International Journal of Science Education Justifying ...mlebron/907016745.pdf · Introduction For I am not so enamored of my own opinions that I disregard what others may think of

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Justifying Alternative Models in Learning Astronomy: A study of K-8science teachers' understanding of frames of referenceJi 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-8science teachers' understanding of frames of reference', International Journal of Science Education, 32: 1, 1 — 29, Firstpublished on: 19 December 2008 (iFirst)To link to this Article: DOI: 10.1080/09500690802412449URL: http://dx.doi.org/10.1080/09500690802412449

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International Journal of Science EducationVol. 32, No. 1, 1 January 2010, pp. 1–29

ISSN 0950-0693 (print)/ISSN 1464-5289 (online)/10/010001–29© 2010 Taylor & Francis DOI: 10.1080/09500690802412449

RESEARCH REPORT

Justifying Alternative Models in Learning Astronomy: A study of K–8 science teachers’ understanding of frames of reference

Ji Shena* and Jere ConfreybaDepartment of Mathematics & Science Education, University of Georgia, Athens, Georgia, USA; bDepartment of Mathematics, Science & Technology Education, North Carolina State University, Raleigh, North Carolina, USATaylor and Francis LtdTSED_A_341412.sgm10.1080/09500690802412449International Journal of Science Education0950-0693 (print)/1464-5289 (online)Research Report2008Taylor & Francis0000000002008Dr. [email protected]

Understanding frames of reference is critical in describing planetary motion and learning astron-omy. Historically, the geocentric and heliocentric models were defended and advocated againsteach other. Today, there are still many people who do not understand the relationship between thetwo models. This topic is not adequately treated in astronomy instruction and is unstudied inscience education research. The present small-scale study suggests that many science teachers ofK–8 hold alternative conceptions about the models of the solar system. Most of the 14 teachers inthe study believed that the geocentric model should not be used in classroom instruction becausethey thought that it was wrong. It was found that they justified their knowledge claims by followingcommon sense, authority, pragmatism, or relativism. Their long-held beliefs, lack of observationalexperience, and resistance in switching between two models made it difficult for them to have adeep understanding of the relationship of the two models. Specific teaching strategies addressingthese 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 ofthem. (Nicholas Copernicus, On the Revolutions of the Heavenly Bodies)

It is well documented that children and adults hold alternative conceptions on sciencetopics (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]

Downloaded By: [Cornell University Library] At: 13:48 18 August 2010

2 J. Shen and J. Confrey

his colleagues maintain a comprehensive collection of literature on students’ and teach-ers’ conceptions on science topics. Astronomy is a field that has intrigued many scienceeducation 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 andNovak (1976) found that children held different notions about the shape of the earthand the meaning of the direction ‘down’ in space. In two later studies, it was confirmedthat both American and Israeli students held these notions (Nussbaum, 1979;Nussbaum & Sharodini-Dagan, 1983). Similar alternative conceptions are heldby teachers as well (Shen, Gibbons & Wiegers, 2003; Summers & Mant, 1995).Vosniadou and colleagues conducted a series of experiments investigating both chil-dren’s and adults’ knowledge of astronomy in the USA and Greece (Brewer, Hendrich,& Vosniadou, 1987; Vosniadou, 1988, 1989, 1991; Vosniadou & Brewer, 1990). Theyfound 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 phenomenonof 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 theauthors’ knowledge has been conducted on frames of reference. The heliocentricmodel of the solar system has been regarded as orthodoxy since Copernicus’ revolu-tion. Regardless of the development of modern physics, many people today acceptthe heliocentric model for the same reason ancient people believed in Ptolemy’sgeocentric model: following authority. Few people understand the connectionbetween the two theories: a matter of frames of reference. The two frames, detachedfrom their historical meanings, are both valid in terms of kinematics. The readershould 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 theuniverse.

The importance of understanding frames of reference in astronomy is not onlymanifested in the historical debates between advocates of the two theories, but alsoembodied in how much learners can tie their knowledge of astronomy into personalexperience of celestial observations. Therefore, this kind of big idea should be empha-sised in school education. Unfortunately, the topic of frames of reference has not beenadequately addressed in learning and teaching astronomy in the US National ScienceEducation Standards (National Research Council, 1996). For K–4, the content stan-dards on earth and space science stress that the focus should be put on observationsand looking for patterns (National Research Council, 1996, p. 130). Nonetheless, inreal classrooms, since science teachers do not want to teach the ‘wrong’ ideas, theyemphasise 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 fromtextbook knowledge. For Grades 5–8, the National Science Education Standardsclearly express the view that the heliocentric model is the only valid model (NationalResearch Council, 1996, p. 159). Students build up all the observational experience


Justifying Alternative Models 3

in a geocentric frame of reference, whereas the heliocentric model is taught as anorthodoxy that is disconnected from observations.

As a start, this study identified some elementary science teachers’ conceptions ofthe geocentric and the heliocentric models of the solar system and investigated whythey believed what they believed. We did not investigate how these teachers’ alterna-tive conceptions affected their students’ learning. We postulate that if teachers holdalternative conceptions, their classroom instruction is very likely problematic. Ourintention of the paper is not meant to be bounded by the particularity of the empiri-cal study. Rather, we hope to provoke the reader to rethink some more fundamentalquestions: What are the big ideas that students should learn in school? How arestudents taught these ideas?

In the following, we first present briefly the development of human understandingof the solar system. This sets the historical context of the study and provides theprescriptive understanding of the development of modelling the solar system. Thenwe describe an empirical study of how K–8 science teachers struggled with thistopic. The analysis of the data and discussion of the results focus on teachers’ under-standing and their justification schemes. Finally, based on research data and class-room observations, we identify difficulties in teaching and learning of the topic andsuggest possible instructional strategies.

Historical Debate

This section briefly sketches the history of human understanding of the geocentricversus the heliocentric models of the solar system. The long-lasting debate over thetwo systems implies that the topic deserves further discussion in both educationaland 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 astronomerswas to explain why the planets have retrograde motion: they stop and move back-wards 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 anumber of concentric spheres with different angular velocities. Aristotle (384–322BC) improved Eudoxus’ spheres and made them physically real. Given that thespheres are concentric, however, both Eudoxus and Aristotle could not explain thevariation of the brightness of the planets (Hoskin, 1999).

