OBSTACLES TO THE DEVELOPMENT OF CONCEPTUAL UNDERSTANDING IN OBSERVATIONAL ASTRONOMY: THE CASE OF SPATIAL REASONING DIFFICULTIES ENCOUNTERED BY PRE-SERVICE TEACHERS Ch. Nicolaou, C. P. Constantinou, Learning in Physics Group, University of Cyprus, Cyprus 1. Introduction Learning in Physics is a complex and multidimensional enterprise which can be analyzed into a number of constituent components: the acquisition of experiences with natural phenomena provides the basis for the subsequent development of concepts; the mental representation of the structure of organization of scientific knowledge that is needed to avoid knowledge fragmentation and meaningless use of jargon comes with the development of epistemological awareness; scientific and reasoning skills provide the strategies and procedures for making operational use of one’s conceptual understanding in order to analyze and understand everyday phenomena but also to undertake critical evaluation of evidence in decision making situations. Finally, positive attitudes towards inquiry feed student motivation and safeguard sustainable engagement with the learning process. Traditionally, our educational systems fail to connect these components into a coherent learning paradigm for physical science. The Learning in Physics Group at the University of Cyprus conducts a coordinated program of research, curriculum development and teaching, which fundamentally relies on the premise that real learning can only emerge when all these components are promoted in unison. This article is part of an on-going research program, through which we aim to investigate the conceptual and reasoning difficulties that pre-service teachers encounter when guided to construct a model for the relative motion of the sun and the earth, which is capable of offering detailed explanation of the phenomenon of day and night. In this part of the project, we recorded the prevalent initial ideas of undergraduate students on the day-night cycle and then exposed them to the Astronomy by Sight module in Physics by Inquiry [1] We subsequently investigated weather the students had developed an appropriate model of the sun-earth relative motion that could account for the day-night cycle. 2. The day-night cycle On a daily basis, we all observe and feel the consequences of the day-night cycle [2] However, only a small percentage of us can explain in an appropriate manner how this happens, probably because of the complexity of the phenomenon itself or of the inherent difficulty in the process of modeling and understanding this phenomenon. • The apparent motion of the sun in the sky. In this approach, we assume that an observation record of the apparent daily motion of the sun in the sky is a pre-requisite to the construction of a model for the day-night cycle. Rise and set times, the altitude and the direction of the sun in the sky are important data which need to be included in the observation record. Such data can serve as a basis for eliciting students’ initial ideas and supporting the process of model construction through negotiated reformulation and evolution of those ideas. The same observational records can also serve as instruments for evaluating the validity of competing models. • An observation record of the apparent motion of the sun in the sky. Shadow plots can be used as convenient records of the apparent motion of the sun in the sky. From this we can infer the direction of the sun in the sky at any one instant. In order to construct a shadow plot we need a flat planar board with a nail to act as gnomon placed perpendicular to the plain of the board. This is the shadow plotting board. We place a sheet of paper on the board so that the nail sticks up roughly through the middle of the paper. We tape the paper onto the board so
•
that it cannot move and we note the height of the nail and the date on the paper. It is also important to state on the paper the locations of several nearby landmarks so that we can subsequently identify the orientation of the paper. During the day we record the shadow of the tip of the nail at intervals of approximately half an hour. The locus of the shadows is directly related to the apparent motion of the sun in the sky. Repeated daily observations of the phenomenon provide important additional information as to the time variation of the apparent motion of the sun. Appropriate accounts of the relative motion of the sun-earth system (two alternative, equivalent models) The information that arises from analysis of the shadow plots and the direct observations of the learner form the basis for the construction of two alternative, equivalent models, each of which is acceptable as an explanatory account of the mechanism of formation of the day-night cycle. In each model the system consists of two bodies: the sun and the earth. Model 1 According to this model, the day-night cycle results from a possible spin of the earth around its own axis at a rate of one complete revolution every 24 hours. In this model, the sun is stationary. Any one point on the earth’s surface faces the sun for 12 hours, the time period needed for half a revolution. During this time interval, this point has daylight. For the twelve hours remaining to complete one revolution, this point on the earth’s surface does no see the sun and experiences nighttime. At every instant in time, half the earth’s surface experiences day and the other hemisphere experiences night. Also at any instant, all points on the earth’s surface that fall along a great circle through the poles experience transition from light to dark or vise versa as they are rotating into the dark or the light, respectively. Model 2 According to this model, the day-night cycle is a result of the rotation of the sun around the earth once every 24 hours. In this model the earth is stationary at the center of the suns circular path. At any one instant in time, half of the earth’s spherical surface is oriented towards the sun and experiences day. The rest of the surface, which does not face the sun, experiences night. A point on the earth’s surface has 12 hours day and 12 hours night, the time periods that correspond to one half of the sun’s rotation.
