The effect of positive error climate on affective domains in mathematics teaching
Year 2022,
Volume: 9 Issue: Special Issue, 236 - 257, 29.11.2022
Merve Özkaya
,
Senem Kalaç
,
Alper Cihan Konyalıoğlu
Abstract
The aim of this study is to investigate the effect of positive error climate in classrooms on middle school students' error orientations and attitudes towards mathematics. The data of the research were collected in the 2021-2022 academic year. The participants of the study consisted of 44 students in two 6th grade classes in a middle school in the city of Van, Türkiye. Quasi-experimental design was used in the research and the pre and post scores of the experimental and comparison groups were compared before and after the study. The data obtained using the "Mathematics Attitude Scale" and the "Error Climate Scale" were analyzed to examine the differences within and between groups. As a result of the findings, it was seen that the positive error climate in the experimental group made a positive significant difference both on the attitude towards mathematics and on error orientations of the students. No significant change was observed at the end of the study in the comparison group in which a neutral error climate was applied. The interviews with the course teacher who carried out the application and the observations made in the classroom reinforced the positive effect of the application. Positive error climate can be seen as a part of formative assessment as it has a corrective effect on teaching in the process.
References
- Akınoğlu, O. (2004). Sınıfta grup etkileşimi [Group interaction in the classroom]. In Z. Kaya (Ed.), Sınıf yönetimi [Class management] (pp. 111-130). Pegem Akademi.
- Akkuşci, Y. E. (2019). Investigation of the effectiveness of using mistake – handling activity applications in classroom in mathematics teaching [Master's dissertation, Ataturk Unıversıty]. YÖK National Thesis Center. https://tez.yok.gov.tr/UlusalTezMerkezi/tezSorguSonucYeni.jsp
- Akpınar, B., & Akdoğan, S. (2010). Negative knowledge concept: Learning from mistakes and failures. The Western Anatolia Journal of Educational Sciences, 1(1), 14-22. https://dergipark.org.tr/en/pub/baebd/issue/3342/46246
- Avcı, E., Coşkuntuncel, O., & İnandı, Y. (2011). Attitudes of twelfth grade students towards mathematics. Mersin University Journal of the Faculty of Education, 7(1), 50-58.
- Baki, A. (2015). Kuramdan uygulamaya matematik eğitimi [Mathematics education from theory to practice] (6th ed.). Harf Eğitim Yayıncılığı.
- Barbieri C.A., & Booth J.L. (2020). Mistakes on display: Incorrect examples refine equation solving and algebraic feature knowledge. Applied Cognitive Psychology, 34(1), 862-878. https://doi.org/10.1002/acp.3663
- Baştürk, S. (2014). Matematik öğretiminde öğrenci hatasının yeri: Hata ve engel kavramı [The place of student error in mathematics teaching: The concept of error and obstacle]. Bilim ve Aklın Aydınlığında Eğitim, 166(1), 14 23. https://www.researchgate.net/publication/312295181
- Borasi, R. (1986). On the educational roles of mathematical errors: Beyond diagnosis and remediation [Doctoral Dissertation, State University of New York]. Ataturk University Libraries. https://www.proquest.com/pagepdf/303527036?accountid=8403
- Borasi, R. (1988, April). Towards a reconceptualization of the role of errors in education: The need for new metaphors [Conference session]. Annual Meeting of the American Educational Research Association. https://eric.ed.gov/?id=ED295969
- Borasi, R. (1989, March). Students’ constructive uses of mathematical errors: A taxonomy [Conference session]. Annual Meeting of the American Educational Research Association, https://eric.ed.gov/?id=ED309069
- Borasi, R. (1994). Capitalizing on errors as "springboards for inquiry": A teaching experiment. Journal for Research in Mathematics Education, 25(21), 166 208. https://doi.org/10.5951/jresematheduc.25.2.0166
- Borasi, R. (1996). Reconceiving mathematics instruction: A focus on errors. Ablex Publishing Corporation.
