Araştırma Makalesi
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Tahmini Öğrenme Yollarının Uygulanması Sürecinde Matematik Öğretmenlerinin Çoklu Temsil Kullanımlarının Gelişimi

Yıl 2021, Cilt: 10 Sayı: 1, 299 - 329, 26.03.2021

Deniz Eroğlu , Dilek Tanışlı

https://doi.org/10.30703/cije.718210
Cited By: 1

Öz

Bu araştırmanın amacı, ortaokul matematik öğretmenlerinin tahmini öğrenme yol haritasına dayalı öğretimlerinde temsil kullanımlarının ve temsiller arası ilişkilendirme becerilerindeki gelişimlerinin incelenmesidir. Araştırma öğretmen gelişim deneyi olarak tasarlanmış ve sürece iki ortaokul matematik öğretmeni katılmıştır. Bu araştırma 10 haftada tamamlanmış ve süreç “planlama, öğretim deneyi ve durum çalışması” olmak üzere 3 farklı aşamada gerçekleştirilmiştir. Birinci aşamada öğretim programındaki kazanımlara uygun olarak, altıncı sınıfta cebir öğrenme alanında yer alan bütün kazanımları kapsayacak ve temsillerin öğretimler sırasında etkin şekilde kullanımını varsayan yol haritaları hazırlanmıştır. İkinci aşamada uzmanlardan biri iki öğretmen ile birlikte öğretim deneyini gerçekleştirmiştir. Üçüncü aşamada öğretmenler yol haritalarına göre hazırlanan öğretim etkinliklerini sınıflarında uygulamıştır. Araştırmanın verileri öğretimler sırasında ve gerçekleştirilen mesleki gelişim toplantılarında çekilmiş videolar aracılığıyla toplanmıştır. Bu araştırmanın sonucunda öğretmenlerin öğrencilerin düşüncelerinden hareketle öğrencileri temsil kullanmaya yönlendirdikleri, öğrencilerin kendi temsil biçimlerini oluşturmalarını sağladıkları ve öğrencilerin temsillere ilişkin ortaya çıkan düşüncelerini organize ederek, temsiller arası ilişki kurmada öğrencilere rehberlik ettikleri görülmüştür.

Anahtar Kelimeler

çoklu temsiller cebir öğretimi öğretmen gelişim deneyi tahmini öğrenme yol haritası ortaokul matematik öğretmenleri

