Subject didactic knowledge (SDK). A heuristic model based on a theory of functional and personal facets of subject-matter education (SME) and its empirical implications

ABSTRACT

Empirical research on teachers’ professional knowledge is mostly conducted worldwide with reference to the construct ‘pedagogical content knowledge’ (PCK) introduced by Lee S. Shulman. In the ‘Consensus Model’ (CM) and the ‘Refined Consensus Model’ (RCM), PCK was further developed and differentiated. Nevertheless, neither PCK nor CM and RCM adequately capture the complexity of teachers’ professional knowledge. Thus, educational-theoretical foundations and goals of subject-specific teaching and learning are not sufficiently taken into account. The same applies to personal, emotional and reflective goals of subject-matter education. Against this background, we propose a more comprehensive model, which we call “subject-specific didactic knowledge” (SDK) and which is based on the distinction between two complementary basic forms of subject-specific education (SME): a functional form of SME in the tradition of PCK and literacy (OECD / PISA) and a personal form of SME, which is characterized by the German educational tradition (sensu Wilhelm von Humboldt) and the US-American philosophy of education (sensu George Herbert Mead and John Dewey). We illustrate the practical implications of this approach for subject-matter education and its investigation, using examples from empirical research in curricular based models of teaching and learning in Germany and other countries.

KEYWORDS:

• Subject didactics
• general subject didactics
• pedagogical content knowledge (PCK)
• subject didactic knowledge (SDK)
• PISA and the literacy concept
• subject-matter education
• biology didactics
• German language and literature didactics
• functional and personal education
• empirical research

1.

What kind of knowledge do teachers need in order to teach successfully? Lee S. Shulman (1986, 1987, 2015) answered this question in a new way for the education system in the USA when, in the 1980s, he brought the long-neglected dimension of subject knowledge within the action knowledge of teachers into the focus of curriculum and education research, proposing the construct of ‘pedagogical content knowledge’ (PCK). However, the PCK construct, which has sometimes been translated as ‘subject didactic knowledge’ (SDK) when referenced in European studies of teacher professionalism, does not adequately describe the complexity of teachers’ professional knowledge. Moreover, it is based on a limited concept of education which also determines the work of the OECD and likewise impacts on the development of curricular concepts. Our central concern is to show how these two conceptual problems of PCK (or a limited understanding of SDK as a synonym of PCK) can be overcome. To do this, we proceed in four steps:

1. This article will first outline essential elements of the PCK construct and reflect on further developments in the current research discourse (cf. Neumann et al., 2018), whereby the ‘Consensus Model’ (CM) and the ‘Refined Consensus Model’ (RCM) (Carlson & Daehler, 2019) play a central role. We also briefly address the equation of PCK with a shortened understanding of ‘subject didactic knowledge’ (SDK), which, as we will show, can be observed in some research approaches in Europe.

2. Against this background, we supplement both the PCK model, which traces back to the American curriculum tradition and has a major influence on curricula worldwide, and the shortened SDK model with subject-specific perspectives from European subject didactics.¹ This allows an extended model of Subject Didactic Knowledge to be developed (Frederking & Bayrhuber, 2020; Frederking, 2022a), in which three levels of SDK are distinguished.

3. In this step we illustrate curricular and practical implications of the extended SDK model in the light of two complementary traditions of subject-based education,² a functional and a personal form. It will be shown how the functional approaches in the sense of PCK and the literacy concept of the OECD can be supplemented by personal forms of subject-matter education along the lines of Humboldt (1793), Mead (1911) and Dewey (1938), with fruitful implications for teaching and curricula.

4. In the final part of the article, possibilities for empirical research on functional and personal subject-matter education are illustrated using examples from science education and first-language education and reflected on in terms of their yield for modelling (design/development) as well as for teacher professional research on the basis of the SDK model. The fact that personal subject-matter education is empirically accessible makes it interesting not only for the debates of teacher professional research, but also for questions of curriculum development.

1. Teacher professional research in the tradition of ‘pedagogical content knowledge‘ (PCK)

In teacher professional research in the PCK tradition, the focus is on the relationship between teachers’ professional knowledge, teaching practice and students’ learning outcomes. In the following, the significance of the PCK model and its current developments will be described (1.1). On this base, we will discuss desiderata and starting points for further development feeding into curriculum and theory of education identified (1.2).

1.1. Pedagogical content knowledge (PCK) and its international development

Pedagogical content knowledge (PCK) was defined by Lee S. Shulman in the 1980s as a central element of professional teacher knowledge (Shulman, 1987, p. 8). In his understanding, PCK is a ‘blending of content and pedagogy’ and a ‘special amalgam of content and pedagogy’ (ibid., p. 8). PCK is guided by the question ‘of how particular topics, problems, or issues are organized, represented, and adapted to the diverse interests and abilities of learners, and presented for instruction’ (ibid., p. 8). PCK thus integrates knowledge about the subject content and pedagogical skills of teachers. It focuses on the knowledge elements of teachers, i.e. on the ‘province of teachers, their own special form of professional understanding’ (ibid., p. 8)—derived from ‘wisdom of practice’ (Shulman, 1986, p. 9). Subject content is to be prepared in such a way that it is interesting and motivating for pupils. The focus is therefore on ‘the ways of representing and formulating the subject that make it comprehensible to others’ (ibid., p. 9).

The concept of pedagogical content knowledge (PCK) is well received worldwide (Cooper & Driel, 2019). International conferences and publications developing on the first elaboration of PCK reflect its unbroken relevance (cf. e.g. Deng, 2018). Two international PCK summits with globally operating researchers, which took place in 2012 and 2015 and dealt with re-examiningand repositioning of pedagogical content knowledge in science education (cf. Berry et al., 2015; Hume et al., 2019), illustrate the extraordinary topicality that Shulman’s PCK approach continues to enjoy throughout the world. The literature overview ‘Towards a Consensus Model’ by Chan and Hume (2019, pp. 3–76) shows impressively how far the PCK model has been used in empirical teaching profession research worldwide. Of 1261 articles in 14 ‘peer-reviewed high-ranking ISI-listed journals in the field of science education and teacher education’, published until the end of 2017, 99 articles have been evaluated in order to examine the reception, application and further development of the PCK approach (Chan & Hume, 2019). Without a doubt, these later studies on teacher knowledge following on from PCK are relevant for a deeper understanding of subject-specific aspects of teaching (Tepner & Sumfleth, 2019; Wilson et al., 2019).

