Middle School Mathematıcs Teachers’ Responding Approaches to Student Thinking on Patterns

Year 2024, Issue: 60, 1622 - 1653, 28.06.2024

Hatice Çetin Argaç , Makbule Gözde Didiş Kabar

https://doi.org/10.53444/deubefd.1412075

Abstract

This study aims to investigate the approaches of five mathematics teachers, who examined students' solutions on figural patterns, in responding to students' thinking and to what extent the teachers take students' current thinking ways into account in their responses. This research was conducted with five middle school mathematics teachers, working in different public schools in a city center in the Central Anatolia Region, in the spring semester of the 2021-2022 academic year. As qualitative research, the data of this study was collected through one-on-one interviews with five mathematics teachers. The interviews were conducted based on students’ written solutions to figural pattern questions and video excerpts including students’ explanations of their solutions. The findings revealed that teachers' general responding approaches were questioning, appreciating, explaining-telling, teaching, showing examples and drawing. The data revealed that teachers occasionally tended to respond to students' solutions by asking questions related to the student's thinking by trying to understand and question their thinking. Teachers dominantly exhibited general approaches such as appreciating, teaching and explaining-telling, which were partially related or unrelated to the student's thinking, and focused directly on whether the solution was correct or wrong. However, teachers' responding tendencies to students' thinking also varied depending on the degree of inaccuracy of the students’ solutions. This research suggests that teachers should be supported with professional development practices to provide high-quality responses that are related to student thinking, move student thinking forward and reveal the conceptual aspects of students' thinking.

Keywords

Middle school mathematics teachers, student thinking, responding, patterns

Ortaokul Matematik Öğretmenlerinin Örüntüler Konusunda Öğrenci Düşüncelerine Yönelik Cevap Verme Yaklaşımları

Abstract

Bu araştırmanın amacı örüntüler konusunda öğrencilerin çözümlerini inceleyen beş matematik öğretmeninin öğrencilerin düşüncelerine yönelik cevap (yanıt) verme yaklaşımlarını ve öğretmenlerin cevaplarında öğrencilerin mevcut düşünme biçimlerini ne kadar dikkate aldıklarını incelemektir. Bu araştırma 2021-2022 eğitim öğretim yılının bahar döneminde, İç Anadolu Bölgesinde yer alan bir ilin merkezinde farklı devlet okullarında görev yapan beş matematik öğretmeniyle gerçekleştirilmiştir. Nitel bir araştırma olan bu çalışmanın verileri beş matematik öğretmeni ile öğrencilerin yazılı çözümleri ve çözümlerinin açıklamalarını içeren video görüntüleri üzerinde yapılan birebir görüşmeler aracılığıyla toplanmıştır. Bulgular şekil örüntüleri ile ilgili inceledikleri öğrenci çözümleri karşısında öğretmenlerin genel olarak cevap verme yaklaşımlarının soru sorma, takdir etme, açıklama/söyleme, anlatma, örnek gösterme ve çizim yaptırma şeklinde olduğunu ortaya koymuştur. Öğretmenler zaman zaman öğrenci düşüncesi ile ilişkili olarak, öğrencinin düşüncesini anlamaya ve sorgulamaya çalışan sorularla cevap verme eğilimi içinde olmuşlardır. Fakat, öğretmenlerin cevap verme eğiliminin ağırlıklı olarak çözümün doğru veya yanlış olması odaklı, öğrenci düşüncesi ile kısmen ilişkili ve ilişkisiz, takdir etme, anlatma, öğretme ve açıklama yapma gibi genel yaklaşımlar olduğu görülmüştür. Öğretmenlerin öğrenci düşünceleri ile ilişkili cevap verme eğilimleri öğrencilerin ortaya koydukları çözümlerin yanlışlık derecesine göre de değişiklik göstermiştir. Bu araştırma, öğretmenlerin öğrenci düşünceleri ile ilişkili, öğrenci düşüncelerini ileriye taşıyan ve öğrencilerin düşüncelerinin kavramsal yönlerini ortaya çıkaran yüksek kaliteli cevaplar verebilmeleri için onlara fırsat sunacak mesleki gelişim uygulamaları ile desteklenmesini önermektedir.

