Research Article
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Year 2024, Volume: 17 Issue: 3, 563 - 591, 25.07.2024
https://doi.org/10.30831/akukeg.1323295

Abstract

References

  • Akhtar, Z., Rashid, A., & Hussain, S. (2020). Writing equations in algebra: Investigation of students’ misconceptions. Sir Syed Journal of Education & Social Research, 3(4), 22-28. https://doi.org/10.36902/sjesr-vol3-iss4-2020(22-28)
  • An, S., & Wu, Z. (2012). Enhancing mathematics teachers’ knowledge of students’ thinking from assessing and analyzing misconceptions in homework. International Journal of Science and Mathematics Education, 10(3), 717-753. https://doi.org/doi:10.1007/s10763-011-9324-x
  • An, S., Kulm, G., & Wu, Z. (2004). The pedagogical content knowledge of middle school mathematics teachers in China and the U.S. Journal of Mathematics Teacher Education, 7 (2), 145–172. https://doi.org/10.1023/B:JMTE.0000021943.35739.1c
  • Aydin-Güç, F., & Aygün, D. (2021). Errors and misconceptions of eighth-grade students regarding operations with algebraic expressions. International Online Journal of Education and Teaching, 8(2), 1106-1126.
  • Baki, A. (1999). Cebirle ilgili işlem yanılgılarının değerlendirilmesi [Evaluation of algebra-related computing misconceptions]. In III. Ulusal Fen Eğitimi Sempozyumu Bildirileri Kitabı [National Science Education Symposium Proceedings Book] (pp.46-49). MEB.
  • Baki, A. (2008). Kuramdan uygulamaya matematik eğitimi [Mathematics education from theory to practice]. Harf Eğitim.
  • Barbieri, C. A., Miller-Cotto, D., & Booth, J. L. (2019). Lessening the load of misconceptions: Design-based principles for algebra learning. Journal of the Learning Sciences, 28(3), 381-417. https://doi.org/10.1080/10508406.2019.1573428
  • Baş, S., Erbaş, A. K. & Çetinkaya, B. (2011). Öğretmenlerin dokuzuncu sınıf öğrencilerinin cebirsel düşünme yapılarıyla ilgili görüşleri [Teachers’ knowledge about ninth grade students’ ways of algebraic thinking]. Education and Science, 36(159), 41-55.
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  • Birgin, O., & Demirören, K. (2020). Sekizinci sınıf öğrencilerinin basit görsel ve cebirsel ifadeler konusundaki hata ve kavram yanılgılarının incelenmesi [Investigation of the preservice science teachers’ views and suggestions on the application of the cooperative learning model in distance education environments]. International Journal of Social and Educational Sciences, 7(14), 233-247.
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  • Brown, C., & Borko, H. (1992). Becoming a mathematics teacher. In D.A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 209-239). Macmillan Publishing.
  • Bukova-Güzel, E. (2016). Matematik eğitiminde matematiksel modelleme [Mathematical modeling in mathematics education]. Pegem.
  • Bursali, G. G., & Gökkurt-Özdemir, B. (2019). Instructional explanations of mathematics teachers and preservice teachers on misconceptions: The subject of probability. Journal of Computer and Education Research, 7(14), 642-672. https://doi.org/ doi: 10.18009/jcer.639384
  • Bush, S. B., & Karp, K. S. (2013). Prerequisite algebra skills and associated misconceptions of middle grade students: a review. The Journal of Mathematical Behavior, 32(3), 613-632. https://doi.org/10.1016/j.jmathb.2013.07.002
  • Çakmak Gürel, Z., & Okur, M. (2018). 7. ve 8. sınıf öğrencilerinin eşitlik ve denklem konusundaki kavram yanılgıları [The misconceptions of 7th and 8th graders on the equality and equation topics]. Cumhuriyet International Journal of Education, 6(4), 479-507. https://doi.org/10.30703/cije.342074
  • Chick, H. L., & Baker, M. K. (2005). Investigating teachers’ responses to student misconceptions. In H. L. Chick, and J. L. Vincent (Eds.), Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education (pp. 249-256). PME.
