Dissertation Defense – Nathan Joseph Wisdom
30 Pryor Street Southwest
Georgia State University, Atlanta, GA 30303
Meta-Didactical Slippages: A Qualitative Case Study of Didactical Situations in a 9th Grade Mathematics Classroom
by Nathan Joseph Wisdom
Research on the mathematical behavior of children over the past forty decades has considerably renewed and augmented the body of evaluative tests of the results of learning (Lester, 2007). Research however, has provided very little knowledge about the means of improving students’ performance on these tests. Nevertheless teachers, students, and others are being pressured to improve students’ performance, but in order to concentrate on basic skills, the learning itself is made more difficult and slower. The combination of requirements has led to a variety of uncontrolled phenomena such as meta-didactical slippage (Brousseau, 2008). The purpose of this study was to: (a) understand the nature of meta-didactical slippage, and how meta-didactical slippages occur in a 9th grade predominantly African American mathematics classroom; and (b) describe how these meta-didactical slippages affect students conceptual understanding on a unit of study of 9th grade mathematics. The study was a descriptive, qualitative, case study that employs ethnographic techniques of data collection and analysis. The theory of didactical situations in mathematics (Brousseau, 1997) served as the theoretical lens that grounded my interpretation of the data, because it enabled me to isolate moments of instruction, action, formulation, validation, and institutionalization in the mathematics teaching and learning process. The study was conducted over a period of 15 weeks in one 9th grade class of 23 predominantly African American students at a high school in a southeastern state. Data was trtangulated using multiple data collection techniques: (a) collection of document artifacts, which included student work samples and teacher lesson plans; (b) interviews conducted with the teacher; (c) researcher introspection; and (d) direct observation. Data was analyzed using ethnographic and discourse analysis techniques, including domain analysis, coding, situated meaning, and the big “D” discourse tool. The study found four themes, which illustrated the nature meta-didactical slippages: (a) over-teaching, (b) situational bypass, (c) language and symbolic representation, and (d) the design of didactical situations. The study presents a discussion of the findings, implications for action, and recommendations for future research.