Heraclides (∼ 390–339 BC) suggested that the earth is a sphere and its rotation givesthe apparent diurnal rotation of the heavens (Hoskin, 1999). At about the sameperiod, Aristarchus (310–230 BC) believed that the sun is actually the centre of theuniverse and all other planets including the earth revolve around the sun—a primitiveheliocentric model. As Aristarchus explained, it was because the stars are too far awaythat 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 itencountered enormous difficulties in incorporating observational data. One difficulty



was to explain the fact that the period from spring-to-summer-to-autumn was threedays longer than the period from autumn-to-winter-to-spring. Hipparchus (190–120BC), an advocate of the geocentric model, was able to offer an explanation, albeit adhoc (see Hoyle, 1973).

It was Ptolemy (∼ 100–200 AD) in his Almagest who made the geocentric model thedominant one. There were three main arguments: the earth is motionless, the earthis approximately at the centre of universe,2 and celestial bodies move in circles andepicycles around the earth. This model was in accordance with the religious beliefthat the earth was motionless and at the centre of the universe. More importantly, itwas able to predict the celestial motions more precisely than the heliocentric model at thetime. For instance, the error due to the heliocentric model at the time for observingMars was about 10°, which was intolerable since by naked eyes the precision couldreach at least 0.5° (Hoyle, 1973).

The geocentric model was constantly revised to account for more observationsand held to be true until Copernicus (1473–1543) formally proposed the heliocen-tric model in his book, de revolutionibus orbium caelestium libri VI. The main pointsinclude the following: the sun, motionless, is at the centre of the universe; stars aremotionless around the edge; the planets including earth revolve around the sun incircles; and the earth rotates on its axis and the moon revolves around the earth in acircle. New observations such as the discovery of the phases of Venus greatlyfavoured the heliocentric model and pushed the geocentric one to the edge.However, Tycho Brahe (1564–1601), who believed that the earth is stationarybecause no observation of parallax of near stars was ever reported,3 revised thePtolemic system to compete against the heliocentric model.4

Up to this point, the issue for astronomy was to describe empirically how the plan-ets move, not why the planets move in the way they do. The predictive powerprovided by the two models was commensurable. However, Copernicus’ theorysecured the platform through which Kepler (1571–1630), Galileo (1564–1642) andNewton (1642–1727) moved forward to the dynamics of planetary motion (Jammer,1957). Since then the heliocentric model gradually won the battle, and was thentaken for granted by the public. The quote in the Encyclopedia of Philosophy capturedwell the significance of Copernicus’ contribution:

With Freud, man lost his Godlike mind; with Darwin his exalted place among the crea-tures 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. Inancient Greece, Aristotle believed that the natural state of an object is to be at restsince all objects on earth have to come to a stop. It was not challenged until 2,000years later Galileo claimed that, based on laboratory observations and thoughtexperiments, being in motion at a constant velocity for an object is as natural asbeing 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 framesof reference. In Galileo and Newton’s system, all inertial frames of reference are



equivalent, and the transformation between any two inertial frames of references isintuitive. Modern physics revolutionised this understanding. To solve the inconsis-tency of the equations for electromagnetic waves under Galilean transformation,Einstein (1879–1955) further postulated that light propagates through empty spacewith a definite speed independent of the speed of the source or observer. He usedthe Lorentz transformation between two inertial frames of reference. What Einsteincontributed on resolving the debate of the geocentric and heliocentric model of thesolar system is well summarised by Sir Fred Hoyle in Nicolaus Copernicus:

The relation of the two pictures (geocentricity and heliocentricity) is reduced to a merecoordinate transformation and it is the main tenet of the Einstein theory that any twoways of looking at the world which are related to each other by a coordinate transforma-tion are entirely equivalent from a physical point of view … Today we cannot say thatthe Copernican theory is ‘right’ and the Ptolemaic theory ‘wrong’ in any meaningfulphysical sense. (Hoyle, 1973, p. 79)

In brief, the two frames of reference of the solar system are equivalent in terms ofbeing able to transform into each other in modern physics (of course they involvedifferent levels of calculations). Hence it calls for a better understanding of the issuein astronomy education.

The historical debate between the geocentric versus heliocentric models suggeststhat the development of physics theories is accompanied by the maximisation ofboth explanatory or predictive power and parsimony; that is, accounting for moreobservations in a simpler and more consistent formulation (Hoskin, 1999; Hoyle,1973; Jammer, 1957). It should be pointed out unambiguously that physicists preferthe heliocentric model because it is consistent with the mechanistic explanationof the planetary motions—gravitational force—and it leads to a much simplerformulation of that explanation. The historical development and its implication maybe ignored in astronomy education, which results in that people accept either one ofthe theories by rote memory or following authority.

The debate between the geocentric and heliocentric advocates is similar to the onebetween 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 theissue has long been resolved since Copernicus’s revolution. As an ‘uncontroversial’topic, the problematic way in which people justify their knowledge claims is fullyreflected in this study.

Theoretical Framework

The theoretical framework of the study originates from the work of conceptualchange research. Students hold a repertoire of alternative ideas on scientificphenomena (Linn, 2006). Education researchers construct different theories toaccount for the process of conceptual change. One debate is about whether studentshave consistent theories in a certain domain, with possibly different interpretationson the term theory and varied approaches about the unit of analysis (e.g., diSessa,



2006; diSessa, Gillespie, & Esterly, 2004; Vosniadou, 2007). In astronomy, the viewthat 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) conducteda cross-cultural (in New Zealand and China) longitudinal study (over a period of13 years) where multiple representational modes were employed (verbal responses,drawings, and modelling with play-dough). They concluded that children createrich, coherent cosmologies to make sense of the world and that the developments ofthese cosmologies across cultures share similar patterns. In this study, we are notparticularly interested in participating in the coherent versus fragmented debate (seeBlown & Bryce, 2006), but we take a broad position that people have alternativeconceptions prior to instruction. We are more interested in how the process ofconceptual change is related to learners’ justification schemes.

