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Justifying Alternative Models in Learning Astronomy: A study of K-8
science teachers' understanding of frames of reference
Ji Shena; Jere Confreyb
a
Department of Mathematics & Science Education, University of Georgia, Athens, Georgia, USA b
Department of Mathematics, Science & Technology Education, North Carolina State University,
Raleigh, North Carolina, USA
First published on: 19 December 2008
To cite this Article Shen, Ji and Confrey, Jere(2010) 'Justifying Alternative Models in Learning Astronomy: A study of K-8
science teachers' understanding of frames of reference', International Journal of Science Education, 32: 1, 1 — 29, First
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International Journal of Science Education
Vol. 32, No. 1, 1 January 2010, pp. 1–29
RESEARCH REPORT
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Justifying Alternative Models in
Learning Astronomy: A study of K–8
science teachers’ understanding of
frames of reference
Ji Shena* and Jere Confreyb
aDepartment
of Mathematics & Science Education, University of Georgia, Athens,
Georgia, USA; bDepartment of Mathematics, Science & Technology Education,
North Carolina State University, Raleigh, North Carolina, USA
[email protected]
0Taylor
00
Dr.
000002008
JiShen
&
Francis
International
10.1080/09500690802412449
TSED_A_341412.sgm
0950-0693
Research
2008
andReport
(print)/1464-5289
Francis
Journal
Ltd
of Science
(online)
Education
Understanding frames of reference is critical in describing planetary motion and learning astronomy. Historically, the geocentric and heliocentric models were defended and advocated against
each other. Today, there are still many people who do not understand the relationship between the
two models. This topic is not adequately treated in astronomy instruction and is unstudied in
science education research. The present small-scale study suggests that many science teachers of
K–8 hold alternative conceptions about the models of the solar system. Most of the 14 teachers in
the study believed that the geocentric model should not be used in classroom instruction because
they thought that it was wrong. It was found that they justified their knowledge claims by following
common sense, authority, pragmatism, or relativism. Their long-held beliefs, lack of observational
experience, and resistance in switching between two models made it difficult for them to have a
deep understanding of the relationship of the two models. Specific teaching strategies addressing
these learning difficulties on this topic are proposed.
Introduction
For I am not so enamored of my own opinions that I disregard what others may think of
them. (Nicholas Copernicus, On the Revolutions of the Heavenly Bodies)
It is well documented that children and adults hold alternative conceptions on science
topics (for comprehensive literature reviews, see e.g., Confrey, 1990; McDermott &
Redish, 1999; Shen, 2006; Wandersee, Mintzes, & Novak, 1994). Duit (2007) and
*Corresponding author. Department of Mathematics & Science Education, University of Georgia,
Athens, Georgia 30605, USA. Email: [email protected]
ISSN 0950-0693 (print)/ISSN 1464-5289 (online)/10/010001–29
© 2010 Taylor & Francis
DOI: 10.1080/09500690802412449
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2 J. Shen and J. Confrey
his colleagues maintain a comprehensive collection of literature on students’ and teachers’ conceptions on science topics. Astronomy is a field that has intrigued many science
education researchers since the beginning of conceptual change research (e.g., Baxter,
1995; Harvard-Smithsonian Centre for Astrophysics & Schneps, 1988; Nussbaum &
Novak, 1976; Vosniadou, 1991) and still draws much attention (e.g., Hannust &
Kikas, 2007; Sharp & Sharp, 2007). By interviewing second graders, Nussbaum and
Novak (1976) found that children held different notions about the shape of the earth
and the meaning of the direction ‘down’ in space. In two later studies, it was confirmed
that both American and Israeli students held these notions (Nussbaum, 1979;
Nussbaum & Sharodini-Dagan, 1983). Similar alternative conceptions are held
by teachers as well (Shen, Gibbons & Wiegers, 2003; Summers & Mant, 1995).
Vosniadou and colleagues conducted a series of experiments investigating both children’s and adults’ knowledge of astronomy in the USA and Greece (Brewer, Hendrich,
& Vosniadou, 1987; Vosniadou, 1988, 1989, 1991; Vosniadou & Brewer, 1990). They
found popular alternative conceptions on topics such as the movement, relative size,
and location of the earth, the sun and the moon, the explanations of the phenomenon
of the day/night cycle, beliefs about gravity, and the shape of the earth.
Given the vast research on astronomy topics,1 surprisingly, none of them to the
authors’ knowledge has been conducted on frames of reference. The heliocentric
model of the solar system has been regarded as orthodoxy since Copernicus’ revolution. Regardless of the development of modern physics, many people today accept
the heliocentric model for the same reason ancient people believed in Ptolemy’s
geocentric model: following authority. Few people understand the connection
between the two theories: a matter of frames of reference. The two frames, detached
from their historical meanings, are both valid in terms of kinematics. The reader
should keep in mind that this paper has nothing to do with defending geocentrism
(e.g., Bouw, 1999), the religious belief that the earth is physically the centre of the
universe.
The importance of understanding frames of reference in astronomy is not only
manifested in the historical debates between advocates of the two theories, but also
embodied in how much learners can tie their knowledge of astronomy into personal
experience of celestial observations. Therefore, this kind of big idea should be emphasised in school education. Unfortunately, the topic of frames of reference has not been
adequately addressed in learning and teaching astronomy in the US National Science
Education Standards (National Research Council, 1996). For K–4, the content standards on earth and space science stress that the focus should be put on observations
and looking for patterns (National Research Council, 1996, p. 130). Nonetheless, in
real classrooms, since science teachers do not want to teach the ‘wrong’ ideas, they
emphasise that what students observe is not ‘right’. They tend to correct students’
observation by saying that ‘the sun is not rising or setting, it’s the earth that is rotating’.
This causes confusion for young students because their observation is detached from
textbook knowledge. For Grades 5–8, the National Science Education Standards
clearly express the view that the heliocentric model is the only valid model (National
Research Council, 1996, p. 159). Students build up all the observational experience
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Justifying Alternative Models 3
in a geocentric frame of reference, whereas the heliocentric model is taught as an
orthodoxy that is disconnected from observations.
As a start, this study identified some elementary science teachers’ conceptions of
the geocentric and the heliocentric models of the solar system and investigated why
they believed what they believed. We did not investigate how these teachers’ alternative conceptions affected their students’ learning. We postulate that if teachers hold
alternative conceptions, their classroom instruction is very likely problematic. Our
intention of the paper is not meant to be bounded by the particularity of the empirical study. Rather, we hope to provoke the reader to rethink some more fundamental
questions: What are the big ideas that students should learn in school? How are
students taught these ideas?
In the following, we first present briefly the development of human understanding
of the solar system. This sets the historical context of the study and provides the
prescriptive understanding of the development of modelling the solar system. Then
we describe an empirical study of how K–8 science teachers struggled with this
topic. The analysis of the data and discussion of the results focus on teachers’ understanding and their justification schemes. Finally, based on research data and classroom observations, we identify difficulties in teaching and learning of the topic and
suggest possible instructional strategies.
Historical Debate
This section briefly sketches the history of human understanding of the geocentric
versus the heliocentric models of the solar system. The long-lasting debate over the
two systems implies that the topic deserves further discussion in both educational
and philosophical senses.
