Overview of information dealing with phases of the Moon

Teachers can use several resources when teaching about phases of the Moon, e.g. charts, models and textbooks, schools usually have more access to textbooks than to these other sources of information. Learning can be enhanced if these resources present accurate information. Furthermore, teaching can be easier when textbooks have all information needed to explain concepts, but might be hampered if textbooks provide less information than required to understand targeted concepts.

This chapter presents analysis of 28 diagrams illustrating phases of the Moon. These diagrams are taken from 24 books. All the diagrams are intended to help learners understand phases of the Moon. Thus, according to Duchastel‘s classification, these diagrams serve an explanatory role. In addition to diagrams, the books use the following types of information to explain phases of the Moon.

 Text: Some books provide textual information dealing with phases of the Moon. Text can

explain the cause of moon phases and describe the shape of the Moon during each phase. Furthermore, text can give information about the sequence of moon phases, and names given to these phases.

 Modelling activities: Some books recommend that learners use models to simulate changing

configurations of the components of the Earth-Moon-Sun system. These activities can give information about the cause and sequence of moon phases.

 Moon chart: Some books recommend that learners observe the Moon daily for a period of a

month, and record observations in a moon chart. These moon charts give information about the sequence of moon phases, but not about the cause of these phases.

Section 3.5.1 (page 73) discusses criteria used to arrange the books in order of complexity of diagrams (from 1 to 24). Simpler diagrams were considered to be those illustrating phases of the Moon only, while complex diagrams were considered to be those illustrating the Earth, the Sun, the Moon orbiting the Earth, and phases of the Moon. Table 6.1 illustrates the extent to which the books used each of the four information sources (diagrams, moon charts, modelling activities and text) when dealing with phases of the Moon.

Table 6.1 Types of information dealing with phases of the Moon in the 24 books

Book number Grade level Moon chart Modelling activity Text Diagram Sun Earth No. of moon

positions No. of moon phases 1 4      4 2 5      4 3 6      4 4 8      14 5 7      8 6 5      8 7 6      6 8 5      8 9 8      11 10 8      8 11 4      4 4 12 5      8 13 7      8 14 4      4 8 15 6      8 8 16 5      4 4 17 4      8 4 18 6      8 8 19 4      8 8 20 6      4 8 21 7      8 8 22 7      8 8 23 7      12 12 24 8      8 8

 Books 1 to 10 have diagrams illustrating the sequence of moon phases, but do not illustrate the Earth, the Sun, and the Moon orbiting Earth (the latter information would help to explain why the Moon appears to change shape as seen from the Earth). All these diagrams supplement

and/or complement other sources of information in the books. Nine of the books have textual information dealing with phases of the Moon; seven books prescribe modelling activities while eight recommend that learners complete a moon charts. Text and modelling activities can be used to explain the cause of moon phases while the diagrams and the moon charts illustrate the sequence of these phases.

 Book 11 has a diagram illustrating the Earth, the Moon in four positions around the Earth, and corresponding phases of the Moon. This diagram can be used to explain that the Moon orbits the Earth, and to further explain that the shape of the Moon appears to change as seen from the Earth. However, information in the diagram is not enough to explain the cause of moon phases since the Sun is not illustrated in the diagram. Martinez-Pena and Gil-Quilez (2001) found that the Sun and/or the Earth were missing in some diagrams. Thus, problems of missing information identified in this study corroborate a problem identified in a previous study. It is worthy to note that the book has textual information dealing with phases of the Moon. This text can be used to explain the cause of moon phases.

 Books 12 and 13 illustrate the Sun, the Earth, and phases of the Moon placed in eight positions around the Earth. The Moon as seen from space is not shown in the diagrams, and no explanation has been provided for this. Martinez-Pena and Gil-Quilez (2001) found a similar problem in diagrams illustrating phases of the Moon. That is, they found that some diagrams illustrating phases of the Moon did not illustrate the Moon as seen from space, and provided no explanation about this matter. Diagrams 12 and 13 can help learners to understand that the shape of the Moon appears to change as seen from Earth in the course of the Moon‘s orbits. Furthermore, these diagrams can help learners to understand the sequence of moon phases. However, information in the diagrams is not enough to explain the cause of moon phases. Each of the two books prescribes a modelling activity for the learners. In addition, Book 12 has textual information dealing with phases of the Moon. These other sources of information can help learners to understand why the Moon appears to change shape as seen from the Earth.

 Books 14, 16, 17 and 20 have diagrams illustrating the Sun, the Earth, the Moon orbiting the Earth, and phases of the Moon. However, each of these diagrams can help to explain only four phases of the Moon. Books 14 and 20 have diagrams illustrating the Moon in four positions around the Earth, and eight phases of the Moon. Book 16 has a diagram illustrating the Moon in four positions around the Earth, and corresponding phases of the Moon. Book 17 has a diagram illustrating the Moon in eight positions around the Earth and four phases of the Moon. All the four books have textual information dealing with phases of the Moon. In addition, Books 14 and 17 recommend that learners complete a Moon chart while Book 17 recommends a modelling activity for the learners. The text can be used to help learners understand the cause of all eight phases. In addition, the modelling activity in Book 17 can be used to help learners understand the cause of all Moon phases.

