Synthesizing Video Data on Students’ Mathematical Reasoning

Principal Investigator: 
Project Overview
Background & Purpose: 

The aims of this project are to: (1) synthesize across two decades of prior research to identify clips of video that are representative of children’s mathematical reasoning, index video according to relevant NCTM content and process standards, and draft analytical commentaries to accompany and contextualize the video episodes; and (2) construct a prototype database that can be searched to find video clips by mathematical content area (e.g., fractions and rational numbers; counting and combinatorics), demographic features (e.g., urban/suburban/working class; age of students, etc.), and type of learning environment (e.g., classroom, informal / after-school, etc.).


Prior research being synthesized includes: 12-year longitudinal study in working-class community with both classroom and after-school settings; 2-year longitudinal study in suburban/rural community in classroom setting; and 3-year longitudinal study in urban community in informal, after-school setting.

Research Design: 

The research design for this project is longitudinal and cross-sectional, and is designed to generate evidence which is descriptive (observational, phenomenological) and synthetic. Prior research studies were re-analyzed using lens of mathematical reasoning to select representative video clips for the project’s prototype database. As part of this process, corresponding transcripts have been included and analytic commentaries have been prepared that contextualize the video clips within their larger study. Clips are indexed according to mathematical content, demographics, educational setting, and relevant NCTM standards.


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.

Publications & Presentations: 

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.

Other Products: 

Prototype database, see “research design.”