Supporting pre-service mathematics teachers to notice and understand the practice of positioning students competently
Bibliographic record
Abstract
Positioning students as competent learners has been shown to be a crucial approach in fostering student learning in mathematics, and has been especially effective in supporting students who express mathematically incorrect understandings (Gresalfi, Martin, Hand, & Greeno, 2009; Kazemi & Hintz, 2014; Lampert, 2003). Few studies have aimed to support pre-service teachers (PSTs) in learning to notice interactions that can deepen their understanding of positioning students competently (PSC). During this qualitative design-based research study, four pre-service teachers from an eastern Canadian university participated in three one-on-one video analysis sessions where they were asked to watch videos and use a framework to support them in attending to and interpreting moments that relate to positioning students competently. Three research questions guided this study: 1) How do pre-service mathematics teachers' conceptualizations of PSC change through their engagement in video viewing sessions? 2) How do pre-service mathematics teachers' noticing of moments of positioning change through their engagement in video viewing sessions? 3) How do the design supports help to contribute to the development of PSTs' understanding and noticing? To answer these questions, audio- and video-footage were collected from pre- and post-interviews, while audio-footage, video-footage, written artifacts, and researcher observations were collected from video analysis sessions. Results showed that: 1) three of the four participants emerged from the study with a deeper understanding of PSC; 2) two participants emerged from the study more consistently attending to the teacher and students, whereas the majority of participants showed improvements in interpreting PSC; 3) most supports were beneficial in supporting PSTs' noticing and understanding of PSC. In addition, a fine-grained analysis of two contrasting episodes from one session showed how the facilitator's role in providing alternative teaching examples and the PST's interactions with the framework (e.g., the definition of PSC) supported one participant in expanding her understanding of PSC. These results have implications for possible resources that can help PSTs cultivate deeper understandings and more focused noticing of interactions of PSC.
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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 | 0.003 | 0.011 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.005 | 0.005 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.002 | 0.005 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 0.002 |
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".