A modelling theory (Shen, 2006; Shen & Confrey, 2007) is employed in thispaper to account for the fact that the teachers held different conceptions about thesolar system. We employed the modelling theory for three reasons. Firstly, we holdthat learners form mental models (Gentner & Stevens, 1983), coherent or not, ofthe world in everyday experience. The meaning of mental models will be discussedshortly. Secondly, people create external representations or models (Lehrer &Schauble, 2000) to explain observations. Especially in astronomy, instructors areencouraged to use a rich set of physical or virtual models to facilitate student learn-ing (Hans, Kali, & Yair, 2008). Thirdly, scientists develop explanatory models(Frigg & Hartmann, 2006) to account for scientific observations (e.g., the geocen-tric 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), differ-ent approaches are taken (e.g., Barab, Hay, Barnett, & Keating, 2000; Clement,2000; Confrey, 2006; Halloun, 1996; Lehrer & Schauble, 2000). The starting pointfor discussion is probably ontology. Some scholars consider a model as a mentalentity, or mental model (Gilbert, 2005; Hestenes, 1987; Passmore & Stewart, 2002),and some others believe that it is the materialised (external) representation thatmatters (Lehrer & Schauble, 2000). Shen (2006) has developed a theory where amodel is considered a hybrid of a physicality and mentality: for example, a physicalmicrocosm of the solar system is a materialisation of our conception, while a thoughtof the solar system may be inherently attached to a physical representation. Physicalityand mentality are not simply two sides of the same coin—one represents the other, orone instantiates the other—for they may be extensions of and complementary to eachother. The totality of the two counts as a complete model.

This synthetic approach has important educational implications. When weconsider the development of students’ mental models, we need to pay particularattention to the tools (e.g., physical models, representational medium) they areinstructed to use to explain phenomena and to communicate with others. Althoughthe operations on mental objects can go beyond experience, the physical materials



that students use form the basis of their experience and hence shape their learningtrajectories. One instantiation is that conceptual change may be triggered by trans-formative modelling of physical representations and artefacts (Shen & Confrey,2007). Another point to note is that any measured outcome of student understand-ing is closely related to the representational modes available to students. A betterapproach should consider multiple ways of eliciting student ideas (Bryce & Blown,2006). For a more comprehensive interpretation of the term model used in thispaper, please refer to Shen (2006). When we talk about teachers’ mental models inthe paper, the reader is referred to their conceptions (i.e., the mental form ofmodels).

Making Choices among Models

In this paper, we only emphasise the sense of how people justify their models. Sincealternative models always exist, a fundamental question arises: ‘Why is a particularmodel favoured over others?’ In this paper, a model is defined as a tool (mental orphysical) used to describe, explain, predict, and communicate with others a naturalphenomenon, an event or an entity. Since intentionality is a natural constituent of atool (Shen, 2006), when choosing among alternatives one has to consider thepurpose of modelling. In the case of the solar system, one may employ the heliocen-tric model to describe not only the kinematics (the motions of the objects) but alsothe dynamics (why they move in such a way). This model unifies the motionpatterns of celestial bodies and terrestrial objects.

Some pragmatic concerns are also involved in making a choice among a pool ofcandidates (van Fraassen, 1991). For instance, on the one hand, the heliocentricmodel provides a succinct explanation for physicists; on the other hand, in terms oftracking the apparent motions of the sun and the moon in the sky, a geocentricframe of reference is simpler, especially for novice learners. Other pragmaticconcerns in choosing models may include accessibility, efficiency, observability,consequences, and social contexts. Furthermore, since a model is a construct thatrepresents the relationship among the constituents of the referent, it only capturescertain traits of its target (Lehrer & Schauble, 2000). Strategies such as simplifica-tion and scaling (Frigg & Hartmann, 2006) are commonly used in modelling. Whenchoosing a model, only the relevant variables are considered. In describing planetarymotions, one ignores the exact shape, the materials, and other properties of the plan-ets. To model the apparent motions of the planets, one projects the planets onto ahypothetical sphere (the sky) without caring about the relative distance betweenthem. One may also deliberately distort the represented world (Frigg & Hartmann,2006). To describe the orbits of the planets, one may only use perfect circles insteadof ellipses.

When comparing and contrasting models, one may switch between them. Thereare two types of transformations. One concerns how models can be transformed ortranslated among alternatives (Shen & Confrey, 2007). If a model is somehowtransformable from another, the two should be considered equivalent under such a



transformation. The other concerns the relationship between a model and the exter-nal world that is modelled (e.g., Roth, Pozzer-Ardenghi, & Han, 2005). It permitsone to see how models are picked based on mapping between reality and humanconstructs.

The historical development of theories and how scientists choose a particulartheory or model certainly inform our theoretical framework. Kuhn (1998) lays out afew objective criteria that were important for scientists to choose among theories:accuracy, consistency, broad scope, simplicity, and fruitfulness. Since these criteriamay be conflicting with each other, insufficient to rule out alternatives, or open todifferent interpretations, Kuhn added that personal experience, social context, andother subjective elements may have a big impact for individual scientists when theydraw a conclusion (Kuhn, 1970). However, the historical perspective about howscientists choose particular theories is dramatically different from the layperson’severyday decision-making. The biggest demarcation is that scientists over the longrun are looking for truth, however defined. As for a layperson, subjective judgementis more dominant. Pragmatic concerns, relative opinions, convenience, time pres-sure, and personal experience are less intimidating than hard theorising, intensecalculation, abstract understanding, and shared community standards that arerequired for getting a theory right.

It is critical to clarify the terms geocentric and heliocentric used in the paperbefore we proceed to present the empirical study. Each term refers to a cluster ofmodels that describe the solar system unless it was specifically pointed out. Theterms heliocentric and geocentric are especially loaded with rich historical andcultural information. For instance, the geocentric model may refer to a spectrum ofmodels from a very primitive one that all celestial objects are revolving around theearth in circles on the same sphere, to an advanced Ptolemaic model where planetsmove around the earth in epicycles, to a Tychonic system that is geometrically simi-lar to the heliocentric model. It depends on the context to figure out what a modelrepresents. In most occasions, in this case, people talked in a fuzzy manner, geocen-tric simply means earth-centred and heliocentric means sun-centred. However, in aformal sense, a geocentric model refers to a system that is kinematically consistentwith the heliocentric system. The two models are parallel: they differ only in prefer-ences 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 problematicways in teaching and learning the topic of frames of reference. The followingresearch 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?



