistent with the relative rankings and content of the structures.

Tables

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Table 2.

Relative schedule of topics, cosmology-related laboratory activities, and data collection points. The schedule was the same for all five semesters of data collection. Interviews with students (labeled A - O) were collected over four semesters.

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Table 2.

Coding scheme for open-response prelab and exam essay questions.

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Table 3.

Laboratory 1 pretest: Half speed of light.

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Table 3.

Laboratory 1 pretest: Half speed of light.

In the future, when space travel is advanced, you have 3 weeks of vacation time and want to visit the star Sirius, in honor of your favorite Harry Potter character. Sirius is 8.6 light-years away. If spaceships in the future could travel at half the speed of light (much faster than current spaceships), would you be able to make the trip to Sirius and back during your vacation?

No. If you were traveling at half of the speed of light it would take you 8.6 × 2 = 17.2 years just to get there, so you definitely could not get there and back in 3 weeks.

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Table 3.

Laboratory 1 pretest: Speed and scale.

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Table 3.

Laboratory 1 pretest: Speed and scale.

What are some other astronomical objects you would be able to visit during your vacation? (Again, in a future spaceship that could travel at half the speed of light.)

Most objects in our Solar System are within a few light-minutes or light-hours away, so you could get to any of those during your futuristic vacation.

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Table 3.

Exam 1: Half speed of light (FIB).

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Table 3.

Exam 1: Half speed of light (FIB).

v1: The star Vega is 25 light-years away. If you were in a spaceship that could travel at half the speed of light, the amount of time it would take you reach Vega is . (Be specific, use a number.)

v2: The star Sirius is 9 light-years away. If you were in a spaceship traveling at half of the speed of light, the amount of time it would take you reach Sirius is . (Be specific, use a number.)

v3: The Whirlpool galaxy is about 30 million light-years away. If you were in a spaceship that could travel at half of the speed of light, the amount of time it would take you reach the Whirlpool galaxy is . (Be specific, use a number.)

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Table 3.

Exam 1: Speed of light (FIB).

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Table 3.

Exam 1: Speed of light (FIB).

Our Galaxy is about 100,000 light-years across. If you could travel at the speed of light, how long would it take you to go across our Galaxy? .

The Whirlpool galaxy is about 30 million light-years away. If you went outside and looked at the Whirlpool, how long ago did the light that just arrived at your eye leave its home? .

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Table 4.

Exam 1: Definition of light-year (MC).

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Table 4.

Exam 1: Definition of light-year (MC).

v1: A television advertisement claiming that a product is light-years ahead of its time does not make sense because

  a. light-years can only be used to talk about light

  b. it doesn't specify the number of light-years

  

  d. a light-year is an astronomically large unit, so a product could not possibly be so advanced

v2: When we look at an object that is 1000 light-years away we see it

  a. as it is right now, but it appears 1000 times dimmer

  b. looking just the same as our ancestors would have seen it 1000 years ago

  c. as it was 1000 light-years ago

  

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Table 4.

Final exam: Half speed of light (FIB).

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Table 4.

Final exam: Half speed of light (FIB).

v1: The star Procyon is about 11 light-years away. If you were in a spaceship that could travel at half of the speed of light, how long would it take you to get to Procyon? .

v2: The star Sirius is 9 light-years away. If you were in a spaceship that could travel at half of the speed of light, the amount of time it would take you reach Sirius is . (Be specific, use a number.)

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Table 4.

Final exam: Speed of light lookback time (FIB).

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Table 4.

Final Exam: Speed of light lookback time (FIB).

The Andromeda galaxy is about 2.5 million light-years away. If you went outside and looked at Andromeda, how long ago did the light that just arrived at your eye leave its home? .

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Table 4.

Final exam: Definition of light-year (MC, v2).

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Table 4.

Final Exam: Definition of light-year (MC, v2).

