feeley thesis

8/11/2019 Feeley Thesis

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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


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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

written permission.

Signature:

Date:


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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 theDegree 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.


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iii

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. Id 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.


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iv

TABLE OF CONTENTS

ACKNOWLEDGMENTS .......................................................................................... iii

LIST OF TABLES.................................................................................................... vii

LIST OF FIGURES..................................................................................................... x

1 INTRODUCTION.............................................................................................. 1

1.1 The Gravity of the Situation......................................................................... 1

1.2 Scope of Thesis............................................................................................ 2

2 THE SEARCH FOR TRUTH ............................................................................. 3

2.1 Literature Review ........................................................................................ 3

2.2 Interviews .................................................................................................... 8

3 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 Gravitys Effect on Objects ................................................................. 35


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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 Pens 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 Planets Atmosphere ............................................. 71

4.5.1.2 Question 12 A Planets Rotation................................................... 71

4.5.1.3 Question 13 A Planets Size ......................................................... 72

4.5.1.4 Question 14 A Planets Mass........................................................ 72

4.5.1.5 Question 15 A Planets 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: Gravitys Effect on Objects ............................ 77


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vii

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


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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 7.1-4: 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 7.1-8: Pearson Chi-squared analysis of Question 5 multiple-choice

responses..................................................................................................98


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x

LIST OF FIGURES

Figure 1: Gravity is arbitrary ........................................................................................99


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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 peoples 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-gravityto zero point energy. Not to worry though, Newtonian

physics and thermodynamics can be granted equal time.

If that isnt 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


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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 didnt 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 masters thesis, much of

the surveys 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.


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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 gravitys role in tides and planetary motion,

as well as holding people to the Earths 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.


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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 childrens 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.

Childrens 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 childs 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


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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 planets gravity is related to its

distance from the Sun, the Suns gravity influences the gravity of the planets that orbit

it, a planets 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, Dupr, & 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).


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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 objects weight increases with height (Ameh, 1987; Bar et al, 1994,

1997), while others believe that an objects 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 Newtons

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 childrens models of motion bygut dynamics, lay dynamicsandphysicists

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 diSessas

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:


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astronauts are weightless in the space shuttle and if there is no force there is no

motion. Physicists dynamics is the counterintuitive world of physics texts,

experiments and problems students solve in class. When learning new concepts, many

students retaingutand layphysics. As Osborne express it,

Gut dynamicsenables one to play hockey, lay dynamicsone totalk about Star Wars, whilephysicists dynamicsenables 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


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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.

Student

Response

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

moons

surface

37% 29% 40% 42% 38% 73% 66% 68% 75%

Away from

astronaut13% 13%

Away from

the moon18% 22% 29% 22% 19% 15% 12% 11% 11%

Floats (no

force)30% 30% 31% 34% 38% 10% 19% 14% 12%

Toward the

astronaut2% 1%

Other

responses3% 5% 0% 2% 5% 2% 3% 7% 1%

Totalresponses

(n = 183) (n = 315) (n = 48) (n = 303) (n = 21) (n = 40) (n = 534) (n = 302) (n = 414)

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


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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 didnt 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 interviews 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 didnt 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 thegravity-air or air-gravitymodel. 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.


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The second, initially labeled the gravity-weightmodel, went on to become the

thresholdmodel. 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 wasnt 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 didnt know what gravity was, but knew

it depended on the planet. Besides, that wouldnt 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 didnt 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.


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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


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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 notbring 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 chestwas replaced with the words the same. The


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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 didnt 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


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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 insidegiant geodesic domes. These domes are filled with air so that

people can live inside the dome without having to wear spacesuits. Suppose someone is standing inside one of the domes,

with a pen in hand. What will happen to the pen if they let goof 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

1The year 2156 was selected as I will be 200 years old that year.


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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.


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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 earths 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 pens lack of heaviness. This lack of heaviness appeared to be a

combination of the pens low mass and the moons 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


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additional question Question 3 read, As you move up and away from the Earths

surface, what happens to the Earths 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 forcewas 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 Newtons law of gravitation, which

states that the force between two masses m1and m2separated by distance r(measured

from each center of mass), has the magnitude, F=Gm

1m

2

r2

, where G is a universal

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


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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 Earths

atmosphere. The creation of these 3 responses required clarification of the initial

...decreasesresponse 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 air-

gravity 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


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Following other questions of the survey, the question was again written in the second

person, and posed as a question. Let gowas 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 feathermight 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, droppedwas 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 droppeddid


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not infer an initial direction. In spite of this, droppedwas replaced by let goto 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,


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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 moons 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 moons minimal gravity. Other student reasoning that may arise is

that since the moon has less or no gravity, things dont 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


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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% Earths mass, and a

diameter 95% Earths diameter. Venus size and mass alone dictate that the

gravitational pull on the surface would be about 90% of Earths. 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 planets surface. This buoyant force is directly related to the objects

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

planets 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 arent 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.