  • Cochran, K. F., DeRuiter, J. A., & King, R. A. (1993). Pedagogical content knowing: An integrative model for teacher preparation. Journal of Teacher Education, 44(4), 263-272. https://doi.org/10.1177/002248719304400400
  • Dede, Y., & Peker, M. (2007). Students’ errors and misunderstanding towards algebra: Pre-service mathematics teachers’ prediction skills of error and misunderstanding and solution suggestions. Elementary Education Online, 6(1), 35-49.
  • Demirören, K. (2019). Investigation of the 8th grade students' mistakes and misconceptions about algebrary expressions [Unpublished master thesis]. Uşak University, Uşak.
  • Di Martino, P., Gregorio, F., & Iannone, P. (2023). The transition from school to university mathematics in different contexts: affective and sociocultural issues in students’ crisis. Educational Studies in Mathematics, 113(1), 79-106. https://doi.org/10.1007/s10649-022-10179-9
  • Driver, R., & Easley, J. (1978). Pupils and paradigms: A review of literature related to concept development in adolescent science students. Studies in Science Education, 5(1978), 61- 84. https://doi.org/10.1080/03057267808559857
  • Ebenezer, J. V., & Fraser, D. M. (2001). First year chemical engineering students' conceptions of energy in solution processes: Phenomenographic categories for common knowledge construction. Science Education, 85(5), 509-535. https://doi.org/10.1002/sce.1021
  • Erdem, Ö., & Sarpkaya Aktaş, G. (2018). Assessment of activity-based instruction in overcoming 7th grade middle school students’ misconceptions in algebra. Turkish Journal of Computer and Mathematics Education, 9(2), 312-338. https://doi.org/ doi: 10.16949/turkbilmat.333612
  • Ersoy, Y., & Erbaş, A. K. (2005). Kassel projesi cebir testinde bir grup Türk öğrencinin genel başarısı ve öğrenme güçlükleri [General achievement and learning difficulties of a group of Turkish students in the Kassel project algebra test]. Elementary Education Online, 4(1), 18-39.
  • Even, R., & Tirosh, D. (1995). Subject matter knowledge and knowledge about students as sources of teacher presentations of the subject-matter. Educational Studies in Mathematics, 29(1), 1-20. https://doi.org/10.1007/BF01273897
  • Fennema, E., & Franke, M. L. (1992). Teachers' knowledge and its impact. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (pp. 47–164). Macmillan.
  • Gelbal, S., & Kelecioğlu, H. (2007). Öğretmenlerin ölçme ve değerlendirme yöntemleri hakkındaki yeterlik algıları ve karşılaştıkları sorunlar [Teachers’ proficiency perceptions of about the measurement and evaluation techniques and the problems they confront]. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi [Hacettepe University Journal of Education], 33, 135-145.
  • Gökkurt-Özdemir, B., & Soylu, Y. (2017). Examination of the pedagogical content knowledge of mathematics teachers. International Online Journal of Primary Education, 6(1), 26-39.
  • Grouws, D., & Schultz, K. (1996). Mathematics teacher education. In J. Sikula (Ed.), Handbook of research on teacher education. Macmillan.
  • Güler, M. (2014). Investigating pre-service teachers' knowledge for teaching mathematics: the sample of algebra [Unpublished master thesis]. Karadeniz Technical University, Trabzon. Gür, H., & Kobak Demir, M. (2019). Matematik öğretmenlerinin öğretim profillerinin belirlenmesi [Determining teaching profiles of mathematics teachers]. Uluslararası Eğitim Bilim ve Teknoloji Dergisi [International Journal of Education Science and Technology], 5(2), 67-105.
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  • Kılıç, H. (2011). Preservice secondary mathematics teachers’ knowledge of students. Turkish Online Journal of Qualitative Inquiry, 2(2), 17-35. https://doi.org/10.17569/tojqi.93311
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Examining the Process of Middle School Math Teachers Diagnosing and Eliminating Student Misconceptions in Algebra

