Building Learning Trajectory Mathematical Problem Solving Ability in Circle Tangent Topic by Applying Metacognition Approach
Bibliographic record
Abstract
Mathematical problem solving ability is one of the most important abilities students must have to process the information provided in solving problems. Before using mathematical problem solving skills, prior knowledge becomes the most crucial thing that makes students able to connect all available information so that they can construct new knowledge through the process of assimilation or accommodation.The purpose of this reseach is to:(1) Analyze prior knowledge what student has so the student can solve the problem of tangent circle given; (2) Know how learning trajectory in student’s mathematical problem solving ability by applying metacognition approach. This reaseacrch is a design research to improve the quality of learning. In this reseacrh researchers gave 3 test questions on students’ mathematical problem solving abilities. One trial was conducted in class VIII-B and trial II was conducted in class VIII-A, each consisting of 30 students junior high school. The result of students answer analysis shows the mast problematic topic that makes the studnts are difficult to solve the problem is about the tangent cicrcle that is the elements of the circle and the concept of circle circumtance there are three phased in learning path of students mathematical problem solving skill that are under standing the problem, making the problem solving plan by prrior knowledge and doing problem solving and evaluating it. From this explanation, it is better for teachers to ensure students have sufficient prior knowledge to make it easier to construct new knowledge, as well as make the learning process fun and meaningful so that students will remember knowledge in long-term memory.
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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 | 0.001 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".