It is important to note that both models can be modified in order to introduce a slant to the spinning axis in order to account for the deviation from equal 12 hour intervals for day and night. It also important to note that based only on observations of the sun-earth system, both models 1 and 2 can explain all of the observations (such as those recorded on a shadow plot) and therefore neither of can be rejected. The two models can also adequately explain all other the personal observations related to the day-night cycle. The equivalence of the two models only breaks down when a third (astronomical) object is entered into the system. The equivalence of the two models (in the context of the two-body system) and as a consequence, their equal validity in explaining shadow plot observations are major epistemological revelations for students in typical astronomy classes. This happens for a number of reasons: students often tend to judge the validity of a model with respect to its correspondence to what they or an expert knows and not in relation to whether it can account for their observations or not. Students also fail to differentiate between a model and a phenomenon; hence they find it difficult to accept that two models can be valid at the same time. Finally, students also encounter conceptual and reasoning difficulties (with respect to model equivalence and reversibility in relative motion, respectively) in their effort to understand the different mechanism underlying the two models.
3. Methodology •
Population The research was conducted at the University of Cyprus during the spring semester 2000. The data was collected in the context of a course on Physical Science in the Elementary Grades attended by 82 Students enrolled in the Primary Education Program at the University of Cyprus. The course used the Greek version of Physics by Inquiry with special emphasis on the module Observational Astronomy: The sun, the earth and the stars. Data was collected through a series of pre-tests administrated throughout the semester at the beginning of every section in the curriculum. • The pre-test In one of the pre-tests, given roughly half way through the semester, the students were asked to respond to the following question: “The sun rises roughly in the east and sets roughly in the west. Therefore, someone located inside a spaceship hovering over the North Pole will observe the earth spinning counter-clockwise. Do you agree or disagree with this statement? State clearly whether you think this statement is correct or not and explain your reasoning. You will find it helpful to include a diagram in your answer.” Only a small percentage of the students were able to identify that the statement is true and explain their reasoning. A typical correct response might include the following: Suppose that someone is positioned at location K on the earth’s surface. Consider also that s/he is looking towards the North Pole. If s/he points her/his right arm towards her/his right parallel to the ground, s/he will be pointing eastwards. On the other hand, if s/he points her/his left hand towards her/his left parallel to the ground, s/he will be pointing westwards. If the earth is spinning around its axis counterclockwise, when observed by another person over the North Pole, the person at location K will see the sun rise from an easterly direction in the morning and set in a westerly direction in the evening. : The face of a person as observed from the front N.P.: North Pole The drawing is not to scale
Top view diagram
earth Α N.P.
.Κ
SUN
D
Figure 1: The rotation of the earth around its axis as a mechanism for formation of the day-night cycle
An alternative way to explain this phenomenon is the following. According to figure 1, country A is located to the east of country D. Country D is located to the west of country K. So, if earth is spinning around it’s axis counterclockwise, when observed over the North Pole, the sun will first appear in the horizon of country A, then country K and then country D. Thus the sun is rising first in the easternmost of the three countries, as it is observed in real life. Since the pre-test was given prior to the intervention both of these responses were deemed appropriate and where evaluated as correct. 4. Data analysis Phenomenographic analysis was used to categorize the student responses. Subsequent qualitative analysis of the responses in each category revealed the models which students used in their attempts to
respond to the question and the difficulties they encountered in the process. The following 4 difficulties [3] were identified through phenomenographic analysis of the student’s responses: 1. Many students interpret the geographical directions as absolute locations or points in space. 2. Many students fail to distinguish the concepts clockwise and anti-clockwise1. 3. Many students orient the four directions erroneously with respect to each other. 4. Many students fail to appreciate the manual reversibility of the relative motion in the two equivalent models. Evidence for difficulty 3 usually appears in diagrammatic representations. One example is shown in figure 2 N
W
E S
Figure 2: Erroneous representation of the four geographical directions. 20% of the students in our sample encountered this difficulty.
