Content structure and analogies in introductory electricity chapters of physics schoolbooks

Introductory electricity is a difficult topic for most lower secondary students, especially the development of an adequate conceptualisation of voltage is seen as a major obstacle. A few instructional concepts concerning the teaching and learning of physics have been proven helpful when it comes to constructing conceptual knowledge. For example, the choice of content structure, meaningful elementarisation of basic concepts or adequate use of analogies. What has not been in the focus is how physics school textbooks consider these factors. In this article, we compare four widely used Austrian physics school textbooks concerning their content structure, definition of basic concepts and their use of analogies. Results show that the concept of ‘content structure diagrams’ is a useful tool to analyse schoolbooks. Although Austria has a compulsory syllabus, the four schoolbooks greatly differ in the amount of covered content and interlinking of concepts. However, a few common approaches regarding the sequencing of the concepts were identified and are reported in this article.


Introduction
Introductory electricity is one of the core elements of lower secondary physics classrooms all over the world. Students' understanding of the concepts current, voltage and resistance presents one of the main goals. However, even after instruction, students show typical misconceptions such as 'electric current is used up' or 'voltage is a quantity of the electric current'. Despites years of research on the teaching and learning of electricity (e.g. [1][2][3][4][5][6]), how physics schoolbooks concerning introductory electricity integrate these findings from educational research has fallen short.
Science teachers and researchers often think of schoolbooks as useful instructional resources that support teachers in planning and carrying out science lessons [7]. However, schoolbooks fulfil a much more important role when it comes to science education: To some extent, textbooks determine student's general perception of science [8].
Furthermore, it is undeniable that schoolbooks frequently act as a 'secret curriculum' and determine what is taught and learned about physics in these classrooms [9,10]. Banilower et al [11] for example reported that in the USA, more than 85% of middle and high school teachers rely on commercially published schoolbooks when it comes to preparing for and organising science lessons. In recent years, science education researchers have investigated various aspects of textbooks. For example aspects regarding the nature of science [7,9,12], misconceptions [13], readability [14], creativity [15] and diversity [16] or gender aspects [17]. However, studies regarding the content structure of physics schoolbooks have not been the focus of research, especially for the topic of introductory electricity.
In this article, we report the analysis of four widely used physics textbooks in Austria. Since introductory electricity is an integral part of the curriculum in year 7, we focused on this level.

Theoretical Framework
In this chapter, theoretical concepts relevant for the quality of schoolbooks are discussed: content structure, content structure diagrams and analogies in science education.

Content structure and content structure diagrams
Although there is a compulsory syllabus in Austria, teachers have a lot of freedom regarding the general structure as well as the sequencing of concepts covered in physics classes. This means that it is the teachers' responsibility to elementarise concepts, plan the sequencing of these concepts, select adequate models, analogies and scientific methods but also integrate aspects of the nature of science. Additionally, historical, technical and social aspects of the current topic should be considered. All of these aspects can be subsummised under the term 'content structure' [18][19][20].
However, there is no single 'content structure' for a specific topic, since it needs to be adapted in order to address students' needs to allow meaningful construction of knowledge in science classrooms. The model of educational reconstruction [21] offers one guideline to construct meaningful, evidence-based content structures. Following this model, it is necessary to analyse the scientific content structure with respect to its support for learning and inclusion of students' conceptions about it. As a tool for planning the content structure of lessons, Duit, Häußler and Kircher [18] proposed so called 'content structure diagrams'. These are flowcharts, in which the lesson content is split up into so-called 'meaningful units', which are subsequently linked using arrows. If the content of a meaningful unit is a logical prerequisite for understanding another, they are connected with an arrow. By using content structure diagrams, it is possible to represent the content of a lesson in a clear manner but also to evaluate physics lessons from a quality perspective.
After their introduction, the concept of content structure diagrams was also used in video studies to analyse the content structure of physics lessons in Germany [20]. Thereby, especially the interlinking of concepts during lessons supported students' gains in content knowledge. Since then, these findings have been replicated in other studies [19], different countries [22] and for different topics [23].
However, this method can easily be adapted to analyse physics textbooks in various categories. Doing so, instead of analysing single physics lessons, sections of textbooks are investigated, which is one focus of this article. Figure 1 shows a small part of a content structure diagram from one of the analysed schoolbooks. The text in the various meaningful units stems from the schoolbooks and was carefully translated into English.

