This project has a longitudinal study design and is designed to generate descriptive [case study, design research, observational] and associative and/or correlational [quasi-experimental] evidence. Original data is collected through survey research [self-completed questionnaires, semi-structured interviews, focus groups] observation [personal, videographic] and assessments of learning or achievement tests, diaries/journals/records kept by study subjects.
To document the teachers’ developing conceptions of argumentation and algebraic justification we will administer a justification assessment instrument developed in the project planning sessions. We will also administer the Knowledge of Algebra for Teaching (KAT) (NSF REC 0337595 and NSF REC 0106709; Ferrini-Mundy, Burrill, Floden, Sandow, & Allen, 2005) to assess teachers’ knowledge of algebra.
During the Year 1 AJA Course, 2-4 interviews will be conducted with each teacher using interview protocols developed in the project planning sessions. Interviews will generally focus on teachers’ developing knowledge of and about algebraic justification and argumentation.
A pre-and post-assessment of students’ conceptions of justification will be administered to all students at the beginning and end of each academic year. This instrument will be an adaptation of one developed by Healy and Hoyles (2000) for the purposes of exploring grade 7-8 students’ conceptions of what makes an acceptable justification.
The study’s analytic plan includes two qualitative approaches: (1) constant comparison and (2) ‘retrospective’ data analysis. The constant comparison design and procedures allow for continual feedback about the development of notions of justification in algebra, teachers’ conceptions of justification in algebra, the development of teaching practice, and students’ learning, while retrospective analysis allows us to bring all data sources from the teachers’ summer sessions, classroom observations and teacher work sessions together for connected analysis. A quantitative quasi-experimental design is used to evaluate student achievement in a pre and posttest analysis, and teacher growth in algebra and justification is assessed by the KAT (described above) and an instrument to be designed by our research team.
Initial analysis of videotaped student discourse will use the instrument (Weaver et al., 2005; Weaver & Dick, 2006) developed for a related research project. Additional mathematical analysis of justifications will use codes developed in project planning sessions. Analysis of transcribed justification videotaped lessons will be coded using Wood et al. (1999) coding categories (developed for NSF RED 9254939) for interaction patterns to identify teaching practices. Simulated recall interviews will be analyzed using a coding rubric developed in project planning sessions for analysis of justification discourse and shifts in pedagogy and teachers’ conceptions of argumentation and justification as disciplinary and learning practice.