Araştırma Makalesi
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Methods of Mathematics Teachers Use in Giving Feedback to Incorrect Solutions Related to Equality Sign

Yıl 2023, Cilt: 4 Sayı: 2, 118 - 133, 30.08.2023

Senanur Ciniviz Ercan Özdemir

Öz

This study determined the methods of mathematics teachers use in giving feedback to incorrect solutions related to the equality sign through scenarios created by the researchers. The researchers used five scenarios with incorrect solutions for common errors related to the equality sign were as a data collection tool. The study was conducted with 8 middle school mathematics teachers. The results determined that mathematics teachers used the methods of telling the error, explaining the correct answer, directing to find the mistake, directing to find the correct answer, re-teaching the subject and incorrect intervention methods in giving feedback to the student mistakes about the equality sign. The results indicated that mathematics teachers mostly used the method of explaining the correct answer in giving feedback to student errors about the equality sign. The study further highlighted that mathematics teachers did not include questions examining students' thoughts in depth and requiring them to justify the solutions they used in giving feedback.

Anahtar Kelimeler

Mathematics teacher equality sign relational thinking giving feedback

Destekleyen Kurum

TÜBİTAK 2209-A Üniversite Öğrencileri Araştırma Projeleri Destekleme Programı

Proje Numarası

1919B012114153

Teşekkür

We thanks to the “TÜBİTAK 2209-A Üniversite Öğrencileri Araştırma Projeleri Destekleme Programı”. This study was produced from the project with the application number "1919B012114153" under the executive of the first author and under the supervision of the second author.