Destekleyen Kurum

Anadolu Üniversitesi

Proje Numarası

1406E301

Kaynakça

  • Ainsworth, S. (1999). The functions of multiple representations. Computers & Education, 33(2), 131-152. https://doi.org/10.1016/S0360-1315(99)00029-9
  • Akkoç, H., Özmantar, F., Bingölbali, E., Yavuz, İ., Baştürk, Ş., ve Demir, S. (2011). Matematik Öğretmen Adaylarına Teknolojiye Yönelik Pedagojik Alan Bilgisi Kazandırma Amaçlı Bir Program Geliştirme. Tübitak Projesi, 107K531, 2008-2011.
  • Arcavi, A., and Schoenfeld, A. H. (2008). Using the unfamiliar to problematize the familiar: The case of mathematics teacher in-service education. Canadian Journal of Science, Mathematics, and Technology Education, 8(3), 280–295. https://doi.org/10.1080/14926150802315122
  • Ball, D. L., Thames, M. H., and Phelps, G. (2008). Content knowledge for teaching: What makes it special. Journal Of Teacher Education, 59(5), 389-407. https://doi.org/10.1177/0022487108324554
  • Borko, H., Jacobs, J., Koellner, K., and Swackhamer, L. (2015). Mathematics professional development: Improving teaching using the problem-solving cycle and leadership preparation models. New York: Teachers College Press.
  • Bulut, D. B., Aygün, B., and İpek, A.S. (2018). Meaning of the Primary and Secondary School Students towards Equal Sign. Turkish Journal of Teacher Education, 7(1), 1-16.
  • Cai, J., and Hwang, S. (2002). Generalized and generative thinking in US and Chinese students’ mathematical problem solving and problem posing. The Journal of Mathematical Behavior, 21(4), 401-421. https://doi.org/10.1016/S0732-3123(02)00142-6
  • Common Core State Standards. (2015). Common Core Standards Initiative. Retrieved from http://www.corestandards.org/.
  • Çelik, D., ve Sağlam-Arslan, A. (2012). Öğretmen adaylarının çoklu gösterimleri kullanma becerilerinin analizi. İlköğretim Online, 11(1), 239-250.
  • Çıkla, O. A., and Çakıroğlu, E. (2006). Seventh grade students' use of multiple representations in pattern related algebra tasks. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 31(31), 13-24.
  • Dündar, S., ve Yılmaz, Y. (2015). Matematik öğretmen adayları hangi gösterim biçiminde daha başarılıdır? İntegral örneği. Turkish Journal of Computer and Mathematics Education, 6(3), 418-445. https://doi.org/10.16949/turcomat.55314
  • Earnest, D., and Balti, A. A. (2008). Instructional strategies for teaching algebra in elementary school. Teaching Children Mathematics, 14(9), 518-522. https://doi.org/10.5951/TCM.14.9.0518
  • Eroğlu, D., ve Tanışlı, D. (2015). Ortaokul matematik öğretmenlerinin temsil kullanımına ilişkin öğrenci ve öğretim stratejileri bilgileri. Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi, 9(1), 275-307. https://doi.org/10.17522/nefefmed.53039
  • Eroğlu, D., Camci, F., ve Tanışlı, D . (2019). Ortaokul altıncı sınıf öğrencilerinin kesir bilgilerinin yapılandırılmasına ilişkin tahmini öğrenme yol haritası: Bir öğretim tasarımı. Pamukkale Üniversitesi Eğitim Fakültesi Dergisi, 45, 116-143. https://doi.org/10.9779/PUJE.2018.225
  • Even, R. (1998). Factors involved in linking representations of functions. The Journal of Mathematical Behavior, 17(1), 105-121. https://doi.org/10.1016/S07323123(99)80063-7
  • Even, R. (1990). Subject matter knowledge for teaching and the case of functions. Educational Studies in Mathematics, 21(6), 521-544. https://doi.org/10.1007/BF00315943
  • Fishman, B. J., Marx, R. W., Best, S., and Tal, R. T. (2003). Linking teacher and student learning to improve professional development in systemic reform. Teaching and teacher education, 19(6), 643-658. https://doi.org/10.1016/S0742051X(03)00059-3
  • Gagatsis, A., and Shiakalli, M. (2004). Ability to translate from one representation of the concept of function to another and mathematical problem solving. Educational psychology, 24(5), 645-657. https://doi.org/10.1080/0144341042000262953
  • Gökkurt, B., ve Soylu, Y. (2016). Ortaokul matematik öğretmenlerinin pedagojik alan bilgilerinin bazı bileşenler açısından incelenmesi: koni örneği. İlköğretim Online, 15(3), 946-973. https://doi.org/10.17051/io.2016.14548
  • Heinze, A., Star, J. R., and Verschaffel, L. (2009). Flexible and adaptive use of strategies and representations in mathematics education. ZDM Mathematics Education, 41, 535-540. https://doi.org/10.1007/s11858-009-0214-4
  • Higgins, J., and Parsons, R. (2009). A successful professional development model in mathematics: A system-wide New Zealand case. Journal Of Teacher Education, 60(3), 231-242. https://doi.org/10.1177/0022487109336894
  • İncikabı, S., and Biber, A. Ç. (2018). Transitions Among The Representations in The Middle School Mathematics Textbooks. Kastamonu Education Journal, 26(3), 729-740. https://doi.org/10.24106/kefdergi.415690
  • İncikabi, S. (2017). Çoklu temsiller ve matematik ögretimi: ders kitaplari üzerine bir inceleme. Cumhuriyet International Journal of Education, 6(1), 66. https://doi.org/10.30703/cije.321438
  • İpek, A. S., and Okumuş, S. (2012). The representations of pre-service elementary mathematics teachers used in solving mathematical problems. Gaziantep University Journal of Social Sciences, 11(3), 681-700.