- Bray, W.S. (2011). A collective case study of the influence of teachers' beliefs and knowledge on error-handling practices during class discussion of mathematics. Journal for Research in Mathematics education, 42(1), 2-38. https://doi.org/10.5951/jresematheduc.42.1.0002
- Bray, W., & Santagata, R. (2013, January 24-26). Developing teaching capacity for making productive use of mathematical errors [Conference session]. Association of Mathematics Teacher Educators Annual Meeting, Orlando Florida, USA.
- Büyüköztürk, Ş. (2020). Sosyal bilimler için veri analizi el kitabı; İstatistik, araştırma deseni SPSS uygulamaları ve yorum [Manual of data analysis for social sciences; Statistics, research design SPSS applications and interpretation] (28th ed.). Pegem Akademi.
- Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Earlbaum Associates.
- Didiş, M. G., Erbaş, A. K., & Çetinkaya, B. (2016). Matematik öğretmen adaylarının öğrenci hatalarına yönelik pedagojik yaklaşımlarının matematiksel modelleme bağlamında incelenmesi [Investigating prospective mathematics teachers’ pedagogical approaches in response to students’ errors in the context of mathematical modeling activities]. Elementary Education Online, 15(4), 1367-1384. https://doi.org/10.17051/io.2016.75429
- Didiş-Kabar, M.G., & Amaç, R. (2018). Investigating pre-service middle-school mathematics teachers’ knowledge of student and instructional strategies: An algebra case. Bolu Abant İzzet Baysal Journal of Education, 18(1), 157 185. https://doi.org/10.17240/aibuefd.2018..-359810
- Ekiz, D. (2009). Bilimsel araştırma yöntemleri [Scientific research methods] (2nd ed.). Anı Yayıncılık.
- Erbaş, A.K., Çetinkaya, B., & Ersoy, Y. (2009). Student difficulties and misconceptions in solving simple linear equations. Education and Science, 34(152), 44-59. http://egitimvebilim.ted.org.tr/index.php/EB/article/view/7
- Fraenkel, J.R., Wallen, N.E., & Hyun, H.H. (2012). How to design and evaluate research in education (8th ed.). McGraw Hill.
- Gedik, S. D. (2014). Effect of mistake-handling activities to mathematics content knowledge development process [Doctoral dissertation, Ataturk University]. YÖK National Thesis Center. https://tez.yok.gov.tr/UlusalTezMerkezi/tezSorguSonucYeni.jsp
- Guzmán-Muñoz, F.J., Gruber, H., Heid, H., Lorenzer, K., Bauer, J., Heinze, A., Tuerling, J.M., Nägele, C., Baumgartner, A., Anja, M., Seifried, J., Link, M., Gartmeier, M., & Wuttke, E. (2009, September 25-30). Learning from errors [Conference session]. ECER, Vienna, Austria. https://eera-ecer.de/ecer-programmes/conference/2/contribution/2488/
- Haser, Ç., & Ubuz, B. (2000, September 6-8). İlköğretim 5. sınıf öğrencilerinin kesirler konusunda kavramsal anlama ve işlem yapma becerileri [Elementary school 5th grade students' conceptual understanding and processing skills about fractions]. IV. Congress of Science Education, Ankara, Turkey.
- Heinze, A. (2005). Mistake-handling activities in German mathematics classroom. In H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 105- 112). PME.
- Heinze, A., & Reiss, K. (2007). Mistake-handling activities in the mathematics classroom: Effects of an in-service teacher training on students’ performance in geometry. In J.-H. Woo, H.-C. Lew, K.-S. Park, & D.-Y. Seo (Eds.), Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 9-16). PME.
