IDENTIFYING STUDENT CONCEPTS OF GRAVITY
By
Roger Eastman Feeley
B.S. University of Maine, 1989
A THESIS
Submitted in Partial Fulfillment of the
Requirements for the Degree of
Master of Science in Teaching
The Graduate School
The University of Maine
May 2007
Advisory Committee:
John R. Thompson, Assistant Professor of Physics, Cooperating Assistant Professor
of Education, Advisor
Michael C. Wittmann, Assistant Professor of Physics: Cooperating Assistant
Professor of Education
Herman Weller, Associate Professor of Science Education
© 2007 Roger Eastman Feeley
All Rights Reserved
ii
LIBRARY RIGHTS STATEMENT
In presenting this thesis in partial fulfillment of the requirements for an advanced
degree at The University of Maine, I agree that the Library shall make it freely
available for inspection. I further agree that permission for “fair use” copying of this
thesis for scholarly purposes may be granted by the Librarian. It is understood that any
copying or publication of this thesis for financial gain shall not be allowed without my
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Signature:
Date:
IDENTIFYING STUDENT CONCEPTS OF GRAVITY
By Roger E Feeley
Thesis Advisor: Dr. John R. Thompson
An Abstract of the Thesis Presented
in Partial Fulfillment of the Requirements for the
Degree of Master of Science in Teaching
May, 2007
This paper discusses a survey developed to investigate student concepts of "gravity"
among AST 109 astronomy students and pre-service K-12 teachers. Survey questions
were developed or modified from those in the literature [Berg 1991, Dostal 2005].
Students were questioned on their reasoning about the behavior of objects on the
surface of a planetary body (e.g., the Earth or the moon) and the causes of this
behavior. Results of the survey successfully elicited student alternate conceptions with
various aspects of gravity. These misconceptions include the tendency to attribute
gravity to the presence of an atmosphere, and the belief that a threshold amount of
gravity, mass, or weight is necessary for free-fall to occur.
ACKNOWLEDGMENTS
Had I been told a decade ago that I would be taking this path, I would have thought
them crazy and asked them what they were smoking . . .
First of all, I would like to thank John Thompson, my advisor, for his role in all this.
He helped keep me on track, despite my bouts of cluelessness and my own best efforts
to impede my progress. I’d also like to thank Michael Wittman, for his encouragement
throughout this process. I also feel indebted to the physics department, for being
supportive of students as a whole.
I am blessed to have the best mom and dad on the planet. They are the epitome of
supportive parents. As for my siblings, thank you Amey, for cracking the whip, as well
as your mastery of the English language. Thank you Arthur and Libby for giving me a
place to put my thoughts into words. And thank you Martha and Tom for giving me
encouragement to get through this. Oh yeah, and thank you all for being guinea pigs –
HA HA.
Finally, I would like to thank Art Bell and George Noory of Coast to Coast AM,
who, with their quest for truth, guarantee me job security.
iii
TABLE OF CONTENTS
ACKNOWLEDGMENTS .......................................................................................... iii
LIST OF TABLES .................................................................................................... vii
LIST OF FIGURES..................................................................................................... x
1
2
3
INTRODUCTION .............................................................................................. 1
1.1
The Gravity of the Situation......................................................................... 1
1.2
Scope of Thesis............................................................................................ 2
THE SEARCH FOR TRUTH ............................................................................. 3
2.1
Literature Review ........................................................................................ 3
2.2
Interviews .................................................................................................... 8
THE GRAVITY SURVEY ............................................................................... 11
3.1
Question 1 – The Mother of all Questions .................................................. 11
3.2
Question 2 – The Mother Question Follow-Up........................................... 13
3.3
Moon Base Alpha – Question 10................................................................ 15
3.4
Multiple-Choice Questions 3 – 5................................................................ 17
3.4.1
Question 3 – Gravity Up and Away from the Earth.............................. 17
3.4.2
Question 4 – Galilean Gravity ............................................................. 20
3.4.3
Question 5 – A Balloon on the Moon................................................... 22
3.5
Venus as a Context for Comparison ........................................................... 24
3.5.1
Questions 6 & 7 – Your Weight and Mass on Venus ........................... 27
3.5.2
Question 8 – Venus’ Gravitational Force ............................................. 28
3.5.3
Question 9 – Free-fall on Venus .......................................................... 29
3.6
The Likert-scale Questions......................................................................... 31
3.6.1
Parameters Affecting Gravity .............................................................. 33
3.6.2
The Existence of Gravity on the Moon ................................................ 34
3.6.3
Gravity’s Effect on Objects ................................................................. 35
iv
4
RESULTS AND DISCUSSION........................................................................ 37
4.1
Initial Categorization ................................................................................. 37
4.2
The Mother of All Questions and initial groupings..................................... 38
4.3
Free-Responses and Student Reasoning ..................................................... 40
4.3.1
Student Reasoning for Question 1 – Why a Pen Floats......................... 40
4.3.2
Question 1 Free-Response ................................................................... 42
4.3.3
Student Reasoning for Question 2 – Why an Astronaut Falls ............... 46
4.3.4
Question 2 Student Free-Response ...................................................... 48
4.3.5
Question 1-2 – The Pen/Astronaut Consistency Check ........................ 52
4.3.6
Question 10 Free-Responses – Why the Pen Falls in the Dome............ 54
4.4
Multiple-choice results............................................................................... 58
4.4.1
Question 3 – Up and Away from Earth ................................................ 58
4.4.2
Question 4 – Galilean Gravity ............................................................. 60
4.4.3
Question 5 – A Balloon on the Moon................................................... 63
4.4.4
Question 6 – Your Weight on Venus ................................................... 67
4.4.5
Question 7 – Your Mass on Venus....................................................... 68
4.4.6
Question 8 – The Gravitational Force of Venus ................................... 69
4.4.7
Question 9 – A Pen’s Free-fall on Venus ............................................. 70
4.5
Likert-scale Questions................................................................................ 70
4.5.1
Questions 11 – 15: Parameters Affecting Gravity ............................... 71
4.5.1.1 Question 11 – A Planet’s Atmosphere ............................................. 71
4.5.1.2 Question 12 – A Planet’s Rotation................................................... 71
4.5.1.3 Question 13 – A Planet’s Size ......................................................... 72
4.5.1.4 Question 14 – A Planet’s Mass........................................................ 72
4.5.1.5 Question 15 – A Planet’s Distance from the Sun ............................. 73
4.5.2
Questions 17 – 19: Gravity on the Moon and Outer Space .................. 74
4.5.2.1 Question 17 – Orbital Zero Gravity ................................................. 74
4.5.2.2 Question 18 – Gravity in Outer Space.............................................. 75
4.5.2.3 Question 19 – Gravity on the Moon................................................. 76
4.5.3
Questions 16 & 20-25: Gravity’s Effect on Objects ............................ 77
v
4.5.3.1 Questions 16 & 23 – Falling Speed.................................................. 77
4.5.3.2 Question 20 – Heavy and Light Objects in Low Gravity.................. 78
4.5.3.3 Question 21 – Heavy and Light Objects in No Gravity .................... 78
4.5.3.4 Question 22 – Heavy and Light Objects in a Vacuum...................... 79
4.5.3.5 Question 24 – Gravity and Weight................................................... 80
4.5.3.6 Question 25 – Heavy Objects and Lifting ........................................ 80
5
ADDITIONAL ANALYSIS ............................................................................. 82
5.1
6
Student Gravity Models ............................................................................. 82
5.1.1
The Venusian Conspiracy.................................................................... 82
5.1.2
The Lunar Divide ................................................................................ 85
CROSSING THE THRESHOLD...................................................................... 88
6.1
The All-in-one Survey ............................................................................... 88
6.2
All-in-one Survey Results .......................................................................... 89
6.3
All-in-one Survey Analysis ........................................................................ 90
7
THE DOUBLE CROSS .................................................................................... 92
8
CONCLUSIONS .............................................................................................. 99
8.1
Student Concepts of Gravity ...................................................................... 99
8.2
Suggestions for future research ................................................................ 102
REFERENCES........................................................................................................ 104
APPENDIX A ......................................................................................................... 112
APPENDIX B ......................................................................................................... 116
BIOGRAPHY OF THE AUTHOR .......................................................................... 118
vi
LIST OF TABLES
Table 2.1-1: Astronaut Question: Berg & Brouwer (1991) with Dostal
(2005)......................................................................................................... 8
Table 4.1-1: Mean "score" of class groups .................................................................... 37
Table 4.1-2: Independent sample t-test for equality of means (p) ................................... 38
Table 4.2-1: Mother of All Questions (Question 1) ........................................................ 39
Table 4.2-2: Independent sample t-test for equality of means (p) .................................. 40
Table 4.3-1: Question 1 multiple-choice responses and student reasoning
(“Float” = A+B+C)................................................................................... 41
Table 4.3-2: Mean "score" of student response groups .................................................. 41
Table 4.3-3: Independent sample t-test for equality of means (p) .................................. 42
Table 4.3-4: Mother Question multiple-choice response distribution with
student reasoning included........................................................................ 45
Table 4.3-5: Question 1 student reasoning to Question 20 (Q20 correct
response is False)...................................................................................... 46
Table 4.3-6: Question 1 multiple-choice responses to Question 2 student
reasoning (“Floaters” = A+B+C) .............................................................. 47
Table 4.3-7: Mean "score" of Question 2 student reasoning groups............................... 48
Table 4.3-8: Independent sample t-test for equality of means (p) for
different reasoning groups in Question 2................................................... 48
Table 4.3-9: Question 2 student reasoning to Question 21 (Q21 correct
response is False)...................................................................................... 51
Table 4.3-10: Question 1 student reasoning to Question 2 student reasoning................. 52
Table 4.4-1: Question 3 ................................................................................................ 59
Table 4.4-2: Question 4 ................................................................................................ 61
vii
Table 4.4-3: Question 4 student responses to Question 21 (Q21 correct
response is False). The “?” refers to the “not sure / do not
know” option. ........................................................................................... 63
Table 4.4-4: Question 5 ................................................................................................ 64
Table 4.4-5: Question 5 responses to Question 22 (Q22 correct response is
False). The “?” refers to the “not sure / do not know” option.................... 65
Table 4.4-6: Original Question 5 with responses........................................................... 66
Table 4.4-7: Question 5 version comparison ................................................................. 67
Table 4.4-8: Question 6 ................................................................................................ 68
Table 4.4-9: Question 7 ................................................................................................ 69
Table 4.4-10: Question 8 .............................................................................................. 69
Table 4.4-11: Question 9 .............................................................................................. 70
Table 4.5-1: Question 11 .............................................................................................. 71
Table 4.5-2: Question 12 .............................................................................................. 72
Table 4.5-3: Question 13 .............................................................................................. 72
Table 4.5-4: Question 14 .............................................................................................. 73
Table 4.5-5: Question 15 .............................................................................................. 74
Table 4.5-6: Question 17 .............................................................................................. 75
Table 4.5-7: Question 18 .............................................................................................. 76
Table 4.5-8: Question 19 .............................................................................................. 76
Table 4.5-9: Question 16 .............................................................................................. 77
Table 4.5-10: Question 23 ............................................................................................ 78
Table 4.5-11: Question 20 ............................................................................................ 78
Table 4.5-12: Question 21 ............................................................................................ 79
viii
Table 4.5-13: Question 22 ............................................................................................ 79
Table 4.5-14: Question 24 ............................................................................................ 80
Table 4.5-15: Question 25 ............................................................................................ 81
Table 5.1-1: Truth Table Twenty-two plus Two............................................................ 83
Table 5.1-2: Truth Table Twenty-two plus Three.......................................................... 85
Table 5.1-3: Truth Table Thirty-two plus Three (False is correct) ................................. 86
Table 5.1-4: Truth Table Thirty-three plus Three (False is correct) ............................... 87
Table 6.2-1: Gravity Survey and All-in-one Survey ranking comparison ...................... 90
Table 7.1-1: Question 4 AST classes to multiple-choice responses ............................... 93
Table 7.1-2: Question 4 Pearson Chi-squared analysis of AST classes .......................... 94
Table 7.1-3: Question 1 AST classes to multiple-choice responses ............................... 95
Table 7.1-4: Question 1 Pearson Chi-squared multiple-choice responses ...................... 95
Table 7.1-5: AST classes to Question 1 student reasoning ............................................ 96
Table 7.1-6: Question 1 constructed student responses Pearson Chi-squared
analysis..................................................................................................... 96
Table 7.1-7: Question 5 AST classes to multiple-choice responses ............................... 97
Table 7.1-8: Pearson Chi-squared analysis of Question 5 multiple-choice
responses .................................................................................................. 98
ix
LIST OF FIGURES
Figure 1: Gravity is arbitrary ........................................................................................ 99
x
1
INTRODUCTION
Chapter 1
INTRODUCTION
1.1 The Gravity of the Situation
This is an age of unparalleled intellectual and scientific advancement. Despite
the richness and ready availability of this information, much of the general public is not
engaged in or utilizing this knowledge. Existing within a physical world, a disconnect
exists between the physical laws and people’s perceptions of those laws – knowing
how they work, or even that they exist.
Being creative creatures, students come to the table of scientific discussion with
preconceived ideas, based on their own experience – what they have seen, heard, lived
– a constructivist attitude that does not allow them to easily embrace new knowledge
imparted to them by the teacher of scientific law. Students are much more willing to
entertain the impossible and claim it as truth. An outcome of this attitude is the
popularity of Coast to Coast AM. Here listeners are exposed to alternate science
theories from anti-gravity to zero point energy. Not to worry though, Newtonian
physics and thermodynamics can be granted equal time.
If that isn’t enough to provoke a response, a motivational story may help. A
student detailed a story in which a philosophy teaching assistant tried to explain that,
while a pen always falls when you drop it on Earth, it would just float away if you let
1
go of it on the Moon. Outside of class, the student took a random survey of other
college students. The respondents who answered that the pen would not fall on the
moon, were also asked why the astronauts didn’t float off the moon. A significant
number of students responded that the astronauts wore heavy boots. (Rapaport, 1995)
1.2 Scope of Thesis
This research is to identify the prevalent models held by students. Given the
length of the survey, the magnitude of data, and that this is a master’s thesis, much of
the survey’s potential will not be realized in this paper. This thesis will look at the data
and try to identify general concepts. An exhaustive analysis of consistency will not
take place, but a general scheme of student reasoning will be noted. The chapter
breakdown is as follows: Chapter 1 will introduce the situation. Chapter 2 includes
the pre-survey research, such as the literature search, and the interviews. The design of
the gravity survey is in Chapter 3. The results are given in Chapter 4, along with
general comments concerning each question. Further analysis on selected portions of
the survey are included in Chapter 5. Chapter 6 talks about the inclusion of another
survey to help determine student reasoning. Chapter 7 discusses the effect of a
curriculum change on student responses. Chapter 8 contains the conclusions.
2
2
THE SEARCH FOR TRUTH
Chapter 2
THE SEARCH FOR TRUTH
2.1 Literature Review
National Science Education Standards (National Research Council, 1996)
suggests that the concept of gravity should be introduced in the fifth grade. By the
eighth grade, students should understand gravity’s role in tides and planetary motion,
as well as holding people to the Earth’s surface (Adams, 2000). The science and
technology standards of the State of Maine Learning Results (Maine Department of
Education, 1997) requires that Maine high school students understand current theories
of gravitational force.
There is relatively little published research on student concepts of gravity.
Most appear to be written by educators, rather than astronomers or physicists. Of the
nearly two dozen papers published, over half were printed prior to 1990, and over three
fourths before 2000. Since 2000, all of the papers addressing student concepts of
gravity have dealt with college students. However, nearly all of the older studies have
usually focused on elementary, middle and secondary school students rather than
college students. These older studies tended to identify various student concepts but
did not investigate how prevalent each concept was. A number of the papers were
continuations of previous research.
3
Since most of the papers were focused on young children, it was not
immediately known if the concepts of gravity held by children would be similar to
those held by older students. Stepans, Beiswenger, and Dyche, (1970) indicate that
misconceptions held by older students are just sophisticated versions of the earlier
alternate conceptions. A review of the Noce, Torosantucci, and Vicentini (1988) paper
indicated that children’s concepts of gravity did not appear to be significantly different
from those of adults. In this paper 264 middle and secondary school students, 64 first
year university Biology students, and 74 adults (including 53 elementary school
teachers) were asked to predict what would happen if an astronaut on the moon lost a
spanner he held in his hand.
Of the 264 students, 223 (84%) held alternate
conceptions, compared to 42 (66%) of the Biology students and 57 (77%) of the adults.
Children’s ideas of gravity are rooted in how they perceive the world. There
have been a number of studies investigating what they think about the Earth.
Nussbaum and Novak (1976) interviewed second graders (n = 26) to develop a model
of the child’s version of Earth. The result was a scheme of five notions, starting with
the most egocentric view: a flat Earth and no concept of space outside the atmosphere.
The notions gradually progress toward a more conceptual view and become more
sophisticated. Notion two is that the Earth is a ball composed of two hemispheres in
space, the lower part solid and the upper part the sky, and we live on the flat part inside
the ball. The third notion is that the Earth is a ball in space, and we live on the top of
the ball. Notion four: the Earth is a ball where people live all around the ball, and
objects either fall to the surface of the Earth or toward the bottom of the ball. The last
4
notion, five, is the notion of a round Earth where objects fall toward the center of the
Earth. This work was followed up by Sneider and Pulos (1983), and by Nussbaum and
Sharoni-Dagan (1983) with students at more advanced grade levels. All researchers
found evidence supporting a progression of conceptual development towards the more
scientific view as age and grade level advanced. The development process started with
a large majority of the students using the most egocentric model (notion one) and
gradually changed to the scientifically compatible notion five.
Gravity is not a readily and well understood concept. Smith and Treagust
(1988) interviewed 24 tenth grade students and tested 113 other students with paper
and pencil. The 4 misunderstandings that arose were: a planet’s gravity is related to its
distance from the Sun, the Sun’s gravity influences the gravity of the planets that orbit
it, a planet’s rotation affects its gravity – zero or slow rotating planets have less gravity
than fast rotating planets, and the rotation of a planet is dependent on its position with
respect to the Sun or to its size.
