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Development of Prospective Mathematis Teachers' Noticing Skills of Students’ Thinking regarding the Mean: A Teaching Experiment

Year 2024, Volume: 21 Issue: 1, 306 - 331, 24.04.2024

Reyhan Tekin Sitrava Neşe Şahin Nafiye Sümeyye Çopur Ayşegül Ayıkol Baykal

https://doi.org/10.33711/yyuefd.1421623

Abstract

This study aims to determine the prospective mathematics teachers’ (PSTs) professional noticing skills regarding mean and to develop their noticing skills through teaching experiment method. In the study, it was focused on teaching arithmetic mean, lasting approximately 4 weeks in an 8-week teaching series including teaching statistics. The data were collected through pre-test, post-test, semi-structured interviews and diaries that PSTs kept during the teaching experiment process from 35 third grade PSTs. The pre-test and post-test, containing questions about three facets of theoretical framework of Professional Noticing of Children’s Mathematical Thinking, include a problem about mean and three student solutions to this problem. The data were analysed using a coding table prepared based on same theoretical framework. The pre-test results showed that before participating in student thinking-focused statistics teaching, PSTs had low skills in attending to students' solution strategies related to mean, interpreting students' mathematical understandings, and responding to students. At the end of the student thinking-focused statistics teaching, it is seen that PSTs significantly improved their attending, interpreting and responding skills. In line with these findings, it can be said that the PST’s noticing skills can be improved with mathematics education courses that are purposefully planned and systematically conducted.

Keywords

Professional noticing skills mean prospective matematics teachers

References

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  • Amador, J. M., & Carter, I. S. (2018). Audible conversational affordances and constraints of verbalizing professional noticing during prospective teacher lesson study. Journal of Mathematics Teacher Education, 21, 5-34.
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  • Aydın, Ş. (2020). Sekizinci sınıf öğrencilerinin merkezi eğilim ölçülerine yönelik istatistiksel düşünmelerinin incelenmesi (Tez No. 644516). [Yüksek lisans tezi, Hacettepe Üniversitesi]. Yüksek Öğretim Kurulu Ulusal Tez Merkezi.
  • Bastian, A., Kaiser, G., Meyer, D., Schwarz, B., & König, J. (2022). Teacher noticing and its growth toward expertise: An expert–novice comparison with pre-service and in-service secondary mathematics teachers. Educational Studies in Mathematics, 110(2), 205-232.
  • Birgin, O., & Eryılmaz, E. (2022). Türkiye’de Matematik Eğitimi Alanında Öğretmenin Fark Etmesi Konusunda Yapılan Çalışmaların Sistematik İncelenmesi. International Journal of Educational Studies in Mathematics, 9(3), 184-203.
  • Birinci, M. (2018). Bir ortaokul matematik öğretmeninin mesleki gelişiminden yansımalar: Kesir öğretiminde fark etme becerisinin işe koşulması [Yayımlanmamış doktora tezi, Karadeniz Teknik Üniversitesi Eğitim Bilimleri Enstitüsü]. Yüksek Öğretim Kurulu Ulusal Tez Merkezi.
  • Blömeke, S., Gustafsson, J.-E., & Shavelson, R. (2015). Beyond dichotomies: Competence viewed as a continuum. Zeitschrift für Psychologie, 223(1), 3–13. https://doi.org/10.1027/2151-2604/a000194
  • Bütüner, S. Ö. (2020). Türkiye’de okutulan ortaokul matematik ders kitaplarının aritmetik ortalama kavramına ilişkin öğrencilere sunduğu öğrenme fırsatları. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 11(1), 157-187.
  • 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.
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  • Doğan-Coşkun, Tekin-Sitrava, R., & Işıksal-Bostan, M. (2023). Pre-service elementary teachers’ noticing expertise of students’ mathematical thinking: The case of fractions. International Journal of Mathematical Education in Science and Technology, 54(6), 982-999.
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  • Dreher, A., & Kuntze, S. (2015). Teachers’ professional knowledge and noticing: The case of multiple representations in the mathematics classroom. Educational Studies in Mathematics, 88, 89-114.
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  • González, G., & Vargas, G. E. (2020). Teacher noticing and reasoning about student thinking in classrooms as a result of participating in a combined professional development ıntervention. Mathematics Teacher Education and Development, 22(1), 5-32
  • Groth, R.E. (2009). Characteristics of teachers' conversations about teaching mean, median, and mode. Teaching and Teacher Education, 25, 707-716.
  • Güner, P., & Akyüz, D. (2017). Ders imecesi (lesson study) mesleki gelişim modeli: Öğretmen adaylarının fark etme becerilerinin incelenmesi. İlköğretim Online, 16(2), 428-452.
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Matematik Öğretmen Adaylarının Öğrencilerin Aritmetik Ortalamaya Yönelik Düşünüşünü Fark Etme Becerilerinin Geliştirilmesi: Bir Öğretim Deneyi

