investigating student difficulties with concepts of gravitation or

INVESTIGATING STUDENT DIFFICULTIES WITH

CONCEPTS OF GRAVITATION

Or...

...DO YOU UNDERSTAND THE GRAVITY OF THIS SITUATION?

Jack Dostal and David Meltzer

Iowa State University

Why Gravitation?

•Lack of research on students’ concepts of gravity

•Similar in nature to Coulomb’s Law

•Subject of interest in both physics and astronomy

Previous Research

Not much! But here are a couple of examples:

Nussbaum, late 1970s - early 1980s (Israel)

Emphasis: Children’s concepts of the earth

•What does Earth look like? Which way is down?

•Instructional method: Audio-tape lessons

Gunstone and White, 1981 (Australia)

Emphasis: First-year college students understanding of gravity

•Students were presented a physical situation and asked to predict what would happen if a certain action was taken.

•Students made observations and were asked to reconcile any discrepancies between their prediction and observation.

Our Goals

•To investigate students’ thoughts about gravitation

•To develop instructional materials which enable students to learn about gravitation more effectively

•To quantitatively evaluate the effectiveness of the materials produced

Pretesting: What are the students thinking?

We have used two main diagnostic instruments:

Multiple choice questions:

•11-question pretest addressing many different aspects of gravitation (inverse square law, Newton’s 3rd Law, more)

•Used at Southeastern Louisiana University, Iowa State University, and Hawkeye Community College

Free-Response questions:

•10 question pretest, all free-response and drawing

•Used at Hawkeye Community College; will use at other schools in the near future

Pretesting: What are the students thinking?

Class profiles:

SE Louisiana: Second-semester algebra-based physics students

(N > 100) Multiple choice questions given on the first day of class

Iowa State: Second-semester algebra-based physics students

(N = 79) Multiple choice questions given on the first day of class

Hawkeye CC: General education astronomy class

(N = 21) Several weeks into course (Newton’s Laws and Universal Law of Gravitation mentioned, but not thoroughly covered)

Selected results from multiple choice questions:

Multiple choice Q1: The mass of the sun is about 3 x 105 times the mass of the earth. How does the magnitude of the gravitational force exerted by the sun on the earth compare with the magnitude of the gravitational force exerted by the earth on the sun? The force exerted by the sun on the earth is:

A. About 9 x 1010 times larger

B. About 3 x 105 times larger

C. Exactly the same

D. About 3 x 105 times smaller

E. About 9 x 1010 times smaller


Multiple choice Q1: The mass of the sun is about 3 x 105 times of the mass of the earth. How does the magnitude of the gravitational force exerted by the sun on the earth compare with the magnitude of the gravitational force exerted by the earth on the sun? The force exerted by the sun on the earth is:

A. About 9 x 1010 times larger

B. About 3 x 105 times larger

C. Exactly the same

D. About 3 x 105 times smaller

E. About 9 x 1010 times smaller


Multiple Choice Q1:

SE Louisiana: less than 10% correct

Iowa State: 14% correct

Hawkeye CC: 19% correct

Students in various settings/backgrounds/courses have the same misconception:

Student thinking: Objects of unequal masses exert unequal forces on one another!


Multiple choice Q8: Which of the following diagrams most closely represents the gravitational forces that the earth and the moon exert on each other? (Note: The mass of the earth is about 80 times that of the moon)

E M

E M

E M

E M

E M

E M

(A) (C) (E)

(B) (D) (F)


Multiple choice Q8: Hawkeye CC results and Iowa State results:

E M

E M

E M

E M

E M

E M

(A) 76%, 38% (C) 14%, 6% (E) 10%, 1%

(B) 0%, 44% (D) 0%, 0% (F) 0%, 0%

Student thinking: Objects of unequal masses exert unequal forces on one another!

Earth

asteroid

Selected results from free-response questions:

Free Response Q2: Refer to the picture above. State whether the magnitude of the force exerted by the Earth on the asteroid is larger than, smaller than, or the same as the magnitude of the force exerted by the asteroid on the Earth. Explain the reasoning for your choice.