In addition to the possible solar and rotational influences, many students
believe that air affects gravity. (Bar, Zinn, & Goldmuntz, 1994; Minstrell, 1982; Noce
et al (1988); Philips, 1991; Ruggiero, Cartelli, Duprè, & Vicentini-Missoni, 1985)
Some students believe the force of gravity needs air to act as a conducting medium
(Bar, Zinn, & Rubin, 1997). Because of this many students believe that there is no
gravity in space or on the moon (Ameh, 1987; Berg & Brouwer, 1991; Dostal, 2005;
Watts & Zylbersztajn, 1981).
5
Bar et al (1994) found through interviews with 400 children between ages 4 and
13 that many do not consider weight and the force of gravity as being the same thing.
This was also seen in other literature (Ameh, 1987; Bar et al, 1997; Noce et al, 1988;
Watts & Zylbersztajn, 1981). Gravity is associated with free fall. Some students
believe that an object’s weight increases with height (Ameh, 1987; Bar et al, 1994,
1997), while others believe that an object’s weight decreases with height (Chandler,
1991). Gunstone and White (1981) asked 458 university students to predict the
movement of a spring scale needle when the scale, holding a bucket of sand, is moved
from the classroom to the top of Mt. Everest. Although 136 (29%) students marked a
correct response, only 56 (12%) gave a correct reason. Wrong student reasoning
included, “Gravitation attraction is constant everywhere,” and Weight = mg and is
independent of height.
Over all age levels and education the majority of people do not use Newton’s
law of gravitation. (Baxter, 1989; Noce et al, 1988; Watts & Zylbersztajn, 1981) This
use of common sense thinking put students at a disadvantage. Roger Osborne (1984)
classifies children’s models of motion by gut dynamics, lay dynamics and physicist’s
dynamics. Gut dynamics is intuitive, spontaneous, non-verbal and allows children to
cope with common occurrences around them. Examples include “heavy things fall
faster” and “things need a push to get them going.” (This idea is similar to diSessa’s
phenomenological primitives (diSessa, 1993).) Lay dynamics is based on form and
content of the language the child speaks and the images conveyed by those they are in
contact with and the media and the books they read. Examples of lay dynamics:
6
“astronauts are weightless in the space shuttle” and “if there is no force there is no
motion.”
Physicist’s dynamics is the counterintuitive world of physics texts,
experiments and problems students solve in class. When learning new concepts, many
students retain gut and lay physics. As Osborne express it,
Gut dynamics enables one to play hockey, lay dynamics one to
talk about Star Wars, while physicist’s dynamics enables one
to do physics assignments.
The creators of the Force Concept Inventory (Hestenes, Wells, & Swackhamer,
(1992) add to this by noting that 1) Common sense beliefs about motion and force are
generally incompatible with Newtonian concepts, 2) Conventional physics instruction
produces little change in these beliefs, and 3) the result is instructor independent of the
instruction as well as the mode of instruction.
Six papers in the reviewed literature contained a question involving an
astronaut dropping something on the moon. Four publications involved dropping a
spanner or wrench (Berg & Brouwer, 1991; Noce et al, 1988; Ruggiero et al, 1985;
Watts & Zylbersztajn, 1981), and 2 involved dropping a pen (Dostal & Meltzer, 2000;
Dostal, 2005). It was never explained why a wrench and pen were chosen for each. A
comparison of the Berg and Brouwer (1991) with the Dostal (2005) results is shown in
Table 2.1-1. The Berg and Brouwer A group is ninth grade students planning to take
physics, the B group is all ninth grade students. These ninth graders were from
Edmonton, Alberta. The Dostal A groups are algebra-based physics classes and the C
groups are calculus-based physics classes, both at Iowa State University. The results of
7
the other papers were not able to be tabulated for comparison. As expected, the
calculus-based physics students appear to have a better understanding of gravity. What
may not be expected is the similarity of the ninth graders with the algebra-based
physics students. This could indicate that both groups of students may not have a solid
understanding of gravity, and that the college students are still struggling with
preconceived notions of gravity they acquired prior to high school.
Berg and
Brouwer
A
Berg and
Brouwer
B
Dostal
A-1
Dostal
A-2
Dostal
A-3
Dostal
C-1
Dostal
C-2
Dostal
C-3
Dostal
C-4
Toward
moon’s
surface
37%
29%
40%
42%
38%
73%
66%
68%
75%
Away from
astronaut
13%
13%
—
—
—
—
—
—
—
Away from
the moon
18%
22%
29%
22%
19%
15%
12%
11%
11%
Floats (no
force)
30%
30%
31%
34%
38%
10%
19%
14%
12%
Toward the
astronaut
2%
1%
—
—
—
—
—
—
—
Other
responses
3%
5%
0%
2%
5%
2%
3%
7%
1%
Total
responses
(n = 183)
(n = 315)
(n = 48)
(n = 303)
(n = 21)
(n = 40)
(n = 534)
(n = 302)
(n = 414)
Student
Response
Table 2.1-1: Astronaut Question: Berg & Brouwer (1991) with Dostal (2005)
2.2 Interviews
One of the more invaluable tools in the design process of the gravity survey
was the gathering of information by interviews (Redish 1999). It was here where the
so-called air-gravity model and threshold models were first formulated. The
interviews for this survey were informal events with no formal protocols or recording
8
devices. The interviewees consisted of nearly 45 adult parents, grandparents, and
children. Ages were between 6 and 81. Interviews were granted by verbal permission,
and took place inside privately owned homes.
All interviews began with the question, “Suppose you were standing on the
moon holding this pen. What would happen if you were to let go of the pen?” After
receiving a sufficient answer from the interviewee, the follow-up question would be
posed, “Do you know about when the astronauts walked on the moon? Why didn’t the
astronauts float off the surface?”
Gleaning information from some of the children was at times difficult. It was
sometimes hard to get definite answers, even after repeating 4 or 5 times. The adults
were a bit easier to interview, but as a rule did not appear to possess a greater
knowledge level.
At the interview’s end, of some of the interviewees were asked if they knew
what caused the tides. It was hoped to get them to consider that the moon must have
had some kind of gravitational effect. Most knew that the moon had something to do
with the tides, but really didn’t know what it was. At least two of the younger
interviewees believed that the wind caused the tides.
At the end of the interview process, two standard gravitational models were
noted. The first is what was called the gravity-air or air-gravity model. The pen
would float because the moon has no air. For some unknown reason air causes gravity,
and since the moon has no air, there is no gravity. This model was common
throughout the literature.
9
The second, initially labeled the gravity-weight model, went on to become the
threshold model. Perhaps the best example of this model came from a middle-school
boy. He initially claimed that the pen would float because of no gravity on the moon.
He was then asked what gravity was and his response was that it was the force that kept
us on the earth. When asked why there wasn’t any gravity on the moon, he considered
for a moment and then recanted. He admitted that there was sort of gravity on the
moon, but not as much as the earth. He really didn’t know what gravity was, but knew
it depended on the planet. Besides, that wouldn’t change his answer anyway. The pen
weighs so little on the earth that it would weigh next to nothing on the moon.
Consequently, it would not be heavy enough to fall, and it would float upward.
Adults and children both held similar views. At least one parent spoke of her
knowledge that she “knew” that the astronauts put lead in their boots before they
ventured out onto the lunar surface. At least two other adults spoke of a link of gravity
to the speed of planetary rotation. The moon had less gravity because it didn’t spin as
fast.
All-in-all, the interview process proved extremely useful in discovering and
verifying the basic models students utilize in their dealings with gravity. A number of
survey questions were the direct result of these interviews.
10
3
THE GRAVITY SURVEY
Chapter 3
THE GRAVITY SURVEY
Since its genesis, the gravity survey has undergone a number of major revisions
as well as minor cosmetic changes. Its initial form was developed through the
utilization of interviews with the general populace as well as an extensive literature
search of pertinent educational and scientific journals.
3.1 Question 1 – The Mother of all Questions
The mother of all the questions (Question 1) that this survey was designed
around concerned the prediction of how a small, light object would behave on the
moon. It was multiple choice with an additional free-response portion, and was similar
to a question found in the literature (Berg & Brouwer, 1991; Dostal, 2005; Noce et al,
1988; Ruggiero et al, 1985; Watts & Zylbersztajn, 1981). The question read, “Suppose
you were standing on the moon holding a pen. If you were to let go of the pen, what
direction will it move?” The directional choices available to the student were, float
upward, float around, staying about the same height, and levitate, but also move away
horizontally, and fall toward the lunar surface. A fifth option was other/none of the
above.
The question was designed as a thought question, and not something that the
students were expected to experience for themselves. The question was written in
11
second person narration to match the original interviews. It was felt that this
perspective might aid in provoking a more descriptive and honest answer as to what the
students believe, since they were being asked to imagine themselves experiencing the
event. The semantics of this question was selected to avoid biasing the student toward
any particular response. The phrase “let go of ” was used instead of “drop” because it
was felt that when something is dropped, it automatically infers that the object would
move down since the direction of a dropped item on the earth is in the down direction.
In the original version of the question, the pen was a Fisher Space Pen™, rather
than any generic pen. The pen was identified as a space pen to add realism to the
question – why would an astronaut not bring a space pen? After the initial test of the
survey, there were indications that one or two students had taken issue with the fact
that it was a space pen. For this reason the product endorsement was removed from
this question.
The given choices of motion were selected from the interviews and literature
search. From the interviews, it was noted that the direction of motion of the pen was
always important. Float upward, float around, and fall were the most common
responses. Prior to the first version of the survey, the original directional choices for
this question were to be, float up/away, float sideways, float in no specific direction,
and fall. The 3 non-falling directional choices were modified to, float upward, float
around, staying about chest height, and levitate, but also move away horizontally, after
consultation with MST and PER students and faculty. After the first version of the
survey was analyzed, the word chest was replaced with the words the same. The
12
question never specified as to the original height of the pen. If the pen originated at a
height other than chest height, there may be no compelling reason for the pen to move
to chest height. It was thought that this change would make the selection more general
and leave the students with three non-falling options – float up, float around, and float
up (levitate) and out.
In addition to their selection of a particular response, students were asked to
explain their response. It was expected that this portion of the question would provide
student reasoning for student responses. The responses could then be additionally
categorized by their explanation. This free response was designed to help determine
what gravity model they were using, and to make sure that the distracters were
interpreted appropriately by the students (i.e., that they chose a particular distracter for
the same reason that we put that distracter in the question in the first place).
3.2 Question 2 – The Mother Question Follow-Up
Question 2 of the survey was designed as a follow-up to the first question. As a
free-response question it was also designed to help determine what gravity model they
were using, but also to evoke cognitive conflict. “Between July 1969 and December
1972 there were six moon landings. Twelve astronauts spent a total of over 80 hours
exploring the lunar surface. Why didn’t the astronauts float off the lunar surface?
Compare this answer to how you answered the question above.” When asked in
interviews, this question originally was phrased to ask the students how they
remembered that the astronauts were kept on the surface. When designing this survey
13
it was pointed out that since the landings were over thirty years ago and most students
are under thirty, the landings are viewed as a part of history rather than as an event.
Consequently, these students were not as likely to assign any special significance to the
landings and not be expected to remember any special details. The number of
astronauts and hours spent on the moon were added to show these students that there
were a number of astronauts and that they spent a significant amount of time on the
moon.
This question went through some minor revisions before ending up with its
current version. The original form asked the student to compare and contrast this
answer to the pen question. The request to contrast the answer was removed since it
might have biased the student into assuming that the answer to this question had to be
different. Another revision involved rewriting the sentence, “What kept the astronauts
from floating off the lunar surface?” to “Why didn’t the astronauts float off the lunar
surface?” It was felt that the original phrasing suggested that the astronauts would
have floated off the surface had there not been something that was keeping them down,
and that the final phrasing conveyed the same thing without leading the student.
It was expected that the students who answered that the pen would not fall in
question 1 would answer that the astronauts remained on the surface because of their
greater mass or weight, or their utilization of air or oxygen, regardless of whether the
student felt that there was gravity present.
14
3.3 Moon Base Alpha – Question 10
Another follow-up question to the pen question was another free-response
question. This appeared in the survey as Question 10. Question 10 posed the same
question as the mother question, but with the addition of an atmosphere. From the
literature (Bar et al, 1994, 1997; Minstrell, 1982; Noce et al, 1988; Ruggiero et al,
1985) as well as interviews, the existence of gravity was tied to the presence of an
atmosphere or some component of air. The interviews indicated that some students
make a connection between the oxygen contained in space suits and gravity. This
question was designed to be exactly like the first question except for the addition of air.
This question was chosen to identify evidence of a gravity-air model of reasoning and
read:
It is the year 2156 and people are living on the moon inside
giant geodesic domes. These domes are filled with air so that
people can live inside the dome without having to wear space
suits. Suppose someone is standing inside one of the domes,
with a pen in hand. What will happen to the pen if they let go
of it?
The year 21561 was chosen to place the scenario in the future, and add to its
credibility, since there are no lunar bases at this time. It was felt that if the scenario
were presented as a thought question, taking place in present time, some students
would take issue with the fact that there were no lunar bases in existence and the
question would become moot. The domes were used in this question to minimize the
1
The year 2156 was selected as I will be 200 years old that year.
15
environmental differences between this question and the original pen question. Since
space suits are totally localized, it was felt that an environment had to be created that
would encompass the immediate surrounding area, thereby removing the suits but also
reducing the sense of being enclosed. Air was used to fill the domes rather than
oxygen to make the atmosphere less exotic and more familiar. By standing inside a
large dome, the person with the pen would essentially be in the open, with a large
volume of air surrounding them. The surroundings would be much more likely to be
perceived as being in an enclosed, climate-controlled, sports stadium or arena. If they
were within a small, oxygen filled, lunar enclosure, they might be more likely to treat
the environment as a space suit, or identify the situation with that of the International
Space Station (ISS) or space shuttle.
Question 10 went through a number of revisions. The original wording of the
reason why the domes were filled with air was to simulate conditions on Earth. It was
originally felt that this text was sufficient in describing the conditions inside the dome.
However, it was found that the lack of descriptive text caused some students to jump to
conclusions and evoke other assumptions. This wording led a substantial number of
students (nearly a third) to believe that simulating earth conditions meant the
environment was the same as the earth in all respects. The pen would fall inside the
dome exactly as it would on earth. The text, to simulate conditions on Earth, was
replaced with, so that people can live inside the dome without having to wear space
suits. This change was expected to address this issue.
16
3.4 Multiple-Choice Questions 3 – 5
Additional questions were added to the survey to substantiate different student
conceptions of gravity as well as check for consistency. As mentioned above, the
interviews and literature (Ameh, 1987; Berg & Brouwer, 1991; Dostal, 2005; Noce et
al, 1988; Ruggiero et al, 1985; Watts & Zylbersztajn, 1981) indicated that one student
explanation for why the pen would not fall is because there is no gravity on the moon.
There were 2 prevalent models as to why the moon has no gravity. One was that the
moon has no atmosphere (or air – freely interchanged with “atmosphere”), and since air
causes gravity the moon has no gravity. In the second model there was no gravity in
“outer space” (outer space being outside the earth’s atmosphere), and since the moon is
in outer space, the moon – by definition – has no gravity. These two models appear to
be related since outer space can be categorized as a vacuum, but students appeared to
distinguish between the two. The other reason why the pen would not fall on the moon
was the pen’s lack of “heaviness.”
This lack of heaviness appeared to be a
combination of the pen’s low mass and the moon’s low (or lack of) gravity (Berg &
Brouwer, 1991; Dostal, 2005).
In addition to these basic models, the initial
information also indicated the existence of perceptions that atmosphere, mass, distance,
and rotation could each affect gravity.
3.4.1 Question 3 – Gravity Up and Away from the Earth
To check for student understanding of the distance dependence of the
gravitational force between two bodies, as well for the air-gravity connection, the first
17
additional question – Question 3 – read, As you move up and away from the Earth’s
surface, what happens to the Earth’s gravitational force on you? Again, the question
was written in the first person. Moving up and away was meant to indicate
displacement, rather than motion. The question was thought to be less hypothetical
than a question based on the moon or other location, and that their responses would
come more from their common sense and gut feeling, rather than their understanding of
a hypothetical situation. Although non-science students appear to be more comfortable
using the colloquial phrase, force of gravity (the original phrasing choice), the
terminology gravitational force was selected for use in the final survey to make the
statement more scientifically accurate. The literature (Baxter, 1989; Noce et al, 1988;
Watts & Zylbersztajn, 1981) suggested that most students do not hold a standard
definition for gravity, or if they are even aware of Newton’s law of gravitation, which
states that the force between two masses m1 and m2 separated by distance r (measured
from each center of mass), has the magnitude, F = Gm12m2 , where G is a universal
r
constant. Given its colloquial nature, “gravity” as a word encompasses a number of
€
different meanings. Some students appeared to identify gravity as a physical force,
while others seemed to use it to describe an environment or state. Most students would
agree that gravitational force and the force of gravity are the two different ways to say
the same thing, but to be technically accurate, gravitational force was used in the final
version of the survey.
The formulation of responses to this question were based on the simplified
logic that there are only two possible avenues to answer the question, either the
18
gravitational force will not change (Gunstone & White, 1981), or it will. And, if the
force changes, it either gets bigger (Ameh, 1987; Bar et al, 1994, 1997) or smaller
(Chandler, 1991). These three options were found in the literature.; So, the initial
responses were selected to be, the gravitational force on you...
...increases,
...decreases, and ...stays the same. To test for the air-gravity connection prompted 3
additional responses. These responses were duplicates of the initial responses, with the
added stipulation that the gravitational force goes to zero once you leave the Earth’s
atmosphere. The creation of these 3 responses required clarification of the initial
...decreases response phrase by adding, but never goes to zero. By adding this text, it
was felt that it reduced the ambiguity that this statement might suggest that the
gravitational force reaches zero in outer space, and that students who supported an airgravity model would be less likely to choose this response. Chandler (1991) indicates
that most students are unaware that gravity reaches to infinity. An additional other
(please explain) response was included in the event the student did not agree with one
of the other 6 choices.
