Investigation of Positive Error Climate in Mathematics Teaching with Mixed Method
Year 2025,
Volume: 19 Issue: 1, 186 - 217, 27.06.2025
Senem Kalaç
,
Alper Cihan Konyalıoglu
Abstract
The purpose of the study is to investigate the effects of the classroom climate created according to the ‘positive error climate framework programme’ on the error orientations of teachers and students in mathematics lessons. Intervention design based on mixed methods was used. The data were collected from four classes (two study and comparison classes) selected by purposive sampling, involving 145 students and 4 mathematics teachers. ‘Classroom Error Climate Scale’ (CECS), lesson observation form and notebook, semi-structured teacher and student interview form were used. At the end of the fifteen-week study, interviews were conducted with the teachers and students in the study groups. T-test results showed positive and significant change in the perceived classroom error climate in the study groups. Qualitative data analyses showed that the error orientations of the study group teachers and students were more positive than the comparison group. Teachers and students stated that positive error climate helps them to comprehend the correct information better, increases participation and self-confidence in the lesson and helps permanent learning.
Ethical Statement
This article is produced from the doctoral thesis of the first author. The thesis was supported by Tubitak with the number 122K776 for one year.
Supporting Institution
TUBİTAK 1002 HIZLI DESTEK PROGRAMI
Thanks
We would like to thank TUBITAK for all their support.
References
-
Abay, J. R., & Clores, M. A. (2022). Beliefs, attitudes and practices of high school teachers in handling students’ errors: Implications for error-tolerant mathematics classrooms. International Journal on Emerging Mathematics Education, 6(2), 101-118. http://dx.doi.org/10.12928/ijeme.v6i2.23995
-
Alvidrez, M.(2019). From mistakes, we learn: Variations in teacher dis/position toward error in mathematics classrooms [Doctoral dissertation, The University Texas El Paso]. ScholarWorks@UTEP. https://digitalcommons.utep.edu/open_etd/2825
-
Boaler, J. (2022). Mathematical mindsets: Unleashing students' potential through creative mathematics, inspiring messages and innovative teaching. John Wiley & Sons.
-
Borasi, R. (1988). Towards a reconceptualization of the role of errors in education: The need for new metaphors. Annual Meeting of the American Educational Research Association, April 5-9. https://files.eric.ed.gov/fulltext/ED295969.pdf
-
Borasi, R. (1989). Students’ constructive uses of mathematical errors: A Taxonomy, Annual Meeting of the American Educational Research Association, San Francisco, 27-31 March, 1-36. https://files.eric.ed.gov/fulltext/ED309069.pdf
-
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
-
Büyüköztürk, Ş. (2020). Sosyal bilimler için veri analizi el kitabı; İstatistik, araştırma deseni SPSS uygulamaları ve yorum (28th ed.). Pegem Akademi.
-
Büyüköztürk, Ş., Kılıç Çakmak, E.,Akgün, Ö.E., Karadeniz & Ş., Demirel, F. (2020). Eğitimde Bilimsel Araştırma Yöntemleri. Pegem Akademi.
-
Creswell, J. W. (2013). Research design: Qualitative, quantitative, and mixed methods approaches (4th ed.). Sage.
-
Creswell, J. (2021). Karma yöntem araştırmalarına giriş (3rd ed.) [Introduction to Mixed Method Research] (M. Sözbilir Trans.). Pegem Akademi.
-
Cohen, J. (1988). The t test for means. Statistical power analysis for the behavioural sciences (2nd ed.) Lawrence Erlbaum Associates.
-
Didiş, M , Erbaş, A ,& Çetinkaya, B . (2016). Investigating prospective mathematics teachers’ pedagogical approaches in response to students’ errors in the context of mathematical modeling activities. Elemantary Education Online , 15(4), 1367-1384. https://doi.org/10.17051/io.2016.75429
-
He, Y. (2020). Constructive error climate. Journal of College Science Teaching , 49(4), 37-40. https://www.jstor.org/stable/27045876
-
Heinze, A., & Reiss, K. (2007, July 8-13). Mistake-handling activities in the mathematics classroom: Effects of an in-service teacher training on students’ performance in geometry [Conference presentation]. 31st Conference of the International Group for the Psychology of Mathematics Education 2007, Seoul, Korea.