Neumann et al. (2018) outline the development of Shulman’s model, in line with van Driel et al. (2014), who have shown that PCK has been addressed in two different lines of research. Under the transformative perspective—following Magnusson et al. (1999) - PCK is considered ‘as the way in which teachers conceptualize science teaching, emphasizing the personal nature of teachers’ orientations’ (Neumann et al., 2018, p. 5). Under the integrative perspective (Hashweh, 2005), which is typical for studies in German-speaking countries, ‘teachers draw on knowledge bases in constructing PCK for classroom use’ (p. 5). Neumann et al. (2018) relate this distinction to the characterization of PCK as ‘knowledge-in-action’ and ‘knowledge-on-action’ (Park & Oliver, 2008) and ‘knowledge of teachers’ and the ‘knowledge for teachers’ (van Driel et al., 2014), respectively.

The Consensus Model of PCK (Gess-Newsome, 2015) brings together the two lines of research. In this model, PCK (personal PCK and PCK & skills) functions as a component of teacher professional knowledge, in the sense of knowledge of teachers. The other components are knowledge for teachers. This includes ‘teacher professional knowledge bases’ (TPKB). TPKB ‘is generic (non content-specific) and normative’ (Gess-Newsome, 2015, p. 32) and includes ‘curricular knowledge’. On the other hand, knowledge of teachers includes ‘topic-specific professional knowledge’ (TSPK), especially about instructional strategies that enable effective learning. In practical teaching, TSPK then becomes PCK of teachers.

The experiences with the Consensus Model of PCK in science education led to an update of the model. At a summit in 2016, the ‘Refined Consensus Model in Science Education (RCM)’ (Carlson & Daehler, 2019) was developed. It was intended to be ‘more useful for guiding a wide variety of research studies that might develop a deeper understanding of teachers’ PCK in science and the implications for teacher education, curriculum, and policy’ (ibid., p. 79). In particular, the term PCK was further differentiated:

A key feature of this model is the identification of three distinct realms of PCK—collective PCK (cPCK), personal PCK (pPCK), and enacted PCK (ePCK)—which describe the specialized professional knowledge held by multiple educators in a field, to the personalized professional knowledge held by an individual teacher in science, and the unique subset of knowledge that a teacher draws on to engage in pedagogical reasoning during the planning of, teaching of, and reflecting on a lesson. (ibid., p. 77)

According to Carlson & Daehler (ibid., p. 82), these differentiations describe “the complex layers of knowledge and experiences that shape and inform teachers’ practice and mediate student outcome.

1.2. Limitations of the PCK model and its later versions CM and RCM

Despite the extraordinary merits of the PCK approach and its further development in the RCM model, we suggest that critical questioning is still necessary on at least two counts, namely in terms of the relationship with the reference disciplines for subject-matter education (1) and with respect to the educational theoretical focus (2) of the approach.

(1) Neither PCK nor RCM specifically reference or comprehensively reflect the respective sciences in which their concepts are grounded or in whose ambit they are located. Following Shulman, PCK is the ‘special amalgam of content and pedagogy’ (Shulman, 1987, p. 8) on the level of personal knowledge of teachers. Thirty years later Shulman called PCK a ‘missing “planet” between content and pedagogy’ (Shulman, 2015, p. 6) and added: ‘I look back on the speculations regarding PCK as similar to the way in which astronomers discovered the planet Neptune’ (ibid.). This metaphor may be apposite for the educational debate in the United States, but outside the USA it does not really hold up, at least not as far as the German- and French-speaking countries and Scandinavia are concerned. Here the ‘missing planet’ had been spotted as early as the 1960s, so well before the advent of PCK, in the shape of subject didactics, the sciences of subject-matter teaching and learning (KVFF Konferenz der Vorsitzenden Fachdidaktischer Fachgesellschaften, 1998, p. 1), anchored in their respective disciplines. Kansanen (2009) describes a much more comprehensive approach of subject didactics in comparison with PCK. Against this background, the equation of PCK and SDK, first observed in psychological research in Germany, proves to be unsatisfactory.

The Refined Consensus Model in Science Education (RCM) (Carlson & Daehler, 2019), although a later development, is also unsatisfactory in its science theory location of PCK. Moreover, it separates PCK from the level of teachers’ professional knowledge base. In the model of Gess-Newsome (2015), PCK is simply part of topic-specific professional knowledge at the level of classroom practice.

Given these limitations and the fact that subject didactics in parts of Europe are distinct academic disciplines with a wealth of experience, we suggest that a far more comprehensive model emerges when the European perspective is taken into account and pedagogical content knowledge (PCK) is integrated into an extended model of subject didactic knowledge (SDK). We will discuss this in more detail in the sections below.

(2) What are the guiding educational goals when teachers apply their knowledge of subject-related teaching and learning in the PCK and RCM models? Shulman himself leaves the aims of teaching and learning in his PCK model relatively vague. The applications of PCK in contemporary empirical teacher professional research, however, are much clearer. A widely known example is the COACTIV study (= Cognitive Activation in the Classroom), a supplementary study to the German PISA surveys of 2003/04 with 198 teachers, investigating teachers’ professional knowledge, cognitively activating mathematics instruction and the development of mathematical competence (Baumert & Kunter, 2006, 2011; Baumert et al., 2010). In these explanations, the interconnection between PCK and the literacy or competence concept of the OECD is very clear. As seen from the perspective of COACTIV, PCK ‘forms a distinct body of instruction- and student-related mathematical knowledge and skills—the knowledge that makes mathematics accessible to students’ (ibid.). In addition: “An important feature of this study [COACTIV] was its embedding in the 2003 PISA student assessment, which made it possible to investigate effects of teacher competence on instructional quality and student-related outcomes“ (Löwen et al., 2013, p. 79).

The representatives of the RCM approach also leave no doubt about the fundamental connection between their approach and the literacy or competence concept: With regard to ‘a framework for future PCK research’ (Wilson et al., 2019, p. 293) the authors stated that ‘scientific literacy, and reasoning’ (ibid.) are important aspects.