The ancient Greek astronomers had two assumptions about celestial movements:
the earth is at rest, and celestial objects have to move in regulation such as circles
(Hoskin, 1999). Under these two assumptions, a difficulty facing these astronomers
was to explain why the planets have retrograde motion: they stop and move backwards for a while during their circulation around the earth. Eudoxus (400–347 BC)
described the motions of the celestial bodies in a satisfactory manner by employing a
number of concentric spheres with different angular velocities. Aristotle (384–322
BC) improved Eudoxus’ spheres and made them physically real. Given that the
spheres are concentric, however, both Eudoxus and Aristotle could not explain the
variation of the brightness of the planets (Hoskin, 1999).
Heraclides (∼390–339 BC) suggested that the earth is a sphere and its rotation gives
the apparent diurnal rotation of the heavens (Hoskin, 1999). At about the same
period, Aristarchus (310–230 BC) believed that the sun is actually the centre of the
universe and all other planets including the earth revolve around the sun—a primitive
heliocentric model. As Aristarchus explained, it was because the stars are too far away
that we could not detect any effect caused by the motion of the earth on the fixed stars
(i.e., parallax of the stars). Nonetheless his theory was soon discarded because it
encountered enormous difficulties in incorporating observational data. One difficulty
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4 J. Shen and J. Confrey
was to explain the fact that the period from spring-to-summer-to-autumn was three
days longer than the period from autumn-to-winter-to-spring. Hipparchus (190–120
BC), an advocate of the geocentric model, was able to offer an explanation, albeit ad
hoc (see Hoyle, 1973).
It was Ptolemy (∼100–200 AD) in his Almagest who made the geocentric model the
dominant one. There were three main arguments: the earth is motionless, the earth
is approximately at the centre of universe,2 and celestial bodies move in circles and
epicycles around the earth. This model was in accordance with the religious belief
that the earth was motionless and at the centre of the universe. More importantly, it
was able to predict the celestial motions more precisely than the heliocentric model at the
time. For instance, the error due to the heliocentric model at the time for observing
Mars was about 10°, which was intolerable since by naked eyes the precision could
reach at least 0.5° (Hoyle, 1973).
The geocentric model was constantly revised to account for more observations
and held to be true until Copernicus (1473–1543) formally proposed the heliocentric model in his book, de revolutionibus orbium caelestium libri VI. The main points
include the following: the sun, motionless, is at the centre of the universe; stars are
motionless around the edge; the planets including earth revolve around the sun in
circles; and the earth rotates on its axis and the moon revolves around the earth in a
circle. New observations such as the discovery of the phases of Venus greatly
favoured the heliocentric model and pushed the geocentric one to the edge.
However, Tycho Brahe (1564–1601), who believed that the earth is stationary
because no observation of parallax of near stars was ever reported,3 revised the
Ptolemic system to compete against the heliocentric model.4
Up to this point, the issue for astronomy was to describe empirically how the planets move, not why the planets move in the way they do. The predictive power
provided by the two models was commensurable. However, Copernicus’ theory
secured the platform through which Kepler (1571–1630), Galileo (1564–1642) and
Newton (1642–1727) moved forward to the dynamics of planetary motion (Jammer,
1957). Since then the heliocentric model gradually won the battle, and was then
taken for granted by the public. The quote in the Encyclopedia of Philosophy captured
well the significance of Copernicus’ contribution:
With Freud, man lost his Godlike mind; with Darwin his exalted place among the creatures on earth; with Copernicus man had lost his privileged position in the universe.
(Edwards, 1967, p. 222)
Parallel events occurred in the conceptual development of frames of reference. In
ancient Greece, Aristotle believed that the natural state of an object is to be at rest
since all objects on earth have to come to a stop. It was not challenged until 2,000
years later Galileo claimed that, based on laboratory observations and thought
experiments, being in motion at a constant velocity for an object is as natural as
being at rest. This was a big step forward and was rephrased as Newton’s first law.
Newton proposed that the basic laws of physics were the same in all inertial frames
of reference. In Galileo and Newton’s system, all inertial frames of reference are
Justifying Alternative Models 5
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equivalent, and the transformation between any two inertial frames of references is
intuitive. Modern physics revolutionised this understanding. To solve the inconsistency of the equations for electromagnetic waves under Galilean transformation,
Einstein (1879–1955) further postulated that light propagates through empty space
with a definite speed independent of the speed of the source or observer. He used
the Lorentz transformation between two inertial frames of reference. What Einstein
contributed on resolving the debate of the geocentric and heliocentric model of the
solar system is well summarised by Sir Fred Hoyle in Nicolaus Copernicus:
The relation of the two pictures (geocentricity and heliocentricity) is reduced to a mere
coordinate transformation and it is the main tenet of the Einstein theory that any two
ways of looking at the world which are related to each other by a coordinate transformation are entirely equivalent from a physical point of view … Today we cannot say that
the Copernican theory is ‘right’ and the Ptolemaic theory ‘wrong’ in any meaningful
physical sense. (Hoyle, 1973, p. 79)
In brief, the two frames of reference of the solar system are equivalent in terms of
being able to transform into each other in modern physics (of course they involve
different levels of calculations). Hence it calls for a better understanding of the issue
in astronomy education.
The historical debate between the geocentric versus heliocentric models suggests
that the development of physics theories is accompanied by the maximisation of
both explanatory or predictive power and parsimony; that is, accounting for more
observations in a simpler and more consistent formulation (Hoskin, 1999; Hoyle,
1973; Jammer, 1957). It should be pointed out unambiguously that physicists prefer
the heliocentric model because it is consistent with the mechanistic explanation
of the planetary motions—gravitational force—and it leads to a much simpler
formulation of that explanation. The historical development and its implication may
be ignored in astronomy education, which results in that people accept either one of
the theories by rote memory or following authority.
The debate between the geocentric and heliocentric advocates is similar to the one
between the evolution theory and the intelligent design believers (e.g., Clines, 2002;
Passmore & Stewart, 2002). Both debates were/are immersed in religious beliefs.
The difference is that the former is under much less spotlight—people think that the
issue has long been resolved since Copernicus’s revolution. As an ‘uncontroversial’
topic, the problematic way in which people justify their knowledge claims is fully
reflected in this study.
Theoretical Framework
The theoretical framework of the study originates from the work of conceptual
change research. Students hold a repertoire of alternative ideas on scientific
phenomena (Linn, 2006). Education researchers construct different theories to
account for the process of conceptual change. One debate is about whether students
have consistent theories in a certain domain, with possibly different interpretations
on the term theory and varied approaches about the unit of analysis (e.g., diSessa,
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6 J. Shen and J. Confrey
2006; diSessa, Gillespie, & Esterly, 2004; Vosniadou, 2007). In astronomy, the view
that students hold naive but relatively stable conceptions is predominant (e.g.,
Vosniadou & Brewer, 1992, 1994; Sharp & Sharp, 2007—for the fragmented side,
see, e.g., Hannust & Kikas, 2007). For instance, Bryce and Blown (2006) conducted
a cross-cultural (in New Zealand and China) longitudinal study (over a period of
13 years) where multiple representational modes were employed (verbal responses,
drawings, and modelling with play-dough). They concluded that children create
rich, coherent cosmologies to make sense of the world and that the developments of
these cosmologies across cultures share similar patterns. In this study, we are not
particularly interested in participating in the coherent versus fragmented debate (see
Blown & Bryce, 2006), but we take a broad position that people have alternative
conceptions prior to instruction. We are more interested in how the process of
conceptual change is related to learners’ justification schemes.