-
Huelser, B.J., & Metcalfe, J., (2012). Making related errors facilitates learning, but learners do not know it. Mem Cogn, 40, 514–527. https://doi.org/10.3758/S13421-011-0167-Z
-
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.
-
Käfer, J., Kuger, S., Klieme, E., & Kunter, M. (2019). The significance of dealing with mistakes for student achievement and motivation: results of doubly latent multilevel analyses. European Journal of Psychology of Education,34(4),731–753 https://doi.org/10.1007/s10212-018-0408-7.
-
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.
-
Konyalıoğlu, A. C. (2021). Error based activities in mathematics education. Osmangazi Journal of Educational Research, 8(1), 1-7. https://dergipark.org.tr/en/download/article-file/1611821
-
Matteucci, M. C., Corazza, M. & Santagata, R. (2015). Learning from mistakes, or not. An analysis of teachers’ error beliefs and mistake-handling strategies through questionnaire and video. Progress in Education, 37(3), 33–54. https://hdl.handle.net/11585/515709
-
McMillan J. H. & Moore S. (2020). Better Being Wrong (Sometimes): Classroom Assessment that Enhances Student Learning and Motivation, The Clearing House: A Journal of Educational Strategies, Issues and Ideas, 93(2), 85-92. https://doi.org/10.1080/00098655.2020.1721414
-
McMillan, J. H., & Schumacher, S. (2010). Research in education: Evidence-based inquiry (7th ed.). Pearson.
Metcalfe, J. (2017). Learning from errors. Annual Review of Psychology, 68, 465-489. https://doi.org/10.1146/annurev-psych-010416-044022
-
Miles, M. B., & Huberman, A. M. (1984). Qualitative data analysis: A source book of new methods. Sage.
-
Moser, J. S., Schroder, H. S., Heeter, C., Moran, T. P., & Lee, Y. H. (2011). Mind your errors: Evidence for a neural mechanism linking growth mind-set to adaptive posterror adjustments. Psychological science, 22(12), 1484-1489. https://doi.org/10.1177/0956797611419520
-
O'Dell, S., (2015). Classroom error climate: Teacher professional development to improve student motivation [Doctoral dissertation, University of Central Florida]. https://stars.library.ucf.edu/etd/704
-
Oser, F., & Spychiger,M. (2005). Lernen ist schmerzhaft: Zur Theorie des Negativen Wissens und zur Praxis der Fehlerkultur [Learning is painful. On the theory of negative knowledge and the culture of mistakes in practice]. Weinheim: Beltz.
-
Özkaya, M. (2015). A study on the impact of mistake-handling activities on mathematics teachers' professional development. (Publication No. 418259) [Doctoral dissertation, Ataturk University]. Council of Higher Education Thesis Center.
-
Özkaya, M., Kalaç, S., & Konyalıoğlu, A. C. (2022). The effect of positive error climate on affective domains in mathematics teaching. International Journal of Assessment Tools in Education, 9(Special Issue), 236-257. https://doi.org/10.21449/ijate.1121828
-
Palkki, R., & Hästö, P. (2018). Mathematics teachers' reasons to use (or not) intentional errors. Teaching Mathematics and Computer Science, 16(2), 263-282. https://doi.org/10.5485/TMCS.2018.0453
-
Rach, S., Ufer, S., & Heinze, A. (2013). Learning from errors: effects of teachers training on students' attitudes towards and their individual use of errors, PNA, 8(1), 21-30. http://dx.doi.org/10.30827/pna.v8i1.6122
-
Santagata, R. (2005). Practices and beliefs in mistake-handling activities: A video study of Italian and US mathematics lessons. Teaching and Teacher Education, 21, 491-508. https://doi.org/10.1016/j.tate.2005.03.004
-
Son, J. W. (2013). How preservice teachers interpret and respond to student errors: Ratio and proportion in similar rectangles. Educational Studies in Mathematics, 84(1), 49–70. https://doi.org/10.1007/s10649-013-9475-5
-
Soncini, A., Matteucci, M.C., & Butera, F. (2021). Error handling in the classroom: An experimental study of teachers’ strategies to foster positive error climate. European Journal of Psychology of Education, 36, 719-738. https://doi.org/10.1007/s10212-020-00494-1
-
Steuer, G., & Dresel, M. (2015). A constructive error climate as an element of effective learning environments. Psychological Test and Assessment Modeling, 57(2), 262–75. https://www.psychologie-aktuell.com/fileadmin/download/ptam/2-2015_20150624/08_Steuer.pdf
-
Steuer, G., Rosentritt-Brunn, G., & Dresel, M. (2013). Dealing with errors in mathematics classrooms: Structure and relevance of perceived error climate. Contemporary Educational Psychology, 38(3), 196-210. https://doi.org/10.1016/j.cedpsych.2013.03.002
-
Tabachnick, B. G., & Fidell, L. S. (2013). Using multivariate statistics. Pearson.