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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 Earths 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


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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 (lotmore, lot less, aboutthe 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 moreon 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 lesson

Venus. The exactly the sameoption 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


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format of Question 6 and Question 7. Responses included,much greater than,much

less than,about the same as,exactly the same as, andthere 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 pens 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


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(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 , andwill 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 objects free-fall will probably be consistent over Questions 8 and 9.


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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


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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.


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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

planets rotation to its gravity. The literature also suggested that some students believe

that a planets distance from the Sun also affects the planets gravity (Smith &

Treagust, 1988; Treagust & Smith, 1989). Newtons law of gravitation, F=Gm

1m

2

r2

,

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 planets . . . 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 planets 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 Newtons


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law of gravitation, and might not realize that the separation distance of the masses is

measured from each objects center of mass. The separation distance between a planet

and an object resting on the planets surface is effectively the radius of the planet.

Given this information, and that a planets radius is a measure of its size, it can be

stated that a planets 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

questions word choice was that it could easily have been misinterpreted. Students

might reasonably equate a planets 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 Earths 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


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moon has no atmosphere to speak of, which would evoke the gravity-air connection. If

gravity ends with the Earths atmosphere, then the moon has no gravity because the

moon is outside the Earths 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 Earths 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 Gravitys 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.


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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 planets

gravitational pull affects an objects falling speed, whereas Question 23 was written,

Gravity affects how fast an object falls. The pairs 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-and-

lead 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 gravitys

effect on weight, and gravitys relationship with height. The literature had indicated

that students associated gravity with free-fall and that an objects 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 Earths

gravitational force increases as you lift.


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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 t-

test 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

Standarddeviation

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


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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.

ClassAST 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.)


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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

A, B, and C combined (floaters) 47% 7.84 2.976 228

D The pen will fall toward the lunar surface. (Correct) 51% 12.70 4.118 249

E Other/None of the above. 2% 9.00 3.251 8

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.


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What direction will the pen move? B C D E

A float up .861 .547 .000 .281

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


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.


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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%

Float (228) 24% (55) 16% (36) 7% (16) 18% (40) 6% (15) 21% (47) 0% 7% (17)

D (249)


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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

MassThreshold

.058 .059 .117 .012

Stasis

Threshold .439 .897 .000

Other

Threshold .562 .000

Other

Reasoning .000


4.3.2 Question 1 Free-Response

Students who reasoned that the pen did not fall because there is no gravitywere

included in the category of the same name. Of the 57 students (12% of all students)

that made up this category, 96% (n = 55) werefloaters. Of the 228floaters, 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 wouldnt fall because there wasnt enough mass, gravity, or weight

something to cause the pen to fall. These 107 students accounted for 47% of the


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comprised 18% of thefloaters. 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

Thresholdcategory. These students made up 6% (n = 15) of thefloaters.

The remaining 21% offloaters(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 possiblyinertia.

I believe the pen would move upward due to the force of

gravity on the moon + because objects tend to moveupward 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-responsefaller responses that were not considered correct

included references to movies, rewriting the multiple-choice answer as their free


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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 butnot very fast because it doesn't have much mass.

There is very little gravity on the moon, so the pen wouldslowly fall to the lunar surface, unless it was too light, in

which case it may drift away or float, like a bubble wouldhere 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 thresholdand 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 studentreasoning included


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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

thresholdreasoning might respond. Of all students with thresholdreasoning, 56% (n =

60 of 107) indicated that they agreed with the Question 20 statement. Only 15% (n =

16) of the thresholdstudents 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 thresholdreasoning 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%

Dont

Know21% 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 isFalse)

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


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complete data is shown in Table 4.3-6. Reasons that floaters gave for why the

astronauts didnt float off the lunar surface included having enough gravity, mass, or

weight (45%, n = 103) and wearing space suits (17%, n = 39). Thefallersresponded

that the astronauts didnt float off the lunar surface because of gravity (39%, n = 98),

lowor lightgravity (29%, n =73), or enoughgravity or mass (22%, n = 56). These

three groups of responses made up 91% (n = 227) of thefallers. 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 thresholdreasoning.

NoGravity

EnoughWeight/Mass

EnoughGravity

Low/LightGravity

SpaceSuits

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

Students3% 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.


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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

score6.311 8.57 11.35 11.44 7.71 13.31 8.92

Standard

deviation2.442 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 differentreasoning 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 students reasoning included components

of more than one category, a determination was made as to which one category the


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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 gravityin 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.

Thresholdthinking was also evident when justifying the behavior of astronauts,

usually in the context that the thresholdwas met. These students reasoned that the

astronauts did not float off the moon because there was enoughgravity, they had

enoughmass 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 gr

feeley thesis

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