- Huelser, B.J., & Metcalfe, J., (2012). Making related errors facilitates learning, but learners do not know it. Memory & Cognition, 40, 514 527. https://sci hub.mksa.top/10.3758/s13421-011-0167-z
- İlhan, M. (2017). The predictive role of students’ perceptions of classroom assessment environment on their attitudes towards school. Kastamonu Education Journal, 25(1), 111-128. https://dergipark.org.tr/tr/pub/kefdergi/issue/27737/308251
- Ingram, J., Pitt, A., & Baldry, F. (2015). Handling errors as they arise in whole- class interactions. Research in Mathematics Education, 17(3), 183 197. https://doi.org/10.1080/14794802.2015.1098562
- Kalaç, S., & Özkaya., M (2021). Sınıf içi olumlu hata iklimi uygulamaları [Positive error climate practices in the classroom]. In A. Kızılkaya Namlı (Ed.), Eğitimin kavramsal temelleri 4: Yöntem ve stratejiler [Conceptual basics of education 4: Methods and strategies] (pp. 231-244). Efe Akademi.
- Kalaç, S., Özkaya, M., & Konyalıoğlu, A.C. (2022). The adaptation of the perceived error climate scale into Turkish. Educational Academic Research, 44(1), 100 109. https://doi.org/10.54614/AUJKKEF.2022.11-22
- Karadağ, Z. (2004, November 24-26). Hatalardan öğrenme yönteminin bilgisayar destekli matematik 664 öğretiminde uygulanması (Koordinat düzlemi ve simetri konusu) [Application of learning from mistakes method in computer assisted mathematics teaching (Coordinate plane and symmetry issue)]. IETC 4th International Educational Technology Conference, Sakarya, Turkey. https://www.iet c.net/publication_folder/ietc/ietc2004.pdf
- Kaya, R. (2015). Investigation of the 6th grade students' misconceptions about representations of the decimal numbers [Master's thesis, Uşak University]. YÖK National Thesis Center. https://tez.yok.gov.tr/UlusalTezMerkezi/tezSorguSonucYeni.jsp
- Kohen, L. (2006). Student and teacher expectations in creating a suitable classroom environment for effective classroom management, an application from universities in Istanbul [Master’s thesis, Yeditepe University]. YÖK National Thesis Center. https://tez.yok.gov.tr/UlusalTezMerkezi/tezSorguSonucYeni.jsp
- McMillan, J.H. (2015). Sınıf içi değerlendirme, etkili ölçütlere dayalı etkili bir öğretim için ilke ve uygulamalar (A. Arı, Trans.). Eğitim Yayınevi (Original work published in 2014).
- McMillan, J.H., & Schumacher, S. (2010). Research in education: Evidence-based inquiry (7. Ed.). Pearson.
- McMillan, J.H., & Workman, D.J. (1998). Classroom assessment and grading practices: A review of the literature. Metropolitan Educational Research Consortium (ERIC Document Reproduction Service No. ED453263). https://files.eric.ed.gov/fulltext/ED453263.pdf
- Metcalfe, J. (2017). Learning from errors. Annual Review of Psychology, 68(1), 465-489. https://doi.org/10.1146/annurev-psych-010416-044022
- National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. NCTM.
- Öcalan, T. (2004). İlköğretimde matematik öğretimi [Mathematics teaching in primary education]. Yeryüzü Yayınevi.
- O'Dell, S. (2015). Classroom error climate: Teacher professional development to improve student motivation [Doctoral thesis, University of Central Florida]. Electronic Theses and Dissertations. https://stars.library.ucf.edu/etd/704/
- Önal, N. (2013). A study on the development of a middle school students’ attitudes towards mathematics scale. Elementary Education Online, 12(4), 938‐948. http://ilkogretim‐online.org.tr
- Oser, F., & Spychiger, M.B. (2005). Lernen ist schmerzhaft: Zur theorie des negativen wissens und zur praxis der fehlerkultur. Beltz-Pädagogik.
- Özdamar, K. (2018). Eğitim, sağlık ve sosyal bilimler için SPSS uygulamalı temel istatistik [SPSS applied basic statistics for education, health and social sciences]. Nisan kitapevi.