With this combination of PCK or RCM on the one hand and the literacy or competence concept on the other hand, empirical research of extraordinary quality has emerged, yielding fundamental insights in the field of teacher professional research. However, the question arises whether the aims associated with the literacy construct are comprehensive enough to capture the totality of teachers’ knowledge required for successful professional teaching and learning. This is especially true if one assumes, for example, that the targets which are typical for the educational tradition in the German-speaking regions (after Humboldt) and in the American education tradition (after Dewey and Mead) are not included: enabling learners to reflect the relevance of subject-matter issues for their own existence, personal development and identity, to consider subject-related objects in their emotional impact and to develop reflexive attitudes in this regard. In line with Deng (2022) and his thesis of ”teaching as unlocking the educational potential of content” (ibid., p. 610) in the context of ‘Bildung-centered Didaktik’ (ibid., p. 606) we aim to show that these are also important elements of teacher professional knowledge, based on subject didactic research in the sense of ‘Fachdidaktik’. They are rooted in an educational and developmental tradition which was influential before PISA, both in Europe and the USA, and to some extent still is. Both traditions complement each other, not only in theoretical terms, as we will show in section 3, but also in quite practical issues of subject-matter teaching and learning, as we will illustrate in section 4, drawing on a number of empirical studies. Building on this, we suggest a more comprehensive extended model of ‘Subject Didactic Knowledge’ (SDK) (Frederking & Bayrhuber, 2020). We believe that this extended heuristic model of SDK, outlined in section 2 using a tripartite typology, is suitable for overcoming the limitations of the PCK approach and its later elaboration in RCM.

2. A typology of subject didactic knowledge within the scope of general subject didactics

What is subject didactic knowledge? The construct was first investigated in studies on the professional knowledge of teachers in German-speaking countries (Baumert & Kunter, 2006, 2011; Blömeke, 2011; Blömeke et al., 2011; Tepner et al., 2012). Subject-matter didactic knowledge was equated here with PCK. In a study on the professional knowledge of maths teachers (Baumert & Kunter, 2006, 2011), subject-matter didactic knowledge was defined as ‘knowledge about explaining and representing’, ‘knowledge about typical student errors and difficulties’ and ‘knowledge about multiple solution potentials of mathematical tasks’ (Krauss et al., 2011, p. 138). These elements of teacher knowledge focussed on in PCK undoubtedly belong to subject-didactic knowledge (SDK) and can also be successfully investigated in their own right, as the research approaches to SDK in the tradition of PCK outlined in Chapter 1 make clear. However, they by no means define SDK comprehensively. Levels or types of SDK are not sufficiently differentiated, a desideratum we pick up on in this chapter, and personal educational goals, which are of particular importance for curricula, are excluded, which we will show in Chapter 3.

In order to understand the term ‘subject didactic knowledge’ (SDK) in its current and comprehensive meaning, it is first necessary to explain what is understood by subject didactics in Europe. Subject didactics are ‘sciences of teaching and learning in the subjects’ (KVFF Konferenz der Vorsitzenden Fachdidaktischer Fachgesellschaften, 1998, p. 1), which have established themselves as academic disciplines at universities in Germany, Austria, Switzerland, France, Sweden, Finland and other European countries since the 1960s (ibid.). In other words: Long before the theory of PCK was developed academic disciplines existed, called subject didactics, which had the aim to gain ‘subject didactic knowledge’ (SDK). How do subject didactics generate this knowledge?³ To answer this question, three types of ‘subject didactic knowledge’ (SDK) must be distinguished (cf. also Frederking & Bayrhuber, 2017, 2020; cf. Figure 1)⁴:

Figure 1. Three types of subject didactic knowledge (SDK).

2.1. SDK type 1: subject didactic knowledge as teachers’ experience-based individual knowledge channeled into everyday theories and theories of practice

Teachers develop theories about successful practice of subject-related teaching and learning by applying what they have learned at university—in their academic disciplines as well as from programmes on subject didactics and pedagogy—and what they have experienced in their own teaching. The result is practice-driven and theory-supported ‘action knowledge’ for subject didactics, based on individual experience. The ’Wisdom of Practice‘ (Shulman, 1986, p. 8) which Shulman processed in the PCK model is located on this level. Type 1 subject didactic knowledge corresponds with ‘knowledge-on-action’ (Park and Oliver (2008) and ‘knowledge of teachers’ (van Driel et al., 2014). It also corresponds with personal PCK (pPCK) in the Refined Consensus Model of PCK in science education.

A teacher’s pPCK is the cumulative and dynamic pedagogical content knowledge and skills of an individual teacher that reflects the teacher’s own teaching and learning experiences, along with the contributions of others, such as teaching colleagues, educational researchers, scientists, and other content specialists in the form of professional exchanges, journal articles, social media, coursework, and professional learning experiences, as well as contributions from all students the teacher has ever taught. (Carlson & Daehler, 2019, p. 85)

2.2. SDK type 2: subject didactic knowledge as research-based disciplinary knowledge at the level of scientific subject didactics

The experience-based subject didactic knowledge of teachers (SDK Type 1) is to be distinguished from the subject didactic knowledge generated by subject didactics as sciences of teaching and learning specific subjects (SDK Type 2). This kind of subject didactic knowledge is created by the European subject didactics at an academic level by scientific means and committed to the criteria of generalizability and verifiability. Subject didactic knowledge of type 2 corresponds roughly to the ‘knowledge for teachers’ (van Driel et al., 2014), which PCK focused on, but it is more. Type 2 subject didactic knowledge comprises the entirety of the theoretically and empirically gained scientific knowledge that a subject didactic discipline generates through basic and application-oriented research. The focus here is on, for example, subject-related teaching and learning processes, subject-related student cognitions and self-concepts of teachers and learners, as well as successful modelling (design/development) to promote acquisition of subject-matter content, goals and methods of gaining knowledge, subject-related research methods for recording teaching activities, research desiderata, etc. In other words: subject didactic knowledge of type 2 covers comprehensively the results of subject didactic research which deals with ‘the transformation of discipline-based subject matter (Fachwissen) into a school subject (Schulfach)’ whereby ‘the totality of the instructional process is of interest’ (Kansanen, 2009, p. 36). Type 2 subject didactic knowledge therefore provides a sound scientific basis for the design of teaching for specific learning objects in different contexts as well as associated recommendations for teacher action (cf. topic-specific professional knowledge in the Consensus Model of PCK; Gess-Newsome, 2015, p. 32). It will also inform sub-areas of a school subject (such as physiology, ecology, evolution, etc. in biology) and feed into revisions of subject curricula.