When we look at an object that is 1000 light-years away we see it

  a. as it was 1000 light-years ago

  

  c. looking just the same as our ancestors would have seen it 1000 years ago

  d. as it is right now, but it appears 1000 times dimmer

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Table 4.

Exam 1: Matching absolute scales.

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Table 4.

Exam 1: Absolute scales (Matching).

Match the distance to each of the following to the closest answer.

  • a.  Nearest galaxy:
  • b.  Nearest star (Alpha Centauri):
  • c.  Size of our Galaxy:
  • d.  Distance to farthest planet in our Solar System:
  • e.  Size of the observable universe:
    • 1.  a few light-minutes
    • 2.  a few light-hours
    • 3.  4 light-years
    • 4.  1000 light-years
    • 5.  100 000 light-years
    • 6.  2.5 million light-years
    • 7.  15 billion light-years
    • 8.  15 trillion light-years

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Table 3.

Exam 1: Object distance ranking task.

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Table 3.

Exam 1: Object distance ranking.

Consider these five objects:

  • a.  The Andromeda Galaxy
  • b.  The Pleiades Star Cluster
  • c.  The Hubble Space Telescope
  • d.  Jupiter
  • e.  The Sun

Rank them by: distance away from Earth (from closest to farthest):

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Table 3.

Exam 1: Object size ranking task.

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Table 3.

Exam 1: Object size ranking.

Consider these seven objects: (1) The Moon, (2) The Andromeda Galaxy, (3) The Coma Cluster of Galaxies, (4) The Hubble Space Telescope, (5) The Pleiades Star Cluster, (6) Saturn, and (7) The Sun. Rank them by size.

(4) The Hubble Space Telescope: man-made, about the size of a bus

(1) The Moon: about 1/4 the size of the Earth

(6) Saturn: about 10 times bigger across than Earth

(7) The Sun: about 100 times bigger across than Earth, (also it's a star, so it's bigger than planets)

(5) Pleiades Star Cluster: contains about 1000 stars-> bigger than the Sun but smaller than a galaxy

(2) Andromeda Galaxy: a galaxy contains billions of stars

(3) Coma Cluster of Galaxies: contains thousands of galaxies

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Table 3.

Final exam: Object distance ranking task.

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Table 3.

Final exam: Object distance ranking.

Consider these five objects:

  • a.  The Andromeda Galaxy
  • b.  The Pleiades Star Cluster
  • c.  The Hubble Space Telescope
  • d.  Jupiter
  • e.  The Sun

Rank them by: distance away from Earth (from closest to farthest):

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Table 3.

Final exam: Object size ranking task.

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Table 3.

Final exam: Object size ranking task.

Consider these five objects:

  • a.  The Andromeda Galaxy
  • b.  The Hubble Space Telescope
  • c.  Jupiter
  • d.  The Pleiades Star Cluster
  • e.  The Sun

Rank them by size (from smallest to largest):

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Table 3.

Laboratory 9 Pretest: Parallax shift.

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Table 3.

Laboratory 9 pretest: Parallax measurements.

Parallax. The following two pictures were taken six months apart. Which star is farther away, A or B?

B is farther away

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Table 3.

Exam 3: Parallax.

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Table 3.

Exam 3: Parallax measurements (FIB).

v1: Parallax. The following two pictures were taken six months apart. Star is farther away.

v2: Parallax. The following two pictures were taken six months apart. Star is closer.

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Table 3.

Exam 3: Parallax, numerical reasoning (MC, v1).

v1: Star X is known to be 10 parsecs away from us and star Y is 50 parsecs away. Which star has the greater parallax shift (angle)?

  

  b. Star Y

  c. There is insufficient information to determine this.

  d. Neither—their parallax angles are the same.

v2: You observe two stars over the course of a year (or more) and find that both stars have measurable parallax angles. Star X has a parallax angle of 1 arc sec. Star Y has a parallax angle of 2 arc sec. Which star is closer?