A modelling theory (Shen, 2006; Shen & Confrey, 2007) is employed in this
paper to account for the fact that the teachers held different conceptions about the
solar system. We employed the modelling theory for three reasons. Firstly, we hold
that learners form mental models (Gentner & Stevens, 1983), coherent or not, of
the world in everyday experience. The meaning of mental models will be discussed
shortly. Secondly, people create external representations or models (Lehrer &
Schauble, 2000) to explain observations. Especially in astronomy, instructors are
encouraged to use a rich set of physical or virtual models to facilitate student learning (Hans, Kali, & Yair, 2008). Thirdly, scientists develop explanatory models
(Frigg & Hartmann, 2006) to account for scientific observations (e.g., the geocentric and the heliocentric models). People learn these scientific models in schools
(Clement, 1993, 2000).
Although there is a shared set of characteristics of modelling as a way of learning
(e.g., modelling is about mapping between a base system and a target system), different approaches are taken (e.g., Barab, Hay, Barnett, & Keating, 2000; Clement,
2000; Confrey, 2006; Halloun, 1996; Lehrer & Schauble, 2000). The starting point
for discussion is probably ontology. Some scholars consider a model as a mental
entity, or mental model (Gilbert, 2005; Hestenes, 1987; Passmore & Stewart, 2002),
and some others believe that it is the materialised (external) representation that
matters (Lehrer & Schauble, 2000). Shen (2006) has developed a theory where a
model is considered a hybrid of a physicality and mentality: for example, a physical
microcosm of the solar system is a materialisation of our conception, while a thought
of the solar system may be inherently attached to a physical representation. Physicality
and mentality are not simply two sides of the same coin—one represents the other, or
one instantiates the other—for they may be extensions of and complementary to each
other. The totality of the two counts as a complete model.
This synthetic approach has important educational implications. When we
consider the development of students’ mental models, we need to pay particular
attention to the tools (e.g., physical models, representational medium) they are
instructed to use to explain phenomena and to communicate with others. Although
the operations on mental objects can go beyond experience, the physical materials
Justifying Alternative Models 7
that students use form the basis of their experience and hence shape their learning
trajectories. One instantiation is that conceptual change may be triggered by transformative modelling of physical representations and artefacts (Shen & Confrey,
2007). Another point to note is that any measured outcome of student understanding is closely related to the representational modes available to students. A better
approach should consider multiple ways of eliciting student ideas (Bryce & Blown,
2006). For a more comprehensive interpretation of the term model used in this
paper, please refer to Shen (2006). When we talk about teachers’ mental models in
the paper, the reader is referred to their conceptions (i.e., the mental form of
models).
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Making Choices among Models
In this paper, we only emphasise the sense of how people justify their models. Since
alternative models always exist, a fundamental question arises: ‘Why is a particular
model favoured over others?’ In this paper, a model is defined as a tool (mental or
physical) used to describe, explain, predict, and communicate with others a natural
phenomenon, an event or an entity. Since intentionality is a natural constituent of a
tool (Shen, 2006), when choosing among alternatives one has to consider the
purpose of modelling. In the case of the solar system, one may employ the heliocentric model to describe not only the kinematics (the motions of the objects) but also
the dynamics (why they move in such a way). This model unifies the motion
patterns of celestial bodies and terrestrial objects.
Some pragmatic concerns are also involved in making a choice among a pool of
candidates (van Fraassen, 1991). For instance, on the one hand, the heliocentric
model provides a succinct explanation for physicists; on the other hand, in terms of
tracking the apparent motions of the sun and the moon in the sky, a geocentric
frame of reference is simpler, especially for novice learners. Other pragmatic
concerns in choosing models may include accessibility, efficiency, observability,
consequences, and social contexts. Furthermore, since a model is a construct that
represents the relationship among the constituents of the referent, it only captures
certain traits of its target (Lehrer & Schauble, 2000). Strategies such as simplification and scaling (Frigg & Hartmann, 2006) are commonly used in modelling. When
choosing a model, only the relevant variables are considered. In describing planetary
motions, one ignores the exact shape, the materials, and other properties of the planets. To model the apparent motions of the planets, one projects the planets onto a
hypothetical sphere (the sky) without caring about the relative distance between
them. One may also deliberately distort the represented world (Frigg & Hartmann,
2006). To describe the orbits of the planets, one may only use perfect circles instead
of ellipses.
When comparing and contrasting models, one may switch between them. There
are two types of transformations. One concerns how models can be transformed or
translated among alternatives (Shen & Confrey, 2007). If a model is somehow
transformable from another, the two should be considered equivalent under such a
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8 J. Shen and J. Confrey
transformation. The other concerns the relationship between a model and the external world that is modelled (e.g., Roth, Pozzer-Ardenghi, & Han, 2005). It permits
one to see how models are picked based on mapping between reality and human
constructs.
The historical development of theories and how scientists choose a particular
theory or model certainly inform our theoretical framework. Kuhn (1998) lays out a
few objective criteria that were important for scientists to choose among theories:
accuracy, consistency, broad scope, simplicity, and fruitfulness. Since these criteria
may be conflicting with each other, insufficient to rule out alternatives, or open to
different interpretations, Kuhn added that personal experience, social context, and
other subjective elements may have a big impact for individual scientists when they
draw a conclusion (Kuhn, 1970). However, the historical perspective about how
scientists choose particular theories is dramatically different from the layperson’s
everyday decision-making. The biggest demarcation is that scientists over the long
run are looking for truth, however defined. As for a layperson, subjective judgement
is more dominant. Pragmatic concerns, relative opinions, convenience, time pressure, and personal experience are less intimidating than hard theorising, intense
calculation, abstract understanding, and shared community standards that are
required for getting a theory right.
It is critical to clarify the terms geocentric and heliocentric used in the paper
before we proceed to present the empirical study. Each term refers to a cluster of
models that describe the solar system unless it was specifically pointed out. The
terms heliocentric and geocentric are especially loaded with rich historical and
cultural information. For instance, the geocentric model may refer to a spectrum of
models from a very primitive one that all celestial objects are revolving around the
earth in circles on the same sphere, to an advanced Ptolemaic model where planets
move around the earth in epicycles, to a Tychonic system that is geometrically similar to the heliocentric model. It depends on the context to figure out what a model
represents. In most occasions, in this case, people talked in a fuzzy manner, geocentric simply means earth-centred and heliocentric means sun-centred. However, in a
formal sense, a geocentric model refers to a system that is kinematically consistent
with the heliocentric system. The two models are parallel: they differ only in preferences of choosing the origin in a particular reference frame.
Research Context and Methodology
Empirical data with a small sample size were collected to showcase the problematic
ways in teaching and learning the topic of frames of reference. The following
research questions shaped the investigation:
●
●
●
What are teachers’ mental models of the solar system?
How do teachers justify their knowledge claims and why?
What are the challenges in teaching and learning the topic of frames of reference
in astronomy?
Justifying Alternative Models 9
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Course Background
The data of this study came from an astronomy course (15 weeks, 2.5 hrs per week)
designed and implemented at the science outreach programme at a Midwest university for science teachers of K–8 (for details of the course, see Shen, 2006). Fourteen
teachers enrolled in the course and the average years of teaching was 12.0 (SD = 6.8,
ranging from two to 25 years). The teachers came from informal science institutions,
and urban and suburban school districts.