2.3. SDK type 3: subject didactic knowledge as transdisciplinary, meta-scientific knowledge at the level of general subject didactics

While types 1 and 2 of subject didactic knowledge have a subject-specific focus, subject didactic knowledge of type 3 is located at a superordinate or more generic scientific level. It is the product of transdisciplinary research in subject didactics at the level of general subject didactics (Bayrhuber et al., 2017; Frederking, 2017; Rothgangel, 2017; Rothgangel & Vollmer, 2020). This research is performed in two ways: (a) as comparisons and (b) as meta-theoretical considerations.

(a) The comparison of elements of subject didactic knowledge of type 2 generated in different individual subject didactics is an essential element of subject didactic knowledge of type 3. One example is the comparison of systemic disciplinary self-descriptions of 17 subject didactics on the basis of grounded theory (Rothgangel et al. 2021) with regard to the history of the subject, the respective subject discipline, the methodological foundations, the educational goals and the interdisciplinary networks (cf. Rothgangel, 2021; Rothgangel & Vollmer, 2020). One finding from systematic comparative work was the discovery that all subject didactics emphasize the specialized and scientific nature of teaching and learning, yet with differing views on the role of their academic reference disciplines themselves. Another surprising finding was the consideration of lifeworld relevance, which evidenced subject-specific variation, not only in the arts and humanities but also in the natural sciences.

A further recent example of comparative studies at the level of type 3 is the comparison of 15 subject didactics in the digital world (Frederking & Romeike, 2022; Rothgangel, 2022). Here, for example, it has become apparent that the specialist subjects and methods are changing fundamentally in the course of digital transformation. However, the changes are manifested in very different ways, varying in each subject. Digital storytelling in first-language education is, of course, fundamentally different from digital generation in technology or digital simulation in chemistry education (Frederking & Romeike, 2022). The contribution of the subjects to digital education is also proving to be different. Two examples are the development of computational thinking skills in computer science didactics (ibid.) and the promotion of digital text competence and digital textual sovereignty in first-language didactics (Frederking, 2022b; Frederking & Krommer, 2022). The recording of similarities and differences is important for cross-subject lesson planning with the aim of not leaving the students alone with the problem of establishing the connection between the subjects in which they are taught

b) However, subject didactic knowledge of type 3 is not only the result of comparisons, but of meta-theoretical considerations. This makes it possible to consider overarching topics and research questions which are of importance for all subject didactics and related research. An example for meta-theoretical reflection of SDK of type 3 concerns the modelling (design/development) of learning objects in subject didactics (cf. Bayrhuber et al., 2017). Subject didactics examine conditions for successful modelling of teaching content and develop concepts for their implementation (type 2). At the level of general subject didactics (type 3), basic principles of didactic modelling are systematically examined, e.g. the analysis of subject-specific objectives, subject-specific competencies, knowledge in subject-related basic research (cf. Bayrhuber, 2017, pp. 172–174). These are the foundations for developing topic-specific professional knowledge (TSPK) in line with the Consensus Model of PCK. However, in the context of subject didactic knowledge of type 3, TPSK is not regarded as a given, but as requiring development and justification. It is an open question which parts of the substantive and the syntactic structure (Schwab, 1964) or which cross-disciplinary dimensions of a discipline are considered relevant for the selection and modelling of subject-related topics from an educational perspective (perspective of Bildung).

Another central element of type 3 subject didactic knowledge on a meta-theoretical level has a specific significance for the present context: knowledge about the educational theoretical foundations and aims of subject-matter teaching based on a theory of subject-matter education. This is of particular importance from a curricular point of view, because the educational concept on which a curriculum is based determines guidelines for the development of subject-specific teaching concepts, as well as recommendations for teachers based on these concepts. Although it is true that ‘all teaching is fundamentally … a moral craft’ (Shulman, , p. 26), it is important to ask what kind of normative orientation determines the planning and implementation of lessons in each case. Therefore, we suggest a more comprehensive model of subject didactic knowledge of type 1 and type 2 on the basis of theoretical analyses of subject-matter education at the level of type 3 (cf. Frederking & Bayrhuber, 2017, 2020).⁵ By this it will be clear that subject didactic knowledge of type 3 can have an effect on curriculum development as well, because the question of aims, contents and methods is of high relevance for both the development of curricula and for the teaching and learning in subject-specific lessons based on a theory of subject-matter education. In the following section, we develop basic features of this model.

3. Subject-matter education as base for a meta-scientific model of subject didactic knowledge of types 1 and 2

‘Education’ does not have a single-term translation into German. In line with international discussions, education translated as Erziehung ‘means centrally those acts that are directed at the growing individual and aim to promote his or her development’ (Miller-Kipp & Oelkers, 2007, pp. 204-211). It takes as a starting point the teacher as actor and teaching as action (cf. Lederer, 2014, p. 40). Education in the sense of Bildung in the tradition of Wilhelm von Humboldt (1793), on the other hand, focuses on the human subjects of learning processes and their development as self-determined learning individuals (cf. Deng, 2022, pp. 605–611; Lederer, 2014, p. 40). Since Humboldt, in German speaking countries Bildung has been associated with ‘self-thinking, self-determination and self-appropriation’ (cf. Meueler, 2009, pp. 148–149). Thus in the German-speaking world the conviction is widespread that Bildung cannot simply be translated as ‘education’ (cf. e.g. Begemann, 2005; Lederer, 2014, p. 43; Oelkers, 2009; Ribolitz, 2011). However, in this section we aim to show that the German concept of Bildung in the tradition of Humboldt has parallels in the English-speaking world, especially in the theories of John Dewey (1938) and George Herbert Mead (1911). They represent an expanded understanding of education, which places the learning subject at the centre, quite similarly to the German concept of Bildung (Frederking & Bayrhuber, 2017, 2020). Integrating Dewey and Mead, therefore, it is possible to translate the word Bildung as education. In this sense we speak here about fachliche Bildung and translate it as ‘subject-matter education’ (SME).