  

  b. Star Y

  c. There is insufficient information to determine this.

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Table 3.

Exam 3: Parallax, numerical reasoning (MC, v2).

Which of the following stars is closest to us?

  a. Procyon (parallax angle = 0.29 arc sec)

  b. Ross 780 (parallax angle = 0.21 arc sec)

  c. Regulus (parallax angle = 0.04 arc sec)

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Table 3.

Final exam: Parallax shift.

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Table 3.

Final exam: Parallax measurements (FIB).

v1: Parallax. The following two pictures were taken six months apart. Star is closer.

v2: Parallax. The following two pictures were taken six months apart. Star is farther away.

v3: Parallax. The following two pictures were taken six months apart. Star is farther away.

       (Figure for v1, v2)                  (Figure for v3)

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Table 3.

Inverse square law.

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Table 3.

Laboratory 9 pretest: Inverse square law.

Star C and Star D have the same luminosity (inherent brightness), but Star C is 5 times farther away than Star D. If the intensity of light is inversely proportional to distance squared, how does the apparent brightness of star D compare to that of star C. Be specific (give a number) and explain your reasoning.

If star C is 5 times farther away, it will be 5 = 25 times dimmer than star D. (Also acceptable: star D will be 25 times brighter than star C.)

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Table 3.

Exam 3: Inverse square law (FIB).

v1: Stars A and B are both Cepheid variable stars. Star A is 6 times farther away than star B. The brightness of star A will be compared to B. (Use a number.)

v2: Stars A and B both have the same spectral class. Star A is 7 times farther away than star B. The brightness of star A will be compared to B. (Give a number.)

v3: Supernova A is 10 times farther away than supernova B. The apparent brightness of supernova A will be compared to B. (Give a number.)

v4: Supernova A is 10 times farther away than supernova B. The apparent brightness of supernova A will be times dimmer than B. (Give a number.)

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Table 3.

Final exam: Inverse square law (FIB).

v1: Stars A and B are both G-type stars. Star A is 3 times closer than star B. The brightness of star A will be compared to B. (Use a number.)

v2: Stars A and B are both Cepheid variable stars. Star A is 5 times closer than star B. The brightness of star A will be compared to B. (Use a number.)

v3: Stars A and B are both Cepheid variable stars. Star A is 6 times closer than star B. The brightness of star A will be compared to B. (Use a number.)

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Table 4.

Precourse survey reanalysis: Solar System.

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Table 4.

Precourse survey reanalysis: Solar System.

 = 17 written responses were collected and analyzed.

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Table 4.

Final exam: Solar System structure (essay).

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Table 4.

Final exam: Solar System structure (essay).

Draw a diagram of our solar system. Label 3 major types of components of the solar system and give the approximate size of at least one of those components.

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Table 4.

Precourse survey reanalysis: galaxy.

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Table 4.

Precourse survey reanalysis: galaxy.

 17 written responses were collected and analyzed.

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Table 4.

Exam 3: Number of stars in Milky Way (MC).

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Table 4.

Exam 3: Number of Stars in Galaxy (MC).

The number of stars in the Milky Way is approximately?

  a. a few hundred million

  b. a few hundred thousand

  

  d. a few hundred

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Table 5.

Exam 3: Galaxy types (MC).

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Table 5.

Exam 3: Galaxy types (MC).

Which of the following is NOT one of the three major categories of galaxies?

  

  b. Spiral Galaxies

  c. Elliptical Galaxies

  d. Irregular Galaxies

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Table 5.

Exam 3: Galaxy types.

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Table 5.

Exam 3: Galaxy types, Spiral Galaxies (FIB).

Use the three images of galaxies shown below (A, B, and C) to answer the following question.

v1: In which of the galaxies shown would you expect to see many bright blue stars?

v2: In which of the galaxies shown would you expect to see regions of abundant gas and dust?

v3: In which of the galaxies shown would you expect to see mostly blue stars?

v4: In which of the galaxies shown below would you expect to see young, hot, blue stars?