Kaynakça

  • Alibali, M. W., Knuth, E. J., Hattikudur, S., McNeil, N. M., & Stephens, A. C. (2007). A longitudinal examination of middle school students’ understanding of the equal sign and equivalent equations. Mathematical Thinking and Learning, 9, 221–247. doi:10.1080/10986060701360902
  • An, S. & Wu, Z. (2008). Approaches to assessing students’ thinking from analyzing errors in homework. In C. E. Malloy (Ed.), Mathematics for every student: Responding to diversity, grades 6–8. NCTM.
  • Ball, D. B., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389-407.
  • Baroody, A. J., & Ginsburg, H. P. (1982). The effects of instruction on children’s understanding of the “equals” sign. Paper presented at the annual meeting of the American Educational Research Association (ERIC Document Reproduction Service No. ED214765
  • Bishop, A. J. (2008). Decision-making, the intervening variable. In P. Clarkson & N. Presmeg (Eds.), Critical issues in mathematics education (pp. 29-35). Springer. https://doi.org/https://doi.org/10.1007/978-0-387-09673-5_3
  • Blanton, M., Levi, L., Crites, T., Dougherty, B. & Zbiek, RM. (2011). Developing Essential Understanding of Algebraic Thinking for Teaching Mathematics in Grades 3-5. Series in Essential Understandings. NCTM.
  • Boaler, J., & Staples, M. (2008). Creating mathematical futures through an equitable teaching approach: The case of railside school. Teachers College Record, 110(3), 608–645.
  • Carpenter, T. P., Franke, M. L., & Levi, L. (2003). Thinking mathematically: ıntegrating arithmetic and algebra in elementary school. Heinemann.
  • Cooney, T. J. & Shealy, B. E. (1997). On understanding the structure of teachers’ beliefs and their relationship to change. In E. Fennema & B. S. Nelson (Eds.), Mathematics teachers in transition (pp. 87–109). Mahwah, NJ: Lawrence Erlbaum.
  • Çelik, D. (2007). Öğretmen adaylarının cebirsel düşünme becerilerinin analitik incelenmesi (Tez No. 212041) [Doktora tezi, Karadeniz Teknik Üniversitesi-Trabzon]. Yükseköğretim Kurulu Başkanlığı Tez Merkezi.
  • Didiş, M.G., Erbaş, A.K. & Çetinkaya, B. (2016). 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.
  • Doğan, O., & Kılıç, H. (2019). Mathematical opportunities: Noticing and acting. Education and Science, 44 (199), 1-19, Doi: 10.15390/EB.2019.7593
  • Driscoll, M. (1999). Fostering algebraic thinking: A guide for teachers, grades 6-10. Heinemann. Fennema, E. & Franke, M. L. (1992). Teachers knowledge and its impact. In D. A. Grouws (Ed.), Handbook of mathematics teaching and learning (pp. 147–164). Macmillan.
  • Herbst, P., Chazan, D., Kosko, K. W., Dimmel, J., & Erickson, A. (2016). Using multimedia questionnaires to study ınfluences on the decisions mathematics teachers make in instructional situations. ZDM, 48(1), 167-183. https://doi.org/10.1007/s11858-015-0727-y
  • Hill, H. C., Rowan, B. & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 388.
  • Jacobs, V. R., Lamb, L. L., & Philipp, R. A. (2010). Professional noticing of children’s mathematical thinking. Journal for Research in Mathematics Education, 41(2), 169-202.
  • Kaput, J.J. (1999). Teaching and learning a new algebra. In. E. Fennema & T.A. Romberg (Eds.), Mathematics classrooms that promote understanding (pp.133-135). Erlbaum.
  • Knuth, E., Alibali, M., McNeil, N., Weinberg, A., & Stephens, A. (2005). Middle school students’ understanding of core algebraic concepts: Equivalence and variable. ZDM, 37(1), 68–76.
  • Ma, L. (1999). Knowing and teaching mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Lawrence Erlbaum Associates. https://doi.org/https://doi.org/10.4324/9781410602589
  • Matthews, P., Rittle-Johnson, B., McEldoon, K., & Roger, T. (2012). Measure for measure: What combining diverse measures reveals about children’s understanding of the equal sign as an ındicator of mathematical equality, Journal for Research in Mathematics Education, 43 (3), 316- 350
  • Milli Eğitim Bakanlığı (MEB), (2018). Matematik Dersi Öğretim Programı (İlkokul ve Ortaokul 1, 2, 3, 4, 5, 6, 7 Ve 8. Sınıflar). MEB Basımevi.
  • National Research Council (2001). Adding it up: Helping children learn mathematics. In J. Kilpatrick, J.
  • Swafford & B. Findell (Eds.), Mathematics learning study committee, center for education, division of behavioral and social sciences and education. National Academy Press.
  • National Council of Teachers of Mathematics (NCTM). (2000). Principles And Standards For School Mathematics. NCTM.
  • Ontorio Ministry of Education (2013). Paying attention to algebraic resasoning: K-12. Support Document For Paying Attention To Mathematics Education. http://www.edugains.ca/resourcesLNS/MathematicsFoundationalPrinciples/PayingAttentiontoAlgebraicReasoning.pdf
  • Özdemir, E. & Dede, E. (2022). Investigation of the ways prospective mathematics teachers respond to students’ errors: an example of the equal sign. International Online Journal of Education and Teaching (IOJET), 9(2). 723-739.
  • Sarkar Arani, M. R., Shibata, Y., Sakamoto, M., Iksan, Z., Amirullah, A. H., & Lander, B. (2017). How teachers respond to students’ mistakes in lessons. International Journal for Lesson and Learning Studies, 6(3), 249-267. https://doi.org/10.1108/IJLLS-12-2016-0058
  • Shulman, L. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.
  • Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1-21.
  • 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.
  • Stephens, A.C., Knuth, E. J., Blanton, M.L., Isler I, Gardiner, A.M., & Marum, T (2013). Equation structure and the meaning of the equal sign: the impact of task selection in eliciting elementary students’ understandings. Journal of Mathematical Behavior, 32, 173– 182.
  • Tulis, M. (2013). Error management behavior in classrooms: teachers' responses to student mistakes. Teaching and Teacher Education, 33, 56-68. https://doi.org/http://dx.doi.org/10.1016/j.tate.2013.02.003
  • Türkdoğan, A., & Baki, A. (2012). İlköğretim ikinci kademe matematik öğretmenlerinin yanlışlara dönüt vermede kullandıkları dönüt teknikleri. Ankara Üniversitesi Eğitim Bilimleri Fakültesi Dergisi, 45(2), 157-182.
  • Van Es, E. A., & Sherin, M. G. (2002). Learning to notice: Scaffolding new teachers’ interpretations of classroom interactions. Journal of Technology and Teacher Education, 10, 571-576.
  • Van de Walle, J., Karp, K., & Bay-Williams, J. (2012). İlkokul ve ortaokul matematiği gelişimsel yaklaşımla öğretim. S. Durmuş (Çev. Ed.), Nobel Yayıncılık.
  • Yıldırım, A., & Şimşek, H. (2008). Sosyal bilimlerde nitel araştırma yöntemleri, Seçkin Yayıncılık, Ankara.

