Research Article
BibTex RIS Cite

Middle School Pre-Service Mathematics Teachers’ Sense Making of Numbers and Operations Through Representations

Year 2023, Volume: 10 Issue: 2, 193 - 207, 31.07.2023

Mesture Kayhan Altay Şerife Sevinç

Abstract

In this study, it is aimed to examine the meanings that middle school pre-service mathematics teachers attribute to numbers and operations while developing their own number systems through a model eliciting activity. For this purpose, pre-service teachers were asked to work on a model eliciting activity in small groups within the scope of a teacher education course. In this activity, preservice teachers are expected to develop a representation system for natural numbers, integers, addition and subtraction operations. The data of the research consists of representations and explanations in the number systems developed by eight groups of pre-service teachers (34 pre-service teachers in total). The data were analyzed by content analysis. As a result of the research, it was seen that pre-service teachers attribute different meanings to numbers and operations in the notations they use in the number systems they have developed. Pre-service teachers exhibited their conceptual understanding by constructing meanings such as cardinality and part-whole relation for numbers and operations in these representations. However, they could not develop their representations for integers and addition-subtraction operations to support the conceptual meaning. These results reveal that pre-service teachers especially have conceptual deficiencies towards negative integers and tend to do algorithm-based addition and subtraction.

Keywords

mathematical symbols meanings of numbers meanings of operations cardinality part-whole relations pre-service teacher education