Analogies
As part of the content structure, analogies play a crucial role when teaching physics, especially introductory electricity [24]. They are powerful tools for teaching abstract concepts [25] and they can be used to explore and develop insights into phenomena which are otherwise intangible [26].
Analogy stems from the ancient greek word 'ἀναλογία' and can loosely be translated into 'according to the ratio' or 'relatively'. An analogy entails a comparison between two phenomena, system or priniciples that share similarities [27,28]. The goal is to describe unknown and/or abstract concepts with the help of already known concepts. Gentner [29] distinguishes between the source domain (or base domain) and target domain of an analogy. Objects and relations between the objects in the target domain are compared with those of the source domain, as shown in figure 2. This means that the effective use of analogies in science education presupposes that at least one domain of the analogy needs to be familiar to students [30].
However, despite the potential of analogies, research has revealed learning obstacles for students' learning processes when analogies are used. For example, students could transfer misconceptions from the source to the target domain of the analogy or the analogy may produce misconceptions itself. For instance, this was shown for 'flat' water circuits (e.g. [31][32][33]). In this analogy, the electric circuit corresponds to pipes, the voltage supply to a pump and the electric current to the waterflow [34]. Furthermore, students could be overwhelmed with the transformation process between the target domain and source domain per se [32,35,36].
However, for introductory electricity, some analogies showed to support students' knowledge construction [1,30]. Hence, a second focus of this article is the analysis of used analogies in the introductory electricity chapters of common Austrian year 7 schoolbooks.

Focus of the study-research questions
We compared the introductory electricity sections of four widely used Austrian physics textbooks for year 7 [37][38][39][40]: 'Big Bang 3 (BB3)', 'Physik 3 (P3)', Physik verstehen 3 (PV3)' and 'Prisma Physik 3 (PP3)'. Thereby we focused on four different aspects: Content structure, interlinking of the content structure, definition of the concepts voltage, current and resistance and analogies used. Those aspects are reflected in the research questions: 1. How can the sequence of core concepts of the introductory electricity sections of the analysed physics schoolbooks be described? 2. How interlinked are the introductory electricity sections of these physics schoolbooks? 3. How are the key concepts voltage, current and resistance elementarised in the schoolbooks? To answer the first two research questions, the content structures of the textbooks were analysed using 'content structure diagrams' which can be compared to flow-diagrams. The resulting diagrams were subsequently analysed using different criteria, in our case the amount of covered content, interlinking of meaningful units and relative amount of 'island-units'.
To answer research questions three and four, the definitions of the concepts and the analogies used were analysed using the meaningful units which cover those aspects. After analysing the textbooks separately, a comparative analysis of the four textbooks was conducted.

