Abstract
Çoğunlukla öğrenme süreçleri ile ilişkili bir kavram olarak ele alınan üstbiliş, bilişsel pek çok süreci içeren öğretim faaliyetlerinin etkili bir şekilde yerine getirilmesinde de önemli bir rol oynar. Araştırmalar genel olarak öğretmenlerin üstbilişsel deneyimlerine (öğretimin planlanması, izlenmesi, değerlendirilmesi gibi) ve bunların nasıl geliştirilebileceğine odaklanmıştır. Bu çalışmada, matematik öğretimi için gerekli üstbilişsel bilgi yapılarını incelemek amaçlanmıştır. Bu kapsamda bir matematik öğretmeninin denk kesirler konusunun öğretimi sırasında işe koştuğu üstbilişsel bilgiler, üstbiliş ve öğretmen bilgisi modelleri çerçevesinde tanımlanmıştır. Nitel araştırma yöntemlerinden durum çalışması deseni kullanılmıştır. Çalışmaya deneyimli bir ortaokul matematik öğretmeni katılmış, veriler öğretmen ile yapılan bire-bir görüşmeler ve denk kesriler konusunun öğretimini içeren ders gözlemleri yoluyla toplanmıştır. Verilerin analizinde içerik analizi kullanılmıştır. Bulgulara dayanarak matematik öğretmeninin üstbilişsel bilgisi ne bildiği, nasıl öğrettiği ve öğretim karar ve eylemleri hakkındaki (neden/ne zaman) bilgi ve farkındalıkları olmak üzere üç ana kategori altında tanımlanmıştır. Öğretmenin “ne bildiği” hakkındaki bilgisi, kendisi, öğrencileri ve genel öğretmen özellikleri ile öğretim sırasında performansına etki edebilecek konu özellikleri (kaynaklar, müfredat, öğretim stratejileri, temsiller ve örnekler) hakkındaki farkındalıklarını içermektedir. Öğretmenin “nasıl öğrettiği” hakkındaki bilgisi, konu ile ilgili tanımların, örnek ve temsillerin nasıl sunulacağı, öğretim yöntem ve stratejilerin nasıl işe koşulacağı, öğretimle ilgili görevlerin nasıl sıralanacağı ve bağlantıların nasıl kurulacağı hakkındaki bilgileri içermektedir. “Öğretim karar ve eylemleri” hakkındaki bilgiler ise öğretmenin öğretimine, öğrenciye ve koşullara ilişkin aldığı kararları, bu kararların nedenleri, zamanlaması ve etkililiği hakkındaki farkındalıklarını içermektedir. Çalışmada tanımlanan üstbilişsel bilgilerin öğretmen bilgisi modellerinde tanımlanan bilgi boyutları ile ilişkili olduğu görülmüştür.
References
- Arends, R. (2012). Learning to teach, 9th edition. New York: Mc-Graw Hill
- Artz, A. F., & Armour-Thomas, E. (1992). Development of a cognitive-metacognitive framework for protocol analysis of mathematical problem solving in small groups. Cognition and instruction, 9(2), 137-175. https://doi.org/10.1207/s1532690xci0902_3
- Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special. Journal of teacher education, 59(5), 389-407. https://doi.org/10.1177/0022487108324
- Baxter, J. A., & Lederman, N. G. (1999). Assessment and measurement of pedagogical content knowledge. In Examining pedagogical content knowledge (pp. 147-161). Springer, Dordrecht.
- Bozorgian, H., & Jafarzade, L. (2013). Teachers’ Metacognitive Knowledge and Education Programs in an Input-poor Environment. In The 11 th TELLSI International Conference.
- Brown, A. L. (1980). Metacognitive development and reading. In R. J. Spiro, B. C. Bruce, & W. F. Brewer (Eds.), Theoretical issues in reading comprehension (pp. 453–481). Hillsdale: Lawrence Erlbaum Associates.
- Carpenter, T. P., & Fennema, E. (1991). Research and cognitively guided instruction. Integrating research on teaching and learning mathematics, 1-16.
- Creswell, J. W., & Poth, C. N. (2018). Qualitative inquiry & research design: Choosing among five approaches (4th ed.). Los Angeles, CA: Sage Publications.
