On the Nature of Students' Digital Mathematical Performances
Bibliographic record
Abstract
In this study I investigate the nature of digital mathematical performances (DMPs) produced by elementary school students (Grades 4-6). A DMP is a multimodal text/narrative (e.g., a video) in which one uses the performance arts to communicate mathematical ideas. I analyze twenty-two DMPs available at the Math + Science Performance Festival in 2008. Assuming a sociocultural/postmodern perspective with emphasis on multimodality, my focus is on the role of the arts and technology in shaping students’ mathematical communication and thinking. Methodologically, I employ qualitative case studies, along with video analysis. I conduct a descriptive analysis of each DMP using Boorstin’s (1990) categories of what makes good films, focusing on surprises, sense-making, emotions, and visceral sensations. I also conduct a cross-case analysis using Boorstin’s categories and the mathematical processes and strands of the Ontario Curriculum. The multimodal nature of DMP is one of its most significant pedagogic attributes. Mathematics is traditionally communicated through print-based texts, but the production of DMPs is an alternative that engages students in conceiving multimodal narratives. The playfulness offers scenarios for students’ collaboration, creativity, and imagination. By making DMPs available online, students share their ideas in a public and social environment, beyond the classrooms. Most of the DMPs only explore Geometry and offer opportunities to experience some surprises, sense-making, emotions, and visceral sensations. The lack of focus on other strands (e.g., Algebra) may be seen as a reflection on what (and how) students are (or not) learning in their classes. The production of conceptual DMPs is a rare event, although I acknowledge that I analyzed only DMPs of the first year of the Festival, that is, students did not have examples or references to produce their DMPs. Some DMPs potentially explore conceptual mathematical surprises, but they appear to have gaps in terms of sense-making. The use of the arts and technologies does not guarantee the mathematical conceptuality of DMPs. This study contributes to mathematics education with an exploratory discussion about how mathematical ideas can be (a) communicated and represented as multimodal texts at the elementary school level and (b) seen through a performance arts lens. The study also points out directions about the pedagogic components for conceiving conceptual DMPs in terms of the performance arts and the components of the Ontario Curriculum.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.012 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.005 | 0.002 |
| Open science | 0.001 | 0.004 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".