  • Karsenty, R. (2018). Professional development of mathematics teachers: Through the lens of the camera. In G. Kaiser, H. Forgasz, M. Graven, A. Kuzniak, E. Simmt, and B. Xu (Eds.), Invited lectures from the 13th international congress on mathematical education (pp. 269–288). Hamburg: Springer. https://doi.org/10.1007/9783319-72170-5_16
  • Leikin, R. (2006). Learning by teaching: The case of Sieve of Eratosthenes and one elementary school teacher. In R. Zazkis and S. Campbell (Eds.), Number theory in mathematics education: Perspectives and prospects (pp.115-140). Mahwah, NJ: Erlbaum.
  • Lesh, R., Post, T. R., and Behr, M. (1987). Dienes revisited: Multiple embodiments in computer environments. In I. Wirsup and R. Streit (Eds.), Development in school mathematics education around the world (pp. 647-680). Reston, VA: National Council of Teachers of Mathematics.
  • Mitchell, R., Charalambous, C. Y., and Hill, H. C. (2014). Examining the task and knowledge demands needed to teach with representations. Journal of Mathematics Teacher Education, 17(1), 37-60. https://doi.org/10.1007/s10857013-9253-4
  • Moon, K., Brenner, M. E., Jacob, B., and Okamoto, Y. (2013). Prospective secondary mathematics teachers’ understanding and cognitive difficulties in making connections among representations. Mathematical Thinking and Learning, 15(3), 201-227. https://doi.org/10.1080/10986065.2013.794322
  • Nathan, M. J., and Knuth, E. J. (2003). A study of whole classroom mathematical discourse and teacher change. Cognition and instruction, 21(2), 175-207. https://doi.org/10.1207/S1532690XCI2102_03
  • National Council of Teachers of Mathematics. (2014). Principles to actions: ensuring mathematical success for all. Reston, VA.
  • Patton, M. Q. (2014). Nitel araştırmada çeşitlilik, kuramsal yönelimler. M. Bütün ve S. B. Beşir (Çev. Ed.). Nitel araştırma ve değerlendirme yöntemleri içinde (ss. 75-142). Ankara: Pegem Akademi Yayıncılık.
  • Powell, A.B., Francisco, J.M., and Maher, C.A. (2003) An analytical model for studying the development of learners mathematical ideas and reasoning using videotape data. The Journal of Mathematical Behavior, 4(22), 405-435. https://doi.org/10.1016/j.jmathb.2003.09.002
  • Schwarts, G., and Karsenty, R. (2020). “Can this happen only in Japan?”: mathematics teachers reflect on a videotaped lesson in a cross-cultural context. Journal of Mathematics Teacher Education, 23(6), 527-554. https://doi.org/10.1007/s10857019-09438-z
  • Seidel, T., Stürmer, K., Blomberg, G., Kobarg, M., and Schwindt, K. (2011). Teacher learning from analysis of videotaped classroom situations: Does it make a difference whether teachers observe their own teaching or that of others? Teaching and Teacher Education, 27(2), 259–267. doi:10.1016/j.tate.2010.08.009.
  • Sherin, M. G., and van Es, E. A. (2009). Effects of video club participation on teachers’ professional vision. Journal of Teacher Education, 60(1), 20–37. https://doi.org/10.1177/0022487108328155
  • Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational researcher, 15(2), 4-14. https://doi.org/10.3102/0013189X015002004
  • Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26, 114–145. https://doi.org/10.5951/jresematheduc.26.2.0114
  • Simon, M. (2000). Research on mathematics teacher development: The teacher development experiment. In A. Kelly , and R. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 335-359). Hillsdale, NJ: Lawrence Erlbaum Associates Publishers.
  • Simon, M. A. (2006). Key developmental understandings in mathematics: A direction for investigating and establishing learning goals. Mathematical thinking and learning, 8(4), 359-371. https://doi.org/10.1207/s15327833mtl0804_1
  • Simon, M. (2014). Hypothetical learning trajectories in mathematics education. Encyclopedia of mathematics education, 272-275. https://doi.org/10.1007/978-94-007-4978-8_72
  • Stein, M. K., and Bovalino, J. W. (2001). Manipulatives: One piece of the puzzle. Mathematics Teaching in the Middle School, 6(6), 356-359. https://doi.org/10.5951/MTMS.6.6.0356
  • Şimsek, N., and Boz, N. (2016). Analysis of Pedagogical Content Knowledge Studies in the Context of Mathematics Education in Turkey: A Meta-Synthesis Study. Educational Sciences: Theory and Practice, 16(3), 799-826.
  • Tanışlı, D. (2013). İlköğretim matematik öğretmeni adaylarının pedagojik alan bilgisi bağlamında sorgulama becerileri ve öğrenci bilgileri. Eğitim ve Bilim, 38(169), 80-95.
  • Tataroglu Tasdan, B., Erduran, A., and Çelik, A. (2015). A daunting task for pre-service mathematics teachers: developing students' mathematical thinking. Educational Research and Reviews, 10(16), 2276-2289.
  • Türnüklü, E. B. (2005). The relationship between pedagogical and mathematical content knowledge of pre-service mathematics teachers. Eurasian Journal of Educational Research, 21, 234-247.
  • Yayla, G., ve Özsevgeç, T. (2015). Ortaokul öğrencilerinin grafik becerilerinin incelenmesi: Çizgi grafikleri oluşturma ve yorumlama. Kastamonu Eğitim Dergisi, 23(3), 1381-1400.
  • Yıldırım, Z., ve Albayrak, M. (2016). Ortaokul Öğrencilerinin Farklı Temsil Biçimlerine Göre Doğrusal İlişki Konusunu Anlama Düzeylerinin İncelenmesi. Adnan Menderes Üniversitesi Eğitim Fakültesi Eğitim Bilimleri Dergisi, 7(2), 11-26.