In the following some basic elements of a theory of subject-matter education will be outlined which we have developed in a theoretical and historical approach and which we regard as a key element of type 3 subject didactic knowledge (cf. Frederking, 2022a; Frederking & Bayrhuber, 2017, 2020). To start with some general findings: A recent reconstruction of historical and current educational discourses shows that there were forms of subject-matter education (fachliche Bildung) long before a general concept of education (Bildung) gained currency in pedagogy or educational science. This finding is significant because it shows how important the subject focus was and still is in educational institutions, in teaching processes and curricula. Two basic orientations of subject-matter education could be identified: functional and personal subject-matter education (cf. Bayrhuber, 2016; Frederking & Bayrhuber, 2017, 2020).⁶ The two basic types can be heuristically characterized as follows: Both types combine subject content with skills of the learning subjects, but they differ in terms of the nature of these skills and the goals associated with them. Functional subject-matter education aims at building subject-matter related knowledge and skills for understanding the world around them, mastering of everyday life and participating in society and culture. Personal subject-matter education focuses on enabling learners to reflect the relevance of subject-matter issues for their own existence, personal development and identity and their relation to the world, to consider subject-related objects in their emotional impact and to develop reflexive attitudes in that regard as well as existential decision-making and action capacity.⁷ It can be assumed that the emphasis on one of the two forms of subject-matter education has consequences for aims and outcomes of a curriculum. In order to demonstrate the curricular importance and to illustrate and concretize the theoretical descriptions above the following sections offer some historical and some current examples of functional and personal forms of subject-matter education in natural sciences and humanities. At the same time, we link these subject-specific examples of functionally and personally oriented educational goals with general developments and approaches. In doing so, we want to show that e.g. PCK and OECD are part of the functional tradition, while Humboldt, Mead or Dewey are famous representatives of the personal tradition. In each case, possibilities for a theoretical foundation of subject didactic knowledge will be derived. It should also become clear that functional subject-matter orientation leads to different curricular and teaching focuses than personal subject-matter orientation. If we consider the two orientations separately, this does not mean that they cannot or should not be considered together when dealing with a topic or in the course of a curriculum. In our understanding, they are to be related to each other in a complementary way (cf. section 4). In order to grasp their special features, however, it makes sense to look at them separately.

3.1. The tradition of functional subject-matter education and its relevance for subject didactic knowledge

3.1.1. Functional subject-matter education

Functional attributes of subject-matter education focusing on the natural sciences can already be found, for example, in the ‘didactica magna’ by Comenius (1657) or in school books from the age of Enlightenment (e.g. Reyher, 1657; von Rochow, 1776) (cf. Bayrhuber, 2020, p. 20). Each of these works had its own approach to facilitate the acquisition of knowledge about nature as a means of coping with life’s practical challenges.

Functional subject goals have also played a decisive role in first-language teaching in Germany since the Middle Ages. In monastic schools, city schools, and humanist schools, rhetoric, stylistics, declamation, and poetics were largely taught as separate sub-disciplines in the sense of the medieval artes, whereas today they are part of first-language teaching with the aim of promoting language and writing skills (cf. Frederking & Abraham, 2021, pp. 71–72). However, it took many centuries for mastery of the first language (in the sense of functional education) to become an integral part of the curriculum in Germany. The new Abitur regulations in Prussia/Germany,⁸ which came into force in 1812, were groundbreaking, because German was represented as an examination subject for the first time. The guiding principles were functional subject-specific goals such as the ‘ability to write pragmatically and orthographically correctly, to read intensively […], to deal with German grammar, and to acquire literary literacy’ (Beisbart, 2014, p. 4).

New accents for functionally oriented subject education were set in Germany and worldwide by the international comparative studies TIMSS and PISA at the end of the 20^th and the beginning of the 21^st century. As a result, the focus of school systems and curricula shifted to subject-related competencies in the sense of competence or ‘literacy’, a term established by the OECD, that encompasses the ‘knowledge and skills for life’ (OECD, 2000; cf.; Klieme et al., 2003). ‘Literacy’ is rightly seen as a ‘functional variant of the general education concept, aimed at developing basic skills for participation in society’ (Tenorth & Tippelt, 2007, p. 486).

With respect to science subjects, the OECD describes scientific literacy as the combination of content knowledge, procedural knowledge and epistemic knowledge (cf. OECD, 2006, p. 6). The Council of Ministers of Education, Canada (1997, p. 158) has defined scientific literacy in a functional sense as ‘an evolving combination of the science-related attitudes, skills, and knowledge students need to develop inquiry, problem-solving, and decision-making abilities, to become lifelong learners, and to maintain a sense of wonder about the world around them’. In Germany, the published national standards for biology education use comparable competencies to capture biological literacy: ‘subject-matter knowledge’, ‘knowledge acquisition’, ‘communication’ and ‘(ethical) evaluation’ (KMK Sekretariat der Ständigen Konferenz der Kultusminister der Länder in der Bundesrepublik Deutschland, 2005, p. 7). Scientific literacy is regarded nationally and internationally as a decisive prerequisite for overcoming practical challenges in life. For example, the Science Framework for PISA 2015 (OECD, 2013, p. 3) refers to water and food supply, combating diseases, energy supply and climate change for practical purposes in a functional sense.

For first-language education, functional manifestations of subject-matter education can also be found. In PISA, reading literacy is defined as ‘understanding, using, and reflecting on written texts, in order to achieve one’s goals, to develop one’s knowledge and potential, and to participate in society’ (OECD, 2000, p. 18). Curricula for first-language education (L1) all over the world are adopting this functional focus on reading. In the USA a National Reading Panel was established in 1997 to foster reading literacy with an evidence-based approach. Special efforts were made with the aim of ‘preventing reading difficulties in young children’ (Snow et al., 1998). In the published national standards for German (L1), reading literacy is one of four central learning fields (KMK Sekretariat der Ständigen Konferenz der Kultusminister der Länder in der Bundesrepublik Deutschland, 2003). The Government of the United Kingdom highlights: ‘The national curriculum for English aims to ensure that all pupils read easily, fluently and with good understanding’ (Government of the United Kingdom, 2014).

3.1.2. Subject didactic knowledge about functional subject-matter education

The historical and contemporary examples listed above confirm the heuristic characterization offered at the beginning of section 3: functional subject-matter education focuses on processes of teaching and learning within a subject which have as their aim the development of subject-specific knowledge and subject-specific competences for understanding the world, mastering everyday life and participating in society and culture.

As a rule, the worldwide approaches to researching teachers’ professional competence in the PCK tradition (cf. the overview in Chan & Hume, 2019) focus on functional subject-matter education, as we showed in section 1 with regard to the COACTIV study and its aim to investigate effects of teacher competence on fostering functional education and student-related outcomes (cf. Löwen et al., 2013, p. 79). The same is true for research based on the consensus model of PCK and the ‘Refined Consensus Model in Science Education (RCM)’ (Carlson & Daehler, 2019). Wilson et al. (2019, p. 293) for example focused on ‘scientific literacy, and reasoning’ (ibid.) as important aspects of ‘a framework for future PCK research’ and they thus underline functional educational goals.