-
Tulis, M. (2013). Error management behavior in classrooms: teachers’ responses to student mistakes. Teaching and Teacher Education, 33, 56-68.
https://doi.org/10.1016/j.tate.2013.02.003.
-
Tulis, M., Steuer, G., & Dresel, M. (2018). Positive beliefs about errors as an important element of adaptive individual dealing with errors during academic learning. Educational Psychology, 38(2),139-158.
https://doi.org/10.1080/01443410.2017.1384536.
-
Türkdoğan A., & Baki A., (2012). Primary school second grade mathematic teachers’ feedback strategies to students’ mistakes. Ankara University Journal of Faculty of Educational Sciences, 45(2), 157-182. https://doi.org/10.1501/Egifak_0000001258
-
Wasilewski, J. A. (2023). The Role of Error Culture in Math Classroom Learning (Publication No. 30314048) [Doctoral dissertation, Northeastern University]. ProQuest Dissertations & Theses Global.
-
Yağar, F., & Dökme, S. (2018). Planning of qualitative researches: research questions, samples, validity and reliability. Gazi Journal of Healty Science, 3(3), 1-9. https://dergipark.org.tr/tr/download/article-file/563245
Matematik Öğretiminde Olumlu Hata İkliminin Karma Yöntem ile Araştırılması
Year 2025,
Volume: 19 Issue: 1, 186 - 217, 27.06.2025
Senem Kalaç
,
Alper Cihan Konyalıoglu
Abstract
Çalışmanın amacı, matematik derslerinde "olumlu hata iklimi çerçeve programına" göre oluşturulan sınıf ikliminin öğretmen ve öğrencilerin hata yönelimlerine etkilerini incelemektir. Karma yöntem desenlerinden müdahale deseni kullanılan araştırmanın verileri, amaçlı örneklem ile seçilmiş dört sınıf (iki çalışma ve iki karşılaştırma sınıfı), bu sınıflarda öğrenim gören 145 öğrenci ve dört matematik öğretmeninden toplanmıştır. Araştırmada "Sınıf Hata İklimi Ölçeği" (SHİÖ), ders gözlem formu ve defteri, yarı yapılandırılmış öğretmen ve öğrenci görüşme formu kullanılmıştır. On beş hafta süren araştırma sonunda çalışma gruplarında yer alan öğretmen ve öğrenciler ile görüşmeler yapılmıştır. T-testi sonucuna göre çalışma gruplarında karşılaştırma gruplarına göre algılanan sınıf hata ikliminde olumlu ve anlamlı bir değişim gözlemlenmiştir. Nitel veri analizlerinde çalışma grubu öğretmenlerinin ve öğrencilerinin hata yönelimlerinin karşılaştırma grubuna göre daha olumlu olduğu görülmüştür. Öğretmen ve öğrenciler, olumlu hata ikliminin doğru bilgiyi daha iyi kavrattığını, derse katılım ve özgüveni artırdığını ve kalıcı öğrenmeye yardımcı olduğunu belirtmiştir.
Ethical Statement
Bu makale birinci yazarın doktora tezinden üretilmiştir. Tez, Tubitak tarafından desteklenen 122K776 numarası ile bir yıl boyunca desteklenmiştir.
Supporting Institution
TUBİTAK 1002 HIZLI DESTEK PROGRAMI
Thanks
TUBİTAK'a verdikleri her türlü desteğinden dolayı teşekkür ederiz.
References
-
Abay, J. R., & Clores, M. A. (2022). Beliefs, attitudes and practices of high school teachers in handling students’ errors: Implications for error-tolerant mathematics classrooms. International Journal on Emerging Mathematics Education, 6(2), 101-118. http://dx.doi.org/10.12928/ijeme.v6i2.23995
-
Alvidrez, M.(2019). From mistakes, we learn: Variations in teacher dis/position toward error in mathematics classrooms [Doctoral dissertation, The University Texas El Paso]. ScholarWorks@UTEP. https://digitalcommons.utep.edu/open_etd/2825
-
Boaler, J. (2022). Mathematical mindsets: Unleashing students' potential through creative mathematics, inspiring messages and innovative teaching. John Wiley & Sons.