The original form of Question 3 was formulated to identify multiple parameters
that were perceived to affect gravity, including, atmosphere, mass, distance, and
rotation. The question was structured in two parts, the first part (a) asking what
happens to the force of gravity, and the second part (b), asking the student to indicate
why they chose their answer, as well as explaining their reasoning. Part (a) of the
question was the original version of the Question 3. The selection of responses for the
this part included, the force of gravity increases, the force of gravity decreases, the
19
force of gravity stays the same, and the force of gravity is zero in outer space. Students
had the option of combining a “directional” answer with the gravity-is-zero option to
help determine a model that most closely fit what the student believed. Since the
question was not designed to determine student reasoning, part (b) was necessary to
fully evaluate (a).
As for student reasoning, the part (b) choices included highlights found in the
literature and interviews, air pressure changes, mass changes, you are further from the
Earth, you are closer to the Sun, the Earth’s rotation has less of an effect, and gravity
is a universal constant. Students were allowed to select multiple responses. The design
of this question was found to be less than desirable. Some students had difficulty
interpreting what the question asked and answered accordingly. The format of the
question made the interpretation of student responses difficult to analyze. As a result,
the final survey questions were not overtly paired, and students were not asked to select
multiple responses.
3.4.2 Question 4 – Galilean Gravity
Question 4 was added to help identify the students who hold the gravity-weight
model –something must be heavy enough to fall. Other students that this question was
designed to identify were those who may realize that objects will fall on the moon, but
may not believe that things fall at the same rate in a vacuum. In order to test for these
Galilean gravity models, as well as issues with dropping and floating, Question 4 read,
“If you let go of a feather and a small piece of lead on the moon, what will happen?”
20
Following other questions of the survey, the question was again written in the second
person, and posed as a question. Let go was used as an action verb rather than dropped
to avoid biasing the question. A feather was chosen as one of the objects because it
was assumed to be light. On the earth, feathers are generally felt to fall through the air
slowly (more slowly than a pen) and have been known to move upward on air currents,
thereby “cheating” earth gravity. Lead was chosen since it is commonly associated
with being “dense,” and has the general perception of being heavier than most other
things. Even a small piece would be perceived to be heavy.
Answers were designed on the basis of how a student might consider the
motion of two objects let go at the same time. With the objects in free-fall, being in a
vacuum, on the lunar surface, the student using correct reasoning would be expected to
answer, both will fall at the same rate. If the student reasoned that the lead is heavy
enough to be attracted to the moon, but the feather was not, the lead will fall slowly,
but the feather will float rather than fall. If the student believed that the moon has no
gravity, or that neither the lead nor the feather were heavy enough to fall, both will
float. If the student were hung up on pre-Galilean concepts, both will fall slowly, but
the lead will fall a little faster than the feather might be selected since it would be
similar to the free-fall of the lead and feather on Earth.
In the original design of this question, dropped was used as the action verb
rather than let go. It was felt that students would not be biased with the use of this
word since the act of dropping an object on the earth just involves letting go of the
object. A review of the responses to this question confirmed that the use of dropped did
21
not infer an initial direction. In spite of this, dropped was replaced by let go to avoid
any perceived biasing – and to be consistent with other questions. Another point that
was considered in the design of the original version was that some students might
believe that, at the instant being let go, an object does not immediately fall. On the
earth, this would account for only a split second, but on the moon, with its weaker
gravity, this time delay could account for a significant time delay. Motion photography
of the astronauts on the moon show them “bouncing around,” getting more “air time”
from a lunar hop than with a comparable earth hop. This could have been perceived as
a type of time delay – on the moon it takes longer for an object to feel the effects of the
lower gravity.
The original answers to the question were similar in nature to the final version.
A problem arose in the wording of some of the responses. The original wording of the
responses, both will start to fall slowly, but then the lead will start to fall faster, and
both would start to fall slowly, but then the feather will float. Were selected to include
the potentially perceived time delay. A number of students took this phrasing to mean
that the lead was somehow accelerated more than normal, or that the rate of fall for
each object was somehow changing.
3.4.3 Question 5 – A Balloon on the Moon
Question 5, designed to search for indications of the gravity-weight model, was
not as much a gravity question as it was a buoyancy question. The question read,
22
“Imagine you are on the moon, holding a balloon filled with Helium. What will
happen to the balloon if you let go of it?” The wording followed the wording of the
original pen question, again written in the first person, and posed as a thought question.
This survey was designed for students outside the science field, and it would be a safe
assumption that many non-science students are unfamiliar with the concept of
buoyancy. Therefore, there is the likelihood that students would attribute the buoyant
properties of “lighter than air” objects such as blimps and balloons to a gravitational
force rather than a buoyant force. The dilemma may not be that the “lighter than air”
object located the moon will not fall, but how fast will it rise. Some students believe,
that on the moon, the reason why the pen floats is because it is too light to be affected
by the moon’s lower gravity. When weighed on the earth, a balloon filled with helium
would be much lighter than the pen because helium is lighter than the air, and when on
the moon the balloon would be even lighter than it would on the earth. The balloon
could rise faster since it is much lighter than it is on the earth, or it may be so light it is
unaffected by the moon’s minimal gravity. Other student reasoning that may arise is
that since the moon has less or no gravity, things don’t move as fast as they do on the
earth. (Ameh, 1987) Therefore, an object that is set to rise will rise more slowly than
it would on earth.
Again, answers to the question were selected as to how a student might reason
this problem, with both direction and relative speeds considered. Responses available
to the student included, the balloon will float up, moving more quickly than it would on
the Earth, the balloon will float up, moving more slowly than it would on the Earth, the
23
balloon will float around, staying about the same height, the balloon will fall toward
the lunar surface, and there is not enough information to answer the question.
This survey question was essentially unchanged from the original version. One
of the answers was replaced. When initially designing this survey, it was considered
that the slow and fast rates of ascension would counteract each other and the balloon
will float up, moving the same rate as it would on the Earth. The minimal response to
this answer prompted the answer to be eliminated and is discussed in greater detail
with the results of the balloon question.
3.5 Venus as a Context for Comparison
The central question of this survey involved the prediction of how an object
behaves in a lunar environment, and that students were expected to perceive that
environment as having little or no gravity. In order to help further substantiate selected
student conceptions gathered from this “micro-gravity” environment, additional
questions posed predictions set within an equally alien environment, one that students
were likely to interpret as being the opposite of the moon. This new environment
would give the opportunity of exploring and possibly identifying other student gravity
models as well as a check student concepts of mass and weight.
This drastically different environment was the surface of Venus. Venus was
selected due to its similar size to Earth, slow rotation, and extremely high atmospheric
pressure. The student gravity models that were potentially present included, the
planetary rotation model, the gravity-air model, and the Newtonian model. It was
24
expected that students with a gravity-air model would key on the extreme atmospheric
pressure of Venus and answer accordingly, and the slow rotation of Venus had the
potential to activate a planetary rotation model (Smith & Treagust, 1988; Treagust &
Smith, 1989).
Venus is only slightly smaller than Earth, with a mass 80% Earth’s mass, and a
diameter 95% Earth’s diameter.
Venus’ size and mass alone dictate that the
gravitational pull on the surface would be about 90% of Earth’s. Venus’ rotational
period is 243 Earth sidereal days, slightly longer than its 225 day period of revolution
about the Sun, making its day 8% longer than its year. The atmospheric pressure at
the surface of Venus is approximately 90 atmospheres (~91 bars or ~1300 psi). This
indicates that Venus’ atmosphere would exert a substantial buoyant force on any object
at or near the planet’s surface. This buoyant force is directly related to the object’s
volume and the density of the surrounding atmosphere, and is equal in magnitude to the
weight of the atmosphere that the object has displaced. It is felt up and away from the
planet’s surface, and in the opposite direction of the gravitational force.
The
combination of these two forces gives the appearance of reducing the apparent
magnitude of the gravitational force. Standing on the surface of Venus, the buoyant
force exerted on a typical high school or college student (assuming they aren’t crushed
by the pressure) could be estimated to reduce their apparent weight by about 10%.
Consequently, this average-sized student on the surface of Venus would weigh on the
order of 80% of their weight on Earth.
25
Although it could be argued that students possess equal levels of knowledge
concerning the moon and Venus, and that students were expected to answer the
questions situated on the moon with no additional information, students were given
selected background information on Venus. The Venus set of questions were designed
to elicit responses that would confirm specific models, and all students needed to have
the same basis to work from. A preface to the Venus set of questions was written and
read, “Venus is sometimes called Earth’s sister planet. It is nearly the same size and
mass, but Venus rotates once on its axis every 243 days, and has an atmospheric
pressure 90 times that of the Earth.”
In the process of designing the Venus preface, the point arose that if the
background information included an analogy that Venus’ atmospheric pressure was
similar to the pressure of the ocean at the depth of about 3200 feet (~1 kilometer), the
student response might be different. It is assumed that most students are aware that
people float and consequently have less apparent weight in the water. It is possible that
students might take this information and apply it to this question. However, it cannot
be assumed that the student population that this survey was given to would understand
the physics behind how submersibles dive and float. On the contrary, it appears that a
general consensus could be that once things are below a threshold depth, the general
properties of sinking and floating may not necessarily apply. The general public seems
to understand that, if a submarine should go below crush depth (easily half a mile) the
ambient oceanic pressure will compress the vessel, causing it to sink to the bottom.
This can suggest that at lower depths, things are held down by the water pressure and
26
do not rise to the surface. Also, as found in other portions of this project, the
likelihood of students applying knowledge not directly related to a set question appears
to be remote. Another argument against using the sea pressure analogy was that this
was a gravity survey and not an ocean survey. Students might have felt that the
information was out of context, which had the possibility of biasing the question.
3.5.1 Questions 6 & 7 – Your Weight and Mass on Venus
The first two Venus questions, Question 6 and Question7, were written as a pair
of 2 independent questions, one asking about weight, and the other about mass. Both
were formatted for the student to complete the sentence with one of 4 responses. Since
they were designed as a pair, to avoid biasing, the answers were exactly the same for
both questions. In keeping with the rest of the survey, these were also written as
thought questions in second person. Question 6 read, “If you could weigh yourself on
Venus, using a standard bathroom scale, you would weigh”, and Question 7 read,
“Your mass on Venus would be”.
The weight question included the condition of using a standard bathroom scale.
Most non-science students are familiar with using standard bathroom scales, but
probably would not understand the mechanics of how the scale works. Since a
standard bathroom scale measures the normal force applied to the scale, students would
be correct in assuming that the scale was measuring the net force down – their apparent
weight. If the scale type had not been stipulated, the student ran the risk of reasoning
this question by invoking a balancing scale – similar to one found in a doctor’s office –
27
in their reasoning. Since a balance scale measures torque, rather than force, the correct
reasoning becomes much more involved and too complex for this survey.
The answers selected for both questions were, a lot more, a lot less, about the
same, exactly the same, and there is not enough information to answer the question.
The answers that were written to be responses to the weight question were purposely
written to encompass a range (lot more, lot less, about the same) rather than being
specific. This was to minimize quantitative reasoning and imply that the information
provided was enough to answer the question. Since an average sized student would
weigh about 80% of their Earth weight on Venus, the correct response to the weight
question was about the same. The gravity-air model suggests that the atmosphere will
push down on everything and one would weigh a lot more on Venus. (The belief that
gravity actually pushed up and the atmosphere pushed down was noted in interviews.)
Since Venus revolves 243 times slower than the earth, the student who believes that
planetary rotation is directly related to gravity might expect to weigh a lot less on
Venus. The exactly the same option was included in both sets of answers to avoid
biasing the correct response to the mass question. The two-question pair was also used
as a consistency check for mass and weight.
3.5.2 Question 8 – Venus’ Gravitational Force
Question 8, the third Venus question, was written as a fill-in-the-blank
statement. The question stated, “The gravitational force of Venus is...
...the
gravitational force of Earth.” Other than that, Question 8 followed the same answer
28
format of Question 6 and Question 7. Responses included, much greater than, much
less than, about the same as, exactly the same as, and there is not enough information
to answer the question. As with the mass and weight responses, the answers used
language written in general terms to encompass a range (much greater, much less,
about the same). Question 8 was included in the Venus section for a number of
reasons. As a direct question, it was meant to determine if students connected
gravitational force with size, mass, rotation or atmosphere. Additionally, Question 8
was used as a consistency check with Question 6, comparing weight to gravitational
force, and Question 9, comparing gravitational force to free-fall.
3.5.3 Question 9 – Free-fall on Venus
Question 9, the final Venus question, asked how a pen would behave on Venus.
Like the pen on the moon, this question was posed as a hypothetical thought question.
Question 9 was written as a complete-the-sentence statement, and required the student
to choose the most appropriate ending. To help clarify their response, most endings
directly compared the movement of the pen on Venus with a similar pen’s movement
on Earth. It read, “Suppose you let go of a pen while standing on the surface of Venus.
Compared to releasing an identical pen at the same height while standing on the surface
of the Earth, the pen on Venus . . .”
Like the other Venus questions, it followed the same general answer format.
Each answer choice that referred to the pen falling on Venus, included a time answer as
well as a speed answer. The answers included, will hit the ground in much less time
29
(fall a lot faster) than the pen on Earth, will hit the ground in much greater time (fall a
lot slower) than the pen on Earth, will hit the ground in about the same amount of time
(fall about the same way) as the pen on Earth, and will hit the ground in exactly the
same amount of time (fall exactly the same way) as the pen on Earth. The options, will
not fall, and There is not enough information to answer the question were also
included. Question 9 was included as a contrast to the pen on the moon, and as a
consistency check with Question 6, and Question 8.
Questions 6, 8, and 9 were designed to work as a group. Students who give the
same response for these three questions would be considered consistent in their
reasoning connecting gravity and gravitational force with free-fall, and weight. Those
who hold a “pure” gravity-air model would also tend to be consistent over the three
questions. Students who do not believe in a gravity-air model but believe that Venus’
atmospheric pressure is great enough to affect the free-fall and weight of an object may
be consistent over only two of the questions. Those who are of the opinion that Venus
has an overly viscous atmosphere might only be consistent over Questions 6 and 8.
Those who overestimate any additional outward or inward non-gravitational external
forces due to the atmosphere might tend to be consistent over questions 6 and 9.
Students who feel that the atmosphere pushes down and crushes objects, but does not
affect an object’s free-fall will probably be consistent over Questions 8 and 9.
30
3.6 The Likert-scale Questions
Through the design process of the survey, it became evident that from an
information-gathering standpoint, it was better to design questions that addressed a
single issue rather than creating ones that required students to reason through multiple
issues.
Of the 10 questions that comprised the heart of the survey, all were
location/environment specific, and most focused on how gravity (or the environment)
affects the motion of, or the force on, an object. All of the multiple-choice questions
asked ‘what’ rather than ‘why,’ leaving the free-response questions as the only ones
that specifically asked for student reasoning. Since the multiple-choice questions did
not directly ask students why they chose their answer, student reasoning was only as
accurate as what was inferred by combining the responses of multiple questions. More
questions were needed to check for the consistency of student responses and get a more
accurate determination of student reasoning.
These additional questions were meant to gather more specific information, and
provide an opportunity to refine the survey data and help determine the reasoning
behind the responses.
These questions were meant to further explore student
understanding by asking direct questions about gravity and the nature of gravity.
Conceptions covered would include the existence of gravity in space and on the moon,
what parameters affect gravity, and how gravity affects objects. In determining the
style of question to add, a number of factors were involved. It was felt that additional
free-response questions, although a more direct method of determining student
reasoning, would make the survey too lengthy for students. Adding multiple-choice
31
questions of the same form and context as the core questions would not only make the
survey too lengthy, but would have added complexity to the determination of student
reasoning. After weighing these and other factors, the Likert psychometric response
scale was determined to be the best format for the additional questions.
In using the Likert scale, questions would be written as true-or-false statements.
Students would specify their level of agreement to those statements. The student could
answer that they were certain that the statement was true or false, or were not so sure
that it was true or false. Their fifth option was that they did not know or were
uncertain. This format had the advantage of allowing the student to pick the answer
they were most comfortable with, and by giving students the option of being unsure, it
was anticipated that students would be more likely to select answers that more
accurately reflected what they actually believed. However, for the data analysis, the
strength of conviction to a true or false answer was not needed, so student response
confidence was disregarded.
A total of 15 Likert-scale questions were added to the original 10 questions of
the core survey. These additional questions fell into 3 general categories. One
category included 5 questions that dealt with some parameters that, as some students
believe, affect gravity. Another category was comprised of 3 questions that addressed
the existence of gravity – on the moon, in outer space, and in earth orbit. The third
category included 7 questions regarding the nature of gravity.
32
3.6.1 Parameters Affecting Gravity
As indicated above, the interviews and literature indicated that a substantial
number of students believe in a gravity-air connection, and that some students link a
planet’s rotation to its gravity. The literature also suggested that some students believe
that a planet’s distance from the Sun also affects the planet’s gravity (Smith &
Treagust, 1988; Treagust & Smith, 1989). Newton’s law of gravitation, F = Gm12m2 ,
r
suggests that only 2 things can affect the gravitational force: mass and separation
€
distance. To investigate how students weighed in on these concepts, the first 5
additional questions (11-15) were included.
All 5 questions had the same general format, “A planet’s . . . affects its
gravitational pull.” “Gravitational pull” was used instead of “gravity” to make the
statement more technically accurate. “Atmosphere,” “rotation,” “mass,” and “distance
from the Sun” were inserted into the general question template to create Question 11,
Question 12, Question 14, and Question 15. “Size” was inserted into Question 13
instead of separation distance for reasons explained below. It was expected that most
of these questions would be used with other survey questions to help identify student
models as well as check for consistency. Exceptions to this were Question 15 (distance
from the Sun) and Question 13 (size). A planet’s distance from the Sun was not
brought up in any other survey questions, so there were no other questions with which
to combine Question 15. Question 13 was not used for reasons explained below.
