Two Secondary School Mathematics Teachers’ Use of Technology through the Lens of Instrumentation Theory
Bibliographic record
Abstract
The primary goal of our research was to gain a sense of the technology that secondary school mathematics teachers in Montreal, Québec are currently using, how they are using it, and some of the reasons why they use the technology that they do, in the ways that they do. The secondary goal was to test the effectiveness of our approach in obtaining this information. The approach consisted of interviewing two local secondary school mathematics teachers. The interview questions prodded at what Instrumentation Theory suggests to be some of the fundamental aspects of one’s interactions with technology; the ‘artifact’ (the particular technology), the subject (the user of that technology), the ‘task’ that the subject tries to complete with the artifact, the ‘instrumented techniques’ that they employ to complete the task (which reveal some of their ‘schemes of use’), and the process through which the subject and the artifact interact and ‘shape’ each other, called ‘an instrumental genesis’. The teachers’ responses to the interview questions revealed that, although they both used most of the same technology (with a few exceptions), significant differences existed between the ways that they used some of them, why certain technologies were used, and why others were not. The two teachers also differed in their views on the value of their instrumented techniques. These findings are discussed in light of the literature review, demonstrating some of the effectiveness of our approach. We believe that our approach was useful as it allowed us to elicit detailed descriptions of these two teachers’ uses of technology and because it facilitated the analysis of the data (as the questions were based on the same theoretical framework that was then used to analyze the teachers’ responses). We conclude with some suggestions for future research. One of the suggestions addresses ways in which our approach could be improved to give researchers who might use it in the future more informative responses.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 teacher head, 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".