-
Borasi, R. (1988). Towards a reconceptualization of the role of errors in education: The need for new metaphors. Annual Meeting of the American Educational Research Association, April 5-9. https://files.eric.ed.gov/fulltext/ED295969.pdf
-
Borasi, R. (1989). Students’ constructive uses of mathematical errors: A Taxonomy, Annual Meeting of the American Educational Research Association, San Francisco, 27-31 March, 1-36. https://files.eric.ed.gov/fulltext/ED309069.pdf
-
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
-
Büyüköztürk, Ş. (2020). Sosyal bilimler için veri analizi el kitabı; İstatistik, araştırma deseni SPSS uygulamaları ve yorum (28th ed.). Pegem Akademi.
-
Büyüköztürk, Ş., Kılıç Çakmak, E.,Akgün, Ö.E., Karadeniz & Ş., Demirel, F. (2020). Eğitimde Bilimsel Araştırma Yöntemleri. Pegem Akademi.
-
Creswell, J. W. (2013). Research design: Qualitative, quantitative, and mixed methods approaches (4th ed.). Sage.
-
Creswell, J. (2021). Karma yöntem araştırmalarına giriş (3rd ed.) [Introduction to Mixed Method Research] (M. Sözbilir Trans.). Pegem Akademi.
-
Cohen, J. (1988). The t test for means. Statistical power analysis for the behavioural sciences (2nd ed.) Lawrence Erlbaum Associates.
-
Didiş, M , Erbaş, A ,& Çetinkaya, B . (2016). Investigating prospective mathematics teachers’ pedagogical approaches in response to students’ errors in the context of mathematical modeling activities. Elemantary Education Online , 15(4), 1367-1384. https://doi.org/10.17051/io.2016.75429
-
He, Y. (2020). Constructive error climate. Journal of College Science Teaching , 49(4), 37-40. https://www.jstor.org/stable/27045876
-
Heinze, A., & Reiss, K. (2007, July 8-13). Mistake-handling activities in the mathematics classroom: Effects of an in-service teacher training on students’ performance in geometry [Conference presentation]. 31st Conference of the International Group for the Psychology of Mathematics Education 2007, Seoul, Korea.
-
Huelser, B.J., & Metcalfe, J., (2012). Making related errors facilitates learning, but learners do not know it. Mem Cogn, 40, 514–527. https://doi.org/10.3758/S13421-011-0167-Z
-
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.
-
Käfer, J., Kuger, S., Klieme, E., & Kunter, M. (2019). The significance of dealing with mistakes for student achievement and motivation: results of doubly latent multilevel analyses. European Journal of Psychology of Education,34(4),731–753 https://doi.org/10.1007/s10212-018-0408-7.
-
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.
-
Konyalıoğlu, A. C. (2021). Error based activities in mathematics education. Osmangazi Journal of Educational Research, 8(1), 1-7. https://dergipark.org.tr/en/download/article-file/1611821
-
Matteucci, M. C., Corazza, M. & Santagata, R. (2015). Learning from mistakes, or not. An analysis of teachers’ error beliefs and mistake-handling strategies through questionnaire and video. Progress in Education, 37(3), 33–54. https://hdl.handle.net/11585/515709
-
McMillan J. H. & Moore S. (2020). Better Being Wrong (Sometimes): Classroom Assessment that Enhances Student Learning and Motivation, The Clearing House: A Journal of Educational Strategies, Issues and Ideas, 93(2), 85-92. https://doi.org/10.1080/00098655.2020.1721414
-
McMillan, J. H., & Schumacher, S. (2010). Research in education: Evidence-based inquiry (7th ed.). Pearson.
Metcalfe, J. (2017). Learning from errors. Annual Review of Psychology, 68, 465-489. https://doi.org/10.1146/annurev-psych-010416-044022
-
Miles, M. B., & Huberman, A. M. (1984). Qualitative data analysis: A source book of new methods. Sage.