A, C.

Use the three images of galaxies shown below (A, B, and C) to answer the following question.

In which of the galaxies would you expect to see mostly red stars?

B.

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Table 5.

Exam 3: Galaxy structure.

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Table 5.

Exam 3: Galaxy structure.

v1: On the following artist's conception of our Galaxy, label the bulge, disk, and halo, and draw a scale bar for size.

v2: Draw a diagram of the Milky Way, both edge on and face on. Be sure to label 3 primary components of the galaxy and the approximate size of at least one of those components.

Figure for v1 Answer

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Table 5.

Final Exam: Galaxy structure, sketch and label (Essay).

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Table 5.

Final exam: Galaxy structure, draw and label (essay).

Draw a diagram of the Milky Way Galaxy. Label 3 major types of components of the Galaxy and give the approximate size of at least one of those components.

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Table 5.

Final exam: Definition of galaxy (MC).

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Table 5.

Final exam: Definition of galaxy (MC).

A typical galaxy is a

  a. nearby object orbiting a planet

  b. large, glowing ball of gas powered by nuclear energy

  c. relatively small, icy object orbiting a star

  

  e. system consisting of one or a few stars orbited by planets, moons, and smaller objects

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Table 4.

Precourse homework essay: Hierarchical structure.

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Table 4.

Homework essay: Hierarchical structure.

 55 essays were collected and analyzed.

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Table 4.

Precourse survey reanalysis: Relationships.

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Table 4.

Precourse survey reanalysis: Relationships.

 17 written responses were collected and analyzed.

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Table 4.

Exam 1: Structure ranking task.

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Table 4.

Precourse survey reanalysis: Relationships.

v1: (FIB)

Consider the following:

  • a.  Galaxy
  • b.  Solar System
  • c.  Universe
  • d.  Earth

Rank them by size, from smallest to largest:

v2: (Essay)

Consider the following: galaxy, solar system, universe. Rank them by size, from smallest to largest. Explain your reasoning, including a description of each item.

solar system < galaxy < universe

A solar system consists of a star, its planets, their moons, and other small debris.

A galaxy contains hundreds of billions of stars (solar systems), gas, dust, and dark matter.

The universe is all of time, space, and its contents. The observable universe includes hundreds of billions of galaxies.

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Table 4.

Final Exam: Solar system and galaxy ranking, including reasoning.

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Table 4.

Final exam: Solar System and Galaxy (ranking task), reasoning.

Which is bigger, the solar system or the galaxy? Explain your reasoning.

The galaxy is bigger than the solar system.

A solar system consists of a star, its planets, their moons, and other small debris.

A galaxy contains hundreds of billions of stars (solar systems), gas, dust, and dark matter.

Abstract

Recently, powerful new observations and advances in computation and visualization have led to a revolution in our understanding of the structure of the Universe. As the field of cosmology advances, it is of interest to study how student ideas relate to scientific understanding. In this paper, we examine in-depth undergraduate students' ideas on distances and structure in the Universe as students progress through a general education astronomy integrated lecture and laboratory course with a focus on active learning. The study was conducted over five semesters at an urban, minority-serving institution. The data collected include individual interviews ( = 15) and course artifacts ( ∼ 60), such as precourse homework essays, prelab surveys, and midterm and final exam questions in a variety of formats. We find that students are fairly successful at tasks involving relative distances, but struggle with absolute distances; have difficulty going beyond an elementary model of the Solar System as the Sun and planets; struggle to visualize galactic halos; but successfully increase their understanding of the hierarchical nature of structure in the Universe throughout the semester.

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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Investigating Student Ideas about Cosmology I: Distances and Structure
http://aip.metastore.ingenta.com/content/aas/journal/aer/12/1/10.3847/AER2012038
10.3847/AER2012038
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