There were three instructors in the course who had co-taught at the science
outreach programme for more than 10 years: a physics professor, an experienced
and retired teacher, and a then science coordinator for a school district. The instructors carefully selected hands-on activities (Gibbons, McMahon, & Wiegers, 2003),
aligned modules with the National Science Education Standards (National Research
Council, 1996) and state standards, and implemented research-based assessments to
diagnose teachers’ understanding (Shen, Gibbons, Wiegers & McMahon, 2007).
The course emphasised the storyline of the science topics, combined everyday
observations and manipulations of physical models, and moved from descriptive
geocentric account to explanatory heliocentric theory. It covered the following topics
in sequence: observations of the sun and moon, mechanisms of shadow, night sky,
and constellations, frames of reference, geocentric and heliocentric models, the
seasons, planetary motions, observational tools, scale models, phases of the moon,
and stellar evolution.
Data Collection
The present study was triggered by a class debate between the teachers and instructors on the correctness of alternative models in describing the solar system. The
discussion stimulated the researchers to further investigate the teachers’ understanding and their reasoning schemes. Therefore, this study only covered six weeks in the
late period of the course.
Multiple sources of data were utilised to triangulate the findings. The data sources
of this study mainly included videotapes, assessment responses, and individual
teacher interviews. Each class was videotaped and the videos were transcribed and
organised in themes by the researcher. For instance, in this study all the clips
containing the topic of frame of reference were combined into a folder. Pre-test and
post-test and four formative assessments were administered. Only the second formative assessment (eight items) and one question from the post-test were relevant to
this study (see Appendix A). The assessment items were created based on research
literature (e.g., Deming, 2002; Shen et al., 2007). The items were tested and revised
to fit the teachers’ knowledge level and course topics (Shen et al., 2003). The results
of the formative assessments were shared with the teachers and instructors. The
teachers were interviewed individually upon agreement. Each interview took about
1–2 hrs and all of the interviews were transcribed. Two interview questions were
relevant to this study (see Appendix A for the list of interview questions).
10 J. Shen and J. Confrey
Table 1.
Week 10
Data collection timeline relevant to this case
Week 11
Week 12
Week 13
Week 14
Week 15
Post-test
Feedback of
Formative
assessment (one
formative
assessment
item on frame
assessment
(Section C) on
of reference)
to teachers
frame of reference
Individual teacher interviews
Classroom observations (field notes and videotapes) and teachers’ journals, artefacts
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Class debate
on alternative
models
There were also other types of data sources that were potentially useful to this
study (but not directly cited). Field notes following structured protocols were made
during classes. The instructors of this course used personal journals as a way of
documenting and examining teachers’ conceptual change. All teachers’ journals
were photocopied each week and organised into categories for further analysis. The
instructors were also interviewed before and after each class. The data collection
timeline is summarised in Table 1.
Data Analysis and Presentation
The analysis of the empirical data was mostly analytic and conceptual. Teachers’
responses to assessments and interviews were quantified to show their mental models
and the distribution of their justification schemes. Tables 2 and 3 present the coding
schemes for categorising teachers’ mental models on the heliocentric models of the
solar system (Table 2) and their justification schemes (Table 3). These codes emerged
from their responses to the relevant assessment items, interviews, and classroom
Table 2.
Coding schemes for teachers’ responses to assessments and interviews: coding scheme
for teachers’ understanding of the heliocentric model
Code
Meaning
Examples (data source)
Sun-O
Viewing the solar system
from the sun
Space-O
Viewing the solar system
from outer space
Non-O
No matter where the
observer stands;
choosing the origin of
the coordinates
‘The heliocentric model is to observe from the sun’
(Formative Assessment).
‘Heliocentric is sun-centered and the view from the sun’
(Formative Assessment).
‘If I jump into space, looking down the solar system,
I would say what I see is a heliocentric model’ (Interview).
‘Heliocentric model is used from the space point of view,
out in the solar system’ (Post-test assessment).
‘Heliocentric means the sun is the center of a model.
Geocentric means the earth is the center of a model.
Neither of these terms means you are located there and are
viewing things from there’ (Post-test assessment).
‘The heliocentric, by definition, is the model where the sun
is the center of whatever base we’re looking at’ (Interview).
Justifying Alternative Models 11
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Table 3.
Coding schemes for teachers’ responses to assessments and interviews: coding scheme
for teachers’ justification schemes
Code
Subcategories
Meaning/notes
Examples from interviews
CS
–
Justify a model by using
common-sense or
everyday experience
RP
–
PP (pragmatic
purposes)
Developmental
appropriateness
Choose/both models
based on relative
perspectives.
Use a developmentally
appropriate model for
instruction.
‘It just appears to move around the
earth, it doesn’t really move around
the earth. It’s an illusion’. (Also see
dialogue of Appendix B)
‘You can’t say one is wrong and one
is right, it’s just different ways of
looking at something’.
‘I think the heliocentric is a concept
you probably shouldn’t bring out
until maybe 8th grade or high school
until students’ minds developed a
little bit more’.
‘And by having those different
frames of reference, you can
understand things better’.
‘You can only understand why they
appear that way by knowing the
heliocentric frame of reference’.
Usage or
understanding
Pick a certain model to
explain the other, to use
in a particular context or
to enhance one’s
understanding.
Simplicity
Pick the simplest model. ‘It was so simplified when we came
up with the heliocentric view point’.
Use currently accepted
‘Because back into the old time,
model, considering the
with Galileo, and all of them, they
historical development. had a lot of ways of understanding
outside the earth.… It’s all part of a
growth that mankind have made to
have a better understanding’.
Learn models from
‘When you have the science books,
textbooks.
they show you different frames of
reference’.
Accept a model by
‘That’s kind of how I feel (that the
following people who
geocentric is wrong), but I’ve been
have more knowledge.
told (by the course instructors) that
I am wrong’.
Choose a model by
‘We do have modern technology…
referring to technology. of viewing the earth … from …
satellite pictures … it’s more factual
than opinion when you use the
modern technology’.
Choose a model by
‘Because you are eager to
referring to
understand theories and equations
mathematics.
and things you can’t just see by your
own eyes’.
Historical
development
AF
(authoritative
forms)
Text or
textbook
People
Technology
Mathematics
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12 J. Shen and J. Confrey
discussions. To track the progress of teachers’ understanding, we used data points on
three occasions. Their initial mental models were represented by their responses to
the formative assessment and their class discussions up to week 11. Then the first
author conducted individual interviews to capture their changes. Finally, we use their
responses to the post-test assessment to capture their understanding at the end of the
course.
To code and calculate the distribution of teachers’ justification schemes, we used
their responses to the formative assessment, class discussion, and individual interviews, only when those are relevant to the topic of frames of reference. The proportion is calculated as the ratio of the number of instances they used for a particular
justification scheme over the total number of the justification instances. Each
instance can be one or more sentences (see examples in Tables 2 and 3). We will
discuss more about the meaning of the coding schemes in the Findings section.
The presentation of the data is mostly descriptive and narrative. All of the analysis, discussions, and the proposed teaching strategies were grounded in classroom
observations, assessments results, and individual interviews. This empirical study is
bounded by the conceptual development of the teachers’ understanding of the solar
system in terms of frame of reference. It is neither a case of any individual in the
class nor a case of the collective as a community of learners.
Findings and Discussions
We first describe the class debate on week 10 that triggered the investigation. This
debate offered a window through which we examined the instructors’ and the teachers’ initial views on using the two frames of reference in learning astronomy. We
then report the teachers’ understanding of the heliocentric frames of reference based
on assessments and interview results. Finally, teachers’ rationales and justification
schemes are categorised and discussed.