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 univer-sity for science teachers of K–8 (for details of the course, see Shen, 2006). Fourteenteachers 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 scienceoutreach programme for more than 10 years: a physics professor, an experiencedand retired teacher, and a then science coordinator for a school district. The instruc-tors carefully selected hands-on activities (Gibbons, McMahon, & Wiegers, 2003),aligned modules with the National Science Education Standards (National ResearchCouncil, 1996) and state standards, and implemented research-based assessments todiagnose teachers’ understanding (Shen, Gibbons, Wiegers & McMahon, 2007).

The course emphasised the storyline of the science topics, combined everydayobservations and manipulations of physical models, and moved from descriptivegeocentric account to explanatory heliocentric theory. It covered the following topicsin sequence: observations of the sun and moon, mechanisms of shadow, night sky,and constellations, frames of reference, geocentric and heliocentric models, theseasons, 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 instruc-tors on the correctness of alternative models in describing the solar system. Thediscussion stimulated the researchers to further investigate the teachers’ understand-ing and their reasoning schemes. Therefore, this study only covered six weeks in thelate period of the course.

Multiple sources of data were utilised to triangulate the findings. The data sourcesof this study mainly included videotapes, assessment responses, and individualteacher interviews. Each class was videotaped and the videos were transcribed andorganised in themes by the researcher. For instance, in this study all the clipscontaining the topic of frame of reference were combined into a folder. Pre-test andpost-test and four formative assessments were administered. Only the second forma-tive assessment (eight items) and one question from the post-test were relevant tothis study (see Appendix A). The assessment items were created based on researchliterature (e.g., Deming, 2002; Shen et al., 2007). The items were tested and revisedto fit the teachers’ knowledge level and course topics (Shen et al., 2003). The resultsof the formative assessments were shared with the teachers and instructors. Theteachers were interviewed individually upon agreement. Each interview took about1–2 hrs and all of the interviews were transcribed. Two interview questions wererelevant to this study (see Appendix A for the list of interview questions).



There were also other types of data sources that were potentially useful to thisstudy (but not directly cited). Field notes following structured protocols were madeduring classes. The instructors of this course used personal journals as a way ofdocumenting and examining teachers’ conceptual change. All teachers’ journalswere photocopied each week and organised into categories for further analysis. Theinstructors were also interviewed before and after each class. The data collectiontimeline 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 modelsand the distribution of their justification schemes. Tables 2 and 3 present the codingschemes for categorising teachers’ mental models on the heliocentric models of thesolar system (Table 2) and their justification schemes (Table 3). These codes emergedfrom their responses to the relevant assessment items, interviews, and classroom

Table 1. Data collection timeline relevant to this case

Week 10 Week 11 Week 12 Week 13 Week 14 Week 15

Class debate on alternative models

Formative assessment (Section C) on frame of reference

Feedback of formative assessment to teachers

Post-test assessment (one item on frame of reference)

Individual teacher interviewsClassroom observations (field notes and videotapes) and teachers’ journals, artefacts

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

‘The heliocentric model is to observe from the sun’ (Formative Assessment).‘Heliocentric is sun-centered and the view from the sun’ (Formative Assessment).

Space-O Viewing the solar system from outer space

‘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).

Non-O No matter where the observer stands; choosing the origin of the coordinates

‘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).



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

‘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)

RP – Choose/both models based on relative perspectives.

‘You can’t say one is wrong and one is right, it’s just different ways of looking at something’.

PP (pragmatic purposes)

Developmental appropriateness

Use a developmentally appropriate model for instruction.

‘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’.

Usage or understanding

Pick a certain model to explain the other, to use in a particular context or to enhance one’s understanding.

‘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’.

Simplicity Pick the simplest model. ‘It was so simplified when we came up with the heliocentric view point’.

Historical development

Use currently accepted model, considering the historical development.

‘Because back into the old time, with Galileo, and all of them, they 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’.

AF (authoritative forms)

Text or textbook

Learn models from textbooks.

‘When you have the science books, they show you different frames of reference’.

People Accept a model by following people who have more knowledge.

‘That’s kind of how I feel (that the geocentric is wrong), but I’ve been told (by the course instructors) that I am wrong’.

Technology Choose a model by referring to technology.

‘We do have modern technology… of viewing the earth … from … satellite pictures … it’s more factual than opinion when you use the modern technology’.

Mathematics Choose a model by referring to mathematics.

‘Because you are eager to understand theories and equations and things you can’t just see by your own eyes’.



discussions. To track the progress of teachers’ understanding, we used data points onthree occasions. Their initial mental models were represented by their responses tothe formative assessment and their class discussions up to week 11. Then the firstauthor conducted individual interviews to capture their changes. Finally, we use theirresponses to the post-test assessment to capture their understanding at the end of thecourse.

To code and calculate the distribution of teachers’ justification schemes, we usedtheir responses to the formative assessment, class discussion, and individual inter-views, only when those are relevant to the topic of frames of reference. The propor-tion is calculated as the ratio of the number of instances they used for a particularjustification scheme over the total number of the justification instances. Eachinstance can be one or more sentences (see examples in Tables 2 and 3). We willdiscuss 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 analy-sis, discussions, and the proposed teaching strategies were grounded in classroomobservations, assessments results, and individual interviews. This empirical study isbounded by the conceptual development of the teachers’ understanding of the solarsystem in terms of frame of reference. It is neither a case of any individual in theclass 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. Thisdebate offered a window through which we examined the instructors’ and the teach-ers’ initial views on using the two frames of reference in learning astronomy. Wethen report the teachers’ understanding of the heliocentric frames of reference basedon assessments and interview results. Finally, teachers’ rationales and justificationschemes 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 systemto describe and explain the corresponding celestial observations. The teachers wereasked to transform these models among themselves to enhance understanding (Shen& Confrey, 2007). In action, when teachers played with geocentric models, they raisedconcerns about teaching the students ‘wrong’ concepts. For instance, a few teacherscommented that, since the sun is not revolving around the earth, one should not rotatethe ‘sun’ in a paper-made geocentric model. In week 10, the instructors started toaddress these concerns by elaborating their rationales about learning astronomy.