We have evidence from other data that this difficulty is related to spatial reasoning. However, for the sake of conciseness we will not discuss it further. According to the fourth category, pre-service teachers do not have “reversibility” in their thinking when they present two alternative models for the day-night cycle. They often mention e.g. that it is the earth, and not the sun, that moves, and then, in the same response, proceed to include a diagram indicating motion of the sun around the earth. Other answers refer to simultaneous motion of the sun and the earth. Other students describe the day-night cycle as a result of the rotation of earth around the sun. The ability to reverse two alternative models is indirectly connected to spatial reasoning ability, mainly as far as spatial rotations in space are concerned. Category 1 and 2 will be analyzed in greater detail below. • Absolute interpretation of the four directions in space Students tent to interpret the four directions (north, south, east, west) as absolute locations in space. They believe that the directions north, south, east, west are permanent points, which are firmly located on the earth or in space. They do not conceive them as directions that change in respect to the position of the observer. According to student’s answers, 59.5% (44/74) of pre-service teachers encounter this difficulty. Figure 3 shows the diagram sketched by student 4. Student 4 clearly presents East and West as points to the left and right side of North Pole respectively. N E E
N
W
E: East W: West N: North Pole S: South Pole
W
earth S
Figure 3: Diagram sketched by student 4 to explain the rotation of earth around it’s axis.
1
In Greek language clockwise rotation is called a right sense rotation and anti-clockwise rotation a left sense rotation.
Student 4 obviously does not consider the position of the observer (points 1 or 2 in figure 4) as relevant to the model. So, if the observer is at point 1 or at point 2 and look towards the north pole, east will be for observer 1 at her/his right hand side and for observer 2 at her/his left hand side. Consequently, country X (figure 4), which is visible by both observers 1 and 2, is located to the east. And, to take this thinking further, if for observer1 the sun rises at 6 a.m. from the east and moves to the West, by noon, the sun will rise for observer 2 from the west! N 2 D
earth
B
E A
Χ W
1 S
Figure 4: Predictions based on the response of student 4. The letters N, S indicate the North and South Pole respectively. The letters E and W indicate easterly and westerly directions respectively.
According to student 15: “The earth is turning around itself during the day. The sun is eastward in the morning and westward in the evening. So, someone in a spaceship, which hovers over the North Pole, will observe the earth N spinning counterclockwise.” W
E S
Earth West-night
East-morning Figure 5: The diagram drawn by student 15 for the earth’s spin around it’s axis.
The response of student 15 leads us to the following thinking: in figure 6 it is morning for Cyprus (C). For another country X, or a point on the surface of the earth, which is positioned diametrically opposite to Cyprus, the sun is in the East. Simultaneously, according to figure 6, it is local noon for Cyprus and midnight for the other country (X). The diagram of the four directions (figure 5) reinforces the idea that student 15 interprets the four directions as absolute locations or as points in or out of the earth. N W Χ
E
C S
West-night
East-morning Figure 6: Predictions based on the answer of student 15.