References

  • Akyüz, D. (2016). Bir öğretmen adayının çözüm stratejileri: Sayıları sekizlik tabanda yeniden keşfetme. İnönü Üniversitesi Eğitim Fakültesi Dergisi, 17(2), 199-216.
  • Albayrak, M., İpek, A. S., & Işık, C. (2006). Onluk sayma sisteminin öğretimi. Atatürk Üniversitesi Kazım Karabekir Eğitim Fakültesi Dergisi, 13, 199-206.
  • Ay, B. (2019). An investigation of seventh grade students’ understanding of negative integers via mathematics history-based model-eliciting activities. Master’s thesis, Middle East Technical University.
  • Aubrey, C. (1993). An investigation of the mathematical knowledge and competencies which young children bring into school. British Educational Research Journal, 19(1), 27-41.
  • Baki, A., & Kartal, T. (2004). Kavramsal ve işlemsel bilgi bağlamında lise öğrencilerinin cebir bilgilerinin karakterizasyonu. Türk Eğitim Bilimleri Dergisi, 2(1), 27-50.
  • Baroody, A. J., & Ginsburg, H. P. (1983). The effects of instruction on children’s understanding of the “equals” sign. The Elementary School Journal, 84(2), 199-212.
  • Baroody, A. J., Lai, M. L., & Mix, K. S. (2006). The development of young children’s early number and operation sense and its implications for early childhood education. In B. Spodek & O.N. Saracho (Eds.), Handbook of research on the education of young children (pp. 187-221). Lawrence Erlbaum Associates Publishers.
  • Berber, M., & Sezgin-Memnun, D. (2018). Ortaokul öğrencilerinin tam sayılar hakkında sahip oldukları metaforlar. 1. Uluslararası Eğitim ve Sosyal Bilimlerde Yeni Ufuklar Kongresi Bildiriler Kitabı, 9-11 Nisan 2018, İstanbul-TÜRKİYE
  • Borromeo Ferri, R. & Blum, W. (2010). Mathematical modelling in teacher education–experiences from a modelling seminar. In Proceedings of the sixth Congress of the European Society for Research in Mathematics Education (pp. 2046-2055).
  • Burton, D. M. (2021). Erken sayı sistemleri ve sembolleri (N. Akal, & Z. E. Özel, çeviri). S. Durmuş (Çeviri Editörü), Matematik Tarihi Giriş (3.baskı) içinde (ss. 1-33). Nobel Yaşam.
  • Chirume, S. (2012). How does the use of mathematical symbols influence understanding of mathematical concepts by secondary school students? International Journal of Social Sciences & Education, 3(1).
  • Chin, K. E., & Pierce, R. (2019). University students’ conceptions of mathematical symbols and expressions. EURASIA Journal of Mathematics, Science and Technology Education, 15(9), em1748.
  • Creswell, J. W. (2021). Nitel Araştırma Yöntemleri, N. A. Mesut Bütün-Selçuk Beşir Demir. çev. Osman Birgin vd. Ankara: Siyasal Kitabevi.
  • De Cruz, H., & De Smedt, J. (2013). Mathematical symbols as epistemic actions. Synthese, 190, 3-19.
  • Douglas, H., Headley, M. G., Hadden, S., & LeFevre, J. A. (2020). Knowledge of mathematical symbols goes beyond numbers. Journal of Numerical Cognition, 6(3), 322-354.
  • Even, R. (1993). Subject-matter knowledge and pedagogical content knowledge: Prospective secondary teachers and the function concept. Journal for Research in Mathematics Education, 24(2), 94-116.
  • Gelman, R. & Gallsitel, C. R. (1978). The Child’s Understanding of Number. Harvard Universtiy Press: Cambridge, Massachusetts, London
  • Gelman, R., & Meck, E. (1983). Preschoolers’ counting: Principles before skill. Cognition, 13 (3), 343-359.
  • Goldin, G. A. (1998). Representational systems, learning, and problem solving in mathematics. The Journal of Mathematical Behavior, 17(2), 137-165.
  • Greenes, C., Schulman, L., & Spungin, R. (1993). Developing sense about numbers. The Arithmetic Teacher, 40(5), 279-284.
  • Hassidov, D., & Ilany, B. S. (2019, February). Between natural language and mathematical symbols (<,>,=): the comprehension of pre-service and preschool teachers’ perspective of “Numbers” and “Quantity”. In Eleventh Congress of the European Society for Research in Mathematics Education (No. 25). Freudenthal Group; Freudenthal Institute; ERME.
  • Hiebert, J. (1988). A theory of developing competence with written mathematical symbols. Educational Studies in Mathematics, 19(3), 333-355.
  • Horzum, T., & Kılıç, Z. N. (2016). Middle school students’ understanding of some geometry symbols. Journal of Research in Education, Science and Technology, 1(2), 113-132.
  • Kaminski, E. (1997). Teacher education students’ number sense: Initial explorations. Mathematics Education Research Journal, 9(2), 225-235.
  • Karaaslan, B. (2015). Doğal sayıların tarihsel gelişimi ve ilköğretim matematik programındaki doğal sayıların öğretimi ile karşılaştırılması (Yüksek Lisans Tezi, Eğitim Bilimleri Enstitüsü).
  • Koellner-Clark, K., & Lesh, R. (2003). A modeling approach to describe teacher knowledge. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 159-174). Lawrence Erlbaum Associates.
  • Lesh, R., & Doerr, H. M. (Eds.). (2003). Beyond constructivism: Models and modeling perspectives on mathematics problem solving learning, and teaching. Lawrence Erlbaum Associates.
  • Lim, S. Y., & Chapman, E. (2010). Using history to enhance student learning and attitudes in Singapore mathematics classrooms. Education Research and Perspectives, (2), 110-132.