Size was used in lieu of separation distance in Question 13 because it was
expected that many students taking the survey would not be familiar with Newton’s
33
law of gravitation, and might not realize that the separation distance of the masses is
measured from each object’s center of mass. The separation distance between a planet
and an object resting on the planet’s surface is effectively the radius of the planet.
Given this information, and that a planet’s radius is a measure of its size, it can be
stated that a planet’s size affects its gravitational pull. However, although technically
correct, the assumptions this statement was based on were not identified in the
question. Without knowing the specific context of the question, students could not be
expected to understand that the intent of the question was to look for separation
distance. This may be a moot point, considering that another consequence of the
question’s word choice was that it could easily have been misinterpreted. Students
might reasonably equate a planet’s size to its mass, and answer the two questions
similarly. For this reason, it was expected that this question would not produce useful
data.
3.6.2 The Existence of Gravity on the Moon
The absence of gravity on the moon and in space are well-documented student
concepts (Ameh, 1987; Berg & Brouwer, 1991; Dostal, 2005; Noce et al, 1988;
Ruggiero et al, 1985; Sharma et al, 2004; Watts & Zylbersztajn, 1981). Numerous
students believe that gravity ends with Earth’s atmosphere. It may be reasonable to
conclude that most of these students hold a gravity-air model. Other students may
consider that gravity is not necessarily influenced by the atmosphere, but reduces to
zero at an appropriate “outer” radius from the Earth. Students who subscribe to any of
the above ideas could reasonably assume that there is no gravity on the moon. The
34
moon has no atmosphere to speak of, which would evoke the gravity-air connection. If
gravity ends with the Earth’s atmosphere, then the moon has no gravity because the
moon is outside the Earth’s atmosphere. If there is no gravity in outer space, and the
moon is defined to be in outer space, then – by definition – the moon has no gravity.
There is no evidence that students have demarcated outer space. Outer space seems to
be a general term for the space outside of the local vicinity of Earth or any other planet.
Since the moon is a substantial distance away from the Earth and not planet-sized,
outer space encompasses lunar space.
Questions 17, 18, and 19 were designed to look for the existence or absence of
gravity just outside Earth’s atmosphere, in outer space, and on the moon. The intent of
this group of questions was to identify student models and check for consistency
utilizing the perspectives of 3 different locations. Question 17 was the location closest
to Earth and read, “When in orbit, the astronauts are in zero gravity.” Question 18
read, “There is no gravity in outer space,” and Question 19 read, “There is no gravity
on the moon.” These 3 questions would be used with other survey questions to help
identify student models as well as check for consistency.
3.6.3 Gravity’s Effect on Objects
The last group of questions added to the survey were added to focus on some of
the conceptions students held about the nature of gravity. These 7 questions were
meant to be used in concert with other survey questions. Two addressed free-fall
speed, 3 were threshold-type questions and 2 related gravity to weight.
35
Question 16 and Question 23 dealt with free-fall as well as gravity terminology.
They were included as a pair of questions. They both asked the same question using
different terminology. Question 16 asked the students to respond to, “A planet’s
gravitational pull affects an object’s falling speed,” whereas Question 23 was written,
“Gravity affects how fast an object falls.” The pair’s purpose was two-fold. Asking
the question twice would provide a consistency check on the concept, and asking it in
two different ways would verify that students considered gravity and gravitational pull
to be the same thing.
Questions 20-22 dealt with the threshold model that arose from the interviews.
Question 20 read, “In low gravity, light objects may be too light to be affected by the
gravitational force,” and Question 21 rephrased the question without gravity, “In an
environment with no gravity, an object must be heavy enough in order to fall.”
Question 22 was added as more of a consistency check on Question 4, the feather-andlead question. It read, “With no atmosphere, heavy objects can fall faster than light
ones.”
The last 2 questions, Question 24 and Question 25 were directed at gravity’s
effect on weight, and gravity’s relationship with height. The literature had indicated
that students associated gravity with free-fall and that an object’s weight was related to
its height above ground (Ameh, 1987; Bar et al, 1994, 1997; Noce et al, 1988; Watts &
Zylbersztajn, 1981). Question 24 read, “Gravity does not affect the weight of an
object,” and Question 25 stated, “Heavy objects are hard to lift because Earth’s
gravitational force increases as you lift.”
36
4
RESULTS AND DISCUSSION
Chapter 4
RESULTS AND DISCUSSION
4.1 Initial Categorization
The initial analysis of the survey results involved checking the correct overall
number of correct responses between classes. Statistical analysis of the data was done
with SPSS. The correct responses were totaled for a “score.” The mean score and
standard deviation for each class is shown in Table 4.1-1. An independent sample ttest for equality of means was performed to identify potential data groups. The results
of this analysis suggest that there is no statistical difference in correct responses across
AST 109 classes or across PHY 101, 102, and 105 classes. A comparison of all
combined AST classes with all combined PHY classes is included in Table 4.1-2. A
direct comparison of the PHY and AST combined groups indicated that there was a
statistically significant difference in the mean score of the two groups.
Class
AST 109
2004
AST 109
2005
AST 109
2006
All AST
PHY 105
2005
PHY 102
2006
PHY 101
2006
All PHY
Mean “score”
10.52
10.92
10.44
10.63
9.19
8.50
7.63
8.66
Standard
deviation
4.10
4.74
4.20
4.35
4.36
3.65
2.94
3.91
n
149
140
128
417
36
16
16
68
Table 4.1-1: Mean "score" of class groups
37
Additional statistical analysis of the data yielded further differences. This
difference was not unexpected given the subject nature of each class. Since the focus of
this thesis is to investigate and identify individual student conceptions of gravity, and
not curriculum development, for most analysis the AST and PHY student data was
pooled together. For a small number of cases, particular groups of AST were separated
from the pool of data and comparative analysis was run on the separate group and the
data pool.
Class
AST 109
2005
AST 109
2006
All PHY
PHY 105
2005
PHY 102
2006
PHY 101
2006
AST 109
2004
.437
.874
—
.088
.061
.007
AST 109
2005
—
.379
—
.049
.050
.007
AST 109
2006
.379
—
—
.122
.080
.010
All AST
—
—
.001
—
—
—
PHY 105
2005
—
—
—
—
.581
.196
PHY 102
2006
—
—
—
—
—
.461
Table 4.1-2: Independent sample t-test for equality of means (p)
4.2 The Mother of All Questions and initial groupings
The responses from the mother of all questions indicated that although most
students felt that a pen would fall on the moon, a substantial portion had other ideas.
The results of all 485 students is shown in Table 4.2-1. (The correct response is D.)
38
An inspection of the multiple-choice responses indicate that 47% (n = 228) of the
students responded that the pen will float or levitate. Correct responses were also
grouped under the Mother Question responses. The overall number of correct
responses between Mother Question responses were also “scored.” The mean score
and standard deviation for each question is also included in Table 4.2-1.
Suppose you were standing on the moon holding a pen.
If you were to let go of the pen, what direction will it move?
All
(485)
Mean
“score”
Standard
deviation
n
A
The pen will float upward from the lunar surface.
13%
7.81
2.872
64
B
The pen will float around, staying about the same height.
25%
7.73
3.047
119
C
The pen will levitate, but also move away horizontally.
9%
8.16
2.977
45
47%
7.84
2.976
228
51%
12.70
4.118
249
2%
9.00
3.251
8
A, B, and C combined (floaters)
D
The pen will fall toward the lunar surface. (Correct)
E
Other/None of the above.
Table 4.2-1: Mother of All Questions (Question 1)
An independent sample t-test for equality of means was performed on the
question groups. These results, shown in Table 4.2-2, suggest that there is no statistical
difference in correct responses across questions A, B, and C. A comparison of
question D to the other questions show a statistically significant difference in correct
responses to all other groups. Student responses from A, B and C were combined into
one group and identified as “floaters”; the students who gave the correct response are
identified as “fallers.” The analysis of most questions involved the comparison of
these two groups in order to check for the consistent use of specific models of gravity
throughout the survey.
39
What direction will the pen move?
B
C
D
E
.861
.547
.000
.281
A
float up
B
float around, about the same height.
—
.424
.000
.258
C
levitate and move horizontally.
—
—
.000
.469
A, B, and C combined (floaters)
—
—
.000
—
D
fall (fallers)
—
—
—
.013
E
Other
—
—
—
—
Table 4.2-2: Independent sample t-test for equality of means (p)
4.3 Free-Responses and Student Reasoning
4.3.1 Student Reasoning for Question 1 – Why a Pen Floats
The multiple-choice responses from the Mother Question indicated that
although most students felt that a pen would fall on the moon, a substantial number of
students had other ideas. The free-response portion of the question was then combined
with the multiple-choice response and used to infer student models of thinking. Each
response combination was reviewed and assigned to a student reasoning category. A
comparison of the multiple-choice responses to the student reasoning categories for the
Mother of All Questions is shown in table 4.3-1.
40
No
Gravity
Gravity
Threshold
Mass
Threshold
Stasis
Threshold
Other
Threshold
Other
Reasoning
Correct
Reasoning
Blank
A (64)
27%
20%
12%
0%
6%
19%
0%
16%
B (119)
24%
10%
6%
34%
2%
18%
0%
7%
C (45)
22%
24%
2%
0%
20%
29%
0%
2%
24% (55)
16% (36)
7% (16)
18% (40)
6% (15)
21% (47)
0%
7% (17)
D (249)
<1%
0%
0%
0%
0%
7%
83%
9%
Other (8)
12%
0%
0%
0%
0%
62%
12%
12%
All (485)
12% (57)
7% (36)
3% (16)
8% (40)
3% (15)
14% (70)
43% (208)
9% (43)
Float (228)
Table 4.3-1: Question 1 multiple-choice responses and student reasoning (“Float” =
A+B+C)
Student reasoning groups were checked and compared for the correct overall
number of correct responses between student reasoning groups. The mean “score” and
standard deviation for each group is shown in Table 4.3-2. An independent sample ttest for equality of means was also performed on these groups; table 4.3-3 contains this
data. The results of this analysis shows a statistical difference in the correct response
group to all other response groups.
Student
reasoning
No
Gravity
Gravity
Threshold
Mass
Threshold
Stasis
Threshold
Other
Threshold
Other
Reasoning
Correct
Reasoning
Mean
“score”
7.00
7.89
10.19
8.75
8.07
8.67
12.80
Standard
deviation
2.542
2.816
2.198
2.619
3.555
3.674
4.056
n
57
36
16
40
15
70
208
Table 4.3-2: Mean "score" of student response groups
41
Student
reasoning
Gravity
Threshold
Mass
Threshold
Stasis
Threshold
Other
Threshold
Other
Reasoning
Correct
Reasoning
No
Gravity
.119
.000
.001
.290
.003
.000
Gravity
Threshold
—
.006
.171
.850
.227
.000
Mass
Threshold
—
—
.058
.059
.117
.012
Stasis
Threshold
—
—
—
.439
.897
.000
Other
Threshold
—
—
—
—
.562
.000
Other
Reasoning
—
—
—
—
—
.000
Table 4.3-3: Independent sample t-test for equality of means (p)
4.3.2 Question 1 Free-Response
Students who reasoned that the pen did not fall because there is no gravity were
included in the category of the same name. Of the 57 students (12% of all students)
that made up this category, 96% (n = 55) were floaters. Of the 228 floaters, 24% (n =
55) used this reasoning. Typical free responses were,
•
“There is no gravity on the moon.”
•
“The pen will float around staying about the same height
because there is no gravity in space.”
A substantial number of students (22% of all students, n = 107) reasoned that
the pen wouldn’t fall because there wasn’t “enough” mass, gravity, or weight –
something – to cause the pen to fall. These 107 students accounted for 47% of the
42
floater group. This reasoning was labeled “threshold” reasoning. In order to help
analyze the data, students with threshold reasoning were separated into multiple
threshold categories. If a student’s reasoning included components of more than one
threshold category, the response was placed in only one of the categories. This
category determination was made on a case-by-case basis.
Students who indicated that there was not enough mass, weight, or heaviness in
describing their threshold were placed in a Mass Threshold category. This category
describes 7% (n = 16) of the floaters. Some examples of a Mass Threshold response
were,
•
“The pen is too light (not massive enough) to be affected by
the weak gravity and just floats around where you put it.”
•
“I think the pen doesn’t have enough mass to fall to the
surface, I just think gravity will pull it in different
directions.”
Thirty-six students (16% of all floaters) claimed that there was not enough
gravity for the pen to fall and were allotted the Gravity Threshold category. Two
examples of Gravity Threshold reasoning were,
•
“Although there is gravity on the moon there is not enough
to affect the pen.”
•
“Because there is little gravity on the moon and it would
have little effect on the pen.”
Students who additionally reasoned that there was not enough gravity to cause
the pen to fall, but there was enough to keep it from floating away were placed in a
separate Stasis Threshold category. There were 40 students in this group, which
43
comprised 18% of the floaters. Interestingly, all students of this group answered B, the
pen will float around, staying about the same height. Typical reasoning included,
•
“There is less gravity on the moon so it will float, but
enough to keep it from floating away.”
•
“The gravity on the moon is weak, but there is enough that
nothing will float away.”
The remaining students who held threshold reasoning, but also included
references to rotation, outside forces and anything else, were given the Other
Threshold category. These students made up 6% (n = 15) of the floaters.
The remaining 21% of floaters (n = 47) held reasoning or responses that would
not fit into any of the other categories. These included references to movies, rewriting
the multiple-choice answer as their free response, and other answers that defied
categorization. Examples of these include,
•
“The pen would levitate, but other factors, such as lunar
wind would drive the pen horizontally as well as vertically.
The other factor would probably be pressure, or possibly
inertia.”
•
“I believe the pen would move upward due to the force of
gravity on the moon + because objects tend to move
upward in movies.”
Of the responses from fallers, 83% (n = 207) included reasoning that was
considered “correct.” Correct reasoning was one that did not include any obvious
errors.
The remaining free-response faller responses that were not considered correct
included references to movies, rewriting the multiple-choice answer as their free
44
response, answers that could be interpreted as wrong, and a handful of fallers who
answered with threshold reasoning.
Examples of threshold reasoning responses
included,
•
“The pen will slowly fall to the ground due to gravity but
not very fast because it doesn't have much mass.”
•
“There is very little gravity on the moon, so the pen would
slowly fall to the lunar surface, unless it was too light, in
which case it may drift away or float, like a bubble would
here on earth.”
It was initially hoped that the identification and categorization of student
thinking would aid in predicting student responses. However, this did not appear to be
the case. A comparison of the multiple-choices of the Mother of All Questions to the
constructed threshold and no gravity reasoning is show in Table 4.3-4. It is apparent
that, with the exception of the students with stasis threshold reasoning, student
responses are nearly evenly distributed among the three choices of the Mother
Question.
A (64)
B (119)
C (45)
D (249)
E (8)
No Gravity
30%
49%
18%
2%
2%
Gravity Threshold
36%
33%
31%
0%
0%
Mass Threshold
50%
44%
6%
0%
0%
Other Threshold
27%
13%
60%
0%
0%
G/M/O Combined
38%
31%
31%
0%
0%
Stasis Threshold
0%
100%
0%
0%
0%
Table 4.3-4: Mother Question multiple-choice response distribution with student
reasoning included
45
After the student responses to the Mother Question were categorized, the
elicited interpretations of student reasoning were then compared to Question 20 of the
Likert questions. Table 4.3-5 shows the comparison of all student reasoning to
Question 20, “In low gravity, light objects may be too light to be affected by the
gravitational force.” This question was written to be an example of how a student with
threshold reasoning might respond. Of all students with threshold reasoning, 56% (n =
60 of 107) indicated that they agreed with the Question 20 statement. Only 15% (n =
16) of the threshold students disagreed with Question 20 and provided a contradictory
answer to their free-response reasoning. Nearly a third of the students who gave
correct free-response answers agreed with the threshold statement. This could suggest
that these 65 students were inconsistent in their response to Question 20 or that they
possibly hold threshold reasoning and that the pen is above that threshold.
No Gravity
Gravity
Threshold
Mass
Threshold
Stasis
Threshold
Other
Threshold
Other
Reasoning
Correct
Reasoning
True
37%
67%
56%
48%
53%
31%
31%
False
25%
8%
13%
23%
13%
31%
47%
Don’t
Know
21%
22%
31%
20%
27%
34%
20%
Blank
2%
3%
0%
0%
7%
3%
2%
Total
100% (57)
100% (36)
100% (16)
100% (40)
100% (15)
100% (70)
100% (208)
Table 4.3-5: Question 1 student reasoning to Question 20 (Q20 correct response is
False)
4.3.3 Student Reasoning for Question 2 – Why an Astronaut Falls
In addition to the free-response portion of the mother question, the astronaut
follow-up question (Question 2) also gave indications of threshold thinking. The
46
complete data is shown in Table 4.3-6. Reasons that floaters gave for why the
astronauts didn’t float off the lunar surface included having enough gravity, mass, or
weight (45%, n = 103) and wearing space suits (17%, n = 39). The fallers responded
that the astronauts didn’t float off the lunar surface because of gravity (39%, n = 98),
low or light gravity (29%, n =73), or enough gravity or mass (22%, n = 56). These
three groups of responses made up 91% (n = 227) of the fallers. When considering the
free-responses of all students to both mother and astronaut questions, 39% (190 of 485)
of the students gave evidence of some type of threshold reasoning.
No
Gravity
Enough
Weight/Mass
Enough
Gravity
Low/Light
Gravity
Space
Suits
Gravity
Other
Blank
A
5%
45%
3%
12%
22%
2%
5%
6%
B
9%
30%
9%
15%
14%
3%
16%
4%
C
2%
40%
16%
16%
18%
0%
7%
2%
Floaters
6%
36%
9%
14%
17%
2%
11%
4%
Fallers (D)
1%
9%
13%
29%
1%
39%
4%
3%
Other
0%
12%
12%
50%
0%
0%
25%
0%
All
Students
3%
22%
11%
23%
8%
21%
8%
4%
Table 4.3-6: Question 1 multiple-choice responses to Question 2 student reasoning
(“Floaters” = A+B+C)
Student reasoning groups were checked and compared for the overall number of
correct responses between student reasoning groups. The mean “score” and standard
deviation for each group is shown in Table 4.3-7. An independent sample t-test for
equality of means was also performed on these groups and is displayed in Table 4.3-8.