- Denzin, N. K., & Lincoln, Y. S. (2018). The Sage handbook of qualitative research (5th ed.). Sage publications.
- Eldar, O., Eylon, B. S., & Ronen, M. (2012). A metacognitive teaching strategy for preservice teachers: Collaborative diagnosis of conceptual understanding in science. In Metacognition in science education (pp. 225-250). Springer, Dordrecht.
- Eldar, O., & Miedijensky, S. (2015). Designing a metacognitive approach to the professional development of experienced science teachers. In Metacognition: Fundaments, applications, and trends (pp. 299-319). Springer, Cham.
- Erenkuş, M. & Şavaşkan, D. (2019). Ortaokul ve imam hatip ortaokulu Matematik 5. sınıf ders kitabı. Koza Yayın.
- Fennema, E., & Franke, M. L. (1992). Teachers' knowledge and its impact. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (pp. 147–164). Macmillan Publishing Co, Inc.
- Flavell, J. H. (1979). Metacognition and cognitive monitoring: A new area of cognitive–developmental inquiry. American psychologist, 34(10), 906.
- Fransman, J. S. (2014). Mathematics teachers' metacognitive skills and mathematical language in the teaching-learning of trigonometric functions in township schools (Doctoral dissertation). North- West University, South Africa.
- Georghiades, P. (2004). From the general to the situated: Three decades of metacognition. International journal of science education, 26(3), 365-383. https://doi.org/10.1080/0950069032000119401
- Hartman, H. J. (2001). Teaching metacognitively. In Metacognition in learning and instruction (pp. 149-172). Springer, Dordrecht.
- Hill, H., & Ball, D. L. (2009). The curious—and crucial—case of mathematical knowledge for teaching. Phi Delta Kappan, 91(2), 68-71. https://doi.org/10.1177/003172170909100
- Jacobs, J. E., & Paris, S. G. (1987). Children's metacognition about reading: Issues in definition, measurement, and instruction. Educational psychologist, 22(3-4), 255-278. https://doi.org/10.1080/00461520.1987.9653052
- Karadağ, Ö., & Tekercioğlu, H. (2019). Türkçe ders kitaplarındaki bilişsel ve üstbilişsel işlevlere dair bir durum tespiti. Mersin Üniversitesi Eğitim Fakültesi Dergisi, 15(3), 628-646. https://doi.org/10.17860/mersinefd.594240
- Kaur, K., & Pumadevi, S. (2009). Examples and conceptual understanding of equivalent fractions among primary school students. In Third International Conference on Science and Mathematics Education (CoSMEd).
- Kieren, T. E. (1993). Rational and fractional numbers: From quotient fields to recursive understanding. In T.P. Carpenter, E. Fennema, & T. A. Romberg (Eds.), Rational numbers: An integration of research (pp.49-84). Hillsdale, NJ: Lawrence Erlbaum.
- Kohen, Z., & Kramarski, B. (2018). Promoting mathematics teachers’ pedagogical metacognition: A theoretical-practical model and case study. In Cognition, Metacognition, and Culture in STEM Education (pp. 279-305). Springer, Cham.
- Lampert, M. (2001). Teaching problems and the problems of teaching. Yale University Press. Ma, L. (1999). Knowing and teaching elementary mathematics: Understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates.
- Millî Eğitim Bakanlığı [MEB], (2018). Matematik dersi öğretim programı (ilkokul ve ortaokul 1., 2., 3., 4., 5., 6., 7. ve 8. sınıflar). http://mufredat.meb.gov.tr/Dosyalar/201813017165445- MATEMAT%C4%B0K%20%C3%96%C4%9ERET%C4%B0M%20PROGRAMI%202018v.pdf
- Merriam, S. B., & Tisdell, E. J. (2016). Qualitative Research: A Guide to Design and Implementation; Kindle Edition. Retrieved from Amazon. com
- Mevarech, Z., & Kramarski, B. (2014). Critical Maths for innovative societies: The role of metacognitive pedagogies, educational research and innovation. Paris: OECD Publishing
- Miles, M. B., Huberman, A. M., & Saldaña, J. (2014). Qualitative data analysis: A methods sourcebook (3rd ed.). Sage publications.
