Mathematics Undergraduate Student Teachers’ Conceptions of Guided Inductive and Deductive Teaching Approaches
Bibliographic record
Abstract
This contribution aimed at developing an understanding of student teachers’ conceptions of guided discoveryteaching approaches. A cross-sectional survey design involving eleven secondary mathematics teachers who hadenrolled for an in-service mathematics education degree was used to address the research question: What areundergraduate student teachers’ conceptions of deductive and inductive teaching approaches? Task-based interviewswere used in conjunction with oral interviews as settings for unravelling students’ conceptions of the two teachingapproaches. Drawing in part from Ausbel’s learning theory and Tall’s notion of a met-before, the study also aimed atassessing the students’ level of grasp of fundamental limitation of empirical explorations despite many benefitsassociated with them such as helping in identifying patterns, use in formulation and communicating of conjecture,and providing insights on what needs to be solved. Verbatim transcriptions from follow up interviews and textualdata from task based interviews were subjected to directed content analysis to infer meaning about students’conceptions of guided teaching approaches. Qualitative data analysis using in part Robert Moore’s notion of conceptusage uncovered conceptual limitations that include inconsistencies in student teachers’ definitions of the teachingapproaches, use of specific examples instead of arbitrary mathematical objects in illustrating analytic teaching.Limitations identified should be given attention by mathematics educators in order to increase understanding of theapproaches among teachers. Research studies into factors contributing to limitations identified can go a long way inimproving the teaching and learning of school mathematics.
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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 | 0.042 | 0.034 |
| Meta-epidemiology (narrow) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.003 | 0.001 |
| Science and technology studies | 0.002 | 0.025 |
| Scholarly communication | 0.011 | 0.008 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".