47
The results of this analysis shows a statistical difference in the correct response group
to all other response groups.
No
Gravity
Enough
Weight/Mass
Enough
Gravity
Low/Light
Gravity
Space
Suits
Gravity
Other
Mean
“score”
6.311
8.57
11.35
11.44
7.71
13.31
8.92
Standard
deviation
2.442
3.678
3.977
3.595
3.344
4.481
3.498
n
16
106
54
110
42
102
38
Table 4.3-7: Mean "score" of Question 2 student reasoning groups
Enough
Weight/Mass
Enough
Gravity
Low/Light
Gravity
Space
Suits
Gravity
Other
No Gravity
.019
.000
.000
.133
.000
.009
Enough
Weight/Mass
—
.000
.000
.195
.000
.606
Enough
Gravity
—
—
.892
.000
.008
.003
Low/Light
Gravity
—
—
—
.000
.001
.000
Space Suits
—
—
—
—
.000
.119
Gravity
—
—
—
—
—
.000
Table 4.3-8: Independent sample t-test for equality of means (p) for different
reasoning groups in Question 2
4.3.4 Question 2 Student Free-Response
As in the mother question, the categories chosen were based on the
interpretation of student free responses. If a student’s reasoning included components
of more than one category, a determination was made as to which one category the
48
response would best fit. There were a handful (6% of floaters (n = 14) and 1% of
fallers (n = 2)) of students who included the words no gravity in their reasoning as to
why the astronauts did not float off the moon. Typically, the response added a
reference to the lack of an outside force, but it seemed that none of the no gravity
reasons utilized much scientific reasoning. Two typical examples of student reasoning
were,
•
“They didnt [sic] float off into the lunar surfaces because
they are at zero gravity.”
•
“Since there is no gravity they can't be forced upward.”
Threshold thinking was also evident when justifying the behavior of astronauts,
usually in the context that the threshold was met. These students reasoned that the
astronauts did not float off the moon because there was enough gravity, they had
enough mass or weight, or were heavy enough. Given the grouping experience with
the free response part of the mother question, the responses with mass, weight and
heaviness were grouped together, and the gravity responses were given their own
category. Of the 107 students who said that there was enough mass or weight, 78% (n
= 83) were floaters and 22% (n = 23) were fallers. Of the 54 students who indicated
that there was enough gravity, 37% (n = 20) were floaters and 61% (n = 33) were
fallers. A typical mass/weight response was,
•
“They weighed enough so that they didn’t float away
although the gravity was low.”
Space suits were not an uncommon reason for explaining why the astronauts
stayed on the moon. A total of 62 students (13% of 485) used space suits in their
49
reasoning, 25% (n = 57) of floaters and 2% (n = 5) of fallers. Suits were used as a sole
reason (8% of 485, n = 41), or used in combination with threshold reasoning (n = 21).
When space suits were combined with another category of reasoning, the other
reasoning took precedence in categorization. Two examples of student reasoning that
included space suit reasoning were,
•
“The astronauts did not float because [of] their space suits.”
•
“The space suits added the extra weight to them to allow
them to stay feet first on the moon.”
Of the students who gave low or light gravity as a reason (n = 110), 30% (n =
33) were floaters and 66% (n = 73) were fallers. “Gravity” without an adjective
modifier was used by 102 students, 4% (n = 4) of them floaters and 96% (n = 98) of
them fallers.
Table 4.3-9 shows the comparison of all student reasoning for the to Question
21, “In an environment with no gravity, an object must be heavy enough in order to
fall.” This question was written to be a possible example of how a student with the
conception that the moon had no gravity would explain why the astronauts would not
float off the moon. Not surprising, students with no gravity reasoning and space suit
reasoning had similar percentages. Those students who noted that gravity was present
on the moon also had similar numbers. Students who fell into the enough weight/mass
category had percentages that were closer to the no gravity and space suit categories
than the gravity categories. This may suggest that students who believe that enough
mass or weight is required to fall, may not necessarily believe weight to be a
consequence of gravity.
50
No
Gravity
Enough
Weight/Mass
Enough
Gravity
Low/Light
Gravity
Space
Suits
Gravity
Other
True
25%
21%
11%
5%
24%
11%
5%
False
44%
53%
70%
74%
46%
70%
74%
Don’t
Know
31%
24%
17%
20%
27%
18%
18%
Blank
0%
1%
0%
0%
0%
0%
0%
Total
100% (16)
100% (107)
100% (54)
100% (110)
100% (41)
100% (102)
100% (38)
Table 4.3-9: Question 2 student reasoning to Question 21 (Q21 correct response is
False)
A comparison of floater and faller reasoning of the mother question to the
astronaut follow-up question is shown in Table 4.3-10. Correlation of student reasoning
for the Mother Question to the student reasoning of the astronaut question proved
difficult due to the lack of recognizable data patterns.
51
No
Gravity
Enough
Weight/Mass
Enough
Gravity
Low/Light
Gravity
Space
Suits
Gravity
Other
Blank
Total
No Gravity
16%
25%
2%
2%
38%
0%
13%
4%
100%
(57)
Gravity
Threshold
3%
50%
14%
19%
8%
0%
3%
3%
100%
(36)
Mass
Threshold
0%
69%
13%
19%
0%
0%
0%
0%
100%
(16)
Stasis
Threshold
0%
28%
18%
28%
8%
5%
15%
0%
100%
(40)
Other
Threshold
0%
40%
33%
20%
7%
0%
0%
0%
100%
(15)
Correct
0%
5%
12%
22%
1%
57%
3%
0
100%
(76)
< Earth
Gravity
0%
3%
10%
38%
1%
45%
1%
1%
100%
(76)
Low/Light
Gravity
0%
16%
18%
31%
0%
27%
7%
2%
100%
(45)
Gravity
Threshold
0%
0%
67%
11%
0%
22%
0%
0%
100%
(9)
Mass
Threshold
0%
67%
33%
0%
0%
0%
0%
0%
100%
(6)
Other
4%
43%
0%
13%
19%
4%
15%
2%
100%
(47)
Blank
11%
16%
0%
11%
11%
0%
21%
32%
100%
(19)
Floaters
Fallers
Table 4.3-10: Question 1 student reasoning to Question 2 student reasoning
4.3.5 Question 1-2 – The Pen/Astronaut Consistency Check
A comparison of individual students across the two questions indicated that the
reasoning of many students was consistent. It was found that 94% (n = 195) of the
students who answered the mother question correctly, also answered the astronaut
52
question correctly. Since all of these students were fallers, 78% of the fallers gave
correct reasoning for both parts of the questions.
Of the floaters, 45% (n = 26) of those who said that the pen floated because of
no gravity reasoned that the astronauts didn’t float off because of their suits. A typical
answer pair of this sort was, “No gravity on moon,” for why the pen wouldn’t fall and,
“Because the suits they had were specially made,” for why the astronauts wouldn’t
float.
An additional 25% (n = 14) of the no gravity students said that the astronauts
stayed on the moon because of their mass or weight. A typical pair of this sort was,
“There is no gravity on the moon, therefore lighter things will float more so than
heavier objects,” for why the pen wouldn’t fall and, “The astronauts are heavier than
the pen, there fore wont [sic] float,” for why the astronauts wouldn’t float.
Students who answered using threshold reasoning for the pen typically did not
appear to stick with one particular response for the astronaut question. An example of
the stasis threshold reasoning was, “I believe that the pen would stay at about the same
height. There is not much of a gravitational pull to make the pen fall, but there is
enough to keep it from floating away,” for why the pen wouldn’t fall and, “They did
not float away because there is gravity on the moon. It is not as strong as here on
earth,” for why the astronauts wouldn’t float.
An example of a mass threshold was, “The pen does not have enough mass for
gravity to hold it down,” for why the pen wouldn’t fall and, “The astronauts did not
float off because they had a great enough weight to be affected and held down by the
53
moon’s gravity (the greater the weight the more area (mass) to be affected by force of
gravity),” for why the astronauts wouldn’t float.
4.3.6 Question 10 Free-Responses – Why the Pen Falls in the Dome
The final free-response question indicated that some students linked gravity to
the presence of an atmosphere or air. Of the floaters, 36% (n = 81) responded that the
pen would float inside the air-filled dome. However, the majority of floaters, 56% (n =
128), responded that the pen would fall inside the dome. Nearly all (94%, n = 234) of
the fallers responded that the pen would also fall within the dome.
The problems beset by the original text of this question did not surface within
the student responses of this survey. The replacement of simulate conditions on Earth
with so that people can live inside the dome without having to wear space suits
appeared to remove most of the bias of the original question. The dome’s temporal
placement appeared to have a minimal affect on student responses, allowing some
students to avoid cognitive conflict.
Eighty-three percent (n = 67) of the floaters who responded that the pen would
also float inside the dome usually reasoned that the addition of air to the surface of the
moon would not change the initial conditions. The responses were similar across all
student reasoning categories.
The remaining floaters gave other reasons or had no response. Two typical
responses, one from a student who held threshold reasoning, and the other from a
student who did not believe in gravity on the moon, “Pen will float because you are
54
still on moon and not much gravity.” “It will float because they have air in the dome
not a change in gravity.”
The reasoning of floaters who responded that the pen would fall inside the
dome included air or atmosphere (38%, n = 49), and the existence of the dome (32%, n
= 41). Student responses involving the atmosphere’s affect on the pen did not always
specify what it was about the air that caused the pen to fall, i.e., whether the air created
gravity or just produced a force. Examples of why the atmosphere causes the pen to
fall are,
•
“It would fall because of the pressure in the dome.”
•
“First, that would be super sweet. . . Anyway, I think the
pen would fall to the ground because with air inside, there
would also be gravity.”
Many floaters attributed the pen’s downward motion to the mere existence of
the dome. It was left to the reviewer as to how the dome caused the pen to fall – if you
build it, gravity will come. There were also a number of floaters who evoked this
justification to quell their cognitive conflict. These students, when confronted with the
scenario of people living on the moon without space suits reasoned that the domes must
somehow contain gravity, rather than confronting and changing their beliefs. “
•
“Well in order to live without spacesuits, they need some
form of gravity, especially to build the domes. The pen
should fall to the ground”
•
“The pen will drop because inside geodesic domes, there
will probably be gravity, since humans prefer it and the
gravity will pull the pen to the floor.”
55
•
“It will drop, if we ever live on the moon we will no doubt
have safe domes where items and people don't float
around.”
Other students solved the conflict by utilizing a temporal loophole. By laying
claim that by the year 2156, humans will have invented artificial gravity, they could
avoid the mental struggle. Typical responses included,
•
“It will fall because by the time we can make geodesic
domes on the moon we would have created artificial
gravity as well.”
•
“Presumably to live on the moon not only would these
domes have air, but also false gravity, since we are still
trying to figure out the effects of gravity on living things.
So from that you can assume the pen will fall much as it
does here.”
•
“The pen would fall because SOMEBODY would have
invented a way to have gravitational pull inside of the
domes. Duh.”
Nearly half (48%, n = 62) of the floaters who felt that the pen would fall inside
the dome indicated that the pen would fall as if it were dropped on Earth. The concern
arose that students were still reading a bias into the question. Students would be
unaware of NASA’s design specifications for lunar domes and encampments, and
might assume that in order to live and work in a dome, all conditions must be similar to
Earth. The fact that the domes were geodesic domes might have triggered students to
establish the domes’ environment – and gravity – as Earth-normal.
A further analysis and interpretation of the data suggests that most students
were not biased toward adding Earth-like conditions to their response. Those students
56
who had reasoned that the dome’s atmosphere is what caused the pen to fall, almost
exclusively attributed the Earth-like parameters to the infusion of air into the dome.
They claimed that the dome had the same conditions as Earth because of the additional
atmosphere.
•
“The pen would fall at an Earth rate, assuming the inside of
the dome had the same amount of air & atmospheric
pressure.”
•
“The same thing that would happen to a pen on earth, it
would drop. If the air is the same for humans as on earth
and creates a gravitational pull to keep people's feet on the
ground.”
•
“Due to the pressure inside the dome, the pen would have
to fall at the same exact rate. . . gravity would also have to
be the same as it is on Earth.”
The reasoning thatfloaters used for claiming that the domes created Earth
conditions were virtually the same as those that did not specify Earth conditions.
•
“The pen will drop. Conditions would have to [be] like
those of Earth in order for people to live.”
•
“The pen will act like it would on Earth. The conditions
inside a dome are altered to be like Earth.”
•
“If the Globes are desined [sic] to replicate earth then I’d
assume they have fixed the Problem with gravity So it
would fall like it did on earth.”
Although nearly all of the fallers responded that the pen would also fall within
the dome, only 59% (n = 137) included the correct reasoning. Eleven percent (n = 26)
indicated that air-atmosphere causes gravity, 18% (n = 43) assumed the pen would fall
as if on Earth, and 14% (n = 34) gave no reason for why the pen falls in the dome. The
57
faller free-responses which included atmosphere causes gravity and Earth conditions
were identical to those free-responses given by floaters.
Concerning the use of the word geodesic in describing the domes, there was
evidence that a handful of students may have felt that the fact that the geo- meant
Earth-like. The responses,
•
“Being in a geodesic dome, the pen would fall to the
ground as though we were on Earth.”
•
“it will fall because they are in geodesic domes.”
•
“The pen will fall to the moon’s surface the same as it
would on earth. The domes, being geodesic, mimic life on
earth.”
may suggest that students felt that gravity was “automatically” added to the
dome. It should be noted that a faller wrote the third student response.
A closer, more detailed analysis of this question proved elusive. The similarity
of student responses across groups and student reasoning types could not be clearly
correlated. Because of the many subsets of student reasoning at this point, exploring
what correlation there is may be a fun and exciting subject for further study for
someone with more time – much more time.
4.4 Multiple-choice results
4.4.1 Question 3 – Up and Away from Earth
As mentioned above, extra questions were added to the survey to substantiate
different student conceptions of gravity as well as check for consistency. The first
58
additional multiple-choice question gave an indication of the air-gravity connection.
Asked what happens to the earth’s gravitational force on you as you move up and away
from the surface, 28% (n = 135) of the students indicated the correct response, A.
Results are displayed in table 4.4-1. However, a majority of the students (59%, n =
285) indicated that earth’s gravitational force is zero outside the earth’s atmosphere.
As you move up and away from the Earth’s surface, what happens to the Earth’s
gravitational force on you?
All
485
Floaters
228
Fallers
249
A
The gravitational force on you decreases, but never goes to zero. (Correct)
28%
25%
31%
B
The gravitational force on you increases.
4%
6%
2%
C
The gravitational force on you stays the same.
8%
8%
7%
D
The gravitational force on you decreases until you leave the Earth’s
atmosphere, where it goes to zero.
19%
19%
19%
E
The gravitational force on you increases until you leave the Earth’s
atmosphere, where it goes to zero.
17%
23%
10%
F
The gravitational force on you stays the same until you leave the Earth’s
atmosphere, where it goes to zero.
23%
18%
28%
G
Other (Please Explain)
2%
<1%
3%
Table 4.4-1: Question 3
In breaking these results down between floaters and fallers, the largest
percentage of both groups of students answered correctly. Also, similar percentages of
floaters (60%, n = 137) and fallers (57%, n = 143) believe that the earth’s gravitational
force is zero outside the earth’s atmosphere.
59
4.4.2 Question 4 – Galilean Gravity
In attempting to address the heaviness issue, the feather-and-lead question
brought up possible issues that some students may have with Galilean gravity models
in addition to the threshold issue. The results for this question are tabulated in Table
4.4-2. Of the 485 that took the survey, 46% (n = 222) students selected the correct
answer, that both would fall at the same rate. Although the majority of fallers (65%, n
= 162) are comfortable with the correct response, over one-fifth (n = 53) of the fallers
appear to have issues with Galilean gravity, choosing the response in which the lead
will fall a little faster than the feather. When comparing the responses of floaters and
fallers directly, it might appear that more than twice as many fallers have this issue
than do their floating peers (n = 21). However, a comment from a floater who
answered C and wrote, “Like, what weighs more . . . a lb of feathers or a lb of rocks?
(lead, in this case),” raises the threshold issue. Since floaters already believe that the
pen floats, one must keep in mind that the feather may be assumed to be lighter than
the pen. A faller assuming this may also believe that if the feather did fall, it would fall
more slowly than the lead.
60
If you let go of a feather and a small piece of lead on the moon, what will happen?
All
485
Floaters
228
Fallers
249
A
Both will fall slowly, but the lead will fall a little faster than the feather.
16%
9%
21%
B
Both will fall at the same rate. (Correct)
46%
25%
65%
C
The lead will fall slowly, but the feather will float rather than fall.
14%
20%
8%
D
Both will float.
20%
39%
2%
E
There is not enough information to answer the question.
5%
7%
3%
Table 4.4-2: Question 4
Student reasoning from the free-responses announced the existence of a falling
threshold. Both floaters and fallers used this reasoning as to why the astronauts don’t
float off the moon. But since the only objects used to purport its existence were vastly
different in size and mass – an astronaut and a pen – an actual size or value for the
threshold is near impossible to determine. By using the data from this question, of the
floaters, 20% (n = 46) say that the lead will fall and the feather will float, and 39% (n =
88) indicate that both the lead and feather will float. Of the fallers, 86% (n = 215)
answer that both the lead and feather will fall. Overall, 62% (n = 299) of all students
indicate the feather will fall, 34% (n = 78) of the floaters and 86% (n = 215) of the
fallers. It would appear that 33% (n = 161) of all students (59% (n = 134) of the
floaters and 10% (n = 26) of the fallers) believe that the feather would float on the
moon. And that 75% (n = 365) of all students (54% of floaters (n = 124), and 94% (n
= 235) of fallers) indicate that the lead would fall. Further analysis of this concept is
continued in another chapter.
61
Question 4 was then compared to Question 22, “With no atmosphere, heavy
objects can fall faster than light ones,” to look for consistency. A comparison of total
responses as well as those split into floater and faller groups is shown in Table 4.4-3.