Matematik Öğretmenlerinin Eşitlik İşareti ile İlgili Hatalı Çözümlere Dönüt Verme Yöntemleri

Yıl 2023, Cilt: 4 Sayı: 2, 118 - 133, 30.08.2023

Senanur Ciniviz Ercan Özdemir

Öz

Bu çalışmada ortaokul matematik öğretmenlerinin eşitlik işareti ile ilgili hatalı çözümlere dönüt verme yöntemleri araştırmacılar tarafından oluşturulan senaryolar aracılığıyla tespit edilmiştir. Veri toplama aracı olarak araştırmacılar tarafından eşitlik işareti ile ilgili yaygın yapılan hatalara yönelik hatalı çözümlerin yer aldığı beş tane senaryo kullanılmıştır. Çalışma 8 ortaokul matematik öğretmeni ile yürütülmüştür. Araştırma sonuçlarına göre matematik öğretmenleri eşitlik işareti ile ilgili öğrenci hatalarına dönüt vermede hatayı söyleme, doğru cevabı açıklama, hatasını bulmaya yönlendirme, doğru cevabı bulmaya yönlendirme, konuyu yeniden öğretme ve yanlış müdahale yöntemlerini kullandıkları tespit edilmiştir. Matematik öğretmenlerinin eşitlik işareti ile ilgili öğrenci hatalarına dönüt vermede en fazla doğru cevabı açıklama yöntemini kullandıkları görülmüştür. Çalışmada matematik öğretmenlerinin dönüt vermede öğrenci düşüncelerini derinlemesine inceleyen ve kullandıkları çözümleri gerekçelendirmelerini gerektirecek sorulara yer vermedikleri de ulaşılan sonuçlar arasındadır.