3.2. The tradition of personal subject-matter education and its relevance for subject didactic knowledge

3.2.1. Personal subject-matter education

Personal subject-matter education has a long tradition, especially in German-speaking and Scandinavian countries (Kansanen, 1999). In the German-speaking regions of Europe, the tradition of personal subject-matter education can be traced back to the Middle Ages (Frederking & Bayrhuber, 2017). Early forms, with religious subjects, can be found in sermons and doctrinal conversations by Meister Eckhart (1314–1323), to whom we owe the German word Bildung (the terminological equivalent of personal education). In the vernacular teaching in schools run by cathedrals, reformers and humanists, personal subject-related educational goals can already be discerned. They supplemented functional educational goals, in that language learning took place through the medium of moral or religious texts. In the 18^th and 19^th centuries, personal subject-related educational goals came into sharper focus, for example, in Johann Gottlieb Herder’s concept of cultural education as the basis of ‘humanity’ (Herder, 1784–87, p. 124) or in Friedrich Schiller’s (Schiller, 1795, p. 643) idea of an aesthetic education with a purpose-free and non-functional orientation.

However, personal approaches are also evident quite early on in educational concepts for the natural sciences. For example, in his ‘didactica magna’ (Comenius, 1657, pp. 31–33), Comenius introduces knowledge, morality and religion as overarching educational goals, whereby knowledge reflects the more functional, application-oriented side of education, morality and religion the personal (Frederking & Bayrhuber, 2017).

This illustrates that personal elements had long been an established supplement to functional goals in subject-matter education when Wilhelm von Humboldt identified the realization of all human powers as the highest goal of education (Bildung) in the sense of the forming and shaping of a human being (Humboldt, 1793). He distinguished between two forms of education, the general and the specific - allgemein and speciell (Humboldt, 1809, p. 188), explaining: ‘Through the general, the powers, i.e. human beings themselves, are to be strengthened […]; through the specific, they are only to receive skills for application’, which serve ‘external need’, not ‘true education’ (ibid.). However, for Humboldt, general education is not something beyond the realm of subject-matter, but develops through engagement with it. According to Humboldt, both ‘general’ and ‘specific’ education take place in the subject lessons.

This reveals a bond between personal and functional subject-matter education that found consideration in the school curricula in Germany in the following two centuries. In the wake of TIMMS and PISA, however, functional educational goals started to dominate subject teaching, and personal educational goals today play a reduced role, both in lessons and in curricula. Nevertheless, across subject didactics, the idea that subject-specific teaching and learning carries a co-responsibility for personal education does still have currency. In biology didactics, for example, there is still talk of ‘science education’ (Bayrhuber, 2020, p. 26), in which the ‘principle of self-education in the spirit of Wilhelm von Humboldt’ (ibid., 28) is the guiding principle. In German language and literature didactics, too, personal ‘forms of linguistic, literary and media education’ (Frederking & Abraham, 2021, p. 76) continue to play a central role. Similar accentuation can be found in some other countries such as Switzerland: ‘Lower secondary education promotes the development and personality formation of young people and encourages them to become lifelong learners’ (Konferenz der kantonalen Erziehungsdirektorinnen und -direktoren EDK & Staatssekretariat für Bildung, Forschung und Innovation SBFI, 2022).

Nevertheless, it is evident that on the whole through TIMSS and PISA, subject-specific personal goals of education have been displaced by a focus on functionality in the literacy tradition. This process, however, is not the result of a widely assumed, irreconcilable opposition between the German concept of education as Bildung and the Anglo-American concept of education as literacy, as is often stated (cf. Begemann, 2005; Lederer, 2014; Oelkers, 2009). In American pragmatism, for example, we see certain correspondences to the tradition of personal subject-matter education in the German-speaking cultural area (cf. Frederking, 2022a). For John Dewey, the ‘progressive organization of subject-matter’ (Dewey, 1938, p. 73) presupposes that learners should have personal experiences during the acquisition of subject-specific knowledge: ‘Anything which can be called a study, whether arithmetic, history, geography, or one of the natural sciences, must be derived from materials which at the outset fall within the scope of ordinary life-experience’ (ibid.). George Herbert Mead illustrates the connection between experience and identity with the example of language teaching: ‘Everything a child gets must come through a problem of his own. […] We must bring language back to the attitudes of individuals acting and reacting to each other. The subject matter itself represents a social product’ (Mead, 1911, p. 178). In other words, when subject-matter becomes relevant in a personal way, functional, subject-driven learning can succeed in a better way.

3.2.2. Subject didactic knowledge about personal subject-matter education

The examples highlighted above, where subject-driven education and personal development can go hand-in-hand, confirm our initial heuristic definition: personal subject-matter education helps learners to relate the subject under study to their own existence and identity and to develop existential decision-making and action capacity. Furthermore, personal subject-matter education develops through reflexive processing of individual experience, operating within the subject in question. This applies both to German and to Anglo-American traditions of education.

In our opinion personal subject-matter education (SME) is a central element of subject didactic knowledge of type 1, 2 and 3. In the following last section we want to demonstrate, how personal subject-matter education can be a part of SDK of type 2 and be fostered and investigated in subject-specific teaching and learning.

4. Functional and personal facets of subject didactic knowledge in subject-specific research and subject-matter education

The analyses in section 3 illustrate that functional and personal types of subject-matter education interact as a complementary single entity. Together they make for successful teaching and learning within subjects. This is not only theoretically plausible, but can also be confirmed empirically. Possible routes for acquiring both types will be illustrated below using examples from theoretical and empirical research in biology didactics and first-language didactics.

4.1. Functional and personal facets of biology didactic knowledge and biology subject-matter education in empirical research (SDK of type 2)

Working with a topic such as ecology can help to elucidate the relationship between subject didactic knowledge (SDK) and subject-matter education in the field of biology.