As the table shows, of all students who agreed with Question 22 (n = 108), over a third
(n = 37) gave the correct answer. For those students who disagreed with Question 22
(n =202), close to two-thirds (n = 128) chose the correct response. This by itself would
suggest that students who know the concepts answer correctly. However, it is perhaps
more interesting to look at the data when separated into groups of floaters and fallers.
The most popular Question 4 answer that floaters gave for all confidence levels was
that the feather and lead both float (D). Given that floaters have already indicated that
the pen does not fall suggests that the lead and feather thresholds are similar, and when
they get around to moving in some direction, they won’t necessarily move at the same
speed. Another detail that arises out of the data is that the number-one answer for all
confidence levels of fallers is the correct answer. Those who were willing to agree
with Question 22 still did not believe that either lead or feather would float, after all,
they are fallers.
62
All
What will happen to the feather
and lead on the moon?
Floaters
Fallers
True
?
False
True
?
False
True
?
False
A
Both fall slow, lead
faster.
18%
20%
12%
4%
15%
7%
32%
27%
14%
B
Both fall same. (Correct)
34%
33%
63%
22%
21%
36%
47%
52%
79%
C
lead falls, feather floats.
19%
19%
6%
23%
23%
13%
13%
14%
3%
D
Both float.
23%
21%
16%
42%
35%
41%
4%
1%
2%
E
Can’t answer.
6%
7%
2%
9%
6%
4%
4%
6%
2%
(108)
(164)
(202)
(55)
(96)
(71)
(53)
(64)
(128)
Total
Table 4.4-3: Question 4 student responses to Question 21 (Q21 correct response is
False). The “?” refers to the “not sure / do not know” option.
4.4.3 Question 5 – A Balloon on the Moon
The balloon question proved to be more difficult than it first appeared.
Apparently, most students have very little understanding of the concept of buoyancy.
The number-one answer for all students, as well as the floater and faller groups was
that the balloon would float up more quickly than on earth. This is where the similarity
appears to end however, since each group gave different percentages for each answer.
Fallers were three times more likely to answer that the balloon would fall, and floaters
were about twice as likely to say that the balloon would float up or just float around.
Table 4.4-4 shows the results.
63
Imagine you are on the moon, holding a balloon filled with Helium.
What will happen to the balloon if you let go of it?
All
485
Floaters
228
Fallers
249
A
The balloon will float up, moving more slowly than it would on the Earth.
15%
18%
11%
B
The balloon will float up, moving more quickly than it would on the Earth.
36%
32%
38%
C
The balloon will float around, staying about the same height.
21%
29%
13%
D
The balloon will fall toward the lunar surface. (Correct)
22%
11%
32%
E
There is not enough information to answer the question.
7%
8%
5%
Table 4.4-4: Question 5
Of all the students, 71% (n = 343) indicate that the balloon would not fall. Of
the floaters, 79% (n = 180) indicate the balloon would not fall and 62% (n = 155) of
the fallers do. Since there was no free-response portion to this question, it was more
difficult to ascertain student response choices. However, as explained below, it is
reasonable to assume that threshold thinking is going on here.
Question 5 was compared to Question 22 to look for consistency.
A
comparison of total responses as well as those split into floater and faller groups is
shown in Table 4.4-5. As the table shows, when both floater and fallers are combined,
the most popular answer for the non-committers and those who believe that all objects
fall at the same rate, is float up quickly (B). It appears that those who think that objects
can fall at different rates, the most popular choice is float around the same height (C).
The floater analysis of Question 4 to Question 22 showed a threshold-thinking pattern
with the feather-and-lead floating response. Adding the assumption that the balloon
could be considered lighter than any of these objects suggests that the balloon would
64
float at least as well as a pen and conceivably rise faster than a pen. A student with
threshold reasoning would be expected to be torn between answers B and C – is it light
enough, or too light? When observing the data of just the floaters in Table 4.4-5,
nearly two-thirds of all floaters chose B or C across all confidence levels. An
evaluation of the fallers shows inconsistency. A majority of fallers who were
uncertain on Question 22 indicated that the balloon should rise, implying that they may
have issues with Galilean concepts. The fallers who appear to have a handle on
Galilean concepts were split between the balloon rising fast and the balloon falling.
All
Floaters
Fallers
What will happen to the balloon?
True
?
False
True
?
False
True
?
False
A
Float up slow
12%
19%
14%
15%
21%
19%
9%
16%
9%
B
Float up quick
29%
41%
34%
26%
34%
33%
32%
51%
35%
C
Float around the same height.
31%
21%
16%
37%
27%
29%
25%
13%
9%
D
Fall (Correct)
22%
11%
30%
13%
9%
13%
32%
14%
40%
E
Can’t answer.
6%
7%
6%
9%
8%
7%
2%
6%
6%
(107)
(162)
(200)
(54)
(95)
(70)
(53)
(63)
(127)
Totals
Table 4.4-5: Question 5 responses to Question 22 (Q22 correct response is False).
The “?” refers to the “not sure / do not know” option.
As was previously mentioned, this question was slightly modified by replacing
one of its multiple-choice answers. Table 4.4-6 shows its original form. The response
to the multiple-choice answer C originally read, the balloon will float up, moving the
same rate as it would on the Earth. This answer was included because when initially
65
designing this survey, it was considered that a student might believe that the slow and
fast balloon ascension rates of choices A & B would counteract each other and the
balloon would rise at a rate comparable to the Earth. Hindsight is 20/20. It was
apparent that, for whatever reason, students did not feel that it was likely that the
balloon would move up at the same rate as it would on the Earth. There was no
compelling reason for students to pick C as their answer. And they didn’t. Only 2% (n
= 1) of the first 40 students to try the first version of the survey chose C. Eighteen
percent (n = 7) felt they had no good options available to them and answered E, there is
not enough information to answer the question.
Imagine you are on the moon, holding a balloon filled with Helium.
What will happen to the balloon if you let go of it?
100% (40)
A
The balloon will float up, moving more slowly than it would on the Earth.
15% (6)
B
The balloon will float up, moving more quickly than it would on the Earth.
42% (17)
C
The balloon will float up, moving the same rate as it would on the Earth.
2% (1)
D
The balloon will fall toward the lunar surface. (Correct)
22% (9)
E
There is not enough information to answer the question.
18% (7)
Table 4.4-6: Original Question 5 with responses
The large percentage of students who answered that there wasn’t enough
information suggested that there was another line of thought that wasn’t addressed by
the other three answers. A comparison of the response choices of this question to the
mother question response choices suggested a solution. Students were allowed to
66
consider that the pen might float around about the same height, so why not the balloon?
C was changed to read, the balloon will float around, staying about the same height.
Twenty-one students took the survey that included the modification. The
difference was significant. A substantial percentage of students did feel that the
balloon would just float around. The percentages of students without a choice they
could call their own dropped to 5% (n = 1). A Pearson Chi-squared analysis
comparing the 40 student responses of the original version of the question to the 21
students who took the revision indicated that the results were statistically significantly
different (p = .037). Table 4.4-7 shows the distribution of responses for the two
versions as well as the responses of the current version. A Chi-squared comparison of
the revision responses with the current version responses indicate that the results are
not statistically different (p = .941). A comparison of the original version responses
with the current survey responses yield a p value of .013.
Imagine you are on the moon, holding a balloon filled with Helium.
What will happen to the balloon if you let go of it?
Up Slower
Up Faster
Up Same as Earth
Float Around
Fall
Other
Original (40)
15%
42%
2%
—
23%
18%
Revision (21)
14%
33%
—
29%
19%
5%
Current (485)
15%
36%
—
21%
22%
7%
Table 4.4-7: Question 5 version comparison
4.4.4 Question 6 – Your Weight on Venus
The results from the question regarding a person’s weight on Venus is shown in
Table 4.4-8. As expected, a large number of students chose the a lot more option,
67
although it was not expected that such a high percentage of all students would choose
that answer. Floaters and fallers were nearly equal in their percentage. Nearly twice
the percentage of fallers chose the about the same option. It was expected that fallers
would choose this option more than floaters since it was the correct response.
If you could weigh yourself on Venus, using a standard
bathroom scale, you would weigh
All
485
Floaters
228
Fallers
249
A
a lot more.
64%
67%
62%
B
a lot less.
14%
18%
10%
C
about the same. (Correct)
16%
12%
21%
D
exactly the same.
1%
1%
<1%
E
There is not enough information to answer the question.
4%
2%
6%
Table 4.4-8: Question 6
4.4.5 Question 7 – Your Mass on Venus
As shown in data Table 4.4-9, about half of all students answered the Venus
mass question correctly. Both fallers and floaters chose the correct answer as their
number-one response, but only four out of ten floaters chose this answer whereas a
majority of the fallers actually answered this. The substantial number of floaters that
answered that the mass was a lot more suggests that these students do not have a
correct concept of mass. A possibility is that they felt that the extreme air pressure
might crush a person, causing them to increase in density or mass.
68
Your mass on Venus would be
All
485
Floaters
228
Fallers
249
A
a lot more.
17%
24%
11%
B
a lot less.
7%
9%
5%
C
about the same.
23%
26%
20%
D
exactly the same. (Correct)
51%
39%
62%
E
There is not enough information to answer the question.
4%
1%
2%
Table 4.4-9: Question 7
4.4.6 Question 8 – The Gravitational Force of Venus
As the data in Table 4.4-10 indicates, the gravitational force of Venus question
suggests that most students believe that air pressure somehow has an effect on
gravitational force. Most of the floaters and nearly half of the fallers believe that
Venus has a much greater gravitational force. As expected, more fallers gave the
correct answer.
The gravitational force of Venus is
of Earth.
the gravitational force
All
485
Floaters
228
Fallers
249
A
much greater than
53%
60%
47%
B
much less than
12%
15%
10%
C
about the same as (Correct)
29%
20%
37%
D
exactly the same as
1%
0%
1%
E
There is not enough information to answer the question.
5%
5%
4%
Table 4.4-10: Question 8
69
4.4.7 Question 9 – A Pen’s Free-fall on Venus
The results to the final Venus question are shown in Table 4.4-11. At least half
of the students from both of the groups felt that the pen would fall faster. Again, this
was felt to be an indication of evidence that atmosphere affects gravity. Over a fourth
of the fallers answered the correct response.
Suppose you let go of a pen while standing on the surface of Venus. Compared to
releasing an identical pen at the same height while standing on the surface of the Earth,
the pen on Venus
All
485
Floaters
228
Fallers
249
A
will hit the ground in much less time (fall a lot faster) than the pen on Earth.
53%
56%
50%
B
will hit the ground in much greater time (fall a lot slower) than the pen on Earth.
14%
15%
14%
C
will hit the ground in about the same amount of time (fall about the same way)
as the pen on Earth. (Correct)
23%
18%
27%
D
will hit the ground in exactly the same amount of time (fall exactly the same way)
as the pen on Earth.
3%
2%
2%
E
will not fall.
2%
4%
2%
F
There is not enough information to answer the question.
5%
5%
5%
Table 4.4-11: Question 9
4.5 Likert-scale Questions
The Likert-scale questions were used to search for and verify evidence of
student models of gravity. It was felt that the strength of conviction to a true or false
answer was not needed and each question’s pair of true answers was combined into
one group as well as each pair of false answers. This simplified the analysis and
interpretation, since now each question had only one true and one false response. It is
believed that the inclusion of the not sure/don’t know option increased the accuracy of
what students were thinking since it allowed students to opt out of a question. Also,
70
due to the scope of this investigation, a detailed analysis of all of these questions was
felt to be beyond the scope of this thesis. Consequently, aside from the general
comments about each question’s tabulated results, this thesis will not have much to say
about most of these questions.
4.5.1 Questions 11 – 15: Parameters Affecting Gravity
4.5.1.1 Question 11 – A Planet’s Atmosphere
As shown in table 4.5-1, most students believe that a planet’s atmosphere
affects its gravitational pull. A majority of floaters and nearly half of the fallers
believe this. The number of fallers who correctly responded that atmosphere does not
affect gravitational force was almost as many as those who believed that it did.
A planet’s atmosphere affects its gravitational pull.
All
485
Floaters
228
Fallers
249
True
55%
66%
46%
False (Correct)
29%
15%
41%
Don’t Know
15%
17%
12%
Blank
1%
1%
1%
Table 4.5-1: Question 11
4.5.1.2 Question 12 – A Planet’s Rotation
Shown in Table 4.5-2, a landslide of students believed that a planet’s rotation
affects its gravitational pull. This may be evidence of the false belief that a body exerts
a centrifugal force when rotating, a belief that has been around since before Newton,
when Huygens coined the term (Stinner, 2001). Huygens believed, like Descartes, that
71
weight is caused by a deficiency of centrifugal force. It is not unreasonable to assume
that this belief is robust enough to have stood the test of time and is still with us today.
A planet’s rotation affects its gravitational pull.
All
485
Floaters
228
Fallers
249
True
77%
80%
74%
False (Correct)
13%
6%
20%
Don’t Know
9%
13%
6%
Blank
1%
1%
<1%
Table 4.5-2: Question 12
4.5.1.3 Question 13 – A Planet’s Size
As tabulated in table 4.5-3, about two thirds of students believe that a planet’s
size affects its gravitational pull. Although this question was designed to model
Newton’s law of gravitation, it is not clear if the students interpreted size as radius – it
is possible that they interpreted size as mass instead.
A planet’s size affects its gravitational pull.
All
485
Floaters
228
Fallers
249
True (Correct)
68%
62%
73%
False
18%
18%
18%
Don’t Know
13%
19%
8%
Blank
1%
1%
1%
Table 4.5-3: Question 13
4.5.1.4 Question 14 – A Planet’s Mass
The results of the question regarding the effect of the mass of a planet on its
gravitational pull (Table 4.5-4) was similar to the results regarding a planet’s size. This
72
question was also designed to model Newton’s law of gravitation, and the greater
percentage of correct responses might be an indication that the question was clearer to
understand than the size question. However, the somewhat larger percentage of
floaters who answered that they didn’t know (26% for mass vs. 19% for size) might
dispute this assessment.
A planet’s mass affects its gravitational pull.
All
485
Floaters
228
Fallers
249
True (Correct)
71%
63%
78%
False
10%
9%
11%
Don’t Know
17%
26%
9%
Blank
1%
1%
1%
Table 4.5-4: Question 14
4.5.1.5 Question 15 – A Planet’s Distance from the Sun
Table 4.5-5 shows the student responses about whether a planet’s distance from
the Sun affects its gravitational pull.
From Newton’s law of gravitation, the
gravitational force that a planet exerts on an object depends only on the mass of the
object, the mass of the planet, and the distance between them. A review of the data for
all students show an almost even split between those who believe that distance from
the sun makes a difference and those who don’t. Breaking it into groups, almost half
the floaters and over a third of the fallers felt that distance had an effect. It was not
expected that such a significant percentage of either group of students would think that
the Sun had an effect. On the other hand, almost half the fallers and nearly a third of
the floaters felt that distance from the Sun did not have an effect. This may suggest
that many students feel that (gravitational) forces are not vector quantities, and thus
73
that the total gravitational pull of a planet is equal to the scalar combination of all
measurable gravitational forces (Smith & Treagust, 1988; Treagust & Smith, 1989).
A planet’s distance from the Sun affects its gravitational pull.
All
485
Floaters
228
Fallers
249
True
41%
47%
35%
False (Correct)
40%
31%
47%
Don’t Know
18%
21%
16%
Blank
1%
1%
2%
Table 4.5-5: Question 15
4.5.2 Questions 17 – 19: Gravity on the Moon and Outer Space
4.5.2.1 Question 17 – Orbital Zero Gravity
About half of all students, over half the floaters and nearly half the fallers
indicated that the astronauts are in zero gravity when they are in orbit. (Table 4.5-6)
Slightly over a third of the fallers gave the correct response. The literature had
indicated that some students equate free-fall to zero gravity (Ameh, 1987; Galili, 1995;
Sharma, 2004). Consequently, this result may indicate that students believe that
astronauts in “zero gravity” because they are in outer space or it may indicate that they
are in “zero gravity” because they are in free-fall. This may be a reason why more
floaters responded that they did not know than the number of floaters who gave the
correct response.
74
When in orbit, the astronauts are in zero gravity.
All
485
Floaters
228
Fallers
249
True
52%
56%
49%
False (Correct)
25%
16%
34%
Don’t Know
21%
26%
16%
Blank
2%
2%
2%
Table 4.5-6: Question 17
4.5.2.2 Question 18 – Gravity in Outer Space
Shown in table 4.5-7, when students were asked to agree with the statement that
there is no gravity in outer space, the data for all students showed a distribution
somewhat similar to the distance from the Sun question. Of the students who answered
the question, close to half of the floaters and 2 out of 5 fallers felt that there was no
gravity in outer space. This significant percentage of fallers might be evidence for the
threshold way of thinking, or suggest that gravity is a localized phenomenon, or that it
needs a medium to act (Bar et al, 1994, 1997). Also, if students are led to assume that
gravity is a force between two objects, how can gravity exist where there are no
objects? Slightly over half the fallers who committed themselves to a true or false
answer (117 of 214) felt that gravity does exist in space, and slightly over half the
floaters who committed themselves to a true or false answer (101 of 179) felt that
gravity does not exist in space.
75
There is no gravity in outer space.
All
485
Floaters
228
Fallers
249
True
42%
44%
39%
False (Correct)
40%
34%
47%
Don’t Know
16%
19%
12%
Blank
2%
3%
2%
Table 4.5-7: Question 18
4.5.2.3 Question 19 – Gravity on the Moon
Most students believe that the moon has gravity. Table 4.5-8 shows how
students responded to the statement that there is no gravity on the moon. Over half the
floaters and more than 5 out of every 6 fallers believed that the moon has gravity. It is
noted that nearly one third of the floaters indicate that there is no gravity on the moon,
but even more interesting is that 6% of fallers also gave that answer.
There is no gravity on the moon.