Year 2024, Volume: 21 Issue: 1, 306 - 331, 24.04.2024

Reyhan Tekin Sitrava Neşe Şahin Nafiye Sümeyye Çopur Ayşegül Ayıkol Baykal

https://doi.org/10.33711/yyuefd.1421623

Abstract

Bu çalışmanın amacı, ilköğretim matematik öğretmen adaylarının aritmetik ortalamaya yönelik mesleki fark etme becerilerinin belirlenmesi ve öğretim deneyi yöntemiyle geliştirilmesidir. Çalışmada, istatistik öğretimini kapsayan 8 haftalık öğretim dizisinde yaklaşık 4 hafta süren aritmetik ortalama öğretimine odaklanılmıştır. Çalışmanın verileri 3. sınıfta öğrenim gören 35 öğretmen adayından ön test, son test, yarı yapılandırılmış görüşmeler ve öğretmen adaylarının öğretim deneyi sürecinde tutmuş oldukları günlükler vasıtasıyla toplanmıştır. Öğrencilerin Matematiksel Düşünmelerine Yönelik Mesleki Fark Etme kuramsal çerçevesinin üç bileşenine yönelik soruların olduğu ön-test ve son-test, aritmetik ortalamaya yönelik bir problem ve bu probleme ait üç öğrenci çözümü içermektedir. Veriler, aynı kuramsal çerçeve temel alınarak hazırlanan kodlama tablosu kullanılarak analiz edilmiştir. Ön-test sonuçları öğretmen adaylarının öğrenci düşünüşü odaklı istatistik öğretimine katılmadan önce öğrencilerin aritmetik ortalamaya yönelik problemlerdeki çözüm stratejilerini dikkate alma, öğrencilerin matematiksel kavrayışlarını yorumlama ve öğrencilere karşılık verme becerilerinin düşük olduğunu göstermektedir. Öğrenci düşünüşü odaklı istatistik öğretiminin sonunda, öğretmen adaylarının, dikkate alma, yorumlama ve karşılık verme becerilerini önemli derecede geliştirdikleri görülmektedir. Bu bulgular doğrultusunda, ,amaca yönelik planlanan ve sistemli bir şekilde yürütülen matematik eğitimi dersleri ile öğretmen adaylarının fark etme becerilerinin geliştirilebileceği söylenebilir.