In terms of functional biological education, school teaching units on ecology aim to build up basic subject knowledge and competences, enabling learners to make sustainable use of the environment in the context of their individual lives and in their role as members of society.⁹ This involves engaging with the relationships between living beings in different habitats and their living and non-living environment. The focus is on basic concepts such as system, climate, ecosystem, biosphere and on sustainable use of the environment. Competences are also to be developed, such as ethical evaluation and knowledge acquisition including ecological modelling. The development of learning offers requires both theoretical and empirical biological knowledge: knowledge elements and competences need to be selected, reduced in complexity and transformed into classroom-ready learning objects. All this is carried out by means of subject didactic modelling (Bayrhuber, 2017, pp. 167–169), taking into account biological didactic knowledge gained through empirical findings from studies in subject didactics. This includes work on biological knowledge acquisition (e.g. Ehmer & Hammann, 2008), on the application of models in biology teaching (e.g. Grünkorn et al., 2014; Krell et al., 2013), on systems thinking in ecology (e.g. Boersma et al., 2011; Hogan, 2000; Sweeney & Sterman, 2007), on the ethical evaluation of environmental actions (e.g. Bögeholz et al., 2017), as well as numerous works on students’ preconceptions, especially in the international context (Duit, 2009; Hammann & Asshoff, 2014; Leach et al., 1995, 1996). This empirical research has provided empirical evidence in essential fields of biology teaching and learning and helped to develop apposite didactic knowledge in the field of functional biology education.

The focus of personal biological education is on relating what is learned to one’s own existence and identity, within a rationality anchored in the subject of biology. Units on ecology will therefore address the learner’s own physical life and personal attitudes in relation to the biotic and abiotic environment. This can be, for example, the insight that we as human beings are part of nature. Individual attitudes towards the sciences also come into play, e.g. regarding the uncertainty of ecological modelling, ethical analyses and justifications in decision-making situations (Bayrhuber, 1992; Bayrhuber et al., 1990, pp. 209–223).¹⁰ Empirical research has been conducted on learners’ interest in living and non-living nature (cf. Scheersoi et al., 2019), on emotions such as well-being or boredom (cf. Holstermann et al., 2012), and on the ability to think in terms of risks and probabilities (Gigerenzer, 2014). At present, more empirical research is needed to develop biology didactic knowledge of type 2 with a focus on personal forms of biology education, e.g. with regard to awareness of belonging to the biosphere (as part of individual human identity) or with regard to the dependence of our own existence on factors in the living and non-living environment, such as the photosynthesis of green plants.

4.2. Functional and personal facets of literature didactic knowledge and literature subject-matter education in empirical research (SDK of type 2)

The role of literature in first language and literature education (L1) has been chosen as an illustration of functional and personal subject-matter education in order to show that empirical research and the generation of evidence-based subject didactic knowledge are also possible in subject-specific learning areas which may often be more difficult to access empirically.

When students are required to engage with literary texts, in many countries it is usually with a view to functional as well as personal literary education. Functional approaches aim at literary comprehension, i.e. the competence to cognitively grasp the content and the formal, semantic and idiolectic features of a literary text. These may include multiple meanings and openness to interpretation, lacunae, linguistic indirectness, fictionality, genre-specific formal elements, a self-referential use of language, literary expertise, or the emotions intended, presented and processed, in the literary text. While in PISA a basic assumption was and is that the understanding of literary texts is part of general reading competence, four empirical studies with 8th and 9th grade students (2008: N = 1083; 2010: N = 1168; 2011: N = 1083; 2012: N = 964) in Germany have since provided evidence to suggest that ‘reading literacy’ and ‘literary literacy’ are two theoretically and empirically clearly separable areas of competence (Frederking et al., 2012, 2016; Meier et al., 2017). This research has provided empirical evidence and helped to develop literary didactic knowledge in the field of functional literary education.

Another focus of functional literary education can be seen in cognitively oriented conversations about literary texts. Nichols (2006) investigates ‘comprehension through conversation’, by purposeful talk in reading workshops. Mills and Jennings (2011) investigated how metacommunicative strategies can improve comprehension processes in conversations about literary texts. Their findings indicate that ‘encouraging teachers and students to reflect on their discussions about books can deepen the power of this popular instructional approach’ (Mills & Jennings, 2011, p. 590). The study of Sedova et al. (2019) with N = 639 9th graders from Czech middle schools confirmed a correlation between individual student engagement in conversations about literature and individual reading comprehension performance.

While all these examples show that functional aspects of ‘literary literacy’ (Frederking et al., 2012) can be studied empirically, it is also possible to gain literary didactic insights into the personal approach to literary experience in a theoretical and empirical way. Literary texts lend themselves in particular to personal types of engagement, because literary production and reception are subjective and emotionally based (cf. e.g. Dewey, 1938). For this reason, literary or aesthetic experiences and forms of subjective, emotional and cognitive activation are predestined to play a special role in literature teaching. Miall and Kuiken (1994) made an early exploration of the correlation between foregrounding and affect in reaction to literary stories, while Kneepkens and Zwaan (1994) focused on the influence of emotions and literary text comprehension. A quasi-experimental study in the USA (Levine, 2014; Levine & Horton, 2015) showed that students (12^th graders) benefit from instruction combined with affect-based interpretive heuristics. However, neither the text-side adequacy of comprehension performance nor the relationship between text- and reader-side emotions and forms of interaction were investigated. A quasi-experimental empirical study with 8th grade students in Germany (N = 699) showed on the basis of quantitative and qualitative methods that subjective, emotional and cognitive activation in literary conversations have very positive effects (Albrecht, 2022; Brüggemann et al., 2017; Frederking et al., 2020). In comparison to functional forms of literary conversations, personal forms of literary talks show significantly larger effects. For example: large effects are seen for empathy towards characters (d = 0.85; e.g. ‘I can empathize well with the lyrical I in the poem’), medium effects for thematic relevance (d = 0.6; e.g. ‘I would like to deal with this topic again in the next lesson’), very large effects for subjective, emotional and cognitive activation (d = 1.11; e.g. ‘Today’s conversation was much more stimulating than other conversations in German lessons’).¹¹ The given examples illustrate that literature didactic knowledge of type 2 can also be gained in connection with empirical research on personal forms of literary education. Further research is required to show the extent to which this also leads to an increase in subject-specific interest and improved performance in the longer term.

In summary, section 4 shows that empirical research can be a good basis for gaining functional and personal forms of subject didactic knowledge. This illustrates how fruitful it can be to model subject-specific educational goals at the level of type 3 subject didactic knowledge and to engage in research at the practical, lesson-oriented level of type 2 subject didactic knowledge.