All
485
Floaters
228
Fallers
249
True
19%
32%
6%
False (Correct)
72%
55%
86%
Don’t Know
7%
10%
5%
Blank
2%
3%
2%
Table 4.5-8: Question 19
76
4.5.3 Questions 16 & 20-25: Gravity’s Effect on Objects
4.5.3.1 Questions 16 & 23 – Falling Speed
As shown in table 4.5-9, almost all students felt that there was a connection
between a planet’s gravitational pull and how fast an object falls. Not surprisingly, a
comparison of the floater and faller groups with a Chi-squared analysis suggests that
the two group’s answers are not statistically different from each other (0.856, 2df, p =
.652). It is interesting to note that many more fallers than floaters responded that there
was no connection between gravitational force and falling speed.
A planet’s gravitational pull affects how fast an object falls
All
485
Floaters
228
Fallers
249
True (Correct)
90%
91%
90%
False
3%
1%
5%
Don’t Know
5%
5%
5%
Blank
2%
3%
1%
Table 4.5-9: Question 16
As with gravitational pull, almost all students felt that there was a connection
between gravity and how fast an object falls. However, table 4.5-10 shows that not as
high a percentage of students make the connection with gravity as they do with a
planet’s gravitational pull. This suggests that a small number of students don’t
necessarily consider “gravity” and “gravitational force” to be the same thing. Further
analysis outside this thesis is suggested. As with the gravitational force question, a
Chi-squared comparison of the floater and faller groups suggests that the two groups
are not statistically different from each other (2.935, 2df, p = .231).
77
Gravity affects how fast an object falls.
All
485
Floaters
228
Fallers
249
True (Correct)
80%
79%
80%
False
9%
8%
10%
Don’t Know
9%
10%
8%
Blank
2%
3%
2%
Table 4.5-10: Question 23
4.5.3.2 Question 20 – Heavy and Light Objects in Low Gravity
Table 4.5-11 shows how students responded to the statement that light objects
may be too light for a low gravitational force to affect them. This threshold thinking
was indicated by nearly a third of the fallers and over 2 out of 5 floaters. Over twice as
many fallers than floaters indicated that there was no such thing as a threshold. Only 1
in 5 floaters rejected the threshold idea, whereas over a third of them were not
confident enough to reject the threshold idea.
In low gravity, light objects may be too light to be affected by the
gravitational force.
All
485
Floaters
228
Fallers
249
True
36%
42%
30%
False (Correct)
34%
21%
47%
Don’t Know
27%
34%
21%
Blank
3%
3%
2%
Table 4.5-11: Question 20
4.5.3.3 Question 21 – Heavy and Light Objects in No Gravity
Most students did not agree with the statement that in an environment with no
gravity, an object must be heavy enough in order to fall. The data are shown in Table
78
4.5-12.
Without a more detailed analysis, it is not clear if the students were
disagreeing with the no gravity issue, the heaviness issue, or both. However, there was
a significant percentage of floaters, and a small percentage of fallers, who agreed with
this statement. These students do not appear to understand the connection of gravity to
weight.
In an environment with no gravity, an object must be heavy enough
in order to fall.
All
485
Floaters
228
Fallers
249
True
13%
21%
7%
False (Correct)
64%
52%
74%
Don’t Know
21%
25%
17%
Blank
2%
3%
2%
Table 4.5-12: Question 21
4.5.3.4 Question 22 – Heavy and Light Objects in a Vacuum
As shown in table 4.5-13, most of the fallers did not believe that heavy objects
can fall faster than light ones in a vacuum. Less than a third of the floaters agreed.
Nearly a fourth of the floaters and over a fifth of the fallers indicated that heavier
things could fall faster than lighter ones. An interesting observation is that more than 2
out of 5 floaters were not willing to commit to either choice.
With no atmosphere, heavy objects can fall faster than
light ones.
All
485
Floaters
228
Fallers
249
True
22%
24%
21%
False (Correct)
42%
31%
51%
Don’t Know
34%
42%
26%
Blank
2%
3%
2%
Table 4.5-13: Question 22
79
4.5.3.5 Question 24 – Gravity and Weight
At least half of all students believe that gravity affects the weight of an object.
Results are in table 4.5-14. If there were a disconnect between gravity and weight in
elementary school, this question may give some evidence to support it, given that not
as many students connect gravity to weight as do gravity to free-fall. Nearly 3 in 10
floaters and 2 in 10 fallers indicate that weight is not affected by gravity.
Gravity does not affect the weight of an object.
All
485
Floaters
228
Fallers
249
True
22%
27%
18%
False (Correct)
61%
50%
71%
Don’t Know
14%
20%
10%
Blank
2%
3%
1%
Table 4.5-14: Question 24
4.5.3.6 Question 25 – Heavy Objects and Lifting
Close to half the floaters and nearly 3 out of 10 fallers agreed that heavy
objects were hard to lift because Earth’s gravitational force increased with lifting. This
data appeared to support the notion found in elementary students. Only slightly more
than half of the fallers and slightly more than a fourth of the floaters rejected this idea.
This data is shown in Table 4.5-15.
80
Heavy objects are hard to lift because Earth’s gravitational force
increases as you lift.
All
485
Floaters
228
Fallers
249
True
37%
45%
29%
False (Correct)
41%
28%
54%
Don’t Know
19%
23%
16%
Blank
3%
4%
1%
Table 4.5-15: Question 25
81
5
ADDITIONAL ANALYSIS
Chapter 5
ADDITIONAL ANALYSIS
5.1 Student Gravity Models
5.1.1 The Venusian Conspiracy
To measure reasoning consistency, the results from Questions 6, your Venus
weight, 8, Venus’ gravitational force, and 9, Venus’ free-fall speed, were compared to
each other. At first glance, the percentages all appeared to be reasonably similar. A
closer look at the data showed that was in fact the case. A comparison of the tabulated
data showed that 270 students gave the same response for this trio of questions, and
were considered consistent in their reasoning connecting weight, gravitational force,
and free-fall speed. The results of the student responses for the triumvirate were then
tabulated into a Truth Table Twenty-two plus Two to help identify any prevalent
student models. The 6 most common combinations are shown. These combinations
comprise 70% of the total student responses (68% floater, 73% faller). The 6
combinations included the 3 consistent groups (Q6/Q8/Q9: AAA, BBB, CCC) as well
as the ACC (n = 29), ACA (n = 22) and AAB (n = 19) groups.
82
Q6
Q8
Q9
N
All 485
Floaters 228
Fallers 249
C
C
C
56
12%
7%
16%
A
A
A
193
40%
43%
37%
B
B
B
21
4%
6%
3%
A
C
C
29
6%
5%
7%
A
C
A
22
4%
3%
6%
A
A
B
19
4%
4%
4%
340
70%
68%
73%
Table 5.1-1: Truth Table Twenty-two plus Two
Each combination of responses was evaluated to come up with a gravitational
model. The models fell into place and are listed in Truth Table Twenty-Two plus
Three. If a student understood that gravitational force, weight, and free-fall drop speed
are determined by Newton’s law of gravitation, then they would be expected to answer
C for all three questions. However, it is reasonable to infer that a student choosing C
on any of these questions is attributing the effect of gravitational force, etc., to the mass
of Venus. It is not reasonable to expect that students making this choice understand
Newton’s law of gravitation explicitly, thus it can not be inferred from this response.
The students in the triple A league would most likely play with the notion that
atmospheric pressure directly affects the gravitational force, and believe that high
atmospheric pressure would increase Venus’ gravitational force. This increased
gravitational force would in turn would increase weight and free-fall drop speed. The
BBB combination had the potential to be easily interpreted multiple ways. One
possible reason for marking this response could be that the student felt that the high
atmospheric pressure would decrease the gravitational force (like some kind of superbuoyant force) and in turn decrease the weight and free-fall drop speed. A more likely
83
interpretation of what students were thinking was that the slow rotation of Venus
decreases its gravitational force along with weight and free-fall drop speed. This
explanation is much more likely since 86% (n = 18) of the 21 students who answered
BBB also indicated that a planet’s rotation affects its gravitational pull.
So much for the consistent students. Students who answered ACC probably
believe that gravitational force is determined by mass. could possibly believe that
gravitational force and free-fall drop speed are both determined by Newton’s law of
gravitation, but Venus’ high atmospheric pressure crushing down increases weight.
ACA would indicate that, again, students would believe the gravitational force is
determined by Newton’s law of gravitation, but the high atmospheric pressure
increases both weight and free-fall drop speed. Lastly, the AAB combination suggests
that students would believe that a high atmospheric pressure increases the gravitational
force and weight, but the free-fall drop speed is somehow decreased, possibly through
viscous drag.
84
Triad
Consistent
n
Possible Student Reasoning
CCC
Yes
56
Gravitational force, weight and free-fall drop speed are determined by
mass.
AAA
Yes
193
High atmospheric pressure increases gravitational force along with weight
and free-fall drop speed
BBB
Yes
21
Slow rotation of Venus decreases gravitational force along with weight
and free-fall drop speed.
ACC
No
29
Gravitational force and free-fall drop speed are determined by mass. High
atmospheric pressure increases weight.
ACA
No
22
Gravitational force is determined by mass. High atmospheric pressure
increases weight and free-fall drop speed.
AAB
No
19
High atmospheric pressure increases gravitational force and weight, but
decreases free-fall drop speed through viscous drag
Table 5.1-2: Truth Table Twenty-two plus Three
5.1.2 The Lunar Divide
The results from Questions 17, 18, and 19 were also compared to each other
using a method similar to the one described above comparing the Venus trio of
questions. Again, the results of the student responses were tabulated into a Truth Table
to help identify any prevalent student models. The 4 most common combinations are
shown in Truth Table Thirty-Two plus Three. These combinations comprise 60% of
the total student responses (53% floater, 67% faller). The 4 combinations included
groups (Q17/Q18/Q19) TTF (n = 112), FFF (n = 86), TFF (n = 56), and TTT (n = 38).
85
Q17
(Orbit)
Q18
(Space)
Q19
(Moon)
n
All 485
Floaters 228
Fallers 249
False
False
False
86
18%
11%
24%
True
False
False
56
12%
11%
24%
True
True
False
112
23%
17%
27%
True
True
True
38
8%
14%
3%
Table 5.1-3: Truth Table Thirty-two plus Three (False is correct)
Evaluating each combination of responses formulated the results that is
included in Truth Table Thirty-Three plus Three. Students who understood that
gravitational force, weight, and free-fall drop speed are determined by Newton’s law of
gravitation, would be expected to disagree with the three questions (FFF). Those who
agreed with Question 17 and disagreed with the other two, answering TFF, would
agree that gravity exists on the moon and in space. Since 75% (n = 42) of these
students also indicated that a planet’s rotation affects its gravitational pull, rather than
this be called inconsistent, they might hold the belief that an object in orbit undergoes a
type of centrifugal force equating to zero gravity, or believe that an object in free-fall
has zero gravity. Answering TTF would suggest that they believe that planetary bodies
have a gravitational force, but there is no gravity in space. By agreeing with the triad,
the student has announced that they believe that there is no gravity on the moon, in
outer space, and that when in orbit, the astronauts are in zero gravity, all concepts
found in the literature.
86
Triad
Possible Student Reasoning
FFF
Gravitational force is possibly determined by Newton’s law of gravitation.
TFF
Gravity exists on the moon and in space, but an object in orbit, undergoing
free-fall experiences zero gravity.
TTF
Planetary bodies have a gravitational force, but there is no gravity in space.
TTT
There is no gravity in space or on the moon.
Table 5.1-4: Truth Table Thirty-three plus Three (False is correct)
87
6
CROSSING THE THRESHOLD
Chapter 6
CROSSING THE THRESHOLD
After weighing the results over multiple areas of the survey, it was apparent
that threshold reasoning was being used by both floaters and fallers. Given their
groupings, it would stand to reason that each group had a different threshold. An
analysis of the data from the mother question and feather-and-lead question was done
to find evidence for a threshold value for falling, that is, a minimum size or amount
that was certain to fall on the moon. To continue in this analysis, an all-in-one survey
was created.
6.1 The All-in-one Survey
The additional survey’s first question asked students to pretend they were on
the moon, standing on a platform about 3 feet above the lunar surface, and holding
various objects out at arm’s length and chest height. They were then to release each
object and describe its motion. The objects included a feather, a pen, a fist size moon
rock, a television size moon rock, and a helium balloon. After releasing the objects, the
astronaut (student) would also become an object by stepping off the platform. Since
the falling and floating assessments of these objects were done by the students and
rather than by an interpretation of the analysis, it was felt that this could provide a more
accurate view of the elusive threshold value. This survey included two more questions,
88
both ranking tasks of the above objects. Question 2 asked to rank the objects’ speed of
falling or rising, and Question 3 asked to rank the motion of the objects within a
pressurized lunar dome. The data and analysis of both the second and third questions
were reserved for future study.
6.2 All-in-one Survey Results
This all-in-one survey was administered to 17 AST 109 students.. Results were
analyzed by categorizing the student descriptions and ranking each object by the
number of students who indicated that it would fall. Both moon rocks had 76% (n =
13) of the students saying that they would fall. The pen was expected to fall by 71% (n
= 12) of the students. Eleven of the students (61%) responded that the astronaut would
fall, and ten (59%) thought the feather would fall. Only 23% (n = 4) of the students
thought that the balloon would fall. This data was compared to the gravity survey data.
Students who indicated that the lead weight would fall (75%, n = 365) on the gravity
survey was close to the percentage of those in the additional survey who thought the
moon rocks would fall. Only 51% (n = 249) of the gravity survey students felt the pen
would float, which is a much smaller percentage than the additional survey students
had for the pen. Both gravity survey values for the feather (62%, n = 299) and the
balloon (21%, n = 104) had percentages reasonably close to the additional survey. A
comparison of the gravity survey to the all-in-one survey is shown in Table 6.1-1.
89
Astronaut
Large Moon
Rock
Small Moon
Rock
Lead
Pen
Feather
Balloon
Gravity Survey (485)
—
—
—
75%
51%
62%
21%
All-in-one Survey (17)
61%
76%
76%
—
71%
59%
23%
Table 6.2-1: Gravity Survey and All-in-one Survey ranking comparison
6.3 All-in-one Survey Analysis
In the analysis, a question arose as to why the moon rocks had the same falling
percentage. Since they were moon rocks it might have been inferred that they would
have to fall on the moon. Another possibility is that density was the issue. Since
density determines sinking and floating, a student may have thought the object would
float because, “There is little gravity on the moon and the object is not that dense.”
Rocks are dense so they fall. On the positive side, this implies that most students treat
the two rocks similarly, perhaps associating similar material (properties?) with similar
behavior. Often, density is the property to start from, rather than weight or size (for
example, in sinking and floating).
Another question that arises from the results is why the astronaut’s falling
percentage was lower than that of the moon rocks. It was expected that the astronaut’s
percentage should have been higher than the rocks, since the astronaut was inferred to
be heavier than the rocks. One idea, related to the paired rock responses above, is
density. Perhaps students who cued on density (explicitly or implicitly) assumed that
rocks have a higher density than astronauts; thus the rocks fall but the astronauts don’t.
Another possible explanation as to why the astronauts wouldn’t fall is the initial
90
conditions. Being 3 ft off the surface might have made a difference. Those students
with the stasis threshold reasoning might have considered 3 feet to be above a
threshold distance for lunar gravity to pull down. A student could be thinking that,
“There was enough gravity to keep them near the surface, but not enough to keep them
on the ground.” A student who believes that there is no gravity on the moon may be
thinking that an outside force is needed, “There is no gravity so it's not pulling the
astronauts in any certain direction. Like being in water, they don't go up, they just
control their direction.”
Most of the results of the two surveys were similar. This could indicate that the
gravity survey can reasonably approximate how students would rank falling objects.
As for discovering a specific threshold amount, these surveys were inconclusive.
Further study and analysis is necessary, work that would be fun for a PhD.
91
7
THE DOUBLE CROSS
Chapter 7
THE DOUBLE CROSS
After reviewing the results of the spring 2004 AST 109 class, the instructor
added a movie of Apollo 15 to the curriculum of the spring 2005 AST 109 class. It
was assumed that the instructor incorporated this movie into the curriculum to directly
address the 2004 results of the mother question and the feather-and-lead question.
When the instructor taught the spring 2006 AST 109 he did not include the movie in
the curriculum, and gave indications that the 2006 class curriculum more closely
followed the 2004 class.
This movie was a 47 second video clip of astronaut David Scott dropping a
falcon feather and hammer on the lunar surface during the third and final EVA of
Apollo 15. (National Aeronautics and Space Administration, n.d.) Scott demonstrated
how objects in a vacuum fall at the same rate by dropping the objects at the same time
and noting that they hit the ground simultaneously. This demonstration was very
similar to the feather-and-lead question on the gravity survey.
The instructor gave no notice that the 2005 AST curriculum had been modified.
The first and only indication that the movie had been shown in the spring 2005 class
came from the first survey reviewed. In their answer to the mother question, the
student explained that the pen would fall because they had seen a movie in class that
showed that things on the moon fall. The initial reaction to this discovery was that the
92
data from the 2005 class would be influenced by the movie and would somehow be
skewed toward the correct answer.
Analysis of the responses across the three astronomy classes for all questions in
the gravity survey indicated that a greater number of 2005 AST students answered the
feather-and-lead question correctly than did students of the other two classes.
A comparison of the percent responses of the feather-and-lead question for the
three astronomy classes is shown in Table 7.1-1. For both the 2004 and 2006 AST 109
classes, 38% of the students gave the correct response, whereas the 2005 students had a
70% correct response rate.
If you let go of a feather and a small piece of lead on the moon, what will happen?
AST Class
Lead falls
faster
Both fall
same rate
Lead falls
feather floats
Both float
Other
Blank
2004 (149)
19%
38%
19%
15%
9%
0%
2005 (140)
16%
70%
3%
14%
2%
1%
2006 (128)
16%
38%
18%
25%
3%
0%
All (417)
15%
49%
13%
18%
5%
<1%
Table 7.1-1: Question 4 AST classes to multiple-choice responses
A Pearson Chi-square analysis was performed on three classes combined and is
shown in Table 7.1-2. The initial analysis of the three classes grouped together
indicated a statistically significant difference within the grouping. Further comparisons
of each AST class to another indicate that the 2004 and 2006 AST classes were not
statistically different from each other, and that the 2005 AST class was statistically
93
significantly different from both 2004 and 2006 classes. This significant difference in
correct responses seems to indicate that students retained the information from the
movie and its associated curriculum, and were able to apply it to a nearly identical
situation.