Instructors’ rationale on the geocentric. The instructors started with a verbal analogyabout frames of reference. The teachers were asked to identify the grammaticalconstituents of a sentence (syntax) written on blackboard and then to discuss what



came to their minds (semantics) when they first saw the nouns in the sentence. Theinstructors explained that, although there were various ways of reading a sentence,the sentence was the same. Analogously, although there were different ways of look-ing at the solar system, there is only one solar system. The instructors emphasisedthat they expected the teachers to be able to switch frames of reference.

The instructors further highlighted that it is celestial observations that connectdifferent frames of reference. They submitted that it is more appropriate for veryyoung students to start with the geocentric model since it is closely connected witheveryday experience and that observations are what young children can do. Oneinstructor said:

Speaking as an educator, I actually prefer (starting with) the geocentric frame of refer-ence until (the) child gets old enough to hold that abstractness of the heliocentric frameof 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 thingseven a little kid can go outside and do it. (Video, 29 March 2005)

They also pointed out that, although observation is especially important in learningastronomy, usually, a lack of observational experience is why astronomy does notmake sense for many students. It is a serious problem in astronomy education sinceregular school time is during daytime, whereas many celestial observations requiregoing out during nights. One instructor asserted:

I am … sure that the general public can spell out the word that the earth rotates aroundits axis and revolves around the sun … My experience has been that a very smallpercentage of people of any age can actually relate those concepts to what they see in thesky, 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 isdivorced from experience is superficial; learning astronomy should connect topersonal experience, especially for very young children; it is very common thatpeople lack observational experience when they start learning astronomy; and learn-ing the geocentric frame of reference provides some help.

Sarah’s objection. Not all teachers agreed with the instructors. Several teachers chal-lenged them. To concentrate on the theme, we only focus on one representativeteacher, Sarah (pseudonyms are used in the paper), in this discussion because hervoice was clearly heard and her arguments were well represented. The reader shouldkeep 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 astron-omy and biology learning. She explained why astronomy was more difficult thanbiology:

When you are looking at the sun, you are looking at the apparent motion—the sunmoves 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 realmotion. That’s not the apparent motion and then translated into this abstract kind ofmotion. (Video, 29 March 2005)



Sarah described learning astronomy as a translational process from an ‘apparent’space (observation) into an ‘abstract’ space (the heliocentric model). The instructorsexplained to Sarah that the ‘apparent’ motion is real—it is just a description from theearth-centred perspective with objects cast on the same spherical surface.

Sarah continued on with her experience of learning astronomy and challenged theinstructors’ argument about the developmental appropriateness of the two models.She believed that many students would not have any trouble in learning the helio-centric model. Clarifying her theory of meaning, one instructor doubted whetherthis kind of learning would make any sense since it is detached from personal experi-ence. Here is some of the verbal exchange between one instructor and Sarah in theclass:

Sarah: I think that we were taught at a heliocentric [model], and that’s interestingbecause I don’t even have a problem with the heliocentric as a child. Notthat we should in any way ignore the geocentric because I think our obser-vations are so important. But I don’t know if a child really has that muchdifficulty in grasping the heliocentric.

Instructor: As a child, they certainly might be able to learn it as a catechism, butwould they be able to relate it to something they see in the sky and use it topredict what they will see tomorrow?

Sarah: Well I don’t recall having much trouble with that and also with my chil-dren. I didn’t teach them the geocentric because I didn’t know the geocen-tric before …

Instructor: What you said though about not knowing that the moon goes around theearth once in a month [referring to a statement Sarah made previously], ifyou were able to tie what you knew heliocentrically about the motion ofthe moon back to observations, you would definitely know [it].

Sarah: Yes.Instructor: 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 andnoticing patterns, you take away the basics by which you can predict whatyou will see in the sky tomorrow or next week or a year from now.

Sarah: Oh, I am not discounting the geocentric; I am just saying my experience isbeing very different. I mean, here I am at my age now doing the geocentricframe of reference.

Instructor: But I guess the point I was making is that you made a statement about notknowing something that if you had that background that would have beenin your knowledge base.

Sarah: 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, Sarahcomplained in individual interview that she was not convinced by the instructors. Afollow-up observation of Sarah’s own fifth-grade classroom showed that she tried toteach 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 themoon goes around the earth once in a month’ was because she was not able to tie herknowledge about the heliocentric frame back with her observation in a geocentricreference frame. Sarah was not alone in the class, and many other teachers expressed



similar thoughts during the debate. Since they had been taught in a way in which theheliocentric model was simply presented as science knowledge in textbooks, they didnot regard the separation between scientific models and personal experiences asproblematic. The translation between the geocentric and heliocentric frames ofreference offered them little advantage, but confusion.

Assessment and Interview Results

Formative assessment and individual interviews further revealed what the teachersknew about the geocentric versus the heliocentric models. The following section willconcentrate on teachers’ mental models about the heliocentric frames of reference.

Teachers’ mental models of the heliocentric model. Eleven teachers took the FormativeAssessment 2 (see Appendix A). The results of the first item showed that all of theteachers knew that geocentric refers to earth-centred and heliocentric to sun-centred. Most of them were able to identify the perspectives for various activities inQuestions 4–6. For Question 7, eight out of 11 teachers knew that the heliocentricmodel would not change if one moved from the earth to the moon.

Teachers’ responses to assessment and interview questions also showed that therewere different mental models of the geocentric and heliocentric frames of reference(for the coding scheme, see Table 2). Since their understanding about the heliocen-tric model was more interesting and differentiated, we only focus on teachers’ viewson the heliocentric model.

