Asia-Pacific Forum on Science Learning and Teaching, Volume 4, Issue 2, Article 2 (Dec., 2003)
Pamela MULHALL, Amanda BERRY and John LOUGHRAN
Frameworks for representing science teachers' pedagogical content knowledge
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Our representations of science teachers' topic specific PCK

To represent successful science teachers' PCK about a particular science topic, we have developed two different but complementary formats. These are the CoRe (Content Representation, shown in Appendix A) which is an overview of the particular content taught when teaching a topic, and PaP-eRs (Pedagogical and Professional-experience Repertoires, an example being that in Appendix B), accounts of practice intended to illuminate aspects of the CoRe in a particular classroom context. The examples shown in these appendices relate to the teaching of the topic, 'Chemical Reactions', to a mixed ability Grade 10 class. It is important to realise that the PaP-eR shown in Appendix B is but one of a number we have developed that are linked to the 'Chemical Reactions' CoRe, each focussing on a different aspect of a successful teacher's PCK in this area.

As noted previously, our approach to data gathering is discussed elsewhere (Loughran et al., 2000, 2001) and it is not within the scope of this paper to detail the ways in which data about science teachers' knowledge of practice was obtained. Suffice to say our representations are a synthesis of our research data (individual and group interviews with experienced, successful science teachers and observations of their science teaching).

About CoRes

A CoRe (Content Representation) provides an overview of how teachers approach the teaching of the whole of a topic and the reasons for that approach - what content is taught and how and why - in the form of propositions. Importantly, a CoRe refers to the teaching of a particular topic to a particular group of students (e.g., mixed ability, Grade 10 general science class).

The CoRe for 'Chemical Reactions' shown in Appendix A refers to the teaching of a typical class at the Grade 10 level. The CoRe was developed by asking teachers to list at the top of each column what they considered to be the "big ideas" for teaching 'Chemical Reactions' to that grade level. Teachers then provided the information shown in the column underneath each big idea as they were asked about the different aspects of their knowledge and practice shown in the left-hand column. The CoRe is a generalisation of teachers' responses. Taken as a whole, the CoRe represents pedagogical content knowledge because of the reasons it provides which link the how, why and what of the content to be taught with the students who are to learn that content. We elaborate on this below.

As we mentioned earlier, our framing of teachers' PCK has been influenced by constructivist perspectives of learning, for which the implications are that teaching for understanding entails teachers developing knowledge about science and learners that enable them to make: (1) curricular decisions; and, (2) instructional decisions (Hollon et al., 1991, p. 149). We use these two groupings to discuss below the kind of information highlighted in each row of the CoRe.

Using knowledge about science and learners to make curricular decisions

Grade level It is important to emphasise that a CoRe refers to a particular type of class, which for the case shown in Appendix A is a Grade 10, mixed ability general science class.

Big science ideas/concepts "Big ideas" is a term often used in science to describe an idea that has had a profound impact on the ways scientists understand and conceptualise the world. Our use of the term is not synonymous with this: we mean the science ideas that the teacher sees as being at the heart of understanding the topic for the particular class under consideration (Smith III & Girod, 2003). (Nevertheless, a big science teaching idea may also be the same as a big science idea.)

What you intend the students to learn about this idea Being specific about what a particular group of students should be able to learn is an important aspect of well developed PCK. In contrast, teachers inexperienced at teaching a topic are often unsure what the students are capable of achieving.

Why it is important for the student to know this In making decisions about what to teach, successful teachers draw on their knowledge of what science content is relevant to students' everyday lives and how the content links with other areas that students study. Related to the latter is "curricular saliency" - how important a particular science idea or topic is to the overall science curriculum (Geddis et al., 1993).

What else you might know about this idea (that you don't intend students to know yet) When selecting what to teach, teachers often make difficult decisions about which content should be omitted (Hollon et al., 1991). Indeed, as noted earlier, constructivist perspectives of learning recognise that teaching for understanding takes time, which places limits on the range of what can be taught.

Using knowledge about science and learners to make instructional decisions

Difficulties/ limitations connected with teaching this idea Shulman (1986) considered that teachers' insights into the potential difficulties when teaching a particular topic to the class in question were an important aspect of teachers' PCK.