The fact that students tent to interpret the four directions as absolute locations or points on or out of earth may occur because in Greek Language they are labeled as the four points of the horizon, a devious term as it implies four points on the earth or in space. This notion is probably reinforced by the educational system through the lack of distinction between the north and south directions and the North and South Pole as points on earth! The first conclusion of the study is that an understand that the four directions of the horizon are not points on or out of the earth, but directions in space, is an important pre-requisite to developing understanding of the day-night cycle. The identification of the four points of the horizon as points inside the earth or in space is of fundamental importance and its resolution should be considered as a prerequisite to the teaching of simple astronomical phenomena, such as the cycle of the day and night. • Differentiation of clockwise and anticlockwise rotation Students believe that the concepts clockwise and anticlockwise are absolute and are defined in respect to right and left. Specifically, they cannot distinguish between rotational relations and relations due to the perspective from the locations of two objects. According to the answers of the students in the pre-test, 39.2% (29/74) of preservice teachers encounter this difficulty. In the Greek language, the clockwise rotation has the meaning of a right sense rotation and anticlockwise rotation the meaning of a left sense rotation. According to student 15 (figure 5): “The earth is turning around itself during the day. The sun is eastward in the morning and westward in the evening. So someone in a spaceship, which hovers over the North Pole, will observe the earth spinning counterclockwise.” Student 15 draws an arrow, which describes a clockwise rotation. However, s/he mentions that the rotation is anticlockwise. Student 31 wrote: «The sun is stationary. I am standing on a point on the surface of the earth and I am moving to the left (not me but earth), the sun will be on my right hand side, that is, westward from the place I am standing. So, the sun rises in the east and sets in the west because of the earth’s anticlockwise rotation. » Student 31 believes that an anticlockwise rotation is one in which an object (in this case the earth) moves towards left. According to this opinion and based on figure 7, moving towards the left is caused both by a clockwise and an anticlockwise spinning of the earth.
Left
Earth
Right (when I look at the sheet)
Figure 7: Predictions based on the response of student 31.
Student 48 states the following: «I agree with the above statement. The earth spins counterclockwise. This is clear from the following diagram. The earth spins counterclockwise so that the sun sets due west. » Student 48 also drew the following sketch (figure 8). The analysis of the explanation of student 48 showed that s/he encounters the two difficulties, which are analyzed in the present article.
N
Earth
W
E S Sun is due east Figure 8: Diagram of student 48 of the spinning of earth around itself.
According to figure 8, the student believes that the position of the sun in space is east. So, s/he thinks that east is a point in space. S/he does not state the position of the observer, for whom at this specific moment, the sun is due east. Moreover, while in figure 8 the arrows indicate a clockwise rotation, at her/his explanation, s/he refers to an anticlockwise rotation. According to the data of pre-test 3 many students cannot distinguish between clockwise and anticlockwise rotation. This happens probably because of the distinctiveness of Greek language. Clockwise in Greek is «δεξιόστροφα» and is a compound word. The word «δεξιά» means “right” and the word «στροφή» means “rotation”. Similarly, anticlockwise in Greek is «αριστερόστροφα» and is a compound word. The word «αριστερά» means “left” and the word «στροφή» means “rotation”. So in Greek the concepts clockwise and anticlockwise are conventional. Often, students do not understand those concepts and even though they refer to a clockwise rotation they draw an anticlockwise rotation and vise versa. There are also students who interpret clockwise rotation of a body in an absolute way. They believe that a rotation is always only counterclockwise or only clockwise despite of the position of the observer.The difficulty has to do with the fact that students think that a body, which turns left is spinning counterclockwise and a second one, which turns right is spinning clockwise. Moreover, students tent to define the two concepts in connection to front and in confrontation to backwards. Someone spins clockwise or counterclockwise if he/she turns from his/her nose to his/her right or left shoulder, respectively. They do not trace differences in description of a motion for different positions of the observers and cannot accept the fact that a clockwise rotation as it is seen when an observer is over a spinning body is counterclockwise as viewed by an observer under the body. 5. Developmental and structural analysis of the curriculum material The Learning in Physics Group at the University of Cyprus is revising the program Physics by Inquiry so that it responds to the conditions and restrains of the Greek Educational System. The underlying aim is to safeguard the development of conceptual understanding, thinking and other abilities relative to the process of learning in physical science. Physics by Inquiry contains narrative, experiments and exercises, and supplementary problems at the end of each module. Through in-depth study of simple physical systems and their interactions, students gain direct experience with the process of science. Starting from their own observations, they develop basic physical concepts, use and interpret different forms of scientific representations, and construct explanatory models with predictive capability. Physics by Inquiry is explicitly designed to develop scientific reasoning skills and to provide practice in relating scientific concepts, representations, and models to real world phenomena. The aim of the module Astronomy by Sight, according to McDermott (1996) [4] is for students to make observations of the motion of the sun, the moon, and the stars in the sky, to identify patterns in the changes that occur during the course of a day and a month and to develop models that enable them to determine the present, past and future appearance of the sky. Physics by Inquiry: Astronomy by Sight is based on a sequence of activities which aim to guide students to overcome the difficulties identified through research, so that real conceptual understanding is achieved for the majority of students. Below we will present a brief structural analysis of the module Observational Astronomy (sections 1-5).
