Two types of teacher knowledge

After coding the teachers’ statements on the three domains of teacher knowledge (general pedagogical knowledge, PCK, and subject matter knowledge of models and modelling), we put together, per domain and per element (for PCK), the coded statements. With this, the variety of statements within each domain became clear. We examined carefully the various sets of statements and identified for each teacher the combinations of codes that arose across the different domains. Next, we compared these combinations across the nine teachers, and two patterns (i.e., specific combinations of codes, which recurred - more or less - strictly) emerged. Using these, we constructed two types of teacher knowledge: Type A and Type B (Tables 2.6 and 2.7). These two types will be described in a general way below. In the next sections, we will describe each type more concretely, portraying the knowledge of two teachers, each of whom was - almost - typical of one of these types.

2.6.1.1 Type A

In Type A, the various knowledge domains are associated with each other in the following way. In the domain of general pedagogical knowledge, we noticed a combination of behaviourist and cognitive perspectives on learning and teaching: behaviourist with regard to the organization of learning environments and cognitive with regard to learning. PCK of instructional strategies includes knowledge that is aimed at the transmission of the content of certain models (i.e., of the solar system), together with knowledge about effective methods and materials to support students’

understanding of the content of these models and to help students connect the models with reality. PCK of students’ understanding of and difficulties with specific concepts is mainly based on the interpretation of the results of written exams. PCK of goals and objectives in the curriculum with regard to models and modelling reflects a combination of positivist and instrumentalist views: models are seen as reductions of reality, aimed at visualizing and explaining different phenomena. PCK of ways to assess students’ understanding includes the same goals: both students’ content knowledge of models and their use of models as ‘tools’ are evaluated using exams and oral presentations.

With regard to the teachers’ subject matter knowledge of models and modelling in science in Type A, we also found a combination of two different views. From the high scores on both scales in the questionnaire, we concluded that the teachers would support the idea that a model is a simplified reproduction of reality, on the one hand, while recognizing that models are the products of human thought, creativity, and communication, on the other hand.

Table 2.6 Type A Teacher Knowledge

General pedagogical knowledge Behaviourist and cognitive perspectives on teaching and learning

PCK-instructional strategies Knowledge about specific multi-media (film, video) and concrete materials to support students' understanding of model content, and knowledge of ways to connect models with reality

PCK-students’ understanding Knowledge about students’ difficulties with the content of specific models, and inability to connect models with reality

PCK-ways to assess students’ understanding Knowledge about examination on model content and model application using written exams, oral presentations, posters, and reports

PCK-goals and objectives in the curriculum Epistemological views which can be understood as positivist and instrumentalist; Knowledge about the use of models to visualize and explain phenomena Subject matter knowledge of models and

modelling in science

A positivist epistemological view, combined with the idea that models are constructed in a social and cultural context

2.6.1.2 Type B

This type of teacher knowledge is dominated by cognitive and constructivist aspects. These show up in the teachers’ general pedagogical knowledge, but also in their PCK. PCK of instructional strategies includes knowledge about motivating and challenging tasks that are aimed at supporting students’ understanding of model content and model production or comparison (debating), and about effective ways to promote

students’ creativity in thinking about the nature of models, and model production. PCK of students’ understanding includes knowledge about students’ motivation, difficulties, and inabilities concerning scientific models and modelling activities, and knowledge about students’ affinity with specific models. This knowledge is based on students’ results in exams, the evaluation of presentations, reports, and portfolios, discussion of their modelling and debating activities, and observation of teamwork.

Table 2.7 Type B Teacher Knowledge

General pedagogical knowledge Cognitive and constructivist perspectives on teaching and learning

PCK-instructional strategies Knowledge about motivating and challenging assignments to promote students’ learning of model content;

Knowledge about effective ways/methods to promote students’ thinking about the nature of models (e.g., debating, modelling activities, computer simulation);

Knowledge about ways to stimulate students’ creativity

PCK-students’ understanding Knowledge about students’ motivation to discover things themselves;

Knowledge about students’ motivation and abilities to participate in modelling and model thinking activities;

Knowledge about student’s affinity with specific models

PCK-ways to assess students’ understanding Knowledge about how to evaluate model content, model production and thinking about the nature of models using exams, oral presentations, reports, portfolios and group observations

PCK-goals and objectives in the curriculum Epistemological views: instrumentalist and relativist;

Knowledge about the use of models to visualize and explain phenomena,

obtain information about phenomena which cannot be observed directly, and derive hypotheses which may be tested Subject matter knowledge of models and

modelling in science

A positivist epistemological view, combined with the idea that models are constructed in a social and cultural context

In the PCK of goals and objectives for teaching models and modelling in the curriculum, not only the visualization and explanation of phenomena are emphasized, but also how to formulate and test hypotheses, and how to obtain information about phenomena. Models are conceived of as instruments but also as ways to view reality (relativist epistemological view). The subject matter knowledge of models and modelling in science in this type is not different from that in Type A.

Following a comparison of the answers and reactions of the nine teachers with the above types of knowledge, we considered the knowledge of five teachers to be typical of Type A, while the knowledge of three was qualified as typical of Type B. The knowledge of one teacher fell outside both categories because of the unique combination of codes we had to apply to his statements. In the next sections, we will describe the knowledge of two teachers in more detail: we have called one teacher “Jim” (representing Type A) and the other teacher “Sam” (representing Type B).

2.6.2 Jim’s knowledge (Type A)

2.6.2.1 General pedagogical knowledge

Jim’s general pedagogical knowledge about learning and teaching can be described as a combination of behaviourist and cognitive perspectives. Although he acknowledged that students play an active role in learning, he reacted more or less negatively to metaphors representing a constructivist or situative perspective. In Table 2.8, we put together some statements that are typical of Jim’s reactions, together with the metaphors he reacted to, and the codes we applied to his reactions.