There were two basic ideas about the heliocentric model in terms of observer’slocation. The first is viewing the solar system from the sun (coded as Sun-O). Thisis parallel to the meaning of the geocentric mostly referred in the class—observingthe apparent motions of celestial bodies from the earth. The second is viewing thesolar system from outer space (coded as Space-O) by stepping outside the wholesystem. Since both models emphasise the role of observer, they can be categorisedas observer-sensitive models. In addition, there was the third group of teachers whobelieved 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 refer-ence, 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 collec-tion timeline. One can see that some teachers changed their mental models alongthe course.

The case of one teacher, Gloria, supported the possibility that there may be aprogression 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 toQuestion 7 of the formative assessment: ‘If your view is from earth it would begeocentric, if your view is from the moon it is lunar-centric, if it is from the sun it isheliocentric’. This is consistent with the instructional sequence that emphasisedobservation. During the individual interview, she expressed her conversion to theNon-O:



The geocentric model should be the model where the earth is the centre, and heliocen-tric, by definition, is the model where the sun is the centre of whatever base we’re look-ing at. At first I thought it meant that’s your frame of reference, that you are on earthlooking 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 thewhole solar system:

I am confused … Suppose you are an alien, you didn’t know … And you are out here inouter 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-Oand Non-O models. When responding to the post-test assessment, however, clearlyshe 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 thecentre. Neither of these terms means you are located there and are viewing thingsfrom 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 partiallysuggested by the overall pattern of Table 4. Although the movement toward Non-O is more explicit, the data suggest that the teachers occasionally flipped theirmental models (especially the Sun-O and Space-O). Probably this is related to theissue of contextuality (diSessa et al., 2004): under different contexts, a subject willassign different meanings to words. There is no further data here to pin down thepattern.

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 Sun-O Sun-O Sun-O2 – Sun-O and Space-O Sun-O3 Sun-O Sun-O –7 Space-O Sun Sun-O1 – – Space-O4 ? – Space-O8 Sun-O Space-O Space-O10 Space-O Space-O Space-O5 Sun-O Sun-O and Space-O ?12 Sun-O Space-O Non-O(i)14 – – Non-O11 Space-O Space-O and Non-O (i) Non-O13 Sun-O Space-O and Non-O Non-O6 ? Non-O Non-O

Note: – = absent; ? = cannot tell; (i) = inferred from context.



Teachers’ views on the validity of the two models. Besides the fact that teachers heldalternative conceptions, many also believed that the geocentric model is wrong.Based on the second question in Formative Assessment 2, eight out of 11 teachersbelieved that the geocentric model is wrong and the heliocentric one is right. Theteachers also believed that the heliocentric framework is the scientific one and couldexplain the geocentric perspective. For instance, in Question 6, nine out of 11 teach-ers believed that Person B was right. They believed that the apparent motions ofcelestial bodies were caused by the rotation of the earth. This is certainly correctunder the heliocentric perspective, but the directionality of this causality is rarelyquestioned.

The next section will present teachers’ justification strategies behind theirbeliefs. The categorisation is not intended to be exhaustive and exclusive. Figure 1presents 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 forcoding scheme). It is not intended to generalise to any other context, and thesejustification strategies need further empirical studies. We will explain each of thejustification 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, followingone’s everyday experience and common-sense. Let us carefully examine the analogyOlivia brought up (for her original dialogue, see Appendix B). When a person sits in

37%

30%

22%

11%

pragmatic use

authoritative forms

common sense

relative

perspectives

Figure 1. Distribution of the teachers’ justification schemes



a car (analogous to the earth) at a parking lot, she is confused about its movementsince 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 goingon. The problem found in this line of reasoning is that people experience the station-ary earth and unconsciously use this experience to reason about motion. In outerspace, the common term ‘at rest’ is non-trivial since everything in the universe is inmotion. The solution is to treat motion relatively: that is, the origin of a frame ofreference to describe motion is arbitrary. Choosing an origin of a reference frame isonly a pragmatic issue. Olivia’s reasoning process gives one kind of justificationscheme: to test whether the theory under scrutiny is in accordance with everydayexperience. It reflects the reasoning from the experienced to the unfamiliar. Theproblem is that people are often unaware of the assumptions they unconsciouslymake. Justifying a theory or model is an argument-like process that requires one tobe clear about the premises (Giere, 1998). The moral is not that we should avoidreferring to our everyday experience, but that the deference to everyday experienceshould be made consciously and its assumptions be often contested (Hammer &Elby, 2003). In addition, a good analogy might be very helpful in comprehendingthe 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 wasdeference 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 ‘wecould trust pictures sent from human machines in the space’. But in fact astronautsor human spacecrafts would only send us the space-craft-centred pictures.

Authority takes different forms. One is people or organisations with specialisedknowledge. During the interviews, some teachers confessed that they accepted bothframes of reference because the instructors said so. Another authoritative form isprinted textbooks. Many textbooks survive after scrutiny, travel across space andtime, and then reach a larger audience. This implies that their contents are probablymore reliable and they function as a good medium for disseminating knowledge. In amodern society, technology becomes another form of authority. One teacheraffirmed when she picked the heliocentric model:

We do have modern technology now or other ways of viewing the earth … from satel-lite pictures … It’s all scientifically based. So to me it’s more factual than opinionwhen 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 positiveattitudes. Oftentimes they provide an economic way of making a sound judgement.Although learners’ reasoning may not necessarily be interfered with their knowledgeof source credibility (Clark & Slotta, 2000), a serious problem with deferring toauthority in learning is that people may weaken their ability to logically reason. Inlearning science concepts, students might listen to whatever their teachers tell them.A related problem is that, instead of gaining conceptual understanding, people



merely use new types of authority to replace old ones. Therefore, those who holdtruth might be easily defeated by those who have power. Conceptual learningbecomes detecting authoritative power. In the study, some teachers were convincedby the instructors that both models are valid simply because they used a new sourceof authority (the instructors in the course) to replace previous sources of authority(their school teachers, textbooks they read, etc.). One teacher commented, ‘I guessPat [one course instructor and a physics professor] is always right’, when talkingabout how she accepted both frames of reference.