Development of Mathematics Teachers' Use of Multiple Representations throughout the Implementations of Hypothetical Learning Trajectories

Yıl 2021, Cilt: 10 Sayı: 1, 299 - 329, 26.03.2021

Deniz Eroğlu , Dilek Tanışlı

https://doi.org/10.30703/cije.718210
Cited By: 1

Öz

The purpose of the research is to examine the development of elementary mathematics teachers’ use of multiple representation and translations between representations throughout the implementations of hypothetical learning trajectories. The research was designed as a teacher development experiment and two elementary school mathematics teachers participated in the process. This research was completed in 10 weeks and the process was carried out in 3 different stages as “planning, teaching experiment and case study”. The first stage of the research consists of preparing hypothetical learning trajectories matching the objectives in the curriculum by covering all the objectives in algebra. All activities in HLT were appropriate to the use of representations during teaching. In the second stage, the teaching experiment was conducted with two teachers under the supervision of one of the experts. In the third stage, teachers implemented teaching activities based on HLT in their classrooms. Videos taken during teaching and at professional development meetings with teachers are the main data sources of the present research. Results reveal that teachers use students' thoughts to direct them to use representation, they allow students to create their own forms of representation, and they guide students to establish translations between representations through organizing students' emerging thoughts about representations.

Anahtar Kelimeler

multiple representations algebra teaching teacher development experiment hypothetical learning trajectory elementary mathematics teachers

