As the major focus of activities is construction of a searchable, synthesized database of video and related metadata from prior research studies, our findings for this project include summaries of database contents and what it yields in terms of video episodes exemplifying the varied ways in which students reason mathematically across a range of situated learning contexts. Clips from video data collected at suburban/rural, urban and working class communities in New Jersey public schools from representative grade levels are included in the database. Across mathematical strands and divergent populations of learners (e.g., elementary grade students from a suburban/rural school district in a classroom setting; and a middle grade students an urban school district in an informal, after-school setting) clips illustrate students’ mathematical reasoning. Common across populations are the forms of reasoning that emerged through students’ explorations, which include direct reasoning, indirect reasoning (e.g., by contradiction), reasoning by cases, reasoning by upper and lower bounds, and reasoning by induction. Overall, there are 250 clips that range from just 30 seconds to several minutes in length, with each featuring a particular form of reasoning.
Maher, C. A. (2008). Video recordings as pedagogical tools in mathematics teacher education. In D. Tirosh and T. Wood (Eds.), International Handbook of Mathematics Teacher Education: Vol. 2: Tools and Processes in Mathematics Teacher Education (pp. 65-83). Rotterdam, The Netherlands: Sense Publishers.
Maher, C. A. (2009). Children’s reasoning: Discovering the idea of mathematical proof. In M. Blanton, D. Stylianou and E. Knuth (Eds.), Teaching and learning proof across the K-16 curriculum (pp. 120-132). New Jersey: Taylor Francis - Routledge.
Mueller, M. & Maher, C. (in press). Convincing and justifying in middle school mathematical reasoning. Mathematics Teaching in the Middle School.
Mueller, M. & Maher, C. (in press). Promoting equity through reasoning. Teaching Children Mathematics.
Weber, K., Maher, C. A., Powell, A. B. & Lee, H. S. (2008). Learning opportunities from group discussions: Warrants become the objects of debate. Educational Studies in Mathematics, 68, 247-261.
Maher, C. A., Powell, A. B. & Uptegrove, E. (Eds.), (submitted). Combinatorics and reasoning: Representing, justifying and building isomorphisms. Springer Publishers.
Prototype database, see “research design.”