- Millî Eğitim Bakanlığı [MEB], (2018). Matematik dersi öğretim programı (ilkokul ve ortaokul 1., 2., 3., 4., 5., 6., 7. ve 8. sınıflar). http://mufredat.meb.gov.tr/Dosyalar/201813017165445- MATEMAT%C4%B0K%20%C3%96%C4%9ERET%C4%B0M%20PROGRAMI%202018v.pdf
- Park, S., & Oliver, J. S. (2008). Revisiting the conceptualisation of pedagogical content knowledge (PCK): PCK as a conceptual tool to understand teachers as professionals. Research in science Education, 38(3), 261-284. https://doi.org/10.1007/s11165-007-9049-6 .
- Patton, M. Q. (2002). Qualitative research & evaluation methods (3rd ed.). Thousand Oaks, CA: Sage.
- Rowland, T., Turner, F., Thwaites, A., & Huckstep, P. (2009). Transformation: Using examples in mathematics teaching. Developing Primary Mathematics Teaching: Reflecting on Practice with the Knowledge Quartet, 67-100.
- Rowland, T. (2013). The knowledge quartet: The genesis and application of a framework for analysing mathematics teaching and deepening teachers’ mathematics knowledge. Sisyphus—Journal of Education, 1(3), 154-43. https://doi.org/10.25749/sis.3705
- Sharma, P., & Mishra, N. (2017). Meta cognitive environment: need of 21 st century. International Journal of Educational Science and Research (IJESR) Vol. 7, Issue 2, Apr 2017, 93-100
- Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational researcher, 15(2), 4-14.
- Schraw, G., & Moshman, D. (1995). Metacognitive theories. Educational psychology review, 7(4), 351-371.
- Schoenfeld, A. H. (2000). Models of the teaching process. Journal of Mathematical Behavior, 18, 243-261. https://doi.org/10.1016/S0732-3123(99)00031-0
- Wilson, N. S., & Bai, H. (2010). The relationships and impact of teachers’ metacognitive knowledge and pedagogical understandings of metacognition. Metacognition and Learning, 5(3), 269-288.
- Yerdelen-Damar, S., Özdemir, Ö. F., & Cezmi, Ü. N. A. L. (2015). Pre-service physics teachers’ metacognitive knowledge about their instructional practices. Eurasia Journal of Mathematics, Science and Technology Education, 11(5), 1009-1026. DOI: 10.12973/eurasia.2015.1370a
- Zohar, A. (1999). Teachers’ metacognitive knowledge and the instruction of higher order thinking. Teaching and teacher Education, 15(4), 413-429.
Abstract
Metacognition, often associated with learning processes, also crucially impacts effective teaching involving cognitive processes. Research primarily focuses on teachers' metacognitive experiences (such as planning, monitoring, and evaluating instruction) and their development. This study examines metacognitive knowledge structures for teaching mathematics within the framework of metacognition and teacher knowledge models. A case study approach was adopted. An experienced middle school mathematics teacher participated in the study, and data were collected through one-on-one interviews with the teacher and classroom observations during the instruction of equivalent fractions. Content analysis was used. Findings categorized the teacher's metacognitive knowledge into "what they know," "how they teach," and "instructional decisions and actions (why/when)." "What they know" includes the teacher's awareness of themselves, students, general teacher characteristics, and topic-related attributes (sources, curriculum, teaching strategies, representations, and examples) that could influence their performance during instruction. The dimension of "how they teach" encompasses the teacher's knowledge about presenting definitions, examples, and representations of the topic, employing teaching methods and strategies, sequencing instructional tasks, and establishing connections between concepts. The dimension of "instructional decisions and actions" encompasses the teacher's awareness of the decisions they make concerning instruction, students, and conditions, including the rationale, timing, and effectiveness of these decisions. The metacognitive knowledge identified in this study is closely related to the knowledge dimensions described in teacher knowledge models.
Keywords
Metacognitive Knowledge Teacher Knowledge Teaching Of Equivalent Fractions Teaching Mathematics.