Proje Numarası

1406E301

Kaynakça

  • Ainsworth, S. (1999). The functions of multiple representations. Computers & Education, 33(2), 131-152. https://doi.org/10.1016/S0360-1315(99)00029-9
  • Akkoç, H., Özmantar, F., Bingölbali, E., Yavuz, İ., Baştürk, Ş., ve Demir, S. (2011). Matematik Öğretmen Adaylarına Teknolojiye Yönelik Pedagojik Alan Bilgisi Kazandırma Amaçlı Bir Program Geliştirme. Tübitak Projesi, 107K531, 2008-2011.
  • Arcavi, A., and Schoenfeld, A. H. (2008). Using the unfamiliar to problematize the familiar: The case of mathematics teacher in-service education. Canadian Journal of Science, Mathematics, and Technology Education, 8(3), 280–295. https://doi.org/10.1080/14926150802315122
  • Ball, D. L., Thames, M. H., and Phelps, G. (2008). Content knowledge for teaching: What makes it special. Journal Of Teacher Education, 59(5), 389-407. https://doi.org/10.1177/0022487108324554
  • Borko, H., Jacobs, J., Koellner, K., and Swackhamer, L. (2015). Mathematics professional development: Improving teaching using the problem-solving cycle and leadership preparation models. New York: Teachers College Press.
  • Bulut, D. B., Aygün, B., and İpek, A.S. (2018). Meaning of the Primary and Secondary School Students towards Equal Sign. Turkish Journal of Teacher Education, 7(1), 1-16.
  • Cai, J., and Hwang, S. (2002). Generalized and generative thinking in US and Chinese students’ mathematical problem solving and problem posing. The Journal of Mathematical Behavior, 21(4), 401-421. https://doi.org/10.1016/S0732-3123(02)00142-6
  • Common Core State Standards. (2015). Common Core Standards Initiative. Retrieved from http://www.corestandards.org/.
  • Çelik, D., ve Sağlam-Arslan, A. (2012). Öğretmen adaylarının çoklu gösterimleri kullanma becerilerinin analizi. İlköğretim Online, 11(1), 239-250.
  • Çıkla, O. A., and Çakıroğlu, E. (2006). Seventh grade students' use of multiple representations in pattern related algebra tasks. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 31(31), 13-24.
  • Dündar, S., ve Yılmaz, Y. (2015). Matematik öğretmen adayları hangi gösterim biçiminde daha başarılıdır? İntegral örneği. Turkish Journal of Computer and Mathematics Education, 6(3), 418-445. https://doi.org/10.16949/turcomat.55314
  • Earnest, D., and Balti, A. A. (2008). Instructional strategies for teaching algebra in elementary school. Teaching Children Mathematics, 14(9), 518-522. https://doi.org/10.5951/TCM.14.9.0518
  • Eroğlu, D., ve Tanışlı, D. (2015). Ortaokul matematik öğretmenlerinin temsil kullanımına ilişkin öğrenci ve öğretim stratejileri bilgileri. Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi, 9(1), 275-307. https://doi.org/10.17522/nefefmed.53039
  • Eroğlu, D., Camci, F., ve Tanışlı, D . (2019). Ortaokul altıncı sınıf öğrencilerinin kesir bilgilerinin yapılandırılmasına ilişkin tahmini öğrenme yol haritası: Bir öğretim tasarımı. Pamukkale Üniversitesi Eğitim Fakültesi Dergisi, 45, 116-143. https://doi.org/10.9779/PUJE.2018.225
  • Even, R. (1998). Factors involved in linking representations of functions. The Journal of Mathematical Behavior, 17(1), 105-121. https://doi.org/10.1016/S07323123(99)80063-7
  • Even, R. (1990). Subject matter knowledge for teaching and the case of functions. Educational Studies in Mathematics, 21(6), 521-544. https://doi.org/10.1007/BF00315943
  • Fishman, B. J., Marx, R. W., Best, S., and Tal, R. T. (2003). Linking teacher and student learning to improve professional development in systemic reform. Teaching and teacher education, 19(6), 643-658. https://doi.org/10.1016/S0742051X(03)00059-3
  • Gagatsis, A., and Shiakalli, M. (2004). Ability to translate from one representation of the concept of function to another and mathematical problem solving. Educational psychology, 24(5), 645-657. https://doi.org/10.1080/0144341042000262953