AST class
All classes
2004/2005
2004/2006
2005/2006
p
.000
.000
.130
.000
Table 7.1-2: Question 4 Pearson Chi-squared analysis of AST classes
However, this singular gain did not appear to transfer to overall knowledge
gain. As noted above in table 4.1-1, the mean scores for each AST classes were not
statistically different. Further evidence for this lack of gain came from the mother
question data. A comparison of the three AST results for the mother question is shown
in table 7.1-3. It shows no significant increase in the percentage of correct responses
from 2004 to 2005, and indicates a decrease in correct answers into 2006. The 2005
AST class had a slightly greater percentage of float up responses. This result runs
counter to expectations. The gain on question 4 did not appear to transfer to the mother
question.
94
Suppose you were standing on the moon holding a pen.
If you were to let go of the pen, what direction will it move?
AST
Float Up
Float
Around
Levitate
Horizontally
Float
Fall
Other
2004 (149)
9%
23%
10%
42%
57%
1%
2005 (140)
16%
16%
6%
38%
59%
4%
2006 (128)
13%
30%
12%
55%
45%
0%
All (417)
13%
23%
9%
45%
54%
1%
Table 7.1-3: Question 1 AST classes to multiple-choice responses
A Pearson Chi-square analysis was performed on the combined AST results of
the mother question. As indicated in table 7.1-4, an analysis of all AST classes gave
evidence of a statistical difference in responses by classes. Examination of the data by
class group indicates that this difference was due to 2006 being different rather than
2005.
AST classes
All classes
2004/2005
2004/2006
2005/2006
Mother Question (p)
.006
.064
.239
.002
Floater vs. Fallers (p)
.004
.177
.066
.002
Table 7.1-4: Question 1 Pearson Chi-squared multiple-choice responses
Further analysis included comparing the three classes with the student
reasoning constructed from the free responses of the mother question. This also
indicated that there was no significant difference in student reasoning for the three
classes. A comparison of the percent responses is shown in table 7.1-5.
95
No
Gravity
Gravity
Threshold
Mass
Threshold
Stasis
Threshold
Other
Threshold
Other
Correct
Response
2004
(149)
5%
8%
4%
10%
5%
15%
51%
2005
(140)
11%
4%
1%
4%
1%
14%
44%
2006
(128)
16%
9%
5%
9%
4%
12%
42%
All
(417)
10%
7%
3%
8%
3%
14%
46%
Table 7.1-5: AST classes to Question 1 student reasoning
A Pearson Chi-square statistical analysis of the constructed responses for all the
AST data is shown in table 7.1-6 below. The groups that were potentially statistically
different for the constructed responses run counter to the groups created by the raw
data.
AST classes
Constructed
Responses
(p)
All classes
2004/2005
2004/2006
2005/2006
.051
.030
.087
.112
Table 7.1-6: Question 1 constructed student responses Pearson Chi-squared analysis
From these results, it was not felt that the inclusion of the video into the 2005
class gave the students any better understanding of gravity. Students did not appear to
transfer any knowledge gained from watching the movie to answer the mother
question.
The lack of any measurable general knowledge transfer from the demonstration
to the mother question, although unexpected was not surprising. However, there was a
totally unexpected gain on Question 5, the balloon question. The apparent transfer to
96
the balloon question was unanticipated and surprising.
Upon discovering this
improvement in student performance, further discussions were held with the instructor
to determine if any other curriculum in the 2005 AST class had been modified. No
other curriculum changes were identified. A comparison of the three classes in table
7.1-7 show a clear change in the distribution of responses for most answers. The
percentage of correct responses (fall) of the 2005 class (33%) was significantly
different from the 2004 and 2006 classes (17% and 20%).
Imagine you are on the moon, holding a balloon filled with Helium.
What will happen to the balloon if you let go of it?
AST
Up Slower
Up Faster
Float
Around
Fall
Other
Blank
2004 (149)
16%
37%
22%
17%
7%
1%
2005 (140)
17%
26%
16%
33%
6%
1%
2006 (128)
11%
41%
22%
20%
6%
0%
All (417)
15%
35%
20%
24%
7%
1%
Table 7.1-7: Question 5 AST classes to multiple-choice responses
A Pearson Chi-squared analysis of the Question 5 responses is shown in table
7.1-8. The p value of the overall responses indicated a statistically significant
difference in one of the classes. Analysis of the classes to each other indicates that for
this question, the 2004 and 2006 astronomy classes were not significantly different
from each other, and the 2005 astronomy class was significantly different from the
other two.
97
AST classes
All classes
2004/2005
2004/2006
2005/2006
p
.043
.030
.733
.028
Table 7.1-8: Pearson Chi-squared analysis of Question 5 multiple-choice responses
It was not surprising that students might apply any knowledge gained from the
movie to the feather and lead survey question. With the exception of student
improvement on the balloon question, these results appear to be consistent with
research on traditional demonstrations (Crouch et al, 2004; Roth et al, 1997). Although
students did appear to learn from the movie, they were only able to apply their new
knowledge to scenarios very similar to what they had seen. They did not appear to be
able to apply their new knowledge to most situations outside of the original context.
As for the balloon question, no student added any free-response comments to their
question to help explain their response. It could be speculated that the movie reminded
students that there was a vacuum on the lunar surface. Consequently, it is unclear how
students utilized the knowledge from the movie and applied it to this question. Perhaps
revisiting the data in more creative ways will suggest a common link between these
student responses.
98
8
CONCLUSIONS
Chapter 8
CONCLUSIONS
Figure 1: Gravity is arbitrary
8.1 Student Concepts of Gravity
College students appear to share many of the gravity concepts held by younger
children.
Students have a remedial sense of gravity, drawing from their own
experiential viewpoint. The two major concepts that this survey identified were the
99
air-gravity model, and the threshold model. However this survey also indicated that
most students were consistent in directly relating gravitational force with weight and
free-fall.
Evidence that students were utilizing the threshold model was only seen in
three papers. Berg and Brouwer (1991) stated that roughly 10% of the students and
teachers believed that the moon’s gravity was too weak to hold down the wrench.
Sharma et al (2004) noted that when describing gravity in an orbiting space ship, some
students claimed that gravity was small enough to give the astronaut a weight of zero
but still significant enough to keep the spacecraft in orbit. Dostal (2005) noted that
students included not enough gravity in some of their reasoning. The question arises,
why hasn’t the threshold been seen before? Of the 6 papers containing the astronaut
question, only 2 give any hint of threshold reasoning.
There are a number of possible reasons why the threshold concept has not been
broached. One possibility is the age of the audience. The three papers discussed above
involved high school and college students. Many of the other papers involve young
children. A child’s conceptual development may be at an immature stage. They could
still hold egocentric notions and not have formulated the necessary vocabulary to
express their models. It is typically difficult to extract information from children
(Haupt, 1950). An argument against this is that older students or adults were subjects
in 4 of the studies that asked questions about astronauts. There was no indication that
older students were unable to express themselves.
100
Another possibility was that the analysis of the data did not go into enough
depth or the researchers were not looking for this idea in student responses and
reasoning. This is unlikely since these papers all appear very thorough in their
analysis. Researchers live to find new facets they can publish and coin new names.
What about the threshold itself? Was the threshold already met? All but two of the
astronauts was holding a spanner or wrench. A wrench, made out of metal, may be
perceived as easily meeting a gravity or mass threshold. With the threshold met, a
justifiable reason for the wrench floating would be the absence of gravity. To put this
in perspective, 20% of all students taking the gravity survey indicated that the lead
would float in the feather-and-lead question. An interesting study may be to pit an
astronaut with a spanner against an astronaut with a pen.
What about this threshold? Was one delineated here? A closer examination of
Table 4.3-10 data, the reasoning as to why the pen floats or falls to the reasoning why
the astronaut doesn’t float, may yield some answers. A check of the fallers shows that
15 gave threshold reasoning when saying why the pen falls. All 15 indicated that the
lead also fell. The pen met the threshold. This seems to indicate that the pen is an
object that is close to some value of threshold.
That said, what do the results of the Mother Question tell? Can this question
serve as an indicator for general or specific student models? Students who answer the
multiple-choice portion of the question wrong have typically held alternate conceptions
that show up on other questions. Apparently, this question easily evokes student
reasoning. As a rule, students who answered incorrectly on the Mother Question
101
(floaters) were found to be less correct overall. Although many floaters appear to hold
multiple views, they generally have been easier to categorize than students who have
answered the multiple-choice correctly (fallers). For example, fallers who used light
or low gravity in their reasoning are most likely not utilizing Newton’s law of
gravitation. When comparing their reasoning of the Mother Question to the Astronaut
Question, about a third of these students indicated that the astronaut had enough mass
or there was enough gravity, and about another third answered low or light gravity.
Only 43 of the fallers who gave correct reasoning for the Mother Question gave a
correct response for the Astronaut Question. That is only 9% of all the students who
took the survey give an indication that they might possibly use Newton’s law of
gravitation. The Mother Question and survey is not really designed to identify correct
student models as much as it is incorrect models.
8.2 Suggestions for future research
One possible step would be to develop the All-in-one survey to help determine
the value for threshold that has so far eluded this research. It appears likely that this
threshold may prove to be an elusive “event horizon.” An unexpected result on the
survey was the 61% who felt that the astronaut would fall if they stepped off the
platform, which was lower than the percentage who said the smaller rocks would fall
when released. It is hypothesized that the reason why only 61% felt the astronaut
would fall has something to do with the force of gravity needing a medium to act
through (Bar et al, 1997). Once the astronaut is no longer in contact with the surface,
102
gravity has no hold. As long as one keeps their feet on (or starts from) the lunar
surface they will stay on (or return to) the surface.
Another possible step would be to make some minor adjustments to the existing
gravity survey, such as replacing and rephrasing questions so that more avenues could
be explored without adding any length to the survey. Looking at the existing plethora
of existing student data in new and creative ways may also provide answers to
questions that have not been asked yet. Given that the survey is opening new doors of
student insight, it has the potential of exploring new worlds of Physics Education
Research.
103
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111
APPENDIX A
APPENDIX A
Gravity Survey Questions
1) Suppose you were standing on the moon holding a pen. If you were to let go of the
pen, what direction will it move?
A. The pen will float upward from the lunar surface.
B. The pen will float around, staying about the same height.
C. The pen will levitate, but also move away horizontally.
D. The pen will fall toward the lunar surface.
E. Other/None of the above.
Please explain your answer.
2) Between July 1969 and December 1972 there were six moon landings. Twelve
astronauts spent a total of over 80 hours exploring the lunar surface. Why didn’t
the astronauts float off the lunar surface? Compare this answer to how you
answered the question above.
3) As you move up and away from the Earth’s surface, what happens to the Earth’s
gravitational force on you?
A. The gravitational force on you decreases, but never goes to zero.
B. The gravitational force on you increases.
C. The gravitational force on you stays the same.
D. The gravitational force on you decreases until you leave the Earth’s atmosphere,
where it goes to zero.
E. The gravitational force on you increases until you leave the Earth’s atmosphere,
where it goes to zero.
F. The gravitational force on you stays the same until you leave the Earth’s
atmosphere, where it goes to zero.
G. Other (Please Explain)
112
4)
A.
B.
C.
D.
E.
If you let go of a feather and a small piece of lead on the moon, what will happen?
Both will fall slowly, but the lead will fall a little faster than the feather.
Both will fall at the same rate.
The lead will fall slowly, but the feather will float rather than fall.
Both will float.
There is not enough information to answer the question.
5) Imagine you are on the moon, holding a balloon filled with Helium. What will
happen to the balloon if you let go of it?
A. The balloon will float up, moving more slowly than it would on the Earth.
B. The balloon will float up, moving more quickly than it would on the Earth.
C. The balloon will float around, staying about the same height.
D. The balloon will fall toward the lunar surface.
E. There is not enough information to answer the question.
Venus is sometimes called Earth’s sister planet. It is nearly the same size and mass,
but Venus rotates once on its axis every 243 days, and has an atmospheric pressure 90
times that of the Earth.
6) If you could weigh yourself on Venus, using a standard bathroom scale, you would
weigh
A. a lot more.
B. a lot less.
C. about the same.
D. exactly the same.
E. There is not enough information to answer the question.
7)
A.
B.
C.
D.
E.
Your mass on Venus would be
a lot more.
a lot less.
about the same.
exactly the same.
There is not enough information to answer the question.
8)
A.
B.
C.
D.
E.
The gravitational force of Venus is
the gravitational force of Earth.
much greater than
much less than
about the same as
exactly the same as
There is not enough information to answer the question.
113
9) Suppose you let go of a pen while standing on the surface of Venus. Compared to
releasing an identical pen at the same height while standing on the surface of the
Earth, the pen on Venus
A. will hit the ground in much less time (fall a lot faster) than the pen on Earth.
B. will hit the ground in much greater time (fall a lot slower) than the pen on Earth.
C. will hit the ground in about the same amount of time (fall about the same way) as
the pen on Earth.
D. will hit the ground in exactly the same amount of time (fall exactly the same way)
as the pen on Earth.
E. will not fall.
F. There is not enough information to answer the question.
10) It is the year 2156 and people are living on the moon inside giant geodesic domes.
These domes are filled with air so that people can live inside the dome without
having to wear space suits.
Suppose someone is standing inside one of the domes, with a pen in hand. What will
happen to the pen if they let go of it?
Please explain your answer.
114
Regarding statements 11 to 25:
If you are certain it is true,
If you think it is true, but are not so sure,
If you do not know, or are uncertain,
If you think it is false but are not sure,
If you are certain it is false,
11)
12)
13)
14)
15)
A
A
A
A
A
B
B
B
B
B
16)
A B C D E
17)
18)
19)
20)
A
A
A
A
21)
A B C D E
22)
A B C D E
23)
24)
25)
A B C D E
A B C D E
A B C D E
B
B
B
B
C
C
C
C
C
C
C
C
C
D
D
D
D
D
D
D
D
D
E
E
E
E
E
E
E
E
E
answer A.
answer B.
answer C.
answer D.
answer E.
A planet’s atmosphere affects its gravitational pull.
A planet’s rotation affects its gravitational pull.
A planet’s size affects its gravitational pull.
A planet’s mass affects its gravitational pull.
A planet’s distance from the Sun affects its gravitational
pull.
A planet’s gravitational pull affects how fast an object
falls.
When in orbit, the astronauts are in zero gravity.
There is no gravity in outer space.
There is no gravity on the moon.
In low gravity, light objects may be too light to be
affected by the gravitational force.
In an environment with no gravity, an object must be
heavy enough in order to fall.
With no atmosphere, heavy objects can fall faster than
light ones.
Gravity affects how fast an object falls.
Gravity does not affect the weight of an object.
Heavy objects are hard to lift because Earth’s
gravitational force increases as you lift.
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APPENDIX B
APPENDIX B
All-in-one Survey Questions
1) Suppose you were on the moon, standing on a platform about 3 feet above the lunar
surface. You are also holding various objects out at arm’s length and chest height.
You release each object to see what happens to it on the moon. The objects are:
a feather
a pen
a small moon rock (the size of your fist)
a large moon rock (the size of a television)
a helium balloon
you become an object yourself by stepping off the platform (after releasing the objects)
For each of these objects, describe the motion of that object after you release it.
In each description, include the object’s direction of motion (e.g. up, down, horizontal,
none) and speed (e.g., quick, slow, very slow, none). Also in each description, explain
your reasoning
Feather
Pen
Small Moon Rock
Large Moon Rock
Helium Balloon
Astronaut (You)
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2) a. If you said that more than one of these objects would fall, rank these objects
according to how quickly they would fall on the moon, from slowest to quickest. If
any objects fall at the same rate, state so explicitly. Explain your reasoning.
b. If you said that more than one of these objects would float up, rank these objects
according to how quickly they would float up on the moon, from slowest to quickest.
If any objects float up at the same rate, state so explicitly. Explain your reasoning.
3. Suppose you built an air-tight dome on the moon, pressurized it with air equal to
Earth’s atmosphere, brought the objects inside the dome, and repeated the
experiments that you had performed when you were outside the dome.
How would you now separate the same six objects? Sort the objects into three groups
– those objects that would definitely fall inside the pressurized dome, those objects that
would definitely float upwards inside the pressurized dome on the moon, and those that
would tend to float about the same height inside the pressurized dome.
Objects that would fall
Objects that would float about the height at which they were released.
Objects that would float up
Briefly explain why you sorted the objects the way you did, especially how your
sorting is different, if at all, from your answers to Question 1.
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BIOGRAPHY OF THE AUTHOR
Roger Eastman Feeley was born in Lewiston, Maine on August 27, 1956. He was
raised in Auburn (a far cry from his birth city across the river) and was rumored to
have graduated from Edward Little High School in 1974. In 1977 he joined the US
Navy’s Nuclear Power Program and spent much of the next 6 years verifying that 70%
of the Earth’s surface is indeed covered with water. After discharge from the Navy,
Roger spent two years at the University of Arizona in Tucson before transferring to
UMaine. In 1989 he graduated with a BS in Engineering Physics.
Before returning to UMaine, Roger worked for the University of Wisconsin –
Madison as a Physics Outreach Specialist, presenting over 525 demonstrations to
nearly 100,000 people in fifteen different states and provinces. While in Madison, he
also taught a course in Radioisotopes at Madison Area Technical College, and was a
Radon Analyst for the State of Wisconsin.
Roger is a member of ΣΠΣ, a physics honor society, as well as the engineering
honor society, ΤΒΠ. Roger is a devotee of Coast to Coast AM – the ‘heavy boots’ in a
world unencumbered by gravity. He also enjoys cooking, playing the piano, singing,
and running. In addition to his world travels, he has visited 49 of the 50 states. He is
currently a candidate for the Master of Science in Teaching degree from The
University of Maine in May 2007.
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