Matematiksel Modelleme Etkinlikleri Bağlamında Öğrenci Düşünmelerine Yönelik Öğretmen Farkındalığı ve Fark Etme Stratejileri
Yıl 2021,
Sayı: 53, 521 - 554, 01.09.2021
Dr. Belma Türker Biber
,
İffet Yetkin Özdemir
Öz
Çalışmanın amacı, öğrencilerin matematiksel düşünme sürecine yönelik öğretmen farkındalıklarını ve fark etme stratejilerini incelemektir. Durum çalışması deseni kullanılan çalışma, Ankara’daki bir ortaokulun yedinci sınıf düzeyinde eğitim veren bir matematik öğretmeninin derslerinde gerçekleştirilmiştir. Çalışmanın verileri öğretmenle yapılan yarı yapılandırılmış görüşmeler, sınıf içi video kayıtları, öğrenci gözlemleri ve öğrenci çalışmalarından elde edilen dokümanlar yoluyla toplanmıştır. Öğrenci düşünmelerini gözlemleme sürecinde istatistik konularını içeren dört modelleme etkinliği kullanılmıştır. Toplanan veriler içerik analizi ve betimsel analiz yöntemiyle analiz edilmiştir. Öğretmenin öğrenci düşünmelerine yönelik neleri fark ettiğine ilişkin 3 kategori elde edilmiştir: (a) Kavramsal anlama (b) işlemsel anlama ve (c) matematiksel dil kullanımı. Öğretmenin öğrenci düşünmeleriyle ilgili farkındalıklarının çoğunlukla kavramsal anlamalar üzerinde yoğunlaştığı tespit edilmiştir. Öğretmenin fark ettiklerini nasıl ifade ettiğiyle ilgili ise şu kategorilere ulaşılmıştır: (a) Tanımlama ve açıklama, (b) değerlendirme ve yorumlama ile (c) gerekçelendirme. Öğretmen uygun model geliştirme sürecindeki öğrencilerinde fark ettiği durumları tekrarlama, fazladan duyma ve taraflı duyma şeklinde tanımlamıştır. Fark ettiği durumlarla ilgili süreci ya da sonucu yorumlamış, çeşitli değerlendirmeler yapmıştır. Öğretmen yorumlarını gerekçelendirirken de, öğrenci söylemleri/davranışlarından kanıtlar sunmuş veya öğrencileriyle ilgili bilgilerinden ve beklentilerinden yola çıkarak tahminde/varsayımlarda bulunmuştur.
Destekleyen Kurum
Hacettepe Üniversitesi
Proje Numarası
014BİYP700001
Teşekkür
Dr. Richard Lesh'e doktora tez sürecime katkılarından dolayı teşekkür ediyorum. Ayrıca Hacettepe Üniversitesi BAP proje koordinatörlüğüne verdiği destekler için teşekkür ederim.
Kaynakça
- Aiken Jr, L. R. (1972). Language factors in learning mathematics. Review of Educational Research, 42(3), 359-385.
- Bali, Ç. G. (2013). Matematik öğretiminde dil. Paper presented at the ufbmek.
- Biembengut, M. S., & Hein, N. (2010). Mathematical Modeling: Implications for Teaching. In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling Students' Mathematical Modeling Competencies. ICTMA 13 (pp. 481 - 490): Springer, US.
- Blythe, T., Allen, D., & Powell, B. S. (1999). Looking together at student work: A companion guide to assessing student learning. New York: Teachers College Press.
- Borko, H., Jacobs, J., Eiteljorg, E., & Pittman, M. E. (2008). Video as a tool for fostering productive discussions in mathematics professional development. Teaching and Teacher Education, 24(2), 417-436. doi:10.1016/j.tate.2006.11.012
- Chamberlin, S. A. (2013). Statistics for Kids: Model Eliciting Activities to Investigate Concepts in Statistics: Prufrock Press.
- Crespo, S. (2000). Seeing More Than Right And Wrong Answers: Prospective Teachers’ Interpretations Of Students’ Mathematicalwork. Journal of Mathematics Teacher Education, 3, 155-181.