Pragmatism. The third type of justification is pragmatism: that is, whatever ispragmatically convenient is the best choice. This is closely connected to a character-istic of modelling: intentionality. Since any model is constructed with an intention inmind, choosing a particular model is definitely associated with its purpose.

Pragmatically, it is convenient to choose the earth as the origin of the referenceframe in everyday life. Theoretically, there is nothing wrong in picking the earth asthe centre. For physicists, it is convenient to choose the sun as the origin of the refer-ence frame. The instructors, as well as some teachers in this study, argued that chil-dren should start with the geocentric model because it provides a natural descriptionof what they observe. Moreover, young children are not developmentally ready forthe abstract heliocentric model. This reasoning emphasises the appropriateness ofinstruction. 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 discardabsolute authority and acknowledge diversity. For instance, one teacher statedduring interview: ‘(the geocentric model) reflects my reality because I’m here onearth, right? So to me that is real’ (Interview, 14 April 2005). To her, the concept ofreality is not universal.

Epistemological relativists deny that ‘there are any objective methodological stan-dards for evaluating theories independently of particular scientific research tradi-tions and their associated belief systems’ (Curd & Cover, 1998, p. 1306). Theteachers are probably not really relativists in a philosophical sense. The point is thatone should not use relativism as an excuse to claim validity for any knowledge state-ment. Scientists are looking for consistency and trying to resolve discrepancy. Thegeocentric and heliocentric frames of reference are both valid in describing the kine-matics of celestial movements. The validity of both frames of reference is built uponthe fact that they are consistent with observations and they can be translated intoeach other.

In summary, this section has addressed a few justification strategies that the teach-ers employed to justify their knowledge; namely, common-sense (analogy), author-ity, 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., nowarrant, weakening one’s own reasoning). One thing to note is that these teachers’



strategies bear something of Kuhn’s (1970) notion of irrational elements. Thesestrategies are very different from the criteria used by scientists to choose a theoryamong alternatives: for example, accuracy, consistency, broad scope, simplicity, andfruitfulness (Kuhn, 1998). This is due to the difference between how a scientifictheory is historically developed and how a scientific model is learned in everyday life.

Difficulties and Teaching Strategies

Based on observations, we will discuss difficulties about the teaching and learning ofthe 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 strategiesemployed by the instructors produced positive learning outcomes, as suggested bythe success of the science outreach programme and indicated by the statistical signif-icance of the pre-test and post-test gain (Shen, 2006). The effectiveness of thesestrategies, however, needs further empirical investigation.

Challenge Long-held Beliefs

Changing belief is the first barrier to accepting the geocentric point of view. Teachersfound it difficult to switch belief systems, as one teacher confessed: ‘It’s almost asuspension of belief. … You have to get rid of your preconceived notion, which isprobably the hardest a teacher does’ (Interview, 1 April 2005). They had this deep-rooted 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 thoseterms, but we’ve always heard that we’re the ones doing the revolving, and it’s not thesun that’s moving. … (Interview, 12 April 2005)

Having been told that the heliocentric model is the correct one for years, the teach-ers 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 idealsolution to this problem. The first step is probably to be Socratic: to challenge long-held beliefs by asking good questions. These questions may stimulate their reflectionon their reasoning process. For instance, when some teachers argued that they couldstep outside the solar system and verify the heliocentric model, the instructorssimply asked where they would stand in the outer space. Good questions may alsokeep the learner pondering for a long time. For instance, in one formative assess-ment, the teachers were asked about what they would observe if they were living onthe moon, which requires them being able to transfer their knowledge about thegeocentric and heliocentric models to the lunar-centric model. Additionally, it isprobably futile to discuss the meaning of belief itself, but more fruitful to focusinstruction on the process of reasoning. Discussions on hidden assumptions that



people make in everyday life may activate students’ awareness of similar premisesthey unconsciously employ in physics problem solving (Hammer & Elby, 2003).

Tie Back to Observations

Observational experience is critical to learn astronomy. It drives the historical devel-opment of human understanding. As we have shown in this study, many teachersactually lacked observational experience. This created a gap between what they seeeveryday and what they learn in textbooks. Several teachers commented that obser-vational practice is one of the most important things they learned in the course andstated that the observational experience totally renewed their understanding.

However, in a normal school setting it is difficult to conduct night sky observa-tions. In addition, teachers are concerned that students’ observations are ‘contradic-tory’ to scientific knowledge. The remedy is not to ask young children to memorisethe heliocentric model, but to focus on positive attitudes of scientific observations, tonurture their habit of being aware of the way they observe—where, when and howthey observe what they see—and to emphasise the practice of data recording andanalysis. Only with these solid experiences are students ready to start to talk aboutdifferent 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 ableto switch back and forth between the two. This produces a common difficulty formany teachers, especially for their students of younger age. For instance, one teachercomplained:

Well, it’s easy for us to see things from the earth, so from geocentric. But when it comesfrom the sun, I found it difficult for myself, and I know it has to be difficult for the chil-dren … (Interview, 10 May 2005)

It is difficult to switch between models because it requires the learner be able toposition himself/herself at different locations and imagine different perceptions.Especially when positioning oneself at locations where one has no experience, a highlevel of abstract thinking is required.

Shen and Confrey (2007) have argued that, in the course, the activities of makinga transformation among various physical models helped the teachers to enhancetheir conceptual understanding. In comparing and contrasting alternatives, theaffordances and limitations of each model are discussed. Another technique ofswitching between models is using mathematics. One simplified way of progressingfrom the geocentric model to the heliocentric one using the knowledge of geometryis illustrated by Hoyle (1973, p. 47–59). If one does not appreciate the beauty andpower of mathematics, one probably would not follow the reasoning. Willhelm,Sherrod, and Walters (2007) have documented a project-based interdisciplinary



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 periodicpatterns) in order to fully understand lunar phases.