Section 1
Section 1 starts with the record of student’s observations for the apparent motion of the sun in the sky during the day using newly constructed shadow plots [5]. Prior to their first shadow plot, students make predictions of how it will look before they construct it. Then, they make and study their plot in comparison with their predictions. Based on the shadow plot, they act out and represent the apparent motion of the sun in the sky during the day. At the end students develop an operational definition[6] of the concept “local noon” Diagram of the epistemological structure of the curriculum material
Section 1 «Sun Shadows»
Shadow Plot
Apparent Motion of the Sun
Section 2 «Observing Changes in the Sky»
Measurements of the sun’s altitude
Consideration: the sun rays reach earth parallel
Section 3 «The Size and Shape of the Earth»
The Shape of Earth Estimation of the Circumference of the EarthEratosthenis’ Method
Measurement of the sun’s azimuth Section 4 «Daily Motion of the Sun» Scientific Model of the Motion of the Earth and the Sun
Record of Moon Observations Patterns of Moon Shapes Section 5 «Phases of the Moon» Relative positions of Sun-Moon according to the Phase of the Moon. Scientific Model of Motion of the motion in the System of Earth-Moon-Sun. Figure 9 Brief structural analysis of Physics by Inquiry: Observational Astronomy, which was designed to guide students to overcome specific difficulties.
Section 2
Section 2 begins with directions for students to measure the altitude of an object with the “fist-overfist” process [7], they develop operational definitions of the concepts “horizontal”, “vertical” and “altitude of an object” and they take measurements of the altitude for different objects. Then students estimate the altitude of the sun for different moments in time during a day using their shadow plots and they come to the conclusion that sunrays reach earth parallel. Finally, discuss what they know about the moon distinguish between their observations, for which they have direct evidence and those facts they know because they were told them or read them. This is done so that they recognize the degree of confidence that our own observations give us and the critical attitude we must have towards anything that is offered as given knowledge. Section 3
The third section has to do with the shape of earth. Firstly, students discuss the disagreement between the measurement of the altitude of a mountain peak by a person who assumes a flat earth and the estimation of its altitude using data from a map. Then they try to explain why some celestial bodies are visible from north and not from south regions of the earth. Based on these observations and exercises, they come to the conclusion that earth’s surface is not flat, but curved. Then they estimate the circumference of the earth with Eratosthenis’ Method and assuming a spherical earth. Section 4
Section 4 starts with the comparison of two or more shadow plots (spanning a period of 3-4 weeks) as far as the general characteristics are concerned with special emphasis on the shortest shadow. Then students define the “azimuth” [8] and estimate the azimuth of several objects. The same process is used for the estimation of the azimuth of the sun through a shadow plot for different times. Then students construct a graph of the azimuth versus time of day, and they discuss the form of the graph and how it represents the observations. Consequently, students construct the scientific model of the motion of sun and the earth, based on which they explain their observations as recorded by the first shadow plot. Finally, they use a compass [9] to find the magnetic declination [10]. Students discover through an exercise two ways of geographical orientation (use of compass and through a shadow plot). Section 5
Before section 5, students observe the Moon for a month and they record their observations in a relevant sheet. At the beginning section 5 students group and order chronologically their observations on a “Moon Observation Summary Chart (MOSC) [11]. Based on MOSC, students look for patterns in the behavior of the moon, which repeat in a period of a day, week or month, and record the phase/form of the moon for this pattern during the synodic period [12]. Then, based on their observations, they trace the position of the moon in relation to the position of the sun, and the direction of the moon for different moments. Consequently, they construct a scientific model for the relevant motion of the bodies in the system sun-earth-moon, based on which they can explain the cycle of moon phases. Students study the sun-moon angle during a synodic period of the moon and estimate the time at which the moon rise and set for its different phases. Finally, they discuss the relative distances between sun, moon and earth and the possible consequences which derive when we alter them in the scientific model we constructed. At the end of the section, students try to construct alternative model that explain their observations. 