5. Conclusion and outlook

Based on a critical reflection of the strengths and limitations of the PCK model (section 1), in this article we present an alternative concept: subject didactic knowledge (SDK). This heuristic model is elaborated in the framework of general subject didactics, as an overarching, transdisciplinary approach (section 2). It comprises subject didactic knowledge of teachers based on individual experience of teaching and learning their subjects (type 1), subject didactic knowledge as a significant result of basic and applied research in subject didactics as academic disciplines (type 2) and transdisciplinary, meta-scientific knowledge about subject didactic aims, methods and principles of research and subject specific education (type 3). All these types of subject didactic knowledge have particular significance from a curricular perspective: They influence the goals, contents, and methods of instruction, thus serving as guidelines for the development and implementation of subject-specific teaching concepts. In this regard, type 3 SDK is of particular importance, as it provides the prerequisites for the reflection and, if necessary, modification of educational goals in subject-specific teaching and learning. In this sense we show in section 3 that, on the basis of theoretical-historical analyses, two basic types of subject-specific education can be distinguished and illustrated in their concrete instructional and curricular implications: functional and personal forms of subject-matter education. Against this background, we used the examples of biology and literature in section 4 to exemplify how functional and personal emphases can be specifically implemented in the classroom and how both can be empirically explored.

The article demonstrates that assumptions and analysis at the type 3 level of subject didactic knowledge (SDK), such as the distinction between functional and personal forms of subject-matter education, have concrete and fruitful implications at the level of classroom practice and subject-specific didactic research (i.e. for SDK types 1 and 2). Further, considering the current worldwide tendency towards allowing a functional focus to dominate in subject-matter education, in the tradition of PISA, while personal facets in the sense of Humboldt, Mead and Dewey have largely disappeared, this article argues for the renewed integration of personal facets of subject-matter education into curriculum and schooling worldwide.

Acknowledgments

The authors would like to express gratitude for the continuing cooperation of his colleagues Ulf Abraham, Werner Jank, Martin Rothgangel and Helmut Johannes Vollmer within our research project “General Subject Didactics”, funded by the Association for Fachdidaktik, Germany, and acknowledge their support.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the ‘Gesellschaft für Fachdidaktik’ (GFD), Germany [WG General subject didactics (AG Allgemeine Fachdidaktik)].

Notes on contributors

Horst Bayrhuber

Horst Bayrhuber is former Director at the Institute for Science Education at the University of Kiel (IPN), Germany, and former Professor of the University of Kiel, where he taught biology didactics.

He initiated and managed extensive national and international curricular and research projects, for example he co-founded and led the European Initiative for Biotechnology Education (EIBE). His current research interests include issues of general subject didactics and of subject-matter education. He was the co-founder and chairman of scientific societies, namely the European Researchers of Didactics of Biology (ERIDOB) and the association for Fachdidaktik (GFD) in Germany. A special concern was the promotion of the empirical turn of the subject didactics in Germany.

Notes

1. For characterizations of these two traditions, see Hopmann and Riquarts (1995), Westbury et al. (2000), Kansanen (1999), Hopmann (2015), Deng (2018). ‘Subject didactics’ is used here in the sense of Fachdidaktik.

2. ‘Education’ is used here in the sense of Bildung in the tradition of Wilhelm von Humboldt (1793; for details see section 3).

3. Within the scope of a single subject didactic such as biology or first language education the question cannot be answered in a general way. This is only possible in the context of a general point of view. This is the horizon of general subject didactics and the analyses and theories associated with it. General subject didactics is a theory or rather a meta-theory encompassing subject didactics of all branches (Frederking, 2017; Rothgangel, 2021). As such, it ‘systematically and comprehensively describes and substantiates the relationship between the subject-matter core of teaching and subject-based theory of education, as well as empirical and theoretical research into subject-based teaching and learning inside and outside school’ (Bayrhuber et al., 2017, p. 5). The analysis of common ground and differences between subject didactics, their scientific foundations and their relationship to other sciences is also part of the research field of general subject didactics (Frederking, 2017; Rothgangel, 2017, 2021; Rothgangel & Vollmer, 2020; Vollmer, 2021).

4. Bayrhuber (1995) described different conceptions of subject didactics in Germany, among them ‘subject didactic as craft’ (p. 338) which correlates with subject didactic knowledge (SDK) of type 1 and ‘subject didactic as science’ (p. 336) which is related to type 2. Furthermore, the three levels of SDK correlate with the three levels of subject didactic observation in Luhmann’s sense (Rothgangel, 2014, 2017, 2021) and subject didactic theories and metatheories in Popper’s sense (Frederking, 2017), but focus on types of knowledge.

5. Klafki (2007, p. 160) points out that didactic conceptions depend as much on developments in the past as on contemporary national and international policies and decisions. Klafki argues for an approach which is both historical and hermeneutical and thus able to work out the historical conditions under which curricula are planned. In a socio-critical and ideology-critical approach, he argues in favour of clarifying the normative orientation as well as the educational policy frameworks in particular periods. This will apply to all forms of subjectmatter teaching, whether functional or personal in orientation.

6. For the characterization of subject didactic knowledge, the consideration of these basic orientations of subject-matter education is sufficient. In the present context, we therefore refrain from assigning them to different educational theories. A description of different theories of education from Humboldt to Klafki is provided, for example, by Sjöström and Eilks (2020). A systematic review of the educational theoretical implications of our theory of technical education will be carried out within the framework of a more comprehensive study, the publication of which is planned for 2024.

7. In our view, the terms ‘functional’ and ‘personal’ education are related to Klafki’s distinction between ‘material education’ and ‘formal education’ (Klafki, 1963, pp. 25–27; Meyer & Meyer, 2007, p. 32). However, the functional as well as the personal subject-matter education includes a material (subject-matter related) as well as a formal (learner related) dimension.

8. Up to the establishment of the German empire in 1871 Prussia was the largest autonomous state in Germany.

9. According to this goal environmental education is part of biology teaching in Germany. A part of the empirical studies mentioned here can be assigned to research in environmental education.

10. Being able to carry out an ethical analysis (functional education) is one thing. The other is to accept that an ethical analysis can result in fundamentally different solutions, e.g. those derived from concepts of well-being or concepts of human dignity, and to apply the procedure in personal life situations (personal education). The same applies to the understanding of a risk analysis on the one hand and the orientation of personal decisions from risk analyses on the other hand (cf. Gigerenzer, 2014).

11. Effect sizes according to Cohen (1988): small effect from d = 0.2; medium effect from d = 0.5; large effect from d = 0.8; very large effect from d = 1.0.