Meaning of Modelling, Reality, and Truth

The meaning of modelling is another barrier for many teachers. This is relevant toviews on the nature of science (Abd-El-Khalick, Bell, & Lederman, 1998; Lederman,1992). Even for the teachers who are comfortable switching back and forth betweenthe two models, they would not accept that both models are valid. The teachers didnot fully understand that building a scientific model always concerns a few character-istics 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 geocentricversus heliocentric models, some discussion on reality and truth is inevitable. Havingdifferent justification schemes is probably due to holding different beliefs about thetruth of people’s knowledge claims. The meaning of truth demarcates the individu-als. For those who follow authority, being true is being in accordance with anaccepted authority; for those who follow experience and common-sense (beginnersof empiricism and rationalism), being true is in accordance with everyday experi-ence; for the naïve relativists, being true is an individual call; for pragmatists, beingtrue is closely tied to one’s purpose and its consequences. What is the meaning oftruth in science? What is reality? These questions always emerge when confrontingfundamental purpose of learning science. A thorough discussion about the meaningof modelling is beyond the scope of the paper.

Conclusion

The present study investigated a small sample of K–8 science teachers’ understand-ings of the geocentric model versus the heliocentric model of the solar system. Theteachers were found to hold different understandings of the heliocentric model interms of observer sensitivity and observer locality. The data also suggested thatbefore instruction the teachers mix the perspective from the sun and the perspectivefrom space, while after instruction they shifted to the independent observer’sperspective. More problematic is that the teachers believed that the geocentricmodel is ‘wrong’ and should not be used in classroom instruction. Many of thembelieved or rejected the heliocentric or geocentric model for various reasons: it is inaccordance with their common-sense; they had been taught it in this way by anauthority figure; it is a personal choice; or it fits their pragmatic concerns.

This problem is connected with the long-lasting historical debate on the geocen-tric versus heliocentric frames of reference in describing the solar system. The waysin which people accept the heliocentric frame nowadays are probably not muchdifferent from those in ancient times when the geocentric one was the orthodoxy. Itis also evident that the idea of frames of reference is not well addressed in astronomy



education according to documents such as national standards. Including frames ofreference in astronomy education can enhance students’ deep understanding ofnature of science and scientific modelling. Students can be taught to make transfor-mations between the heliocentric model and the geocentric one, while beingconscious about the justification schemes they employ. Meaningful learning occurswhen students tie their understandings to their own experiences.

Acknowledgements

This material is partially based upon work supported by the US National ScienceFoundation under Award No. ESI-0227619. Any opinions, findings, and conclu-sions or recommendations expressed in this publication are those of the author anddo not necessarily reflect the views of the National Science Foundation. The authorswish to thank Patrick Gibbons, Jack Wiegers, and anonymous reviewers whoprovided constructive comments on early drafts of this paper.

Notes

1. 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 ofresearch is not terribly relevant to this study since we only focus on the topic of frames ofreference.

2. Owing to the construct of eccentric, the earth is slightly off the geometric centre in Ptolemy’smodel (http://en.wikipedia.org/wiki/Ptolemaic_system).

3. It does exist but could not be observed due to the limited technology at that time.4. See http://en.wikipedia.org/wiki/Tycho_Brahe.

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Appendix A. Assessment and interview questions

Formative Assessment 2, Part C: Heliocentric VS Geocentric

1 Geocentric means earth-centred, heliocentric means sun-centred.(A) True (B) False (C) Not Sure (D) Don’t know2 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 knowFor questions 3 to 5 below, indicating the models heliocentric or geocentric (if it is amixed model, please explain):

3 The apparent path of the sun (see figure): The sun rises at different points alongthe eastern horizon, reaches different maximum heights, and sets at different pointsin 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 themiddle 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 isbecause the sky is a fixed celestial sphere circling the earth. Person B argues that thisis because the earth rotates on its axis once per day. Who do you agree with? Stateyour reasoning.7 If you lived on the moon rather than the earth, would the heliocentric view of thesolar system change? It would be ____ as the heliocentric view for a person living onthe earth?(A) the same (B) different (C) Not Sure (D) Don’t knowWhy do you think so?8 Suppose you were living on the moon, not the earth. Can you draw a picture ordescribe it to show the ‘lunar-centric’ view of your world: how the sun, the earth andthe stars appear to move?



Relevant Individual Interview Questions

5. In my observation, I saw the instructors used many analogies or models, do youremember some? And how did they facilitate or hinder your learning?14. Can you describe the geocentric model and heliocentric model? Is one of themtrue and the other wrong?

Relevant Post-test Question

17. Please state briefly about your understanding of the meanings of heliocentricmodel, geocentric model and the relationship between the two [feel free to drawpictures]:

Appendix B. Olivia’s moving car analogy

Olivia: I think from a frame of reference point, I can understand that. I stillthink, you know, the true model is the heliocentric model becausethat’s the way the solar system works. Obviously the geocentric iswhat 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’snot really what’s happening. What’s really happening is we’re goingaround the sun.

Interviewer: So, you are saying, can you say more? Because you said the heliocen-tric model is the true one, that’s what’s happening in the nature, andthe geocentric is what you see on the earth….

Olivia: That’s kind of how I feel, but I’ve been told I am wrong, so [bothlaugh]. I think it goes back to what we talked about in class. Geocentricis what the kids can see and when they’re younger that’s kind of whatyou have to (teach)…. Whereas (teaching) heliocentric when they areable to think more abstractly, you can move into “this is what’s reallyhappening.” I know it has to do with frames of reference, I just feel like… what’s really happening is the heliocentric.

Interviewer: Can you say more about what do you mean by really happening?Olivia: 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 ismoving. Have you ever had this kind of experience? But I am reallynot, so it’s not what’s really truly going on.

Interviewer: Now, when you are saying you are really not, what do you mean bythat?

Olivia: I’m not moving.Interviewer: You are not moving, but the other car,Olivia: The other car is, which makes, gives me the feeling that I’m moving.

It’s probably a terrible analogy.Interviewer: That’s a very good analogy, I think.



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 oppositethough. I am the one actually doing the moving. So watching the sunrise and set, yes that’s what I’m seeing, but it’s not what really what’sgoing on. What’s really going on is, I know it’s what I’m seeing, butit’s doing that because I’m the one doing the moving. (INTERVIEW,4-12-05)


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International Journal of Science Education Justifying ...mlebron/907016745.pdf · Introduction For I am not so enamored of my own opinions that I disregard what others may think of