Keywords

Ortaokul matematik öğretmenleri, öğrenci düşüncesi, cevap verme, örüntüler

References

• Altıntaş, Ş., & Keskin, C. (2019). 7.sınıf matematik kitabı. Ankara: Ekoyay.
• Amit, M., & Neria, D. (2008). “Rising to the challenge”: Using generalization in pattern problems to unearth the algebraic skills of talented pre-algebra students. ZDM, 40, 111-129.
• Barnhart, T., & van Es, E. (2015). Studying teacher noticing: Examining the relationship among pre-service science teachers' ability to attend, analyze and respond to student thinking. Teaching and Teacher Education, 45, 83-93.
• Boaler, J., & Brodie, K. (2004). The importance, nature and impact of teacher questions. In D. E. McDougall & J. A. Ross (Eds.). Proceedings of the Twenty-Sixth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol 1., pp. 774-782). Toronto: Ontario Institute of Studies in Education/University of Toronto.
• Bywater, J. P., Chiu, J. L., Hong, J., & Sankaranarayanan, V. (2019). The teacher responding tool: Scaffolding the teacher practice of responding to student ideas in mathematics classrooms. Computers & Education, 139, 16-30. https://doi.org/10.1016/j.compedu.2019.05.004
• Callejo, M. L., & Zapatera, A. (2017). Prospective primary teachers’ noticing of students’ understanding of pattern generalization. Journal of Mathematics Teacher Education, 20(4), 309-333.
• Casey, S., Lesseig, K., Monson, D., & Krupa, E. E. (2018). Examining preservice secondary mathematics teachers' responses to student work to solve linear equations. Mathematics Teacher Education and Development, 20(1), 132-153.
• Crespo, S. (2002). Praising and correcting: Prospective teachers investigate their teacherly talk. Teaching and Teacher Education, 18(6), 739-758.
• Driscoll, M., & Moyer, J. (2001). Using students' work as a lens on algebraic thinking. Mathematics Teaching in the Middle School, 6(5), 282-287.
• Ellis, A., Özgür, Z., & Reiten, L. (2019). Teacher moves for supporting student reasoning. Mathematics Education Research Journal, 31(2), 107-132. https://doi.org/10.1007/s13394-018-0246-6.
• El Mouhayar, R., & Jurdak, M. (2015). Variation in strategy use across grade level by pattern generalization types. International Journal of Mathematical Education in Science and Technology, 46(4), 553–569.
• Jacobs, V. R., & Ambrose, R. C. (2008). Making the most of story problems. Teaching Children Mathematics, 15(5), 260–266. https://doi.org/10.5951/TCM.15.5.0260
• Jacobs, V. R., Lamb, L. C., & Philipp, R. A. (2010). Professional noticing of children’s mathematical thinking. Journal for Research in Mathematics Education, 41(2), 169–202. https://doi.org/10.5951/jresematheduc.41.2.0169
• Kaput, J. J. (1995). A research base supporting long term algebra reform? In D. T. Owens, M. K. Reed, & G. M. Millsaps (Eds.), Proceedings of the 17th Annual Meeting of PME-NA (Vol. 1, pp. 71-94). Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.
• Kaput, J. J. (2008). What is algebra? What is algebraic reasoning?. In J. J. Kaput, D. W. Carraher & M. L. Blanton (Eds.), Algebra in the early grades (pp. 5–17). Lawrence Erlbaum Associates.
• Keskin-Oğan, A., & Öztürk, S. (2019). 7. Sınıf matematik ders kitabı. Ankara: MEB.
• Kieran, C. (1996). The changing face of school algebra. In C. Alsina, J. Alvarez, B. Hodgson, C. Laborde, & A. Pérez (Eds.), 8th International Congress on Mathematical Education: Selected lectures (pp. 271-290). Seville, Spain: S.A.E.M. Thales.
• Kieran, C. (2004). Algebraic thinking in the early grades: what is it?, The Mathematics Educator, 8(1), 139-151.
• Krebs, A. S. (2005). Analyzing student work as a professional development activity. School Science and Mathematics, 105(8), 402–411.
• Land, T. J., Tyminski, A. M., & Drake, C. (2019). Examining aspects of teachers’ posing of problems in response to children’s mathematical thinking. Journal of Mathematics Teacher Education, 22(4), 331-353. https://doi.org/10.1007/s10857-018-9418-2.
• Lesseig, K., Casey, S., Monson, D., Krupa, E. E., & Huey, M. (2016). Developing an interview module to support secondary pst's noticing of student thinking. Mathematics Teacher Educator, 5(1), 29-46.
• Mason, J. (1996). Expressing generality and roots of algebra. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching (pp. 65–86). Dordrecht: Kluwer Academic.