-
Moser, J. S., Schroder, H. S., Heeter, C., Moran, T. P., & Lee, Y. H. (2011). Mind your errors: Evidence for a neural mechanism linking growth mind-set to adaptive posterror adjustments. Psychological science, 22(12), 1484-1489. https://doi.org/10.1177/0956797611419520
-
O'Dell, S., (2015). Classroom error climate: Teacher professional development to improve student motivation [Doctoral dissertation, University of Central Florida]. https://stars.library.ucf.edu/etd/704
-
Oser, F., & Spychiger,M. (2005). Lernen ist schmerzhaft: Zur Theorie des Negativen Wissens und zur Praxis der Fehlerkultur [Learning is painful. On the theory of negative knowledge and the culture of mistakes in practice]. Weinheim: Beltz.
-
Özkaya, M. (2015). A study on the impact of mistake-handling activities on mathematics teachers' professional development. (Publication No. 418259) [Doctoral dissertation, Ataturk University]. Council of Higher Education Thesis Center.
-
Özkaya, M., Kalaç, S., & Konyalıoğlu, A. C. (2022). The effect of positive error climate on affective domains in mathematics teaching. International Journal of Assessment Tools in Education, 9(Special Issue), 236-257. https://doi.org/10.21449/ijate.1121828
-
Palkki, R., & Hästö, P. (2018). Mathematics teachers' reasons to use (or not) intentional errors. Teaching Mathematics and Computer Science, 16(2), 263-282. https://doi.org/10.5485/TMCS.2018.0453
-
Rach, S., Ufer, S., & Heinze, A. (2013). Learning from errors: effects of teachers training on students' attitudes towards and their individual use of errors, PNA, 8(1), 21-30. http://dx.doi.org/10.30827/pna.v8i1.6122
-
Santagata, R. (2005). Practices and beliefs in mistake-handling activities: A video study of Italian and US mathematics lessons. Teaching and Teacher Education, 21, 491-508. https://doi.org/10.1016/j.tate.2005.03.004
-
Son, J. W. (2013). How preservice teachers interpret and respond to student errors: Ratio and proportion in similar rectangles. Educational Studies in Mathematics, 84(1), 49–70. https://doi.org/10.1007/s10649-013-9475-5
-
Soncini, A., Matteucci, M.C., & Butera, F. (2021). Error handling in the classroom: An experimental study of teachers’ strategies to foster positive error climate. European Journal of Psychology of Education, 36, 719-738. https://doi.org/10.1007/s10212-020-00494-1
-
Steuer, G., & Dresel, M. (2015). A constructive error climate as an element of effective learning environments. Psychological Test and Assessment Modeling, 57(2), 262–75. https://www.psychologie-aktuell.com/fileadmin/download/ptam/2-2015_20150624/08_Steuer.pdf
-
Steuer, G., Rosentritt-Brunn, G., & Dresel, M. (2013). Dealing with errors in mathematics classrooms: Structure and relevance of perceived error climate. Contemporary Educational Psychology, 38(3), 196-210. https://doi.org/10.1016/j.cedpsych.2013.03.002
-
Tabachnick, B. G., & Fidell, L. S. (2013). Using multivariate statistics. Pearson.
-
Tulis, M. (2013). Error management behavior in classrooms: teachers’ responses to student mistakes. Teaching and Teacher Education, 33, 56-68.
https://doi.org/10.1016/j.tate.2013.02.003.
-
Tulis, M., Steuer, G., & Dresel, M. (2018). Positive beliefs about errors as an important element of adaptive individual dealing with errors during academic learning. Educational Psychology, 38(2),139-158.
https://doi.org/10.1080/01443410.2017.1384536.
-
Türkdoğan A., & Baki A., (2012). Primary school second grade mathematic teachers’ feedback strategies to students’ mistakes. Ankara University Journal of Faculty of Educational Sciences, 45(2), 157-182. https://doi.org/10.1501/Egifak_0000001258
-
Wasilewski, J. A. (2023). The Role of Error Culture in Math Classroom Learning (Publication No. 30314048) [Doctoral dissertation, Northeastern University]. ProQuest Dissertations & Theses Global.
-
Yağar, F., & Dökme, S. (2018). Planning of qualitative researches: research questions, samples, validity and reliability. Gazi Journal of Healty Science, 3(3), 1-9. https://dergipark.org.tr/tr/download/article-file/563245