- Doerr, H., & English, L. D. (2003). A Modeling perspective on students’ mathematical reasoning about data. Journal of Research in Mathematics Education, 34(2), 110-136.
- English, L. D. (2006). Mathematical Modeling in the primary school. Educational Studies in Mathematics, 63(3), 303-323.
- Even, R., & Wallach, T. (2004). Between student observation and student assessment: A critical reflection. Canadian Journal of Science, Mathematics, and Technology Education(4), 483–495.
- Garfield, J., delMas, R., & Zieffler, A. (2012). Developing statistical modelers and thinkers in an introductory, tertiary-level statistics course. ZDM, 44(7), 883-898. doi:10.1007/s11858-012-0447-5
- Genç, G., & Erdem, A. R. (2016). Matematik Öğretiminde Olumlu Söylem Ortamı ve Söylem Analizi. Uluslararası Toplum Araştırmaları Dergisi, 6(10).
- Hjalmarson, M. A., Moore, T. J., & Delmas, R. (2011). Statistical analysis when the data is an image: Eliciting student thinking about sampling and variability. Statistics Education Research Journal, 10(1), 15-34.
- Jacobs, V., & Philipp, R. (2011). Mathematics Teacher Noticing: Seeing Through Teachers' Eyes. Association of Mathematics Teacher Educators.
- Jones, G. A., Thornton, C. A., Langrall, C. W., Mooney, E. S., Perry, B., & Putt, I. J. (2000). A Framework for Characterizing Children's Statistical Thinking. Mathematical Thinking and Learning, 2(4), 269-307. doi:10.1207/S15327833MTL0204_3
- Konold, C., & Pollatsek, A. (2002). Data Analysis as the Search for Signals in Noisy Processes. Journal for Research in Mathematics Education, 33(4), 259-289. doi:10.2307/749741
- Koparan, T. (2014). Difficulties in learning and teaching statistics: teacher views. International Journal of Mathematical Education in Science and Technology, 46(1), 94-104. doi:10.1080/0020739x.2014.941425
- Lehrer, R., & Romberg, T. (1996). Exploring Children's Data Modeling. Cognition and Instruction, 14(1), 69-108.
- Leinhardt, G., Putnam, R. T., Stein, M., & Baxter, J. (1991). Where subject knowledge matters. In P. Peterson, E. Fennema, & T. Carpenter (Eds.), Advances in research on teaching (pp. 87 - 113). Greenwich, CT: JAI Press.
- Lesh, R. (2006). Modeling students modeling abilities: The teaching and learning of complex systems in education. Journal of the Learning Sciences, 15(1), 45-52. doi:DOI 10.1207/s15327809jls1501_6
- Lesh, R., & Kelly, A. E. (1997). Teacher's evolving conceptions of one-to-one tutoring: A three-tiered teaching experiment. Journal for Research in Mathematics Education, 28(4), 398-430. doi:Doi 10.2307/749681
- Luna, M., Russ, R. S., & Colestock, A. A. (2009). Teacher noticing in the moment of instruction: The case of one high school science teacher. Paper presented at the Paper to be presented at annual meeting of the National Association for Research in Science Teaching.
- NCTM. (2000). Principles and Standards for School Mathematics. (0873534808). Reston, VA: NCTM.
- Nicol, C., & Crespo, S. (2003). Learning in and from practice: Pre-service teachers investigate their mathematics teaching. Paper presented at the International Group for the Psychology of Mathematics Education 27, Honolulu, Hawaii.
- Schorr, R. Y., & Lesh, R. (1998). Using thought-revealing activities to stimulate new instructional models for teachers. Paper presented at the 20th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Raleigh, NC.
- Schorr, R. Y., & Lesh, R. (2003). A modeling approach for providing teacher development. In R. Lesh & H. Doerr (Eds.), Beyond Constructivism: A models & modeling perspective on mathematics problem solving, learning & teaching (pp. 141 - 157). Mahwah, NJ: Lawrence Erlbaum Associates.