References
- Arends, R. (2012). Learning to teach, 9th edition. New York: Mc-Graw Hill
- Artz, A. F., & Armour-Thomas, E. (1992). Development of a cognitive-metacognitive framework for protocol analysis of mathematical problem solving in small groups. Cognition and instruction, 9(2), 137-175. https://doi.org/10.1207/s1532690xci0902_3
- Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special. Journal of teacher education, 59(5), 389-407. https://doi.org/10.1177/0022487108324
- Baxter, J. A., & Lederman, N. G. (1999). Assessment and measurement of pedagogical content knowledge. In Examining pedagogical content knowledge (pp. 147-161). Springer, Dordrecht.
- Bozorgian, H., & Jafarzade, L. (2013). Teachers’ Metacognitive Knowledge and Education Programs in an Input-poor Environment. In The 11 th TELLSI International Conference.
- Brown, A. L. (1980). Metacognitive development and reading. In R. J. Spiro, B. C. Bruce, & W. F. Brewer (Eds.), Theoretical issues in reading comprehension (pp. 453–481). Hillsdale: Lawrence Erlbaum Associates.
- Carpenter, T. P., & Fennema, E. (1991). Research and cognitively guided instruction. Integrating research on teaching and learning mathematics, 1-16.
- Creswell, J. W., & Poth, C. N. (2018). Qualitative inquiry & research design: Choosing among five approaches (4th ed.). Los Angeles, CA: Sage Publications.
- Denzin, N. K., & Lincoln, Y. S. (2018). The Sage handbook of qualitative research (5th ed.). Sage publications.
- Eldar, O., Eylon, B. S., & Ronen, M. (2012). A metacognitive teaching strategy for preservice teachers: Collaborative diagnosis of conceptual understanding in science. In Metacognition in science education (pp. 225-250). Springer, Dordrecht.
- Eldar, O., & Miedijensky, S. (2015). Designing a metacognitive approach to the professional development of experienced science teachers. In Metacognition: Fundaments, applications, and trends (pp. 299-319). Springer, Cham.
- Erenkuş, M. & Şavaşkan, D. (2019). Ortaokul ve imam hatip ortaokulu Matematik 5. sınıf ders kitabı. Koza Yayın.
- Fennema, E., & Franke, M. L. (1992). Teachers' knowledge and its impact. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (pp. 147–164). Macmillan Publishing Co, Inc.
- Flavell, J. H. (1979). Metacognition and cognitive monitoring: A new area of cognitive–developmental inquiry. American psychologist, 34(10), 906.
- Fransman, J. S. (2014). Mathematics teachers' metacognitive skills and mathematical language in the teaching-learning of trigonometric functions in township schools (Doctoral dissertation). North- West University, South Africa.
- Georghiades, P. (2004). From the general to the situated: Three decades of metacognition. International journal of science education, 26(3), 365-383. https://doi.org/10.1080/0950069032000119401
- Hartman, H. J. (2001). Teaching metacognitively. In Metacognition in learning and instruction (pp. 149-172). Springer, Dordrecht.
- Hill, H., & Ball, D. L. (2009). The curious—and crucial—case of mathematical knowledge for teaching. Phi Delta Kappan, 91(2), 68-71. https://doi.org/10.1177/003172170909100
- Jacobs, J. E., & Paris, S. G. (1987). Children's metacognition about reading: Issues in definition, measurement, and instruction. Educational psychologist, 22(3-4), 255-278. https://doi.org/10.1080/00461520.1987.9653052
- Karadağ, Ö., & Tekercioğlu, H. (2019). Türkçe ders kitaplarındaki bilişsel ve üstbilişsel işlevlere dair bir durum tespiti. Mersin Üniversitesi Eğitim Fakültesi Dergisi, 15(3), 628-646. https://doi.org/10.17860/mersinefd.594240
- Kaur, K., & Pumadevi, S. (2009). Examples and conceptual understanding of equivalent fractions among primary school students. In Third International Conference on Science and Mathematics Education (CoSMEd).
- Kieren, T. E. (1993). Rational and fractional numbers: From quotient fields to recursive understanding. In T.P. Carpenter, E. Fennema, & T. A. Romberg (Eds.), Rational numbers: An integration of research (pp.49-84). Hillsdale, NJ: Lawrence Erlbaum.