  • Merriam, S. B. (1998). Qualitative research and case study applications in education. San Francisco: Jossey-Bass Publishers
  • Miles, M. B., Huberman, A. M., & Saldana, J. (2014), Qualitative data analysis: A Methods Sourcebook (4th ed.). Sage.
  • Ministry of National Education [MNE]. (2018). Matematik dersi öğretim programı. Ankara: MEB.
  • Mutodi, P., & Mosimege, M. (2021). Learning mathematical symbolization: conceptual challenges and instructional strategies in secondary schools. Bolema: Boletim de Educação Matemática, 35, 1180-1199.
  • National Council of Teachers of Mathematics (NCTM) (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
  • Nesher, P., Greeno, J. G., & Riley, M. S. (1982). The development of semantic categories for addition and subtraction. Educational Studies in Mathematics, 13(4), 373-394.
  • Olkun, S., Fidan, E., & Özer, A. B. (2013). 5-7 yaş aralığındaki çocuklarda sayı kavramının gelişimi ve saymanın problem çözmede kullanımı. Eğitim ve Bilim, 38(169), 236-248.
  • Özdemir, A.Ş., & Göktepe Yıldız, S. (2015). Sınıfta matematik tarihinin kullanımına bir örnek: Babil sayma sistemi. Amasya Üniversitesi Eğitim Fakültesi Dergisi, 4(1), 26-49.
  • Pape, S. J., & Tchoshanov, M. A. (2001). The role of representation (s) in developing mathematical understanding. Theory into practice, 40(2), 118-127.
  • Postlewait, K. B., Adams, M. R., & Shih, J. C. (2003). Promoting meaningful mastery of addition and subtraction. Teaching Children Mathematics, 9(6), 354-357.
  • Powell, S. R. (2015). The influence of symbols and equations on understanding mathematical equivalence. Intervention in School and Clinic, 50(5), 266-272.
  • Savizi, B. (2007). Applicable Problems in the History of Mathematics: Practical Examples for the Classroom. Teaching Mathematics and Its Applications: An International Journal of the IMA, 26(1), 45-50.
  • Schleppegrell, M. J. (2007). The linguistic challenges of mathematics teaching and learning: A research review. Reading & Writing Quarterly, 23(2), 139-159.
  • Schorr, R., & Lesh, R. (2003). A modeling approach for providing teacher development. Beyond constructivism: A models and modeling perspective. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 141-158). Lawrence Erlbaum Associates.
  • Seggie, F. N., & Bayyurt, Y. (Eds.). (2017). Nitel araştırma: Yöntem, teknik, analiz ve yaklaşımları. Anı Yayıncılık.
  • Sevinc, S., & Ay, B. (2021). Integration of mathematics history into model-eliciting activities for making sense of negative integers. In D. Olanoff, K. Johnson, & S. Spitzer (Eds.), Proceedings of the Forty-Third Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA 43) (pp. 235-244). Philadelphia, PA, October 14-17.
  • Sevinc, S., & Brady, C. (2019). Kindergarteners’ and first graders’ development of numbers representing length and area: Stories of measurement. In K. Robinson, H. Osana, & D. Kotsopoulos (Eds), (pp. 115–137). Springer. https://doi.org/10.1007/978-3-030-12895-1_8
  • Shulman, L. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1–22.
  • Sullivan, P., Clarke, D., & Clarke, B. (Eds.). (2012). Teaching with tasks for effective mathematics learning. Springer. https://doi.org/10.1007/978-1-4614-4681-1
  • Steiner, C. J. (2009). A Study of pre-service elementary teachers’ conceptual understanding of integers (Unpublished doctoral dissertation). Kent State University, Kent.
  • Steinke, D. (2008). Using part-whole thinking in math. Focus on Basics Connecting Research & Practice. 9(A), 1-7.
  • Thanheiser, E., & Rhoads, K. (2009). Exploring preservice teachers’ conceptions of numbers via the Mayan number system. Proceedings of the North American Chapter of the International Group for the Psychology of Mathematics Education, 1220-1227.
  • Treacy, K., & Willis, S. G. (2003). A model of early number development. In Annual conference of the Mathematics Education Research Group of Australasia 2003 (pp. 674-681). Deakin University.
  • Tsamir, P., Tirosh, D., Levenson, E., Tabach, M., & Barkai, R. (2015). Analyzing number composition and decomposition activities in kindergarten from a numeracy perspective. ZDM, 47, 639-651.
  • Yağcı, Z. N. (2018). Ortaokul öğrencilerinin bazı geometri sembollerine geometri problemleri içerisinde yükledikleri anlamlar. (Yayınlanmamış Yüksek Lisans Tezi). Necmettin Erbakan Üniversitesi, Konya.
  • Yang, D. C., Reys, R. E., & Reys, B. J. (2009). Number sense strategies used by pre-service teachers in Taiwan. International Journal of Science and Mathematics Education, 7, 383-403.
  • Young-Loveridge, J. (2001). Helping children move beyond counting to part-whole strategies. Teachers and Curriculum, 5, 72-78.
  • Wessman-Enzinger, N. M., & Tobias, J. M. (2020). The dimensions of prospective elementary and middle school teachers’ problem posing for integer addition and subtraction. Journal of Mathematics Teacher Education, 25, 1-33. https://doi.org/10.1007/s10857-020-09477-x
  • Zawojewski, J., Lesh, R., & English, L. (2003). A models and modeling perspective on the role of small group learning activities. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: A models and modelling perspective on mathematics problem solving; learning and teaching (pp. 337–358). Lawrence Erlbaum Associates.