A Class Debate on Learning the Geocentric and Heliocentric Models
Before week 10, the instructors introduced multiple physical models of the solar system
to describe and explain the corresponding celestial observations. The teachers were
asked to transform these models among themselves to enhance understanding (Shen
& Confrey, 2007). In action, when teachers played with geocentric models, they raised
concerns about teaching the students ‘wrong’ concepts. For instance, a few teachers
commented that, since the sun is not revolving around the earth, one should not rotate
the ‘sun’ in a paper-made geocentric model. In week 10, the instructors started to
address these concerns by elaborating their rationales about learning astronomy.
Instructors’ rationale on the geocentric. The instructors started with a verbal analogy
about frames of reference. The teachers were asked to identify the grammatical
constituents of a sentence (syntax) written on blackboard and then to discuss what
Justifying Alternative Models 13
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came to their minds (semantics) when they first saw the nouns in the sentence. The
instructors explained that, although there were various ways of reading a sentence,
the sentence was the same. Analogously, although there were different ways of looking at the solar system, there is only one solar system. The instructors emphasised
that they expected the teachers to be able to switch frames of reference.
The instructors further highlighted that it is celestial observations that connect
different frames of reference. They submitted that it is more appropriate for very
young students to start with the geocentric model since it is closely connected with
everyday experience and that observations are what young children can do. One
instructor said:
Speaking as an educator, I actually prefer (starting with) the geocentric frame of reference until (the) child gets old enough to hold that abstractness of the heliocentric frame
of reference … To start with going outside looking up, making a series of observations,
… to look at what you see, where you see it, and when you see it—those are three things
even a little kid can go outside and do it. (Video, 29 March 2005)
They also pointed out that, although observation is especially important in learning
astronomy, usually, a lack of observational experience is why astronomy does not
make sense for many students. It is a serious problem in astronomy education since
regular school time is during daytime, whereas many celestial observations require
going out during nights. One instructor asserted:
I am … sure that the general public can spell out the word that the earth rotates around
its axis and revolves around the sun … My experience has been that a very small
percentage of people of any age can actually relate those concepts to what they see in the
sky, and when they see it, where they see it and why they see it. (Video, 29 March 2005)
In summary, the instructors’ points were straightforward: any knowledge that is
divorced from experience is superficial; learning astronomy should connect to
personal experience, especially for very young children; it is very common that
people lack observational experience when they start learning astronomy; and learning the geocentric frame of reference provides some help.
Sarah’s objection. Not all teachers agreed with the instructors. Several teachers challenged them. To concentrate on the theme, we only focus on one representative
teacher, Sarah (pseudonyms are used in the paper), in this discussion because her
voice was clearly heard and her arguments were well represented. The reader should
keep in mind that in fact many teachers participated in the debate. For instance,
Sarah started to comment on the contrast made by the instructors between astronomy and biology learning. She explained why astronomy was more difficult than
biology:
When you are looking at the sun, you are looking at the apparent motion—the sun
moves across the sky. (When) you are talking about life sciences, you look at a plant,
you are not looking at an apparent plant when you see a flower open, that’s the real
motion. That’s not the apparent motion and then translated into this abstract kind of
motion. (Video, 29 March 2005)
14 J. Shen and J. Confrey
Sarah described learning astronomy as a translational process from an ‘apparent’
space (observation) into an ‘abstract’ space (the heliocentric model). The instructors
explained to Sarah that the ‘apparent’ motion is real—it is just a description from the
earth-centred perspective with objects cast on the same spherical surface.
Sarah continued on with her experience of learning astronomy and challenged the
instructors’ argument about the developmental appropriateness of the two models.
She believed that many students would not have any trouble in learning the heliocentric model. Clarifying her theory of meaning, one instructor doubted whether
this kind of learning would make any sense since it is detached from personal experience. Here is some of the verbal exchange between one instructor and Sarah in the
class:
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Sarah:
Instructor:
Sarah:
Instructor:
Sarah:
Instructor:
Sarah:
Instructor:
Sarah:
I think that we were taught at a heliocentric [model], and that’s interesting
because I don’t even have a problem with the heliocentric as a child. Not
that we should in any way ignore the geocentric because I think our observations are so important. But I don’t know if a child really has that much
difficulty in grasping the heliocentric.
As a child, they certainly might be able to learn it as a catechism, but
would they be able to relate it to something they see in the sky and use it to
predict what they will see tomorrow?
Well I don’t recall having much trouble with that and also with my children. I didn’t teach them the geocentric because I didn’t know the geocentric before …
What you said though about not knowing that the moon goes around the
earth once in a month [referring to a statement Sarah made previously], if
you were able to tie what you knew heliocentrically about the motion of
the moon back to observations, you would definitely know [it].
Yes.
So that’s the predictive power of being able to bounce back and forth
between the two. And when you take away the geocentric observations and
noticing patterns, you take away the basics by which you can predict what
you will see in the sky tomorrow or next week or a year from now.
Oh, I am not discounting the geocentric; I am just saying my experience is
being very different. I mean, here I am at my age now doing the geocentric
frame of reference.
But I guess the point I was making is that you made a statement about not
knowing something that if you had that background that would have been
in your knowledge base.
Well that’s true but probably because I really haven’t thought about it.
(Video, 29 March 2005)
The conversation became intensified and Sarah gave up. Later this week, Sarah
complained in individual interview that she was not convinced by the instructors. A
follow-up observation of Sarah’s own fifth-grade classroom showed that she tried to
teach her students the heliocentric model, but her students could not grasp the idea.
In the discussion, the instructor pointed out that Sarah ‘not knowing that the
moon goes around the earth once in a month’ was because she was not able to tie her
knowledge about the heliocentric frame back with her observation in a geocentric
reference frame. Sarah was not alone in the class, and many other teachers expressed
Justifying Alternative Models 15
similar thoughts during the debate. Since they had been taught in a way in which the
heliocentric model was simply presented as science knowledge in textbooks, they did
not regard the separation between scientific models and personal experiences as
problematic. The translation between the geocentric and heliocentric frames of
reference offered them little advantage, but confusion.
Assessment and Interview Results
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Formative assessment and individual interviews further revealed what the teachers
knew about the geocentric versus the heliocentric models. The following section will
concentrate on teachers’ mental models about the heliocentric frames of reference.
Teachers’ mental models of the heliocentric model. Eleven teachers took the Formative
Assessment 2 (see Appendix A). The results of the first item showed that all of the
teachers knew that geocentric refers to earth-centred and heliocentric to suncentred. Most of them were able to identify the perspectives for various activities in
Questions 4–6. For Question 7, eight out of 11 teachers knew that the heliocentric
model would not change if one moved from the earth to the moon.
Teachers’ responses to assessment and interview questions also showed that there
were different mental models of the geocentric and heliocentric frames of reference
(for the coding scheme, see Table 2). Since their understanding about the heliocentric model was more interesting and differentiated, we only focus on teachers’ views
on the heliocentric model.
There were two basic ideas about the heliocentric model in terms of observer’s
location. The first is viewing the solar system from the sun (coded as Sun-O). This
is parallel to the meaning of the geocentric mostly referred in the class—observing
the apparent motions of celestial bodies from the earth. The second is viewing the
solar system from outer space (coded as Space-O) by stepping outside the whole
system. Since both models emphasise the role of observer, they can be categorised
as observer-sensitive models. In addition, there was the third group of teachers who
believed that the heliocentric frame has nothing to do with where the observer is
(coded as Non-O). This model puts the sun at the origin of one’s frame of reference, and places other celestial objects in relation to the sun under this assumption.
