Investigating eighth-grade students’ conceptual understanding of cartesian coordinates in junior high school mathematics
Bibliographic record
Abstract
Understanding mathematical concepts is a crucial aspect of learning mathematics, as it enables students to solve problems, reason logically, and apply knowledge in various contexts. This study aimed to analyze eighth-grade students’ conceptual understanding of Cartesian coordinate material. The population of this research consisted of junior high school students in a school located in the Karawang district, with a sample of 30 students from class VIII. Data were collected using a mathematical comprehension test consisting of four questions, each designed to assess specific indicators of conceptual understanding, including identifying points, determining direction and distance, and analyzing the relative positions of lines. The results showed that students frequently made errors in several areas: many struggled to accurately identify points on the Cartesian plane, had difficulty determining direction and distance from a given point, and often misinterpreted the positions of lines relative to one another. These findings indicate that students’ conceptual understanding of Cartesian coordinates remains limited, which may hinder their overall mathematical performance. Therefore, it is recommended that teachers implement more targeted instructional strategies, such as visual representations, guided practice, and interactive exercises, to enhance students’ comprehension and strengthen their mathematical reasoning skills. The contribution of this study lies in providing empirical evidence on students’ specific misconceptions related to Cartesian coordinates and offering pedagogical implications that can inform the development of more effective instructional approaches in mathematics classrooms.
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 | 0.001 | 0.004 |
| 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 | 0.002 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".