Proje Numarası

1919B012114153

Kaynakça

  • Alibali, M. W., Knuth, E. J., Hattikudur, S., McNeil, N. M., & Stephens, A. C. (2007). A longitudinal examination of middle school students’ understanding of the equal sign and equivalent equations. Mathematical Thinking and Learning, 9, 221–247. doi:10.1080/10986060701360902
  • An, S. & Wu, Z. (2008). Approaches to assessing students’ thinking from analyzing errors in homework. In C. E. Malloy (Ed.), Mathematics for every student: Responding to diversity, grades 6–8. NCTM.
  • Ball, D. B., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389-407.
  • Baroody, A. J., & Ginsburg, H. P. (1982). The effects of instruction on children’s understanding of the “equals” sign. Paper presented at the annual meeting of the American Educational Research Association (ERIC Document Reproduction Service No. ED214765
  • Bishop, A. J. (2008). Decision-making, the intervening variable. In P. Clarkson & N. Presmeg (Eds.), Critical issues in mathematics education (pp. 29-35). Springer. https://doi.org/https://doi.org/10.1007/978-0-387-09673-5_3
  • Blanton, M., Levi, L., Crites, T., Dougherty, B. & Zbiek, RM. (2011). Developing Essential Understanding of Algebraic Thinking for Teaching Mathematics in Grades 3-5. Series in Essential Understandings. NCTM.
  • Boaler, J., & Staples, M. (2008). Creating mathematical futures through an equitable teaching approach: The case of railside school. Teachers College Record, 110(3), 608–645.
  • Carpenter, T. P., Franke, M. L., & Levi, L. (2003). Thinking mathematically: ıntegrating arithmetic and algebra in elementary school. Heinemann.
  • Cooney, T. J. & Shealy, B. E. (1997). On understanding the structure of teachers’ beliefs and their relationship to change. In E. Fennema & B. S. Nelson (Eds.), Mathematics teachers in transition (pp. 87–109). Mahwah, NJ: Lawrence Erlbaum.
  • Çelik, D. (2007). Öğretmen adaylarının cebirsel düşünme becerilerinin analitik incelenmesi (Tez No. 212041) [Doktora tezi, Karadeniz Teknik Üniversitesi-Trabzon]. Yükseköğretim Kurulu Başkanlığı Tez Merkezi.
  • Didiş, M.G., Erbaş, A.K. & Çetinkaya, B. (2016). 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.
  • Doğan, O., & Kılıç, H. (2019). Mathematical opportunities: Noticing and acting. Education and Science, 44 (199), 1-19, Doi: 10.15390/EB.2019.7593
  • Driscoll, M. (1999). Fostering algebraic thinking: A guide for teachers, grades 6-10. Heinemann. Fennema, E. & Franke, M. L. (1992). Teachers knowledge and its impact. In D. A. Grouws (Ed.), Handbook of mathematics teaching and learning (pp. 147–164). Macmillan.
  • Herbst, P., Chazan, D., Kosko, K. W., Dimmel, J., & Erickson, A. (2016). Using multimedia questionnaires to study ınfluences on the decisions mathematics teachers make in instructional situations. ZDM, 48(1), 167-183. https://doi.org/10.1007/s11858-015-0727-y
  • Hill, H. C., Rowan, B. & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 388.
  • Jacobs, V. R., Lamb, L. L., & Philipp, R. A. (2010). Professional noticing of children’s mathematical thinking. Journal for Research in Mathematics Education, 41(2), 169-202.
  • Kaput, J.J. (1999). Teaching and learning a new algebra. In. E. Fennema & T.A. Romberg (Eds.), Mathematics classrooms that promote understanding (pp.133-135). Erlbaum.
  • Knuth, E., Alibali, M., McNeil, N., Weinberg, A., & Stephens, A. (2005). Middle school students’ understanding of core algebraic concepts: Equivalence and variable. ZDM, 37(1), 68–76.
  • Ma, L. (1999). Knowing and teaching mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Lawrence Erlbaum Associates. https://doi.org/https://doi.org/10.4324/9781410602589
  • Matthews, P., Rittle-Johnson, B., McEldoon, K., & Roger, T. (2012). Measure for measure: What combining diverse measures reveals about children’s understanding of the equal sign as an ındicator of mathematical equality, Journal for Research in Mathematics Education, 43 (3), 316- 350
  • Milli Eğitim Bakanlığı (MEB), (2018). Matematik Dersi Öğretim Programı (İlkokul ve Ortaokul 1, 2, 3, 4, 5, 6, 7 Ve 8. Sınıflar). MEB Basımevi.
  • National Research Council (2001). Adding it up: Helping children learn mathematics. In J. Kilpatrick, J.
  • Swafford & B. Findell (Eds.), Mathematics learning study committee, center for education, division of behavioral and social sciences and education. National Academy Press.
  • National Council of Teachers of Mathematics (NCTM). (2000). Principles And Standards For School Mathematics. NCTM.
  • Ontorio Ministry of Education (2013). Paying attention to algebraic resasoning: K-12. Support Document For Paying Attention To Mathematics Education. http://www.edugains.ca/resourcesLNS/MathematicsFoundationalPrinciples/PayingAttentiontoAlgebraicReasoning.pdf
  • Özdemir, E. & Dede, E. (2022). Investigation of the ways prospective mathematics teachers respond to students’ errors: an example of the equal sign. International Online Journal of Education and Teaching (IOJET), 9(2). 723-739.
  • Sarkar Arani, M. R., Shibata, Y., Sakamoto, M., Iksan, Z., Amirullah, A. H., & Lander, B. (2017). How teachers respond to students’ mistakes in lessons. International Journal for Lesson and Learning Studies, 6(3), 249-267. https://doi.org/10.1108/IJLLS-12-2016-0058
  • Shulman, L. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.
  • Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1-21.
  • 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.
  • Stephens, A.C., Knuth, E. J., Blanton, M.L., Isler I, Gardiner, A.M., & Marum, T (2013). Equation structure and the meaning of the equal sign: the impact of task selection in eliciting elementary students’ understandings. Journal of Mathematical Behavior, 32, 173– 182.
  • Tulis, M. (2013). Error management behavior in classrooms: teachers' responses to student mistakes. Teaching and Teacher Education, 33, 56-68. https://doi.org/http://dx.doi.org/10.1016/j.tate.2013.02.003
  • Türkdoğan, A., & Baki, A. (2012). İlköğretim ikinci kademe matematik öğretmenlerinin yanlışlara dönüt vermede kullandıkları dönüt teknikleri. Ankara Üniversitesi Eğitim Bilimleri Fakültesi Dergisi, 45(2), 157-182.
  • Van Es, E. A., & Sherin, M. G. (2002). Learning to notice: Scaffolding new teachers’ interpretations of classroom interactions. Journal of Technology and Teacher Education, 10, 571-576.
  • Van de Walle, J., Karp, K., & Bay-Williams, J. (2012). İlkokul ve ortaokul matematiği gelişimsel yaklaşımla öğretim. S. Durmuş (Çev. Ed.), Nobel Yayıncılık.
  • Yıldırım, A., & Şimşek, H. (2008). Sosyal bilimlerde nitel araştırma yöntemleri, Seçkin Yayıncılık, Ankara.
Toplam 36 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Eğitim Psikolojisi
Bölüm Araştırma Makaleleri
Yazarlar

Senanur Ciniviz Bu kişi benim 0009-0003-8948-782X

Ercan Özdemir 0000-0003-4797-9327

Proje Numarası 1919B012114153
Yayımlanma Tarihi 30 Ağustos 2023
Kabul Tarihi 30 Ağustos 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 4 Sayı: 2

Kaynak Göster

APA Ciniviz, S., & Özdemir, E. (2023). Matematik Öğretmenlerinin Eşitlik İşareti ile İlgili Hatalı Çözümlere Dönüt Verme Yöntemleri. Eurasian Journal of Teacher Education, 4(2), 118-133.
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