Table 4 summarises the mental models held by the teachers along the data collection timeline. One can see that some teachers changed their mental models along
the course.
The case of one teacher, Gloria, supported the possibility that there may be a
progression of the mental models: the Sun-O is the starting point, then the Space-O,
and finally the Non-O. Initially, she held the Sun-O, as indicated by her response to
Question 7 of the formative assessment: ‘If your view is from earth it would be
geocentric, if your view is from the moon it is lunar-centric, if it is from the sun it is
heliocentric’. This is consistent with the instructional sequence that emphasised
observation. During the individual interview, she expressed her conversion to the
Non-O:
16 J. Shen and J. Confrey
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Table 4.
Teachers’ mental models on the heliocentric model
Teacher
code
Formative Assessment and class
discussion (29 March 2005)
Interview (date)
(1–26 April 2005)
Post-test assessment
(26 April 2005)
9
2
3
7
1
4
8
10
5
12
14
11
13
6
Sun-O
–
Sun-O
Space-O
–
?
Sun-O
Space-O
Sun-O
Sun-O
–
Space-O
Sun-O
?
Sun-O
Sun-O and Space-O
Sun-O
Sun
–
–
Space-O
Space-O
Sun-O and Space-O
Space-O
–
Space-O and Non-O (i)
Space-O and Non-O
Non-O
Sun-O
Sun-O
–
Sun-O
Space-O
Space-O
Space-O
Space-O
?
Non-O(i)
Non-O
Non-O
Non-O
Non-O
Note: – = absent; ? = cannot tell; (i) = inferred from context.
The geocentric model should be the model where the earth is the centre, and heliocentric, by definition, is the model where the sun is the centre of whatever base we’re looking at. At first I thought it meant that’s your frame of reference, that you are on earth
looking at what’s going on, but really it’s whether or not it’s the base. (Interview,
6 April 2005)
But at the same time she was also confused when thinking about standing above the
whole solar system:
I am confused … Suppose you are an alien, you didn’t know … And you are out here in
outer space, and you’re looking at (the solar system). Then … the sun is in the centre,
and then the earth around. So we’ll be heliocentric. (Interview, 6 April 2005)
These comments suggest at the point she was still struggling between the Space-O
and Non-O models. When responding to the post-test assessment, however, clearly
she believed that it was not important about where one stands. She wrote:
Heliocentric means the sun is the centre of a model, geocentric means the earth is the
centre. Neither of these terms means you are located there and are viewing things
from there. It’s just a matter of frame of reference you choose. (Post-test assessment,
26 April 2005)
The conjecture that there is a progression of the mental models is only partially
suggested by the overall pattern of Table 4. Although the movement toward NonO is more explicit, the data suggest that the teachers occasionally flipped their
mental models (especially the Sun-O and Space-O). Probably this is related to the
issue of contextuality (diSessa et al., 2004): under different contexts, a subject will
assign different meanings to words. There is no further data here to pin down the
pattern.
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Justifying Alternative Models 17
Teachers’ views on the validity of the two models. Besides the fact that teachers held
alternative conceptions, many also believed that the geocentric model is wrong.
Based on the second question in Formative Assessment 2, eight out of 11 teachers
believed that the geocentric model is wrong and the heliocentric one is right. The
teachers also believed that the heliocentric framework is the scientific one and could
explain the geocentric perspective. For instance, in Question 6, nine out of 11 teachers believed that Person B was right. They believed that the apparent motions of
celestial bodies were caused by the rotation of the earth. This is certainly correct
under the heliocentric perspective, but the directionality of this causality is rarely
questioned.
The next section will present teachers’ justification strategies behind their
beliefs. The categorisation is not intended to be exhaustive and exclusive. Figure 1
presents the proportion of the justification schemes used by the teachers in this study,
based on their responses to individual interviews and assessments (see Table 3 for
coding scheme). It is not intended to generalise to any other context, and these
justification strategies need further empirical studies. We will explain each of the
justification schemes in the following.
Figure 1.
Distribution of the teachers’ justification schemes
A common analogy in teachers’ reasoning. The analogy used by one teacher, Olivia,
reflected a common strategy of many people to justify their knowledge, following
one’s everyday experience and common-sense. Let us carefully examine the analogy
Olivia brought up (for her original dialogue, see Appendix B). When a person sits in
11%
pragmatic use
37%
authoritative forms
22%
common sense
relative
perspectives
30%
Figure 1.
Distribution of the teachers’ justification schemes
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18 J. Shen and J. Confrey
a car (analogous to the earth) at a parking lot, she is confused about its movement
since it might be the case that the car next to her (analogous to the sun) is moving.
She could figure this out by stepping out of the car and seeing what is really going
on. The problem found in this line of reasoning is that people experience the stationary earth and unconsciously use this experience to reason about motion. In outer
space, the common term ‘at rest’ is non-trivial since everything in the universe is in
motion. The solution is to treat motion relatively: that is, the origin of a frame of
reference to describe motion is arbitrary. Choosing an origin of a reference frame is
only a pragmatic issue. Olivia’s reasoning process gives one kind of justification
scheme: to test whether the theory under scrutiny is in accordance with everyday
experience. It reflects the reasoning from the experienced to the unfamiliar. The
problem is that people are often unaware of the assumptions they unconsciously
make. Justifying a theory or model is an argument-like process that requires one to
be clear about the premises (Giere, 1998). The moral is not that we should avoid
referring to our everyday experience, but that the deference to everyday experience
should be made consciously and its assumptions be often contested (Hammer &
Elby, 2003). In addition, a good analogy might be very helpful in comprehending
the target, but it doesn’t count as a formal proof of the claim (Clement, 1993).
Authoritative forms. Another popular type of justification used by the teachers was
deference to authority. The teachers argued that ‘when one steps outside the earth,
one sees the heliocentric model’. Never doing that, the teachers then argued that ‘we
could trust pictures sent from human machines in the space’. But in fact astronauts
or human spacecrafts would only send us the space-craft-centred pictures.
Authority takes different forms. One is people or organisations with specialised
knowledge. During the interviews, some teachers confessed that they accepted both
frames of reference because the instructors said so. Another authoritative form is
printed textbooks. Many textbooks survive after scrutiny, travel across space and
time, and then reach a larger audience. This implies that their contents are probably
more reliable and they function as a good medium for disseminating knowledge. In a
modern society, technology becomes another form of authority. One teacher
affirmed when she picked the heliocentric model:
We do have modern technology now or other ways of viewing the earth … from satellite pictures … It’s all scientifically based. So to me it’s more factual than opinion
when you use the modern technology to understand the heliocentric view. (Interview,
26 April 2005)
Authority, in many occasions, is a source of knowledge, information, and positive
attitudes. Oftentimes they provide an economic way of making a sound judgement.
Although learners’ reasoning may not necessarily be interfered with their knowledge
of source credibility (Clark & Slotta, 2000), a serious problem with deferring to
authority in learning is that people may weaken their ability to logically reason. In
learning science concepts, students might listen to whatever their teachers tell them.