2.6.2.2 PCK

We discuss Jim’s PCK based on his reactions to the interview questions about learning and teaching models and modelling with regard to the solar system, in the context of the ANtWoord chapter on the solar system and universe. PCK is divided into the above-mentioned four elements.

Knowledge about instructional strategies: Jim had much knowledge of instructional strategies to effectively transmit and explain knowledge to his students, using physical models of the solar system, films, and videos: “We let them play, in structured assignments, with wooden sticks and balls and a lamp. They like it, and they get more insight into the model”. His lessons on ‘Models of the Solar System’ were mainly aimed at teaching and explaining the Copernicus’ heliocentric model. He developed new, more structured material for his students because, in his opinion, the ANtWoord exercises are “too vague”. He stressed the observation of phenomena (positions of moon, sun, stars) by the students. The usefulness of various models of the solar system on explaining these observations should be tested in the lessons.

Because of unfavourable weather conditions and organizational problems, the observational part of his lessons was not successful and he was unhappy with this: “It is hard to take that they (the students) have a model in mind while they don’t even know what can be seen, because we were not able to design an effective observation task”. According to Jim, students’ production of their own models and a classroom debate on models of the solar system make no sense.

Table 2.8 Examples of Jim’s general pedagogical knowledge

Question or metaphor Jim’s response Applied code

What do you think is the best way for students to learn?

Something new has to fit into an existing framework, and you (the teacher) are the one who has to make this link

Learning-cognitivist: understanding and learning of new material depend strongly on what students already know Teaching-cognitivist: it is the job of the teacher to base instruction on students’ prior knowledge Learning is joint work, as done

by ants collaborating to achieve a result which is beneficial to all

I think the result of this work is not clear to students; they have to see the point of it, and for them the result of learning is a good mark Motivation- behaviourist: students’ active participation occurs mainly because of extrinsic motivation i.e. rewards and punishments, as well as expected outcomes of their engagement Teaching is like a tourist guide

who negotiates a destination and a route with the tourists

No, the destination is laid down in the programme, and you should not discuss the route too much, because that will be too confusing for them [the students].

Teaching-behaviourist: it is the job of the curriculum and the teacher to organize students’ practices, and to provide clear plans and goals.

Teaching is a game of billiards; you have to know how to play in order to send the balls in the right direction

Yes, but balls roll systematically, and students do not. Yet, you want to send them in a certain direction; to make order out of chaos

Learning-cognitivist: students differ in their learning strategies, and in the interest and

understanding they bring to school activities.

Teaching-behaviourist: it is the job of the curriculum and the teacher to organize students’ practices, and to provide clear plans and goals.

Learning is building Yes, piling up knowledge Learning-behaviourist: learning is an increase of the quantity of knowledge

Knowledge about students’ understanding: Jim showed little specific knowledge of his students’ understanding of the heliocentric model and some historical models (i.e., Ptolemy’s geocentric model) of the solar system. He stated that, in the context of this chapter, his students “need concrete manipulative materials, small and concrete assignments, and questions with concrete answers. They also need clear learning goals, in order to be well prepared for their exams”.

Knowledge about ways to assess students: Jim’s assessment of his students’ understanding of this chapter consisted of exams with knowledge and application questions about concepts contained in the heliocentric model and some historical models of the solar system. His students also had to carry out various tasks during the lessons, the results of which he evaluated, too. Finally, Jim assessed students’ writing of letters to an astronomer about their views on the theory of the Big Bang.

Knowledge about goals and objectives in the curriculum: Jim used models in the curriculum to explain phenomena. Jim conceived of models as reductions of reality, and not as truths: “I always try to emphasize two viewpoints: a scientific, rational view and an irrational way of thinking (i.e., wonderment and respect for the creation of earth and heaven)”.

2.6.2.3 Subject matter knowledge of models and modelling in science

On the questionnaire’s scale ‘relationship between model and target’, Jim’s main score was 2.9. At item level, we noticed that Jim gave the highest score (4 = always) to the following statements: ‘A model is a simplified reduction of reality’, ‘One attempts to keep a model as simple as possible’, ‘A model is meant to explain a phenomenon’, and ‘When developing a model, one attempts to exclude as many irrelevant aspects of its target as possible’. Jim gave a score of 1 (= never) on the item ‘In the course of development, the model corresponds more to its target’. On the other scale, about the ‘construction and use of models’, his main score was 2.6. Here, he gave a score of 4 to the statement ‘A model is meant to give an overview of complex phenomena’, and of 1 to ‘A model is meant to represent an abstract concept’.

We conclude that Jim holds a mainly positivist epistemological view of models: above all, he understands models in relation to empirical data, and not to concepts and ideas. He sees models, primarily, as reductions of reality, which are aimed at explaining phenomena.

In sum, it may be said that Jim’s PCK of teaching and learning models and modelling in the context of a chapter on the solar system and universe can be understood as model-content oriented. Expressing behaviourist and cognitive perspectives on learning and teaching, Jim applied teaching methods, which are aimed at the transmission of knowledge content, and the structuring of students’ activities. His knowledge about students’ understanding reflects behaviourist and cognitive perspectives on learning, too. His methods of assessment are related mainly to knowledge and understanding of concepts contained in the heliocentric model and some historical models (e.g., Ptolemy’s geocentric model) of the solar system, also reflecting his focus on model content. His knowledge about goals and objectives for teaching this specific topic in

the curriculum reflects a positivist way of thinking, which corresponds to the way he answered the questionnaire on models and modelling in science.