Teaching Probability by Using Geogebra Dynamic Tool and Implemanting Critical Thinking Skills
Bibliographic record
Abstract
In this paper we explore the use of GeoGebra (as a visual dynamic tool) and critical thinking skills for supporting high school students' understanding of probability, more specifically, understanding of conditional probability and Bayes' theorem. The research presented is part of a broader research project on improving high school students' risk literacy and critical thinking. Decisions that involve the understanding of risk are made in all aspects of life including health (e.g. whether to continue with the course of medication), finances (paying for extra insurance) and politics (preemptive strikes versus political dialogue). These decisions are not only common, but they are also critical for individual and societal health and well being. Some studies have shown that people are routinely exposed to medical risk information and that their understanding of this information can have serious implications on their health. Despite its importance, most people are unable to adequately interpret and communicate risk. The goal of our research is to substantiate the claim that dynamic learning environment enables student to grasp abstract mathematical concept by manipulating mathematical objects constructed within these systems and implementing critical thinking skills.
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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 | 0.002 | 0.012 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.004 | 0.005 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.019 | 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".