Elementary student teachers' science content representations

This purpose of this study was to examine the ways in which three prospective teachers who had early opportunities to teach science would approach representing science content within the context of their student teaching experiences. The study is framed in the literature on pedagogical content knowledge and learning to teach. A situated perspective on cognition is applied to better understand the influence of context and the role of the cooperating teacher. The three participants were enrolled in an experimental teacher preparation program designed to enhance the teaching of science at the elementary level. Qualitative case study design guided the collection, organization, and analysis of data. Multiple forms of data associated with student teachers' content representations were collected, including audiotaped planning and reflection interviews, written lesson plans and reflections, and videotaped teaching experiences. Broad analysis categories were developed and refined around the subconstructs of content representation (i.e., knowledge of instructional strategies that promote learning and knowledge of students and their requirements for meaningful science learning). Findings suggest that when prospective teachers are provided with opportunities to apply and reflect substantively on their developing considerations for supporting children's science learning, they are able to maintain a subject matter emphasis. However, in the absence of such opportunities, student teachers abandon their subject matter emphasis, even when they have had extensive background and experiences addressing subject‐specific considerations for teaching and learning. © 2002 Wiley Periodicals, Inc. J Res Sci Teach 39: 443–463, 2002     

On the conclusive validation of symbol manipulative processes (How do you know it has to work?)

This paper discusses the ramifications of the problem of proving that the design of a symbol manipulating processor conclusively does what the designer intended. More specifically, it explores such questions as: (1) What different interpretations can be given to the expression “the intent of the process”? (2) Does the process, or should the process end? In either event, how do we prove it? (3) If the process does end, how do we prove that it does what was intended? This question may be meaningful even if the process does not end. (4) Is there a whole class of processes that stand or fall together? Can we adapt our proof of conclusiveness to cover the whole class? (5) Do the processes of the class yield the same or different results, and whichever it is, how do we prove it? The example of formal differentiation from the calculus is used to illustrate these problems; and question number four is developed in detail to illustrate the mixture of mathematical, logical, linguistic, computer science, procedural and even psychological insights involved. References are given for the methods of attack on the other questions.