Knowledge about students' thinking that influences your teaching of this idea This part of the CoRe makes explicit the influence on their decision-making of teachers' experience in teaching this topic. When planning lessons, teachers draw on their knowledge about commonly held ideas about the topic that students bring to class (the importance of which is highlighted by the "alternative conceptions" literature mentioned earlier) and also the usual responses (including level of interest) of students to specific teaching and learning situations.

Other factors that influence your teaching of this idea Contextual knowledge about students and general pedagogical knowledge that influences the teaching approach are indicated in this part of the CoRe.

Teaching procedures (and particular reasons for using these to engage with this idea) The term "procedures" is used in the sense of that in the PEEL project (Baird & Northfield, 1992): it acknowledges that from a constructivist perspective, student change in terms of learning is gradual and involves the student's active engagement with the science ideas under consideration. Teaching procedures cannot guarantee learning: rather their purpose from a constructivist perspective is to influence student thinking in ways that promote better understanding of science ideas (Leach & Scott, 1999).

Specific ways of ascertaining students understanding or confusion around this idea Teachers need to constantly monitor the progress of students' understanding so that they can determine the effectiveness of their teaching of the topic and plan future lessons. While summative assessment is usually explicit, teachers' formative assessment is often unacknowledged and implicit, and probably more specific to the topic being studied.

We note that some parts of the CoRe have more detail than others, in part a consequence of the difficulty of exploring teachers' PCK (Loughran et al., 2000, 2001; Mulhall, Milroy, Berry, Gunstone, & Loughran, 2000). However, the form of representation of a CoRe allows additions and changes to be made as further insights from expert, successful teachers are gained. This does not imply that there is only one CoRe for each topic. Indeed we have found more than one CoRe seems to be applicable to 'Chemical Reactions' (Loughran, Mulhall, & Berry, 2002). This is not surprising in view of the developing research literature on the role of beliefs and contextual factors in teachers' understandings and practice (e.g., Tobin et al., 1994; Tobin, 1998).

The CoRe enables an overview of teachers' PCK for a topic to be made, and provides some insights into the decisions that teachers make when teaching a particular topic, including the linkages between the content, the students and teachers' practice. However, because the information is represented in the form of propositions, it is limited in terms of providing insight into teachers' experiences of practice. It was for this reason that we developed PaP-eRs (Pedagogical and Professional-experience Repertoires), which we now discuss.

About PaP-eRs

In our research, PaP-eRs are narrative accounts of a teacher's PCK for a particular piece of science content. Each PaP-eR "unpacks" the teacher's thinking around an element of PCK for that content, and is based on classroom observations and comments made by teachers during the interviews from which the CoRes were developed. PaP-eRs are intended to represent the teacher's reasoning, that is, the thinking and actions of a successful science teacher in teaching a specific aspect of science content. The function of the narrative is to elaborate and give insight into the interacting elements of the teacher's PCK in ways that are meaningful and accessible to the reader, and that may serve to foster reflection in the reader about the PCK under consideration, and to open the teacher reader to possibilities for change in his/her own practice.

The example of a PaP-eR from the topic area of 'Chemical Reactions' shown in Appendix B has been annotated using "call out" boxes to highlight the interpretive frames we have used in its construction. (The shaded call-out boxes do not form part of the PaP-eR.) The "voice" of this PaP-eR is that of a teacher reflecting on her/his understanding about the problematic nature of the concept of substance, an understanding developed through experience of practice. The "voice" of the call-out boxes is that of the researchers elaborating what they intended to illustrate in the different parts of the PaP-eR. It is important to realise that this PaP-eR is but one of a number that are linked to the 'Chemical Reactions' CoRe, each focussing on different aspects of a successful teacher's PCK.

PaP-eRs offer one way of capturing the holistic nature and complexity of PCK, more than is possible in the CoRe. PaP-eRs have the capacity to represent a "narrative whole", and function to explain in a text what one knows in action as a teacher. Many of the PaP-eRs involve teachers coming to see experience differently, or "reframing" (Barnes, 1992) over a "widened range of attention" (Dewey, 1933) what goes on in the learning of particular science concepts. In so doing, the reader is afforded insights into teachers' development of pedagogical content knowledge of that science topic.

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