Merve ÖZKAYA, Senem KALAÇ, Alper Cihan KONYALIOĞLU

The effect of positive error climate on affective domains in mathematics teaching

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.

Anahtar Kelimeler:

Middle school students, Positive error climate, Attitudes towards mathematics, Error orientation

The effect of positive error climate on affective domains in mathematics teaching

Keywords:

Positive error climate, Attitudes towards mathematics, Error orientation, Middle school students,

PDF

___

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
Palkki, R., & Hastö, P. (2018). Mathematics teachers’ reasons to use (or not) intentional errors. Teaching Mathematics and Computer Science, 6(2), 263 282. http://www.problemsolving.fi/pp/intentionalErrors.pdf
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://hdl.handle.net/11162/101713
Rittle-Johnson, B., & Star, J.R. (2009). Compared with what? The effects of different comparisons on conceptual knowledge and procedural flexibility for equation solving. Journal of Educational Psychology, 101(3), 529–544. https://doi.org/10.1037/a0014224
Santagata, R. (2004). “Are you joking or are you sleeping?” Cultural beliefs and practices in Italian and U.S. teachers’ mistake-handling strategies. Linguistics and Education, 15, 141–164. https://doi.org/10.1016/j.linged.2004.12.002
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
Son, J.W., & Sinclair, N. (2010). How preservice teachers interpret and respond to student geometric errors. School Science and Mathematics, 110(1), 31 46. https://doi.org/10.1111/j.1949-8594.2009.00005.x
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(3), 719-738. https://doi.org/10.1007/s10212-020-00494-1
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, 196–210. https://doi.org/10.1016/j.cedpsych.2013.03.002
Tezbaşaran, A. (1997). Likert tipi ölçek geliştirme kılavuzu [Likert type scale development guide]. Türk Psikologlar Derneği.
Trisha, M. (1999). Changing student attitudes towards mathematics. Primary Educator, 5(4), 2–6.
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
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
Turkish Ministry of National Education [MoNE]. (2018). Matematik dersi öğretim programı (İlkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar) [Mathematics lesson curriculum (1, 2, 3, 4, 5, 6, 7 and 8th grades)]. MoNE.
Yenil, T. (2020). The correction of 6th-grade students' misconceptions on decimal notation with digital concept cartoons designed according to the 5E model [Master’s dissertation, Bartın University]. YÖK National Thesis Center. https://tez.yok.gov.tr/UlusalTezMerkezi/tezSorguSonucYeni.jsp
Yıldırım, İ. (2019). The effect of erroneous solution method on the achievement of some istatistical concepts of 7th grade students [Master’s dissertation, Adiyaman University]. YÖK National Thesis Center. https://tez.yok.gov.tr/UlusalTezMerkezi/tezSorguSonucYeni.jsp