A related problem is that, instead of gaining conceptual understanding, people
Justifying Alternative Models 19
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merely use new types of authority to replace old ones. Therefore, those who hold
truth might be easily defeated by those who have power. Conceptual learning
becomes detecting authoritative power. In the study, some teachers were convinced
by the instructors that both models are valid simply because they used a new source
of authority (the instructors in the course) to replace previous sources of authority
(their school teachers, textbooks they read, etc.). One teacher commented, ‘I guess
Pat [one course instructor and a physics professor] is always right’, when talking
about how she accepted both frames of reference.
Pragmatism. The third type of justification is pragmatism: that is, whatever is
pragmatically convenient is the best choice. This is closely connected to a characteristic of modelling: intentionality. Since any model is constructed with an intention in
mind, choosing a particular model is definitely associated with its purpose.
Pragmatically, it is convenient to choose the earth as the origin of the reference
frame in everyday life. Theoretically, there is nothing wrong in picking the earth as
the centre. For physicists, it is convenient to choose the sun as the origin of the reference frame. The instructors, as well as some teachers in this study, argued that children should start with the geocentric model because it provides a natural description
of what they observe. Moreover, young children are not developmentally ready for
the abstract heliocentric model. This reasoning emphasises the appropriateness of
instruction. The practical fulfilment does not guarantee the truthfulness of a theory.
Relativism. There is a fourth kind of justification used by the teachers—relativism:
that is, reality is personal, my ‘real’ might not be your ‘real’. These people discard
absolute authority and acknowledge diversity. For instance, one teacher stated
during interview: ‘(the geocentric model) reflects my reality because I’m here on
earth, right? So to me that is real’ (Interview, 14 April 2005). To her, the concept of
reality is not universal.
Epistemological relativists deny that ‘there are any objective methodological standards for evaluating theories independently of particular scientific research traditions and their associated belief systems’ (Curd & Cover, 1998, p. 1306). The
teachers are probably not really relativists in a philosophical sense. The point is that
one should not use relativism as an excuse to claim validity for any knowledge statement. Scientists are looking for consistency and trying to resolve discrepancy. The
geocentric and heliocentric frames of reference are both valid in describing the kinematics of celestial movements. The validity of both frames of reference is built upon
the fact that they are consistent with observations and they can be translated into
each other.
In summary, this section has addressed a few justification strategies that the teachers employed to justify their knowledge; namely, common-sense (analogy), authority, relativism, and pragmatism. Each of these strategies provides certain merits (e.g.,
tying to personal experience, being cost efficient) but also poses limitations (e.g., no
warrant, weakening one’s own reasoning). One thing to note is that these teachers’
20 J. Shen and J. Confrey
strategies bear something of Kuhn’s (1970) notion of irrational elements. These
strategies are very different from the criteria used by scientists to choose a theory
among alternatives: for example, accuracy, consistency, broad scope, simplicity, and
fruitfulness (Kuhn, 1998). This is due to the difference between how a scientific
theory is historically developed and how a scientific model is learned in everyday life.
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Difficulties and Teaching Strategies
Based on observations, we will discuss difficulties about the teaching and learning of
the topic observed in the course. Additionally, drawing on literature on modelling
(Clement, 2000; Confrey, 2006; Hestenes, 1987; Lehrer & Schauble, 2000; Shen &
Confrey, 2007), we will also propose possible solutions. These teaching strategies
employed by the instructors produced positive learning outcomes, as suggested by
the success of the science outreach programme and indicated by the statistical significance of the pre-test and post-test gain (Shen, 2006). The effectiveness of these
strategies, however, needs further empirical investigation.
Challenge Long-held Beliefs
Changing belief is the first barrier to accepting the geocentric point of view. Teachers
found it difficult to switch belief systems, as one teacher confessed: ‘It’s almost a
suspension of belief. … You have to get rid of your preconceived notion, which is
probably the hardest a teacher does’ (Interview, 1 April 2005). They had this deeprooted conception because of the way they were taught, or ‘told’:
It’s just really hard to undo 30 plus years of being told that we revolve around the sun …
We were taught from day one that heliocentric is what’s going on. We never use those
terms, but we’ve always heard that we’re the ones doing the revolving, and it’s not the
sun that’s moving. … (Interview, 12 April 2005)
Having been told that the heliocentric model is the correct one for years, the teachers would never ask why this is so.
Deep-rooted beliefs are hard to change as if they belong to a private universe
(Harvard-Smithsonian Centre for Astrophysics & Schneps, 1988). There is no ideal
solution to this problem. The first step is probably to be Socratic: to challenge longheld beliefs by asking good questions. These questions may stimulate their reflection
on their reasoning process. For instance, when some teachers argued that they could
step outside the solar system and verify the heliocentric model, the instructors
simply asked where they would stand in the outer space. Good questions may also
keep the learner pondering for a long time. For instance, in one formative assessment, the teachers were asked about what they would observe if they were living on
the moon, which requires them being able to transfer their knowledge about the
geocentric and heliocentric models to the lunar-centric model. Additionally, it is
probably futile to discuss the meaning of belief itself, but more fruitful to focus
instruction on the process of reasoning. Discussions on hidden assumptions that
Justifying Alternative Models 21
people make in everyday life may activate students’ awareness of similar premises
they unconsciously employ in physics problem solving (Hammer & Elby, 2003).
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Tie Back to Observations
Observational experience is critical to learn astronomy. It drives the historical development of human understanding. As we have shown in this study, many teachers
actually lacked observational experience. This created a gap between what they see
everyday and what they learn in textbooks. Several teachers commented that observational practice is one of the most important things they learned in the course and
stated that the observational experience totally renewed their understanding.
However, in a normal school setting it is difficult to conduct night sky observations. In addition, teachers are concerned that students’ observations are ‘contradictory’ to scientific knowledge. The remedy is not to ask young children to memorise
the heliocentric model, but to focus on positive attitudes of scientific observations, to
nurture their habit of being aware of the way they observe—where, when and how
they observe what they see—and to emphasise the practice of data recording and
analysis. Only with these solid experiences are students ready to start to talk about
different models. In this way, the learner will understand the purpose of modelling—
to understand, explain, or predict what one sees.
Switch between Models
Since there are two basic models of the solar system, a necessary skill is to be able
to switch back and forth between the two. This produces a common difficulty for
many teachers, especially for their students of younger age. For instance, one teacher
complained:
Well, it’s easy for us to see things from the earth, so from geocentric. But when it comes
from the sun, I found it difficult for myself, and I know it has to be difficult for the children … (Interview, 10 May 2005)
It is difficult to switch between models because it requires the learner be able to
position himself/herself at different locations and imagine different perceptions.
Especially when positioning oneself at locations where one has no experience, a high
level of abstract thinking is required.
Shen and Confrey (2007) have argued that, in the course, the activities of making
a transformation among various physical models helped the teachers to enhance
their conceptual understanding. In comparing and contrasting alternatives, the
affordances and limitations of each model are discussed. Another technique of
switching between models is using mathematics. One simplified way of progressing
from the geocentric model to the heliocentric one using the knowledge of geometry
is illustrated by Hoyle (1973, p. 47–59). If one does not appreciate the beauty and
power of mathematics, one probably would not follow the reasoning. Willhelm,
Sherrod, and Walters (2007) have documented a project-based interdisciplinary
22 J. Shen and J. Confrey
learning environment for pre-service teachers on the topic of the phases of the moon.
They argued that one has to develop four mathematical and spatial concepts
(geometric spatial visualisation, spatial projection, cardinal directions, and periodic
patterns) in order to fully understand lunar phases.