Keywords

Mesleki fark etme becerisi aritmetik ortalama matematik öğretmen adayları

References

  • Amador, J. M., Carter, I., & Hudson, R. A. (2016). Analyzing preservice mathematics teachers’ professional noticing. Action in Teacher Education, 38(4), 371- 383.
  • Amador, J. M., & Carter, I. S. (2018). Audible conversational affordances and constraints of verbalizing professional noticing during prospective teacher lesson study. Journal of Mathematics Teacher Education, 21, 5-34.
  • Anantharajan, M. (2020). Teacher noticing of mathematical thinking in young children’s representations of counting. Journal for Research in Mathematics Education, 51(3), 268-300.
  • Aydın, Ş. (2020). Sekizinci sınıf öğrencilerinin merkezi eğilim ölçülerine yönelik istatistiksel düşünmelerinin incelenmesi (Tez No. 644516). [Yüksek lisans tezi, Hacettepe Üniversitesi]. Yüksek Öğretim Kurulu Ulusal Tez Merkezi.
  • Bastian, A., Kaiser, G., Meyer, D., Schwarz, B., & König, J. (2022). Teacher noticing and its growth toward expertise: An expert–novice comparison with pre-service and in-service secondary mathematics teachers. Educational Studies in Mathematics, 110(2), 205-232.
  • Birgin, O., & Eryılmaz, E. (2022). Türkiye’de Matematik Eğitimi Alanında Öğretmenin Fark Etmesi Konusunda Yapılan Çalışmaların Sistematik İncelenmesi. International Journal of Educational Studies in Mathematics, 9(3), 184-203.
  • Birinci, M. (2018). Bir ortaokul matematik öğretmeninin mesleki gelişiminden yansımalar: Kesir öğretiminde fark etme becerisinin işe koşulması [Yayımlanmamış doktora tezi, Karadeniz Teknik Üniversitesi Eğitim Bilimleri Enstitüsü]. Yüksek Öğretim Kurulu Ulusal Tez Merkezi.
  • Blömeke, S., Gustafsson, J.-E., & Shavelson, R. (2015). Beyond dichotomies: Competence viewed as a continuum. Zeitschrift für Psychologie, 223(1), 3–13. https://doi.org/10.1027/2151-2604/a000194
  • Bütüner, S. Ö. (2020). Türkiye’de okutulan ortaokul matematik ders kitaplarının aritmetik ortalama kavramına ilişkin öğrencilere sunduğu öğrenme fırsatları. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 11(1), 157-187.
  • 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.
  • Carpenter, T. P., Fennema, E., Peterson, P. L., Chiang, C. P., & Loef, M. (1989). Using knowledge of children’s mathematics thinking in classroom teaching: An experimental study. American Educational Research Journal, 26(4), 499-531.
  • Cobb, P., Confrey, J., DiSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9-13.
  • Confrey, J., & Lachance, A. (2000). Transformative teaching experiments through conjecture-driven research design. In A. Kelly & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 231–265). Mahwah, NJ: Lawrence Erlbaum Associates.
  • Cooper, S. (2009). Preservice teachers' analysis of children's work to make instructional decisions. School Science and Mathematics, 109(6), 355-362.
  • Doğan-Coşkun, Tekin-Sitrava, R., & Işıksal-Bostan, M. (2023). Pre-service elementary teachers’ noticing expertise of students’ mathematical thinking: The case of fractions. International Journal of Mathematical Education in Science and Technology, 54(6), 982-999.
  • Czarnocha, B., & Maj, B. (2008). A teaching experiment. In B. Czarnocha (Ed.), Handbook of mathematics teaching research -a tool for teachers- researchers (pp. 47–58). Poland: University of Reszów.
  • Fernández, C., Llinares, S., & Valls, J. (2013). Primary school teacher’s noticing of students’ mathematical thinking in problem solving. The Mathematics Enthusiast, 10(1), 441–468.
  • Dick, L. K. (2017). Investigating the relationship between professional noticing and specialized content knowledge. In E. Schack, M. Fisher, & J. Wilhelm (Eds.), Teacher noticing: Bridging and broadening perspectives, contexts, and frameworks (pp. 339-358). Springer.
  • Dişbudak-Kuru, Ö., Ucuzoğlu, A. N., Işıksal-Bostan, M., Yemen-Karpuzcu, S., & Tekin-Sitrava, R. (2022). Ortaokul matematik öğretmenlerinin mesleki fark etme becerileri: dikdörtgenler prizmasının hacmine ilişkin problem durumu. Mersin Üniversitesi Eğitim Fakültesi Dergisi, 18(2), 154-174.