- Sherin, M. G. (2001). Developing a professional vision of classroom events. In T. Wood, B. S. Nelson, & J. Warfield (Eds.), Beyond classical pedagogy: Teaching elementary school mathematics (pp. 75 - 93). Hillsdale, NJ: Erlbaum.
- Star, J. R., & Strickland, S. K. (2007). Learning to observe: using video to improve preservice mathematics teachers’ ability to notice. Journal of Mathematics Teacher Education, 11(2), 107-125. doi:10.1007/s10857-007-9063-7
- Straker, A. (1993). Talking points in mathematics: Cambridge University Press.
- 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.
- Wallach, T., & Even, R. (2005). Hearıng students: the complexity of understanding what they are saying, showing, and doing. Journal of Mathematics Teacher Education, 8, 393–417.
Teacher’s Noticing and Noticing Strategies about Student's Thinking in the Context of Mathematical Modeling Activitie
Yıl 2021,
Sayı: 53, 521 - 554, 01.09.2021
Dr. Belma Türker Biber
,
İffet Yetkin Özdemir
Öz
This study aims to examine teacher's noticing and noticing strategies towards student's mathematical thinking process. The case study was conducted in the lessons of a mathematics teacher teaching at the seventh grade level of a middle school in Ankara. Data was collected through semi-structured interviews with the teacher, in-class video recordings, student observations, and documents obtained from student studies. Four modeling activities relating statistical subjects were used to observe student's thinking process. The collected data were analyzed by content analysis and descriptive analysis method. There were figured out 3 categories of teacher’s noticing about student thinking: (a) conceptual understanding (b) procedural understanding (c) mathematical language use. It has been found that the teacher's noticing about student's thinking is mostly focused on conceptual understandings. Regarding the teacher's noticing strategies, the following categories were reached: a) Identification and description, (b) evaluation and interpretation, and (c) justification. The teacher defined the situations that she noticed in her students during the appropriate model development process as repetition, overhearing, and biased hearing. She interpreted the process or result of the situations she noticed and made various assessments. In justifying her comments, she presented evidence from students' rhetoric/behavior or offered predictions/assumptions based on her knowledge and expectations about their students.
Proje Numarası
014BİYP700001
Kaynakça
- Aiken Jr, L. R. (1972). Language factors in learning mathematics. Review of Educational Research, 42(3), 359-385.
- Bali, Ç. G. (2013). Matematik öğretiminde dil. Paper presented at the ufbmek.
- Biembengut, M. S., & Hein, N. (2010). Mathematical Modeling: Implications for Teaching. In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling Students' Mathematical Modeling Competencies. ICTMA 13 (pp. 481 - 490): Springer, US.
- Blythe, T., Allen, D., & Powell, B. S. (1999). Looking together at student work: A companion guide to assessing student learning. New York: Teachers College Press.
- Borko, H., Jacobs, J., Eiteljorg, E., & Pittman, M. E. (2008). Video as a tool for fostering productive discussions in mathematics professional development. Teaching and Teacher Education, 24(2), 417-436. doi:10.1016/j.tate.2006.11.012
- Chamberlin, S. A. (2013). Statistics for Kids: Model Eliciting Activities to Investigate Concepts in Statistics: Prufrock Press.
- Crespo, S. (2000). Seeing More Than Right And Wrong Answers: Prospective Teachers’ Interpretations Of Students’ Mathematicalwork. Journal of Mathematics Teacher Education, 3, 155-181.
- Doerr, H., & English, L. D. (2003). A Modeling perspective on students’ mathematical reasoning about data. Journal of Research in Mathematics Education, 34(2), 110-136.
- English, L. D. (2006). Mathematical Modeling in the primary school. Educational Studies in Mathematics, 63(3), 303-323.
- Even, R., & Wallach, T. (2004). Between student observation and student assessment: A critical reflection. Canadian Journal of Science, Mathematics, and Technology Education(4), 483–495.
- Garfield, J., delMas, R., & Zieffler, A. (2012). Developing statistical modelers and thinkers in an introductory, tertiary-level statistics course. ZDM, 44(7), 883-898. doi:10.1007/s11858-012-0447-5
- Genç, G., & Erdem, A. R. (2016). Matematik Öğretiminde Olumlu Söylem Ortamı ve Söylem Analizi. Uluslararası Toplum Araştırmaları Dergisi, 6(10).