Earth

asteroid


Same as: 10%

Smaller than: 5%

Larger than: 86%

76% of all students explicitly reasoned that because the Earth was larger or more massive, it exerted a greater force on the asteroid.

LARGER objects exert MORE force on SMALLER objects...

...than SMALLER objects exert on LARGER objects.

Free Response Q8: Imagine that you are standing on the surface of the moon holding a pen in one hand.

A) If you let go of the pen, what happens to the pen? Why?

B) After you let go of the pen, what happens to you? Why?


Free Response Q8:Imagine that you are standing on the surface of the moon holding a pen in one hand.

A) If you let go of the pen, what happens to the pen? Why?

DROPS TO THE SURFACE

FLOATS

FLOATS AWAY

45%

31%

24%

Free Response Q8:Imagine that you are standing on the surface of the moon holding a pen in one hand. A) If you let go of the pen, what happens to the pen? Why?

DROPS TO THE SURFACE•Most cite the moon’s lesser gravity•“Like the astronauts”

FLOATS or FLOATS AWAY•Low gravity•Not enough gravity•No gravity•Weightlessness

Free Response Q8:Imagine that you are standing on the surface of the moon holding a pen in one hand.

B) If you let go of the pen, what happens to you? Why?

YOU STAY ON THE SURFACE

YOU FLOAT

YOU FLOAT AWAY

71%

5%

5%

19%OTHER

Students do not automatically consider gravitation to be universal!

Free Response Q1:

In the picture above, a person is standing on the Earth holding a ball in one hand. Draw the direction of the force exerted by the Earth on the ball in the picture above.

Earth


Earth

Free Response Q1:

Correct (downward):

Incorrect (upward):

Incorrect (balanced):

67%

29%

5%

Do students really think that the ball will fall up? No.

This appears to be a confusion of what is meant by a “force exerted by the Earth on the ball.”

Free Response Q7(A): Two large masses M1 and M2 are in space as shown.

•Where (if anywhere) can you place a third mass M3 to

increase the total gravitational pull on M2? (This would

increase the push or pull experienced by M2.)

•Draw M3 in that position on the picture above and

explain your reasoning for choosing that position.

M1 M2


M1 M2

Free Response Q7(A):

Correct answers: 67%Correct answers with correct reasoning (superposition of forces): 14%

M3 M3M3

M3M3

M3

M3

•“Tension” response: “M2 must now pull both M1 and M3, so there more force on M2”

M1 M2 M3

Free Response Q7(A):

•Closeness: “M3 is closer to M2 than M1, so there is more force on M2”

M1 M2M3

M3M3

M3

Free Response Q7(B): Two large masses M1 and M2 are in space as shown. •Where (if anywhere) can you place a third mass M3 to decrease the total gravitational pull on M2? (This would decrease the push or pull experienced by M2.) •Draw M3 in that position on the picture above and explain your reasoning for choosing that position.

M1 M2


M1 M2


Free Response Q7(B):

Correct answers: 38%Correct answers with correct reasoning (superposition/cancellation of forces): 29%

M3M3

M3

M3

M3 M3

M3

M3

M3

Free Response Q7(B) -- Reasoning for some incorrect answers:

•Force Distribution I: “M1’s force is ‘used up’ on M3, so M1

pulls on M2 with less force.”

M1 M2

M3

M3

•Force Transmission : “M3 pulls on M1, so M1 pulls on M2 with

less force.”

M1 M2M3

Free Response Q7(B) -- Reasoning for some incorrect answers:

•Force Distribution II: “M2 has to pull two objects, so the pull

is less.”

M1 M2M3

M1’s force on M2 depends

in some way on M3!

What’s next?

•Create workbook-style instructional materials to teach gravitation

•Field-test instructional materials in both physics and astronomy classroom settings

•Evaluate the effectiveness of these materials

•Further investigate student understanding through interviews and additional diagnostics

investigating student difficulties with concepts of gravitation or

Documents