Year 2024, Volume: 17 Issue: 3, 563 - 591, 25.07.2024
https://doi.org/10.30831/akukeg.1323295

Abstract

The aim of this study is to examine how middle school mathematics teachers diagnose and attempt to eliminate students' misconceptions in algebra. The study employed a case study method and embedded single-case design within its scope. The research was conducted with three mathematics teachers working in different state schools and having different professional experiences, as well as ten students from the eighth-grade classes of the same schools. The data collection instruments used in the study included the Diagnostic Test developed by researchers to identify students with misconceptions, the Assessment Framework prepared for the evaluation of teacher performances in diagnosing and eliminating student misconceptions, and Semi-Structured Interviews conducted between students and teachers, which were recorded and made available in audio/video format. The study revealed that teachers generally resorted to conventional methods in the process of diagnosing and eliminating students' misconceptions. In most cases, teachers superficially addressed students' errors and did not fully focus on students' thinking. Regarding the processes aimed at eliminating student misconceptions, it was observed that teachers preferred to directly inform students that their answers were incorrect, rather than facilitating students in recognizing their own errors. The findings of this study highlight the need to increase teachers' awareness and student knowledge regarding misconceptions in algebra.

References

  • Akhtar, Z., Rashid, A., & Hussain, S. (2020). Writing equations in algebra: Investigation of students’ misconceptions. Sir Syed Journal of Education & Social Research, 3(4), 22-28. https://doi.org/10.36902/sjesr-vol3-iss4-2020(22-28)
  • An, S., & Wu, Z. (2012). Enhancing mathematics teachers’ knowledge of students’ thinking from assessing and analyzing misconceptions in homework. International Journal of Science and Mathematics Education, 10(3), 717-753. https://doi.org/doi:10.1007/s10763-011-9324-x
  • An, S., Kulm, G., & Wu, Z. (2004). The pedagogical content knowledge of middle school mathematics teachers in China and the U.S. Journal of Mathematics Teacher Education, 7 (2), 145–172. https://doi.org/10.1023/B:JMTE.0000021943.35739.1c
  • Aydin-Güç, F., & Aygün, D. (2021). Errors and misconceptions of eighth-grade students regarding operations with algebraic expressions. International Online Journal of Education and Teaching, 8(2), 1106-1126.
  • Baki, A. (1999). Cebirle ilgili işlem yanılgılarının değerlendirilmesi [Evaluation of algebra-related computing misconceptions]. In III. Ulusal Fen Eğitimi Sempozyumu Bildirileri Kitabı [National Science Education Symposium Proceedings Book] (pp.46-49). MEB.
  • Baki, A. (2008). Kuramdan uygulamaya matematik eğitimi [Mathematics education from theory to practice]. Harf Eğitim.
  • Barbieri, C. A., Miller-Cotto, D., & Booth, J. L. (2019). Lessening the load of misconceptions: Design-based principles for algebra learning. Journal of the Learning Sciences, 28(3), 381-417. https://doi.org/10.1080/10508406.2019.1573428
  • Baş, S., Erbaş, A. K. & Çetinkaya, B. (2011). Öğretmenlerin dokuzuncu sınıf öğrencilerinin cebirsel düşünme yapılarıyla ilgili görüşleri [Teachers’ knowledge about ninth grade students’ ways of algebraic thinking]. Education and Science, 36(159), 41-55.
  • Baykul, Y. (2014). Ortaokulda matematik öğretimi (5-8. sınıflar) [Teaching mathematics in secondary school (5th-8th grades)]. Pegem.
  • Bingölbali, F. (2010). The causes of students’ difficulties encountered during the task implementation in mathematics teaching and types of teachers’ interventions [Unpublished master thesis]. Gaziantep University, Gaziantep.
  • Birgin, O., & Demirören, K. (2020). Sekizinci sınıf öğrencilerinin basit görsel ve cebirsel ifadeler konusundaki hata ve kavram yanılgılarının incelenmesi [Investigation of the preservice science teachers’ views and suggestions on the application of the cooperative learning model in distance education environments]. International Journal of Social and Educational Sciences, 7(14), 233-247.
  • Borko, H., & Putnam, R. T. (1996). Learning to teach. In D.C. Berliner and R.C. Calfee (Eds.), Handbook of educational psychology (pp. 673–708). Simon and Schuster Macmillan.
  • Brown, C., & Borko, H. (1992). Becoming a mathematics teacher. In D.A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 209-239). Macmillan Publishing.
  • Bukova-Güzel, E. (2016). Matematik eğitiminde matematiksel modelleme [Mathematical modeling in mathematics education]. Pegem.
  • Bursali, G. G., & Gökkurt-Özdemir, B. (2019). Instructional explanations of mathematics teachers and preservice teachers on misconceptions: The subject of probability. Journal of Computer and Education Research, 7(14), 642-672. https://doi.org/ doi: 10.18009/jcer.639384
  • Bush, S. B., & Karp, K. S. (2013). Prerequisite algebra skills and associated misconceptions of middle grade students: a review. The Journal of Mathematical Behavior, 32(3), 613-632. https://doi.org/10.1016/j.jmathb.2013.07.002
  • Çakmak Gürel, Z., & Okur, M. (2018). 7. ve 8. sınıf öğrencilerinin eşitlik ve denklem konusundaki kavram yanılgıları [The misconceptions of 7th and 8th graders on the equality and equation topics]. Cumhuriyet International Journal of Education, 6(4), 479-507. https://doi.org/10.30703/cije.342074