- Hjalmarson, M. A., Moore, T. J., & Delmas, R. (2011). Statistical analysis when the data is an image: Eliciting student thinking about sampling and variability. Statistics Education Research Journal, 10(1), 15-34.
- Jacobs, V., & Philipp, R. (2011). Mathematics Teacher Noticing: Seeing Through Teachers' Eyes. Association of Mathematics Teacher Educators.
- Jones, G. A., Thornton, C. A., Langrall, C. W., Mooney, E. S., Perry, B., & Putt, I. J. (2000). A Framework for Characterizing Children's Statistical Thinking. Mathematical Thinking and Learning, 2(4), 269-307. doi:10.1207/S15327833MTL0204_3
- Konold, C., & Pollatsek, A. (2002). Data Analysis as the Search for Signals in Noisy Processes. Journal for Research in Mathematics Education, 33(4), 259-289. doi:10.2307/749741
- Koparan, T. (2014). Difficulties in learning and teaching statistics: teacher views. International Journal of Mathematical Education in Science and Technology, 46(1), 94-104. doi:10.1080/0020739x.2014.941425
- Lehrer, R., & Romberg, T. (1996). Exploring Children's Data Modeling. Cognition and Instruction, 14(1), 69-108.
- Leinhardt, G., Putnam, R. T., Stein, M., & Baxter, J. (1991). Where subject knowledge matters. In P. Peterson, E. Fennema, & T. Carpenter (Eds.), Advances in research on teaching (pp. 87 - 113). Greenwich, CT: JAI Press.
- Lesh, R. (2006). Modeling students modeling abilities: The teaching and learning of complex systems in education. Journal of the Learning Sciences, 15(1), 45-52. doi:DOI 10.1207/s15327809jls1501_6
- Lesh, R., & Kelly, A. E. (1997). Teacher's evolving conceptions of one-to-one tutoring: A three-tiered teaching experiment. Journal for Research in Mathematics Education, 28(4), 398-430. doi:Doi 10.2307/749681
- Luna, M., Russ, R. S., & Colestock, A. A. (2009). Teacher noticing in the moment of instruction: The case of one high school science teacher. Paper presented at the Paper to be presented at annual meeting of the National Association for Research in Science Teaching.
- NCTM. (2000). Principles and Standards for School Mathematics. (0873534808). Reston, VA: NCTM.
- Nicol, C., & Crespo, S. (2003). Learning in and from practice: Pre-service teachers investigate their mathematics teaching. Paper presented at the International Group for the Psychology of Mathematics Education 27, Honolulu, Hawaii.
- Schorr, R. Y., & Lesh, R. (1998). Using thought-revealing activities to stimulate new instructional models for teachers. Paper presented at the 20th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Raleigh, NC.
- Schorr, R. Y., & Lesh, R. (2003). A modeling approach for providing teacher development. In R. Lesh & H. Doerr (Eds.), Beyond Constructivism: A models & modeling perspective on mathematics problem solving, learning & teaching (pp. 141 - 157). Mahwah, NJ: Lawrence Erlbaum Associates.
- Sherin, M. G. (2001). Developing a professional vision of classroom events. In T. Wood, B. S. Nelson, & J. Warfield (Eds.), Beyond classical pedagogy: Teaching elementary school mathematics (pp. 75 - 93). Hillsdale, NJ: Erlbaum.
- Star, J. R., & Strickland, S. K. (2007). Learning to observe: using video to improve preservice mathematics teachers’ ability to notice. Journal of Mathematics Teacher Education, 11(2), 107-125. doi:10.1007/s10857-007-9063-7
- Straker, A. (1993). Talking points in mathematics: Cambridge University Press.
- 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.
- Wallach, T., & Even, R. (2005). Hearıng students: the complexity of understanding what they are saying, showing, and doing. Journal of Mathematics Teacher Education, 8, 393–417.