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Meaning of Modelling, Reality, and Truth
The meaning of modelling is another barrier for many teachers. This is relevant to
views on the nature of science (Abd-El-Khalick, Bell, & Lederman, 1998; Lederman,
1992). Even for the teachers who are comfortable switching back and forth between
the two models, they would not accept that both models are valid. The teachers did
not fully understand that building a scientific model always concerns a few characteristics of the world that one is interested in (Confrey, 2006; Lehrer & Schauble, 2000).
When it comes to fundamental debates such as the one between the geocentric
versus heliocentric models, some discussion on reality and truth is inevitable. Having
different justification schemes is probably due to holding different beliefs about the
truth of people’s knowledge claims. The meaning of truth demarcates the individuals. For those who follow authority, being true is being in accordance with an
accepted authority; for those who follow experience and common-sense (beginners
of empiricism and rationalism), being true is in accordance with everyday experience; for the naïve relativists, being true is an individual call; for pragmatists, being
true is closely tied to one’s purpose and its consequences. What is the meaning of
truth in science? What is reality? These questions always emerge when confronting
fundamental purpose of learning science. A thorough discussion about the meaning
of modelling is beyond the scope of the paper.
Conclusion
The present study investigated a small sample of K–8 science teachers’ understandings of the geocentric model versus the heliocentric model of the solar system. The
teachers were found to hold different understandings of the heliocentric model in
terms of observer sensitivity and observer locality. The data also suggested that
before instruction the teachers mix the perspective from the sun and the perspective
from space, while after instruction they shifted to the independent observer’s
perspective. More problematic is that the teachers believed that the geocentric
model is ‘wrong’ and should not be used in classroom instruction. Many of them
believed or rejected the heliocentric or geocentric model for various reasons: it is in
accordance with their common-sense; they had been taught it in this way by an
authority figure; it is a personal choice; or it fits their pragmatic concerns.
This problem is connected with the long-lasting historical debate on the geocentric versus heliocentric frames of reference in describing the solar system. The ways
in which people accept the heliocentric frame nowadays are probably not much
different from those in ancient times when the geocentric one was the orthodoxy. It
is also evident that the idea of frames of reference is not well addressed in astronomy
Justifying Alternative Models 23
education according to documents such as national standards. Including frames of
reference in astronomy education can enhance students’ deep understanding of
nature of science and scientific modelling. Students can be taught to make transformations between the heliocentric model and the geocentric one, while being
conscious about the justification schemes they employ. Meaningful learning occurs
when students tie their understandings to their own experiences.
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Acknowledgements
This material is partially based upon work supported by the US National Science
Foundation under Award No. ESI-0227619. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the author and
do not necessarily reflect the views of the National Science Foundation. The authors
wish to thank Patrick Gibbons, Jack Wiegers, and anonymous reviewers who
provided constructive comments on early drafts of this paper.
Notes
1.
2.
3.
4.
The reader can refer to Blown and Bryce (2006), to Sharp and Sharp (2007), to and Hans,
Kali, and Yair (2008) for summaries on conceptual change studies in astronomy. This body of
research is not terribly relevant to this study since we only focus on the topic of frames of
reference.
Owing to the construct of eccentric, the earth is slightly off the geometric centre in Ptolemy’s
model (http://en.wikipedia.org/wiki/Ptolemaic_system).
It does exist but could not be observed due to the limited technology at that time.
See http://en.wikipedia.org/wiki/Tycho_Brahe.
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Justifying Alternative Models 27
Appendix A.
Assessment and interview questions
Formative Assessment 2, Part C: Heliocentric VS Geocentric
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1 Geocentric means earth-centred, heliocentric means sun-centred.
(A) True (B) False (C) Not Sure (D) Don’t know
2 Geocentric is the wrong model of the solar system but heliocentric is the right one.
(A) True (B) False (C) Not Sure (D) Don’t know
For questions 3 to 5 below, indicating the models heliocentric or geocentric (if it is a
mixed model, please explain):
3 The apparent path of the sun (see figure): The sun rises at different points along
the eastern horizon, reaches different maximum heights, and sets at different points
in the west, during the year. This is a ______centric model.
4 Aristarchus (270 B.C.) developed a solar system model (see figure). This is a
______centric model.
5 The activity similar to what you did in this class: one student ‘is’ the sun in the
middle and many other students ‘are’ the 13 zodiac constellations in a circle.
Another student holding a globe acts like the earth. This is a _____centric model.
6 Stars rise in the east and set in the west over 24 hours. Person A argues that this is
because the sky is a fixed celestial sphere circling the earth. Person B argues that this
is because the earth rotates on its axis once per day. Who do you agree with? State
your reasoning.
7 If you lived on the moon rather than the earth, would the heliocentric view of the
solar system change? It would be ____ as the heliocentric view for a person living on
the earth?
(A) the same (B) different (C) Not Sure (D) Don’t know
Why do you think so?
8 Suppose you were living on the moon, not the earth. Can you draw a picture or
describe it to show the ‘lunar-centric’ view of your world: how the sun, the earth and
the stars appear to move?
28 J. Shen and J. Confrey
Relevant Individual Interview Questions
5. In my observation, I saw the instructors used many analogies or models, do you
remember some? And how did they facilitate or hinder your learning?
14. Can you describe the geocentric model and heliocentric model? Is one of them
true and the other wrong?
Relevant Post-test Question
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17. Please state briefly about your understanding of the meanings of heliocentric
model, geocentric model and the relationship between the two [feel free to draw
pictures]:
Appendix B.
Olivia:
Interviewer:
Olivia:
Interviewer:
Olivia:
Interviewer:
Olivia:
Interviewer:
Olivia:
Interviewer:
Olivia’s moving car analogy
I think from a frame of reference point, I can understand that. I still
think, you know, the true model is the heliocentric model because
that’s the way the solar system works. Obviously the geocentric is
what we’re seeing because of our frame of reference here on earth.
That’s what we see, you know, things move around us … but that’s
not really what’s happening. What’s really happening is we’re going
around the sun.
So, you are saying, can you say more? Because you said the heliocentric model is the true one, that’s what’s happening in the nature, and
the geocentric is what you see on the earth….
That’s kind of how I feel, but I’ve been told I am wrong, so [both
laugh]. I think it goes back to what we talked about in class. Geocentric
is what the kids can see and when they’re younger that’s kind of what
you have to (teach)…. Whereas (teaching) heliocentric when they are
able to think more abstractly, you can move into “this is what’s really
happening.” I know it has to do with frames of reference, I just feel like
… what’s really happening is the heliocentric.
Can you say more about what do you mean by really happening?
I can be in a car, and I stopped, and a car can move, come out next to
me, and I can feel like I am moving because this car next to me is
moving. Have you ever had this kind of experience? But I am really
not, so it’s not what’s really truly going on.
Now, when you are saying you are really not, what do you mean by
that?
I’m not moving.
You are not moving, but the other car,
The other car is, which makes, gives me the feeling that I’m moving.
It’s probably a terrible analogy.
That’s a very good analogy, I think.
Justifying Alternative Models 29
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Olivia:
I guess that’s kind of how I see between geocentric and heliocentric:
this is what I see moving, but the reality is kind of the opposite
though. I am the one actually doing the moving. So watching the sun
rise and set, yes that’s what I’m seeing, but it’s not what really what’s
going on. What’s really going on is, I know it’s what I’m seeing, but
it’s doing that because I’m the one doing the moving. (INTERVIEW,
4-12-05)