• Merriam, S. B. (2002). Introduction to qualitative research. In S. B. Merriam and Associates (Eds.), Qualitative research in practice: Examples for Discussion and Analysis (3-16). San Francisco, CA: Jossey-Bass
• Milewski, A., & Strickland, S. (2016). (Toward) developing a common language for describing instructional practices of responding: A teacher-generated framework. Mathematics Teacher Educator, 4(2), 126-144.
• Millî Eğitim Bakanlığı [MEB]. (2018). Matematik dersi öğretim programı (İlkokul ve Ortaokul 1,2,3,4,5,6,7, ve 8. Sınıflar). Ankara: MEB.
• Monson, D., Krupa, E., Lesseig, K., & Casey, S. (2020). Developing secondary prospective teachers’ ability to respond to student work. Journal of Mathematics Teacher Education, 23(2), 209-232. https://doi.org/10.1007/s10857-018-9420-8.
• National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Reston, VA: Author.
• Özel, Z., Işıksal-Bostan, M., & Tekin-Sitrava, R. (2022). Prospective teachers’ instructional responses on the basis of students’ functional thinking: The context of pattern generalization. International Journal for Mathematics Teaching and Learning, 23(2), 40-58.
• Papic, M. (2007). Promoting repeating patterns with young children-more than just alternating colours!. Australian Primary Mathematics Classroom, 12(3), 8-13.
• Radford, L. (2006). Algebraic thinking and the generalization of patterns: A semiotic perspective. Alatorre, S., Cortina, J.L., Sáiz, M., and Méndez, A. (Eds) (2006). Proceedings of the 28th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Mérida, México: Universidad Pedagógica Nacional.
• Radford, L. (2014). The progressive development of early embodied algebraic thinking. Mathematics Education Research Journal, 26, 257-277.
• Rivera, F., & Becker, J. R. (2008). Middle school children’s cognitive perceptions of constructive and deconstructive generalizations involving linear figural patterns. ZDM, 40(1), 65–82.
• Sahin, A., & Kulm, G. (2008). Sixth grade mathematics teachers’ intentions and use of probing, guiding, and factual questions. Journal of Mathematics Teacher Education, 11(3), 221-242.
• Sherin, M. G., & van Es, E. A. (2005). Using video to support teachers’ ability to notice classroom interactions. Journal of Technology and Teacher Education, 13(3), 475-491.
• Son, J. W., & Sinclair, N. (2010). How preservice teachers interpret and respond to student geometric errors. School Science and Mathematics, 110(1), 31-46.
• Stacey, K. (1989). Finding and using patterns in linear generalising problems. Educational Studies in Mathematics, 20(2), 147-164.
• Sun, L. (2020). Teachers’ responses to student mathematical thinking in Chinese elementary mathematics classrooms. School Science and Mathematics, 120(1), 45-54.
• Şengül, S. (2022). Ortaokul matematik derslerinin öğretme-öğrenme sürecinde öğrenci düşüncesini ortaya çıkarma ve yorumlama. [Yayımlanmamış Yüksek Lisans Tezi]. Trabzon Üniversitesi.
• Tanışlı, D. (2008). İlköğretim beşinci sınıf öğrencilerinin örüntülere ilişkin anlama ve kavrama biçimlerinin belirlenmesi. [Yayımlanmamış Doktora Tezi]. Anadolu Üniversitesi.
• Tanışlı, D., & Yavuzsoy-Köse, N. (2011). Lineer şekil örüntülerine ilişkin genelleme stratejileri: Görsel ve sayısal ipuçlarının etkisi. Eğitim ve Bilim, 36(160), 184-19.
• Tataroğlu-Taşdan, B., & Didiş-Kabar, M. G. (2022). Pre-service mathematics teachers’ responding to student thinking in their teaching experiences. Journal of Pedagogical Research, 6(1), 87-109.
• 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(4), 571–596.
• van Es, E. A., & Sherin, M. G. (2008). Mathematics teachers’“learning to notice” in the context of a video club. Teaching and teacher education, 24(2), 244-276.
• van Es, E. A., & Sherin, M. G. (2024). Expanding on prior conceptualizations of teacher noticing. ZDM–Mathematics Education, 53, 17-27.
• Walkoe, J. (2015). Exploring teacher noticing of student algebraic thinking in a video club. Journal of Mathematics Teacher Education, 18, 523-550.
• Walkoe, J., Sherin, M., & Elby, A. (2020). Video tagging as a window into teacher noticing. Journal of Mathematics Teacher Education, 23(4), 385-405.
• Warren, E., & Cooper, T. (2006). Using repeating patterns to explore functional thinking. Australian Primary Mathematics Classroom, 11(1), 9-14.
• Yıldırım, A. & Şimşek, H. (2006). Sosyal bilimlerde nitel araştırma yöntemleri (5. Baskı). Ankara: Seçkin Yayıncılık. Yin, R. K. (2009). Case study research: design and methods (4th edition). US: Sage Publication.