6. Discussion A basic conclusion deriving from this research is the existence of reasoning difficulties, which complicate student’s efforts to construct understanding in Astronomy and Physics. There are certain common difficulties that many students encounter that should be made explicit and where appropriate confronted in a learning environment so that conceptual understanding is achieved. Very often reasoning difficulties are not identified either by the students or by the teachers and therefore remain in the conceptual ecology of the learners and affect or even determine the learning process. The design of
curriculum should include the development of strategies and activities that encourage students to express their opinion. Through the expression of students opinion difficulties come up and enable learners and teachers to discuss them openly. Pre-tests like the one presented in this article can contribute much as instruments of revealing thinking and other difficulties. On the other hand, the results of this research indicate the importance of integrated development of conceptual understanding and scientific reasoning as well as other abilities closely connected to learning in physical science. Moreover, in physical science there is a need to emphasize more the development of connections between the formal information, the epistemological structure of the subject, the means of representation of the information and the real phenomena. Physics by Inquiry is a program in which students themselves make observations and use them in combination with specific reasoning patterns and concepts that they formulate to construct conceptual models with predictive capability. The models are gradually refined through application and further observations of related but more complex systems. As a result of this process students emerge with experientially developed intuitions of inquiry as the process of science, which is constructed according to clear epistemological criteria. In contrast to traditional instruction, the method of inquiry does not emphasize on the transmission of information, which if preoccupied, stay functionally unutilized for the explanation of everyday phenomena and their application in decision making. References [1] L. C. MacDermott and the Physics Education Group, Physics by Inquiry, J. Willey, New York, (1996). [2] M. Summers, J. Mant, A survey of British primary school teachers’ understanding of the Earth’s place in the universe, Educational Research, 37, (1), (1995), 3 – 19. A. Lightman, Ph. Sadler, The earth is round? Who are you kidding?, Science and Children, (1988), 24 – 26. St. Vosniadou, Designing curricula for conceptual restructuring: Lessons from the study of knowledge acquisition in astronomy, J. Curriculum Studies, 23, (3), (1991), 219 – 237. St. Vosniadou, Mental models of the earth: a study of conceptual change in childhood, Cognitive Psychology, 24, (1992), 535 – 585. J. G. Sharp, R. Bowker and J. Merrick, Primary astronomy: conceptual change and learning in three 10 – 11 year olds, Research in Education, 57, (1997), 67 – 83. [3] L. C. McDermott, Millikan Lecture 1990: What we teach and what is learned – Closing the gap. American Journal of Physics, 59 (4), (1991), 301-315. [4] C. McDermott and the Physics Education Group, Physics by Inquiry, J. Wiley, New York, (1996). [5] Shadow plot is the diagram, which is created by the changing of the track of the top of the shadow of an object caused by the sun during the day. [6] Operational definition is a set of instructions which allow anyone to measure the specific dimension, identify an example of the concept or alter it for others. An operational definition cannot be misunderstood. [7] Fist over fist process is a method of measuring angles in space. The method is based on counting of our fist in degrees, having our arm stretched in front of us. [8] Azimuth of an object is the angle measured clockwise from north, as viewed for above) to the object. [9] Compass is the scientific instrument with which we orient, as it points always toward magnetic North. [10] Magnetic declination is the angle between magnetic north and the true north. [11] Moon Observation Summary Chart (MOSC) is a chart on which we record daily, for a specific period, moon observations. [12] Synodic period of the moon is the cycle from the new moon, through the full moon and back to the new moon in about 30 days. Local noon is the time of the day for which the sun is located at its highest position in the sky.
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