- Kohen, Z., & Kramarski, B. (2018). Promoting mathematics teachers’ pedagogical metacognition: A theoretical-practical model and case study. In Cognition, Metacognition, and Culture in STEM Education (pp. 279-305). Springer, Cham.
- Lampert, M. (2001). Teaching problems and the problems of teaching. Yale University Press. Ma, L. (1999). Knowing and teaching elementary mathematics: Understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates.
- Millî Eğitim Bakanlığı [MEB], (2018). Matematik dersi öğretim programı (ilkokul ve ortaokul 1., 2., 3., 4., 5., 6., 7. ve 8. sınıflar). http://mufredat.meb.gov.tr/Dosyalar/201813017165445- MATEMAT%C4%B0K%20%C3%96%C4%9ERET%C4%B0M%20PROGRAMI%202018v.pdf
- Merriam, S. B., & Tisdell, E. J. (2016). Qualitative Research: A Guide to Design and Implementation; Kindle Edition. Retrieved from Amazon. com
- Mevarech, Z., & Kramarski, B. (2014). Critical Maths for innovative societies: The role of metacognitive pedagogies, educational research and innovation. Paris: OECD Publishing
- Miles, M. B., Huberman, A. M., & Saldaña, J. (2014). Qualitative data analysis: A methods sourcebook (3rd ed.). Sage publications.
- Millî Eğitim Bakanlığı [MEB], (2018). Matematik dersi öğretim programı (ilkokul ve ortaokul 1., 2., 3., 4., 5., 6., 7. ve 8. sınıflar). http://mufredat.meb.gov.tr/Dosyalar/201813017165445- MATEMAT%C4%B0K%20%C3%96%C4%9ERET%C4%B0M%20PROGRAMI%202018v.pdf
- Park, S., & Oliver, J. S. (2008). Revisiting the conceptualisation of pedagogical content knowledge (PCK): PCK as a conceptual tool to understand teachers as professionals. Research in science Education, 38(3), 261-284. https://doi.org/10.1007/s11165-007-9049-6 .
- Patton, M. Q. (2002). Qualitative research & evaluation methods (3rd ed.). Thousand Oaks, CA: Sage.
- Rowland, T., Turner, F., Thwaites, A., & Huckstep, P. (2009). Transformation: Using examples in mathematics teaching. Developing Primary Mathematics Teaching: Reflecting on Practice with the Knowledge Quartet, 67-100.
- Rowland, T. (2013). The knowledge quartet: The genesis and application of a framework for analysing mathematics teaching and deepening teachers’ mathematics knowledge. Sisyphus—Journal of Education, 1(3), 154-43. https://doi.org/10.25749/sis.3705
- Sharma, P., & Mishra, N. (2017). Meta cognitive environment: need of 21 st century. International Journal of Educational Science and Research (IJESR) Vol. 7, Issue 2, Apr 2017, 93-100
- Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational researcher, 15(2), 4-14.
- Schraw, G., & Moshman, D. (1995). Metacognitive theories. Educational psychology review, 7(4), 351-371.
- Schoenfeld, A. H. (2000). Models of the teaching process. Journal of Mathematical Behavior, 18, 243-261. https://doi.org/10.1016/S0732-3123(99)00031-0
- Wilson, N. S., & Bai, H. (2010). The relationships and impact of teachers’ metacognitive knowledge and pedagogical understandings of metacognition. Metacognition and Learning, 5(3), 269-288.
- Yerdelen-Damar, S., Özdemir, Ö. F., & Cezmi, Ü. N. A. L. (2015). Pre-service physics teachers’ metacognitive knowledge about their instructional practices. Eurasia Journal of Mathematics, Science and Technology Education, 11(5), 1009-1026. DOI: 10.12973/eurasia.2015.1370a
- Zohar, A. (1999). Teachers’ metacognitive knowledge and the instruction of higher order thinking. Teaching and teacher Education, 15(4), 413-429.
Details
| Primary Language | Turkish |
|---|---|
| Subjects | Mathematics Education |
| Journal Section | Articles |
| Authors | |
| Publication Date | March 15, 2024 |
| Submission Date | June 25, 2023 |
| Published in Issue | Year 2024 Volume: 24 Issue: 1 |