  • Gökkurt, B., ve Soylu, Y. (2016). Ortaokul matematik öğretmenlerinin pedagojik alan bilgilerinin bazı bileşenler açısından incelenmesi: koni örneği. İlköğretim Online, 15(3), 946-973. https://doi.org/10.17051/io.2016.14548
  • Heinze, A., Star, J. R., and Verschaffel, L. (2009). Flexible and adaptive use of strategies and representations in mathematics education. ZDM Mathematics Education, 41, 535-540. https://doi.org/10.1007/s11858-009-0214-4
  • Higgins, J., and Parsons, R. (2009). A successful professional development model in mathematics: A system-wide New Zealand case. Journal Of Teacher Education, 60(3), 231-242. https://doi.org/10.1177/0022487109336894
  • İncikabı, S., and Biber, A. Ç. (2018). Transitions Among The Representations in The Middle School Mathematics Textbooks. Kastamonu Education Journal, 26(3), 729-740. https://doi.org/10.24106/kefdergi.415690
  • İncikabi, S. (2017). Çoklu temsiller ve matematik ögretimi: ders kitaplari üzerine bir inceleme. Cumhuriyet International Journal of Education, 6(1), 66. https://doi.org/10.30703/cije.321438
  • İpek, A. S., and Okumuş, S. (2012). The representations of pre-service elementary mathematics teachers used in solving mathematical problems. Gaziantep University Journal of Social Sciences, 11(3), 681-700.
  • Karsenty, R. (2018). Professional development of mathematics teachers: Through the lens of the camera. In G. Kaiser, H. Forgasz, M. Graven, A. Kuzniak, E. Simmt, and B. Xu (Eds.), Invited lectures from the 13th international congress on mathematical education (pp. 269–288). Hamburg: Springer. https://doi.org/10.1007/9783319-72170-5_16
  • Leikin, R. (2006). Learning by teaching: The case of Sieve of Eratosthenes and one elementary school teacher. In R. Zazkis and S. Campbell (Eds.), Number theory in mathematics education: Perspectives and prospects (pp.115-140). Mahwah, NJ: Erlbaum.
  • Lesh, R., Post, T. R., and Behr, M. (1987). Dienes revisited: Multiple embodiments in computer environments. In I. Wirsup and R. Streit (Eds.), Development in school mathematics education around the world (pp. 647-680). Reston, VA: National Council of Teachers of Mathematics.
  • Mitchell, R., Charalambous, C. Y., and Hill, H. C. (2014). Examining the task and knowledge demands needed to teach with representations. Journal of Mathematics Teacher Education, 17(1), 37-60. https://doi.org/10.1007/s10857013-9253-4
  • Moon, K., Brenner, M. E., Jacob, B., and Okamoto, Y. (2013). Prospective secondary mathematics teachers’ understanding and cognitive difficulties in making connections among representations. Mathematical Thinking and Learning, 15(3), 201-227. https://doi.org/10.1080/10986065.2013.794322
  • Nathan, M. J., and Knuth, E. J. (2003). A study of whole classroom mathematical discourse and teacher change. Cognition and instruction, 21(2), 175-207. https://doi.org/10.1207/S1532690XCI2102_03
  • National Council of Teachers of Mathematics. (2014). Principles to actions: ensuring mathematical success for all. Reston, VA.
  • Patton, M. Q. (2014). Nitel araştırmada çeşitlilik, kuramsal yönelimler. M. Bütün ve S. B. Beşir (Çev. Ed.). Nitel araştırma ve değerlendirme yöntemleri içinde (ss. 75-142). Ankara: Pegem Akademi Yayıncılık.
  • Powell, A.B., Francisco, J.M., and Maher, C.A. (2003) An analytical model for studying the development of learners mathematical ideas and reasoning using videotape data. The Journal of Mathematical Behavior, 4(22), 405-435. https://doi.org/10.1016/j.jmathb.2003.09.002
  • Schwarts, G., and Karsenty, R. (2020). “Can this happen only in Japan?”: mathematics teachers reflect on a videotaped lesson in a cross-cultural context. Journal of Mathematics Teacher Education, 23(6), 527-554. https://doi.org/10.1007/s10857019-09438-z