  • Dreher, A., & Kuntze, S. (2015). Teachers’ professional knowledge and noticing: The case of multiple representations in the mathematics classroom. Educational Studies in Mathematics, 88, 89-114.
  • Enisoğlu, D. (2014). Yedinci sınıf öğrencilerinin sütun grafiği gösteriminde verilen aritmetik ortalama, ortanca ve tepe değer kavramları ile ilgili problemleri çözerken kullandıkları olası çözüm stratejileri, yaptıkları hatalar ve yanlış yorumlamaları (Tez No: 381685) [Yüksek lisans tezi, Orta Doğu Teknik Üniversitesi]. Yüksek Öğretim Kurulu Ulusal Tez Merkezi.
  • Fernández, C., Llinares, S., & Valls, J. (2013). Primary school teacher’s noticing of students’ mathematical thinking in problem solving. The Mathematics Enthusiast, 10(1), 441-468.
  • Gal, I. (1995). Statistical tools and statistical literacy: The case of the average. Teaching Statistics, 17(3), 97-99.
  • Girit-Yildiz, D., Osmanoglu, A., & Gundogdu Alayli, F. (2023). Providing a video-case-based professional development environment for prospective mathematics teachers to notice students’ misconceptions in measurement. Journal of Mathematics Teacher Education, 26(2), 179-209.
  • González, G., & Vargas, G. E. (2020). Teacher noticing and reasoning about student thinking in classrooms as a result of participating in a combined professional development ıntervention. Mathematics Teacher Education and Development, 22(1), 5-32
  • Groth, R.E. (2009). Characteristics of teachers' conversations about teaching mean, median, and mode. Teaching and Teacher Education, 25, 707-716.
  • Güner, P., & Akyüz, D. (2017). Ders imecesi (lesson study) mesleki gelişim modeli: Öğretmen adaylarının fark etme becerilerinin incelenmesi. İlköğretim Online, 16(2), 428-452.
  • Güner, P., & Akyüz, D. (2020). Noticing student mathematical thinking within the context of lesson study. Journal of Teacher Education, 71(5), 568–583. https://doi.org/10.1177/0022487119892964
  • Gürbüz, S. ve Şahin, F. (2018). Sosyal bilimlerde araştırma yöntemleri (5. baskı). Ankara: Seçkin Yayıncılık.
  • Gürel, R. (2016). Ortaokul matematik öğretmenlerinin merkezi eğilim ve yayılım ölçülerine ilişkin öğretim bilgilerinin incelenmesi. (Tez No: 443569). [Yüksek lisans tezi, Hacettepe Üniversitesi]. Yüksek Öğretim Kurulu Ulusal Tez Merkezi.
  • Gürsoy, P. (2019). Bir matematik öğretmeninin cebir öğretim sürecinden yansımalar: Fark etme becerisi. [Yayımlanmamış Yüksek Lisans Tezi, Karadeniz Teknik Üniversitesi Eğitim Bilimleri Enstitüsü]. Yüksek Öğretim Kurulu Ulusal Tez Merkezi.
  • Hino, K., Stylianides, G. J., Eilerts, K., Lajoie, C., & Pugalee, D. (2017). Topic study group no. 47: Pre-service mathematics education of primary teachers. In G. Kaiser (Ed.), Proceedings of the 13th International Congress on Mathematical Education, ICME-13 Monographs (pp. 593–597). https://doi.org/10.1007/978-3-319-62597-3_74
  • Hoth, J., Kaiser, G., Busse, A., Doehrmann, M., Koenig, J., & Blömeke, S. (2017). Professional competences of teachers for fostering creativity and supporting high-achieving students. ZDM, 49, 107-120.
  • Ivars, P., Fernández, C., & Llinares, S. (2020). A learning trajectory as a scaffold for pre-service teachers’ noticing of students’ mathematical understanding. International Journal of Science and Mathematics Education, 18, 529-548.
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There are 64 citations in total.

Details

Primary Language Turkish
Subjects Mathematics Education
Journal Section Articles
Authors

Reyhan Tekin Sitrava 0000-0002-1285-2791

Neşe Şahin 0000-0002-0261-2954

Nafiye Sümeyye Çopur 0000-0002-1296-3336

Ayşegül Ayıkol Baykal 0000-0002-9673-3780

Early Pub Date April 20, 2024
Publication Date April 24, 2024
Submission Date January 17, 2024
Acceptance Date April 1, 2024
Published in Issue Year 2024 Volume: 21 Issue: 1

Cite

APA Tekin Sitrava, R., Şahin, N., Çopur, N. S., Ayıkol Baykal, A. (2024). Matematik Öğretmen Adaylarının Öğrencilerin Aritmetik Ortalamaya Yönelik Düşünüşünü Fark Etme Becerilerinin Geliştirilmesi: Bir Öğretim Deneyi. Van Yüzüncü Yıl Üniversitesi Eğitim Fakültesi Dergisi, 21(1), 306-331. https://doi.org/10.33711/yyuefd.1421623
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