Developing Multimedia Case Studies for Preservice Teacher Education 

Mathematics
teacher educators face several practical problems in their work with preservice
teachers. For example, when placed in exemplary classrooms to work and
observe, student teachers lack the experience base necessary to meaningfully
observe the complex and rapid interactions that can occur. In addition,
during their student teaching experiences, preservice teachers lack a
common experience upon which they can reflect with their fellow student
teachers. This situation limits their ability to reflect on their own practice
and also limits their opportunities to analyze the processes of teaching
and learning more generally. While at considerable risk for oversimplifying
a complex problem, we believe that CDROMbased case materials appear to
hold great potential for bringing the complexities of a classroom into
focus. 

Case
1: 1day lesson filmed in 7th grade mathematics classrom
Case 2: 4day lesson sequence filmed in an 8th grade prealgbera classroom 

The overarching goal of this research is to better understand how multimedia case studies can be used to support the development of effective practice among preservice mathematics teachers. As preservice teachers enter into the professional practice of teaching, they are developing their own models of pedagogical reasoning, grounded in part in their growing base of experience as practitioners. The casebased reasoning used by experienced teachers is a combination of decisionmaking in action and an integrated base of pedagogical content knowledge built through practice. We are investigating how multimedia case studies of classroom teaching can support the development of casebased reasoning among preservice teachers.  
How
do multimedia case studies further the development of pedagogical reasoning
among preservice teachers? How do multimedia case studies support the creation of shared classroom experiences for preservice teachers? To what extent do multimedia case studies support reflection on the part of preservice teachers? What is the scope and structure of an effective case study? What is the nature of an effective implementation of a multimedia case study? 

Case 1: The case of the Sneakers Purchase Setting: 7th Grade classroom in Nashville, TN The Sneakers Problem involves the task of deciding on the criteria or factors that students would consider in purchasing a pair of sneakers, followed by a ranking of the criteria. The primary mathematics content of this lesson is data analysis, including ranking of data and aggregating ranked data. Other mathematical ideas involved are average and the relationship between totaling the data ranks and averaging the data ranks. The primary mathematical goal of the lesson is for students to be engaged in analyzing data within the context of purchasing a pair of sneakers by generating ranked data and then compiling one class list of ranked data from the group lists of ranked data. Case 2: Making Weighty Decisions Setting: 8th Grade Classroom in Nashville, TN This lesson sequence is part of a unit on data analysis. The primary focus is on ranking data and aggregating ranked data with attention being given to weighted ranks. In thinking about a learning trajectory for this initial lesson sequence, it is important to highlight the mathematical issues involved in comparing ranked lists which have been created from (1) summing ranks across lists and (2) averaging ranks across lists. Students' understandings of average are typically grounded in an algorithmic approach which does not highlight the importance of average in terms of what it tells you about a data set. In addition, the relation of the sum to the average is not understood. Most students think that the sum is more accurate and that an average is an approximation. These mathematical issues can be teased out in the first problem by having students compare the results of aggregating ranked lists by both summing and averaging. While it is not expected that this comparison will clarify students' understandings, it should provide an initial activity to raise the issue which can then be revisited in the subsequent problems in this lesson sequence and later in this unit. 

This
project is funded by NSF Grant #9725512. Principal Investigators: Janet Bowers (San Diego State University), Helen M. Doerr, Joanna Masingila (Syracuse University, Mathematics Education); Kay McClain (Vanderbilt University). Programmer:
Jeff Sale 