INVESTIGATION OF MISTAKES AND MISCONCEPTIONS OF 8TH GRADE STUDENTS ACCORDING TO STUMP'S SLOPE PERCEPTION CLASSIFICATION
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Bibliographic record
Abstract
The aim of this research is to investigate eighth graders’ mistakes and misconceptions of the concept that take place in the mathematics curriculum and to make recommendations for solution. According to this purpose, the sample of the research consisted of 165 eighth graders from 4 different public schools located in Palandoken district of Erzurum province. The students of the sample were those, who were ready at the school on the day at which the research was carried out. To determine the mistakes and misconceptions of the students on the slope, a “Slope Test” consisting of 7 multiple choice questions and 8 open-ended questions, was created in accordance with the gains. Expert opinions were applied during developing the test, and validity and reliance studies were carried out through a pilot study. In the research, the Slope Test was applied to the students and this test was used as the data collection tool. The descriptive scanning method was employed in the research and as the interview was held with some of the students if necessary, the mixed method was the method of the study. The obtained data were analyzed with the descriptive analysis and content analysis techniques. The mistakes and misconceptions of the students were examined according to the results of the study and some recommendations were made considering the results. Keywords: Slope, misconception, eighth grade students, mathematics education. REFERENCES Barr, G. (1981). Some student ideas on the concept of gradient. Mathematics in School . 10 (1), 14-17. Cheng, D. S. (2010). Connecting proportionality and slope: Middle school students' reasoning about steepness . Boston: Boston University. Clement, J. (1985, July). Misconceptions in graphing. In Proceedings of the ninth international conference for the psychology of mathematics education (Vol. 1, pp. 369-375). Utrecht, the Netherlands: Utrecht University. Crawford, A. R., & Scott, W. E. (2000). Making sense of slope. The Mathematics Teacher , 93(2), 114-118. Creswell, J. W., & Clark, V. L. P. (2007). Designing and conducting mixed methods research . CA, Sage publications. Duncan, B., & Chick, H. L. (2013). How do adults perceive, analyse and measure slope?. In 36 th annual conference of Mathematics Education Research Group of Australasia , 258-265. Greene, J. C., Caracelli, V. J., & Graham, W. F. (1989). Toward a conceptual framework for mixed-method evaluation designs. Educational Evaluation and Policy Analysis , 11(3), 255-274. Hoffman, T. W. (2015). Concept image of slope: Understanding middle school mathematics teachers' perspective through task-based interviews. (Unpublished doctoral dissertation). The University of North Carolina at Charlotte. Milli Egitim Bakanligi (MEB) (2017). Ilkogretim matematik dersi 5-8. siniflar ogretim programi ve kilavuzu . Ankara: Devlet Kitaplari Mudurlugu Basimevi. Morse, J. M. (1991). Approaches to qualitative–quantitative methodological triangulation. Nursing Research , 40, 120–123. Ozbellek, G. (2003). Ilkogretim 6. ve 7. sinif duzeyindeki aci konusunda karsilasilan kavram yangilari, eksik algilamalarin tespiti [Confronted conceptions mistakes about angle, determaniation and elimination methods of deficient perceptions at 6 th and 7 th grades in primary education], (Unpublished Master Dissertation). Dokuz Eylul University, Izmir. Stump, S. (1999). Secondary mathematics teachers’ knowledge of slope. Mathematics Education Research Journal, 11 (2), 124-144. Styers, J. L., Nagle, C. R., & Moore-Russo, D. (2020). Teachers’ noticing of students’ slope statements: attending and interpreting. Canadian Journal of Science, Mathematics and Technology Education, 20 (3), 504-520. Yenilmez, K., & Yasa, E. (2008). Ilkogretim ogrencilerinin geometrideki kavram yanilgilari [Primary school students’ misconceptions about geometry]. Journal of Uludag University Faculty of Education, 21 (2), 461-483. Yildirim, A., & Simsek, H. (2016). Sosyal bilimlerde nitel arastirma yontemleri [Qualitative research methods in social sciences], 9 th Edition, Ankara: Seckin Publishing 256-272. Zandieh, M. J. (2000). A theoretical framework for analyzing student understanding of the concept of derivative. CBMS Issues in Mathematics Education , 8, 103-127.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it