Objective and subjective probability: Undergraduate students’ descriptions, examples, and arguments
Bibliographic record
Abstract
My thesis addresses several issues of importance to probability education, presented in four separate studies.The first study attends to definitions and examples of probability offered through resources and produced by undergraduate students.The findings suggest that the everyday notion of probability predates and dominates students' conception of mathematical probability and point out the important role learner-generated examples play in identifying the scope of learners' understanding of probability.The second study examines the distinction between mathematical and everyday aspects of zero-probable and one-probable (extreme) events as featured in a variety of resources and as exemplified by prospective secondary school teachers.Moreover, different types of probability apparent from examples are identified and discussed.The results suggest that the participants use a range of subjective, theoretical, and logical approaches to construct probability examples in everyday and mathematical contexts.The results identified the need for a clear distinction between the notions of 'zero-probable' and 'impossible' in probability instruction and call for pedagogical attention to this issue.The third study provides an overview of some of the ways in which randomness is defined in mathematics.The study examines and interprets undergraduate students' examples, definitions, and ideas related to randomness by analyzing the participants' written responses, verbal communications, and gestures.The findings were strongly related to those of previous research.The gesture analysis further identified some aspects of randomness that were less apparent in participants' verbal responses.The fourth study examines undergraduate students' arguments concerning the probability of a fixed and unknown event.The goal of the study was to identify ambiguity caused by the interaction between everyday and mathematical probability in participants' responses.The findings suggest that reflective tasks in which students are asked to examine and reflect on opposing probability arguments may help learners to reconcile some conflicting probability ideas.Overall, my research provides enhanced understanding of how participants perceived probability related ideas, as evident in their examples, definitions and gestures.Based on the results of my research, I present ideas and tasks for instructional implementation aimed at provoking discussion about different interpretations of probability and strengthening student understanding.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.004 | 0.016 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.004 | 0.003 |
| Open science | 0.001 | 0.004 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".