- Özkaya, M. (2015). A study on the impact of mistake-handling activities on mathematics 697 teachers' professional development [Doctoral thesis, Ataturk University]. National Thesis Center. https://tez.yok.gov.tr/UlusalTezMerkezi/tezSorguSonucYeni.jsp
- Özkaya, M., & Konyalıoğlu, A.C. (2019). Mistake handling activities in the development of middle school mathematics teachers’ subject matter knowledge: Addition operation with fractions. Journal of Bayburt Education Faculty, 14(27), 23 52. https://doi.org/10.35675/befdergi.475076
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The effect of positive error climate on affective domains in mathematics teaching
Year 2022,
Volume: 9 Issue: Special Issue, 236 - 257, 29.11.2022
Merve Özkaya
,
Senem Kalaç
,
Alper Cihan Konyalıoğlu
Abstract
The aim of this study is to investigate the effect of positive error climate in classrooms on middle school students' error orientations and attitudes towards mathematics. The data of the research were collected in the 2021-2022 academic year. The participants of the study consisted of 44 students in two 6th grade classes in a middle school in the city of Van, Türkiye. Quasi-experimental design was used in the research and the pre and post scores of the experimental and comparison groups were compared before and after the study. The data obtained using the "Mathematics Attitude Scale" and the "Error Climate Scale" were analyzed to examine the differences within and between groups. As a result of the findings, it was seen that the positive error climate in the experimental group made a positive significant difference both on the attitude towards mathematics and on error orientations of the students. No significant change was observed at the end of the study in the comparison group in which a neutral error climate was applied. The interviews with the course teacher who carried out the application and the observations made in the classroom reinforced the positive effect of the application. Positive error climate can be seen as a part of formative assessment as it has a corrective effect on teaching in the process.
References
- Akınoğlu, O. (2004). Sınıfta grup etkileşimi [Group interaction in the classroom]. In Z. Kaya (Ed.), Sınıf yönetimi [Class management] (pp. 111-130). Pegem Akademi.
- Akkuşci, Y. E. (2019). Investigation of the effectiveness of using mistake – handling activity applications in classroom in mathematics teaching [Master's dissertation, Ataturk Unıversıty]. YÖK National Thesis Center. https://tez.yok.gov.tr/UlusalTezMerkezi/tezSorguSonucYeni.jsp
- Akpınar, B., & Akdoğan, S. (2010). Negative knowledge concept: Learning from mistakes and failures. The Western Anatolia Journal of Educational Sciences, 1(1), 14-22. https://dergipark.org.tr/en/pub/baebd/issue/3342/46246
- Avcı, E., Coşkuntuncel, O., & İnandı, Y. (2011). Attitudes of twelfth grade students towards mathematics. Mersin University Journal of the Faculty of Education, 7(1), 50-58.
- Baki, A. (2015). Kuramdan uygulamaya matematik eğitimi [Mathematics education from theory to practice] (6th ed.). Harf Eğitim Yayıncılığı.
- Barbieri C.A., & Booth J.L. (2020). Mistakes on display: Incorrect examples refine equation solving and algebraic feature knowledge. Applied Cognitive Psychology, 34(1), 862-878. https://doi.org/10.1002/acp.3663
- Baştürk, S. (2014). Matematik öğretiminde öğrenci hatasının yeri: Hata ve engel kavramı [The place of student error in mathematics teaching: The concept of error and obstacle]. Bilim ve Aklın Aydınlığında Eğitim, 166(1), 14 23. https://www.researchgate.net/publication/312295181
- Borasi, R. (1986). On the educational roles of mathematical errors: Beyond diagnosis and remediation [Doctoral Dissertation, State University of New York]. Ataturk University Libraries. https://www.proquest.com/pagepdf/303527036?accountid=8403
- Borasi, R. (1988, April). Towards a reconceptualization of the role of errors in education: The need for new metaphors [Conference session]. Annual Meeting of the American Educational Research Association. https://eric.ed.gov/?id=ED295969
- Borasi, R. (1989, March). Students’ constructive uses of mathematical errors: A taxonomy [Conference session]. Annual Meeting of the American Educational Research Association, https://eric.ed.gov/?id=ED309069
- Borasi, R. (1994). Capitalizing on errors as "springboards for inquiry": A teaching experiment. Journal for Research in Mathematics Education, 25(21), 166 208. https://doi.org/10.5951/jresematheduc.25.2.0166
- Borasi, R. (1996). Reconceiving mathematics instruction: A focus on errors. Ablex Publishing Corporation.