 Seven books (15, 18, 19, 21, 22, 23 and 24) have diagrams illustrating the Sun, the Earth, the Moon in at least eight positions around the Earth, and corresponding phases of the Moon. These diagrams can be used to explain all the eight phases of the Moon. Six of these books have textual information dealing with phases of the Moon. In addition, one of the six books

prescribes a modelling activity, while three books recommend that learners complete moon charts. Textual information and modelling activity can give additional information about the cause of moon phases. The diagram in a book that has no other information about phases of the Moon (Book 18) should illustrate all the concepts needed to understand moon phases. However, this is not the case because, for example, the names of moon phases are not presented in the diagram. This suggests that learning can be hampered if teachers do not provide additional information.

The curriculum requires learners in the Intermediate Phase to know the sequence of moon phases and to understand that these phases can be explained by the motion of the Moon relative to the Earth and the Sun. This curriculum requires Senior Phase learners to understand that motions of the Earth and the Moon can explain concepts such as phases of the Moon.

The discussion presented in this chapter shows that 13 books have simple diagrams mainly illustrating the sequence of moon phases, but occasionally giving information about the Moon‘s orbit around the Earth. Eight of these diagrams are in books designed for use in the Intermediate Phase while four are in books designed for use in the Senior Phase. All the 13 books present textual information and/or modelling activities to help learners understand the cause of moon phases. It appears that the diagrams are intended to supplement text and/or modelling activities by pictorially illustrating the sequence of moon phases.

Further analysis shows that four books have fairly complex diagrams that can explain four phases of the Moon while seven books have complex diagrams that can explain all the eight phases of the Moon. Understanding information illustrated in the complex diagrams requires learners to imagine looking at the Earth-Moon-Sun system from different perspectives, to mentally spin the Earth on its axis and to orbit the Moon around the Earth. These processes require learners to undertake processes at Piaget‘s formal operational level (Piaget‘s findings suggest that 12-year olds function at this level). Seven of the complex diagrams are in books designed for use in the Intermediate Phase while four are in books designed for use in the Senior Phase (Intermediate Phase learners are roughly 9-to-11 year old while senior phase learners are roughly 12-to-14 years old). According to Piaget‘s levels of development, complex diagrams are likely to be above the thinking ability of learners in the Intermediate Phase. One would expect publishers to use text and modelling activities to explain the cause of moon phases to these learners, and to provide simpler diagrams illustrating the sequence of these phases. The publishers would then use complex diagrams to explain the cause of moon phases for senior phase learners who operate at Piaget‘s formal operational level. However, this is not the case in the books surveyed in this study.

Analysis of Table 6.1 shows that 15 books deal with moon phases in the Intermediate Phase while nine deal with the topic in the Senior Phase. There appears to be no link between diagram complexity and grade level. That is, complex diagrams are found in books designed for lower grades (e.g. Diagram 19 in a Grade 4 book) and in books designed for senior grades (e.g. Diagram 24 in a Grade 8 book). In the same way, simpler diagrams are found in books designed for lower grades (e.g. Diagram 1 in a Grade 4 book) and in books designed for senior grades (e.g. Diagram 4 in a Grade 8 book). This observation corroborates Martinez-Pena and Gil-Quilez‘s (2001)

observation that the same diagram is found in books used by learners at different levels of education.

Analysis Diagrams 11 to 24 shows that artists illustrated the Earth‘s orbital path on the same plane as the Moon‘s orbital path. As a result, the Moon‘s orbit appears to be aligned with the ecliptic in these diagrams, so that New Moon erroneously occupies the position that results in a solar eclipse while Full Moon erroneously occupies the position that results in a lunar eclipse. Several researchers have made a similar observation, and proposed that this representation might enhance a common misconception in which people associate phases of the Moon‘s with the Earth‘s shadow (e.g. Dove, 2002; Engeström, 1991; Martinez-Pena & Gil-Quilez, 2001; Trundle et al., 2002). In reality, the Moon‘s orbit is tilted at 5o

to the plane of the Earth‘s orbit. However, it is difficult to illustrate the Earth and the Moon‘s orbits in different planes while keeping diagrams simple enough to be understood by school learners. The theory of models suggests that differences between diagrams and the Earth-Moon-Sun system conceptualized by scientists should be explained to diagram users. However, the books analyzed in this study provided no information explicating the differences. This means that teachers should help learners to see these differences (but this might be difficult if teachers do not understand the topic). If the differences are not pointed out, learners might consider diagrams as exact replicas of the system.

Further analysis shows that relative sizes and distances between the Earth, the Sun and the Moon are not maintained in Diagrams 11 to 24. As a result, the Earth-Moon-Sun system illustrated in the diagrams differs from the system as conceptualized by scientists. Some researchers have noted this problem in diagrams illustrating phases of the Moon (e.g. Dove, 2002; Engeström, 1991 and Subramaniam & Padalkar, 2009). Engeström argues that this representation fails to indicate that the probability of the Earth‘s shadow falling on the Moon is very small. Furthermore, Engeström (1991) and Subramaniam and Padalkar (2009) argue that this representation could enhance a view that the Earth‘s shadow causes phases of the Moon.