Results
The content structures of the schoolbooks were analysed on a detailed (using meaningful units) and on a general level in order to get a better overview of the underlying sequencing of the concepts. First, results of the analysis of the general content structure are reported. The chapters of all four schoolbooks were double-coded reaching an accordance between .91 < κ < .94. Figure 3 shows an example for a sequencing structure of the schoolbook 'Big Bang 3'. The sequencing of the other four schoolbooks can be found in the supplementary materials (stacks.iop.org/ PhysEd/54/065023/mmedia).
The analysis of the sequencing of core concepts revealed that all four schoolbooks share some aspects while others are diverse. Three of the four schoolbooks (BB3, PV3, PP3) start the electricity chapter with introducing electric charges and forces related to the atomic model in order to explain electric current on a microscopic level. The schoolbook P3 also starts with electric charges and forces but chooses to introduce the atomic model only at a later part of the chapter, after the introduction of the basic quantities voltage, current and resistance.
Concerning the introduction of these basic quantities, three schoolbooks (BB3, P3, PP3) introduce them in the same order as shown in figure 4. Followed by Ohm's law and series/parallel circuits.
The fourth schoolbook PV3 chooses to introduce voltage first, followed by electric cur rent. Afterwards, batteries and accumulators as well as solar-, thermal-and piezoelectricity are covered, these concepts are not covered in the other schoolbooks. There, only then electric resistance, parallel-and series circuits and Ohm's law are introduced.
Next, the analysis of the detailed content structure diagrams using meaningful units is described. We double-coded 15% of all schoolbook-sections and found an accordance of κ = .74. These diagrams were further analysed, three different aspects of this analysis are reported in this article. The first aspect analysed concerns the amount of covered content in the different schoolbooks, a summary of the number of analysed pages and meaningful units is shown in table 1.
We operationalised the covered content as the amount of meaningful units and further distinguished between relative and absolute amount of covered content. The absolute amount As shown in figure 5, BB3 shows the largest relative amount of covered content, more than a standard deviation above the mean. In contrast, PP3 covers three meaningful units per page, which is a standard deviation below the mean. This result may also be due to the pages analysed, since in BB3 the introductory electricity chapter covers 16 pages while in PP3 it covers 33 pages. However, when comparing two schoolbooks with the same amount of covered pages (P3 and BB3) there is also a difference of 0.7 for the relative amount of covered content.
Next, we analysed the interlinking of meaningful units of the four schoolbooks. The interlinking of meaningful units is operationalised as the average amount of arrow connections per meaningful unit ( x = 1.6, sd = 0.3 units). Figure 6 shows the interlinking of the four analysed schoolbooks. While BB3 and PP3 show a relatively high amount of interlinking with about 1.8, P3 and PV3 shows a value of about 1.3.
The last aspect we analysed concerns the relative amount of 'island units' as shown in figure 7 ( x = 0.08, sd = 0.05 units). A meaningful unit counts as an island unit, when this unit is not logically linked to any other meaningful units.
A comparison between figures 6 and 7 shows that the books with a high interlinking also have a relative low amount of island-units. PV3 shows    the greatest relative amount of island-units with a value of 0.14.
To answer research question three and four, the elementarisations of the basic quantities voltage, current and resistance in the schoolbooks were analysed. For the flow of electricity, three schoolbooks use an analogy. The range of different analogies can be seen in table 2.
Regarding voltage, also three schoolbooks use an analogy. BB3 uses a height analogy and  'electrical height difference' synonymous to volt age, comparing it to a pumped-storage power plant. P3 uses the analogy of water pressure in a pipe, voltage is conceptualised as the 'cause of the flow of an electric current'. PP3 also uses a closed water circuit analogy. However, voltage is elementarised as a measure of 'how much the electrons are driven'. PV3 does not use any analogies, voltage is defined as 'the propulsion of the electrons i.e. the reason why electrons can move'.
Furthermore, we analysed the definitions of electrical resistance in the four schoolbooks. All four schoolbooks define it as a quantity of a mat erial to hinder the electrical current or the flow of electrons. In addition, PP3 distinguishes between the electrical resistance (as a phenomenon) and the value of the electrical resistance, which is defined by Ohm's law in this schoolbook. Although PV3 does not differentiate between these two aspects, it links the definition of electric resistance to Ohm's law.

Conclusion and outlook
Overall, we demonstrated that the concept of 'content structure diagrams' can be a meaningful tool to analyse physics schoolbooks.  The analysis shows that the content structures of the four analysed schoolbooks are similar regarding some aspects on a general level. As far as the sequence of concepts is concerned, three schoolbooks first introduce the atomic model of a conductor in order to explain electric current on a microscopic level, while the remaining textbook introduces this atomic model only after the introduction of the concepts voltage, current and resistance.
Another result worth mentioning is the fact that also three schoolbooks show the same sequence of concepts regarding the introduction of the concepts voltage, electric current, resistance and Ohm's law. Especially interesting is that these aspects are listed in the same order in the Austrian compulsory syllabus. One reason for the sequencing in the schoolbooks could be that although the content listed in the syllabus, which is supposed to be covered in physics classes in year 7, does not prescribe a specific sequence, the authors of the schoolbooks just used this sequencing. Additionally, it is interesting that although the national syllabus does not mention parallel or series circuits, all four schoolbooks cover this aspect.
Furthermore, the analysis shows that the four textbooks greatly differ in the amount of covered content, interlinking of meaningful units and also in the amount of island-units. For example, for the relative amount of covered content, meaning the average amount of meaningful units per page, the values lie between 1.28 und 5.63 meaningful units per page.
Regarding the introduction of the key concepts flow of electricity, electric current, volt age and electric resistance and parallel/series circuits, three of the four schoolbooks use analogies. Although the used analogies use quite different source domains ranging from 'flow of students' to 'airflow' and 'traffic flow', water related analogies dominate. This is especially interesting since the use of certain water-related analogies have proven to be counterproductive in supporting students' understanding of simple circuits [30]. Additionally, BB3 is the only schoolbook that uses the same analogy for the introduction of more than one of these key concepts.
These findings result in a few desiderata for future physics education research: First, further research is needed that links the content structure of schoolbooks, usage of schoolbooks by teachers in science classrooms and how this relates to students' learning. While this article aims to compare and analyse the content structure of different schoolbooks, research of this kind would answer the question whether the interlinking of concepts in schoolbooks at least partially translate to the interlinking of concepts in physics lessons. Second, more evidence is needed regarding the sequencing of the basic quantities voltage, current and resistance and whether these aspects influence student learning. For example, Burde and Wilhelm [30] argue that an introduction of voltage before electric current benefits student learning.