  • Chick, H. L., & Baker, M. K. (2005). Investigating teachers’ responses to student misconceptions. In H. L. Chick, and J. L. Vincent (Eds.), Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education (pp. 249-256). PME.
  • Cochran, K. F., DeRuiter, J. A., & King, R. A. (1993). Pedagogical content knowing: An integrative model for teacher preparation. Journal of Teacher Education, 44(4), 263-272. https://doi.org/10.1177/002248719304400400
  • Dede, Y., & Peker, M. (2007). Students’ errors and misunderstanding towards algebra: Pre-service mathematics teachers’ prediction skills of error and misunderstanding and solution suggestions. Elementary Education Online, 6(1), 35-49.
  • Demirören, K. (2019). Investigation of the 8th grade students' mistakes and misconceptions about algebrary expressions [Unpublished master thesis]. Uşak University, Uşak.
  • Di Martino, P., Gregorio, F., & Iannone, P. (2023). The transition from school to university mathematics in different contexts: affective and sociocultural issues in students’ crisis. Educational Studies in Mathematics, 113(1), 79-106. https://doi.org/10.1007/s10649-022-10179-9
  • Driver, R., & Easley, J. (1978). Pupils and paradigms: A review of literature related to concept development in adolescent science students. Studies in Science Education, 5(1978), 61- 84. https://doi.org/10.1080/03057267808559857
  • Ebenezer, J. V., & Fraser, D. M. (2001). First year chemical engineering students' conceptions of energy in solution processes: Phenomenographic categories for common knowledge construction. Science Education, 85(5), 509-535. https://doi.org/10.1002/sce.1021
  • Erdem, Ö., & Sarpkaya Aktaş, G. (2018). Assessment of activity-based instruction in overcoming 7th grade middle school students’ misconceptions in algebra. Turkish Journal of Computer and Mathematics Education, 9(2), 312-338. https://doi.org/ doi: 10.16949/turkbilmat.333612
  • Ersoy, Y., & Erbaş, A. K. (2005). Kassel projesi cebir testinde bir grup Türk öğrencinin genel başarısı ve öğrenme güçlükleri [General achievement and learning difficulties of a group of Turkish students in the Kassel project algebra test]. Elementary Education Online, 4(1), 18-39.
  • Even, R., & Tirosh, D. (1995). Subject matter knowledge and knowledge about students as sources of teacher presentations of the subject-matter. Educational Studies in Mathematics, 29(1), 1-20. https://doi.org/10.1007/BF01273897
  • Fennema, E., & Franke, M. L. (1992). Teachers' knowledge and its impact. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (pp. 47–164). Macmillan.
  • Gelbal, S., & Kelecioğlu, H. (2007). Öğretmenlerin ölçme ve değerlendirme yöntemleri hakkındaki yeterlik algıları ve karşılaştıkları sorunlar [Teachers’ proficiency perceptions of about the measurement and evaluation techniques and the problems they confront]. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi [Hacettepe University Journal of Education], 33, 135-145.
  • Gökkurt-Özdemir, B., & Soylu, Y. (2017). Examination of the pedagogical content knowledge of mathematics teachers. International Online Journal of Primary Education, 6(1), 26-39.
  • Grouws, D., & Schultz, K. (1996). Mathematics teacher education. In J. Sikula (Ed.), Handbook of research on teacher education. Macmillan.
  • Güler, M. (2014). Investigating pre-service teachers' knowledge for teaching mathematics: the sample of algebra [Unpublished master thesis]. Karadeniz Technical University, Trabzon. Gür, H., & Kobak Demir, M. (2019). Matematik öğretmenlerinin öğretim profillerinin belirlenmesi [Determining teaching profiles of mathematics teachers]. Uluslararası Eğitim Bilim ve Teknoloji Dergisi [International Journal of Education Science and Technology], 5(2), 67-105.
  • Kaya, D. (2015). A study on the effects of multiple representations-based instruction on students’ algebraic reasoning skills, algebraic thinking levels and attitudes towards mathematics [Unpublished master thesis]. Dokuz Eylül University, İzmir.
  • Kieran, C. (1992). The learning and teaching of school algebra. In D.A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp.390-419). Macmillan.
  • Kılcan, S. A. (2006). The levels of elementary mathematics teachers' conceptual knowledge of the division with fractions [Unpublished master thesis]. Abant İzzet Baysal University, Bolu.
  • Kılıç, H. (2011). Preservice secondary mathematics teachers’ knowledge of students. Turkish Online Journal of Qualitative Inquiry, 2(2), 17-35. https://doi.org/10.17569/tojqi.93311
  • Kimii, C., & Declark. G. (1985). Young children reinvent arithmetic: Implications of Piaget’s theory. Teachers College Press.
  • Kinach, B. M. (2002a). A cognitive strategy for developing pedagogical content knowledge in the secondary mathematics methods course: Toward a model of effective practice. Teaching and Teacher Education, 18(1), 51-71. https://doi.org/10.1016/S0742-051X(01)00050-6
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There are 73 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Hüseyin Kabadaş 0000-0002-1679-6088

Hayal Yavuz Mumcu 0000-0002-6720-509X

Publication Date July 25, 2024
Submission Date July 5, 2023
Published in Issue Year 2024 Volume: 17 Issue: 3

Cite

APA Kabadaş, H., & Yavuz Mumcu, H. (2024). Examining the Process of Middle School Math Teachers Diagnosing and Eliminating Student Misconceptions in Algebra. Journal of Theoretical Educational Science, 17(3), 563-591. https://doi.org/10.30831/akukeg.1323295