- Bray, W.S. (2011). A collective case study of the influence of teachers' beliefs and knowledge on error-handling practices during class discussion of mathematics. Journal for Research in Mathematics education, 42(1), 2-38. https://doi.org/10.5951/jresematheduc.42.1.0002
- Bray, W., & Santagata, R. (2013, January 24-26). Developing teaching capacity for making productive use of mathematical errors [Conference session]. Association of Mathematics Teacher Educators Annual Meeting, Orlando Florida, USA.
- Büyüköztürk, Ş. (2020). Sosyal bilimler için veri analizi el kitabı; İstatistik, araştırma deseni SPSS uygulamaları ve yorum [Manual of data analysis for social sciences; Statistics, research design SPSS applications and interpretation] (28th ed.). Pegem Akademi.
- Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Earlbaum Associates.
- Didiş, M. G., Erbaş, A. K., & Çetinkaya, B. (2016). Matematik öğretmen adaylarının öğrenci hatalarına yönelik pedagojik yaklaşımlarının matematiksel modelleme bağlamında incelenmesi [Investigating prospective mathematics teachers’ pedagogical approaches in response to students’ errors in the context of mathematical modeling activities]. Elementary Education Online, 15(4), 1367-1384. https://doi.org/10.17051/io.2016.75429
- Didiş-Kabar, M.G., & Amaç, R. (2018). Investigating pre-service middle-school mathematics teachers’ knowledge of student and instructional strategies: An algebra case. Bolu Abant İzzet Baysal Journal of Education, 18(1), 157 185. https://doi.org/10.17240/aibuefd.2018..-359810
- Ekiz, D. (2009). Bilimsel araştırma yöntemleri [Scientific research methods] (2nd ed.). Anı Yayıncılık.
- Erbaş, A.K., Çetinkaya, B., & Ersoy, Y. (2009). Student difficulties and misconceptions in solving simple linear equations. Education and Science, 34(152), 44-59. http://egitimvebilim.ted.org.tr/index.php/EB/article/view/7
- Fraenkel, J.R., Wallen, N.E., & Hyun, H.H. (2012). How to design and evaluate research in education (8th ed.). McGraw Hill.
- Gedik, S. D. (2014). Effect of mistake-handling activities to mathematics content knowledge development process [Doctoral dissertation, Ataturk University]. YÖK National Thesis Center. https://tez.yok.gov.tr/UlusalTezMerkezi/tezSorguSonucYeni.jsp
- Guzmán-Muñoz, F.J., Gruber, H., Heid, H., Lorenzer, K., Bauer, J., Heinze, A., Tuerling, J.M., Nägele, C., Baumgartner, A., Anja, M., Seifried, J., Link, M., Gartmeier, M., & Wuttke, E. (2009, September 25-30). Learning from errors [Conference session]. ECER, Vienna, Austria. https://eera-ecer.de/ecer-programmes/conference/2/contribution/2488/
- Haser, Ç., & Ubuz, B. (2000, September 6-8). İlköğretim 5. sınıf öğrencilerinin kesirler konusunda kavramsal anlama ve işlem yapma becerileri [Elementary school 5th grade students' conceptual understanding and processing skills about fractions]. IV. Congress of Science Education, Ankara, Turkey.
- Heinze, A. (2005). Mistake-handling activities in German mathematics classroom. In H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 105- 112). PME.