  • Seidel, T., Stürmer, K., Blomberg, G., Kobarg, M., and Schwindt, K. (2011). Teacher learning from analysis of videotaped classroom situations: Does it make a difference whether teachers observe their own teaching or that of others? Teaching and Teacher Education, 27(2), 259–267. doi:10.1016/j.tate.2010.08.009.
  • Sherin, M. G., and van Es, E. A. (2009). Effects of video club participation on teachers’ professional vision. Journal of Teacher Education, 60(1), 20–37. https://doi.org/10.1177/0022487108328155
  • Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational researcher, 15(2), 4-14. https://doi.org/10.3102/0013189X015002004
  • Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26, 114–145. https://doi.org/10.5951/jresematheduc.26.2.0114
  • Simon, M. (2000). Research on mathematics teacher development: The teacher development experiment. In A. Kelly , and R. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 335-359). Hillsdale, NJ: Lawrence Erlbaum Associates Publishers.
  • Simon, M. A. (2006). Key developmental understandings in mathematics: A direction for investigating and establishing learning goals. Mathematical thinking and learning, 8(4), 359-371. https://doi.org/10.1207/s15327833mtl0804_1
  • Simon, M. (2014). Hypothetical learning trajectories in mathematics education. Encyclopedia of mathematics education, 272-275. https://doi.org/10.1007/978-94-007-4978-8_72
  • Stein, M. K., and Bovalino, J. W. (2001). Manipulatives: One piece of the puzzle. Mathematics Teaching in the Middle School, 6(6), 356-359. https://doi.org/10.5951/MTMS.6.6.0356
  • Şimsek, N., and Boz, N. (2016). Analysis of Pedagogical Content Knowledge Studies in the Context of Mathematics Education in Turkey: A Meta-Synthesis Study. Educational Sciences: Theory and Practice, 16(3), 799-826.
  • Tanışlı, D. (2013). İlköğretim matematik öğretmeni adaylarının pedagojik alan bilgisi bağlamında sorgulama becerileri ve öğrenci bilgileri. Eğitim ve Bilim, 38(169), 80-95.
  • Tataroglu Tasdan, B., Erduran, A., and Çelik, A. (2015). A daunting task for pre-service mathematics teachers: developing students' mathematical thinking. Educational Research and Reviews, 10(16), 2276-2289.
  • Türnüklü, E. B. (2005). The relationship between pedagogical and mathematical content knowledge of pre-service mathematics teachers. Eurasian Journal of Educational Research, 21, 234-247.
  • Yayla, G., ve Özsevgeç, T. (2015). Ortaokul öğrencilerinin grafik becerilerinin incelenmesi: Çizgi grafikleri oluşturma ve yorumlama. Kastamonu Eğitim Dergisi, 23(3), 1381-1400.
  • Yıldırım, Z., ve Albayrak, M. (2016). Ortaokul Öğrencilerinin Farklı Temsil Biçimlerine Göre Doğrusal İlişki Konusunu Anlama Düzeylerinin İncelenmesi. Adnan Menderes Üniversitesi Eğitim Fakültesi Eğitim Bilimleri Dergisi, 7(2), 11-26.
Toplam 48 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Bölüm Araştırma Makalesi
Yazarlar

Deniz Eroğlu 0000-0001-7863-5055

Dilek Tanışlı 0000-0002-2931-5079

Proje Numarası 1406E301
Yayımlanma Tarihi 26 Mart 2021
Yayımlandığı Sayı Yıl 2021Cilt: 10 Sayı: 1

Kaynak Göster

APA Eroğlu, D., & Tanışlı, D. (2021). Tahmini Öğrenme Yollarının Uygulanması Sürecinde Matematik Öğretmenlerinin Çoklu Temsil Kullanımlarının Gelişimi. Cumhuriyet Uluslararası Eğitim Dergisi, 10(1), 299-329. https://doi.org/10.30703/cije.718210

Cited By

ÇOKLU GÖSTERİMLERLE DESTEKLENMİŞ ÖĞRETİMİN ÜNİVERSİTE ÖĞRENCİLERİNİN BAZI DUYUŞSAL DEĞİŞKENLERİ ÜZERİNE ETKİSİ
Dokuz Eylül Üniversitesi Buca Eğitim Fakültesi Dergisi
https://doi.org/10.53444/deubefd.1436962
 Kapak Resmi İndir

e-ISSN: 2147-1606

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