- Heinze, A., & Reiss, K. (2007). Mistake-handling activities in the mathematics classroom: Effects of an in-service teacher training on students’ performance in geometry. In J.-H. Woo, H.-C. Lew, K.-S. Park, & D.-Y. Seo (Eds.), Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 9-16). PME.
- Huelser, B.J., & Metcalfe, J., (2012). Making related errors facilitates learning, but learners do not know it. Memory & Cognition, 40, 514 527. https://sci hub.mksa.top/10.3758/s13421-011-0167-z
- İlhan, M. (2017). The predictive role of students’ perceptions of classroom assessment environment on their attitudes towards school. Kastamonu Education Journal, 25(1), 111-128. https://dergipark.org.tr/tr/pub/kefdergi/issue/27737/308251
- Ingram, J., Pitt, A., & Baldry, F. (2015). Handling errors as they arise in whole- class interactions. Research in Mathematics Education, 17(3), 183 197. https://doi.org/10.1080/14794802.2015.1098562
- Kalaç, S., & Özkaya., M (2021). Sınıf içi olumlu hata iklimi uygulamaları [Positive error climate practices in the classroom]. In A. Kızılkaya Namlı (Ed.), Eğitimin kavramsal temelleri 4: Yöntem ve stratejiler [Conceptual basics of education 4: Methods and strategies] (pp. 231-244). Efe Akademi.
- Kalaç, S., Özkaya, M., & Konyalıoğlu, A.C. (2022). The adaptation of the perceived error climate scale into Turkish. Educational Academic Research, 44(1), 100 109. https://doi.org/10.54614/AUJKKEF.2022.11-22
- Karadağ, Z. (2004, November 24-26). Hatalardan öğrenme yönteminin bilgisayar destekli matematik 664 öğretiminde uygulanması (Koordinat düzlemi ve simetri konusu) [Application of learning from mistakes method in computer assisted mathematics teaching (Coordinate plane and symmetry issue)]. IETC 4th International Educational Technology Conference, Sakarya, Turkey. https://www.iet c.net/publication_folder/ietc/ietc2004.pdf
- Kaya, R. (2015). Investigation of the 6th grade students' misconceptions about representations of the decimal numbers [Master's thesis, Uşak University]. YÖK National Thesis Center. https://tez.yok.gov.tr/UlusalTezMerkezi/tezSorguSonucYeni.jsp
- Kohen, L. (2006). Student and teacher expectations in creating a suitable classroom environment for effective classroom management, an application from universities in Istanbul [Master’s thesis, Yeditepe University]. YÖK National Thesis Center. https://tez.yok.gov.tr/UlusalTezMerkezi/tezSorguSonucYeni.jsp
- McMillan, J.H. (2015). Sınıf içi değerlendirme, etkili ölçütlere dayalı etkili bir öğretim için ilke ve uygulamalar (A. Arı, Trans.). Eğitim Yayınevi (Original work published in 2014).
- McMillan, J.H., & Schumacher, S. (2010). Research in education: Evidence-based inquiry (7. Ed.). Pearson.
- McMillan, J.H., & Workman, D.J. (1998). Classroom assessment and grading practices: A review of the literature. Metropolitan Educational Research Consortium (ERIC Document Reproduction Service No. ED453263). https://files.eric.ed.gov/fulltext/ED453263.pdf
- Metcalfe, J. (2017). Learning from errors. Annual Review of Psychology, 68(1), 465-489. https://doi.org/10.1146/annurev-psych-010416-044022
- National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. NCTM.
- Öcalan, T. (2004). İlköğretimde matematik öğretimi [Mathematics teaching in primary education]. Yeryüzü Yayınevi.
- O'Dell, S. (2015). Classroom error climate: Teacher professional development to improve student motivation [Doctoral thesis, University of Central Florida]. Electronic Theses and Dissertations. https://stars.library.ucf.edu/etd/704/
- Önal, N. (2013). A study on the development of a middle school students’ attitudes towards mathematics scale. Elementary Education Online, 12(4), 938‐948. http://ilkogretim‐online.org.tr
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