İlköğretim Matematik Öğretmen Adaylarının Sayıları ve İşlemleri Gösterimler Yoluyla Anlamlandırması

Year 2023, Volume: 10 Issue: 2, 193 - 207, 31.07.2023

Mesture Kayhan Altay Şerife Sevinç

Abstract

Bu çalışmada ilköğretim matematik öğretmen adaylarının bir modelleme etkinliği aracılığıyla kendi sayı sistemlerini geliştirirken sayılara ve işlemlere yükledikleri anlamları incelemek amaçlanmıştır. Bu amaçla bir ders kapsamında öğretmen adaylarından grup çalışmasıyla bir modelleme etkinliği üzerinde çalışmaları istenmiştir. Bu modelleme etkinliğinde öğretmen adaylarından doğal sayılar, tam sayılar, toplama ve çıkarma işlemleri için bir temsil sistemi geliştirmeleri beklenmektedir. Araştırmanın verilerini, sekiz grup matematik öğretmen adayı (toplam 34 öğretmen adayı) tarafından geliştirilen sayı sistemlerindeki gösterimler ve açıklamalar oluşturmaktadır. Veriler içerik analizi ile çözümlenmiştir. Araştırmanın sonucunda öğretmen adaylarının geliştirdikleri sayı sistemlerinde kullandıkları gösterimlerde sayılara ve işlemlere farklı anlamlar yükledikleri görülmüştür. Öğretmen adayları bu gösterimlerde sayılar ve işlemler için kardinalite ve parça-bütün ilişkisi gibi anlamlar oluşturarak kavramsal anlamalarını ortaya koymuşlardır. Ancak tam sayılar ve toplama-çıkarma işlemleri için gösterimlerini kavramsal anlamı destekleyecek şekilde geliştirememişlerdir. Bu sonuçlar öğretmen adaylarının özellikle negatif tam sayılara yönelik kavramsal eksikliklerini ve algoritmaya dayalı toplama ve çıkarma işlemi yapma eğiliminde olduklarını ortaya koymaktadır.

Keywords

matematiksel semboller sayıların anlamları işlemlerin anlamları kardinalite parça-bütün ilişkisi öğretmen adayları

References

  • Akyüz, D. (2016). Bir öğretmen adayının çözüm stratejileri: Sayıları sekizlik tabanda yeniden keşfetme. İnönü Üniversitesi Eğitim Fakültesi Dergisi, 17(2), 199-216.
  • Albayrak, M., İpek, A. S., & Işık, C. (2006). Onluk sayma sisteminin öğretimi. Atatürk Üniversitesi Kazım Karabekir Eğitim Fakültesi Dergisi, 13, 199-206.
  • Ay, B. (2019). An investigation of seventh grade students’ understanding of negative integers via mathematics history-based model-eliciting activities. Master’s thesis, Middle East Technical University.
  • Aubrey, C. (1993). An investigation of the mathematical knowledge and competencies which young children bring into school. British Educational Research Journal, 19(1), 27-41.
  • Baki, A., & Kartal, T. (2004). Kavramsal ve işlemsel bilgi bağlamında lise öğrencilerinin cebir bilgilerinin karakterizasyonu. Türk Eğitim Bilimleri Dergisi, 2(1), 27-50.
  • Baroody, A. J., & Ginsburg, H. P. (1983). The effects of instruction on children’s understanding of the “equals” sign. The Elementary School Journal, 84(2), 199-212.
  • Baroody, A. J., Lai, M. L., & Mix, K. S. (2006). The development of young children’s early number and operation sense and its implications for early childhood education. In B. Spodek & O.N. Saracho (Eds.), Handbook of research on the education of young children (pp. 187-221). Lawrence Erlbaum Associates Publishers.
  • Berber, M., & Sezgin-Memnun, D. (2018). Ortaokul öğrencilerinin tam sayılar hakkında sahip oldukları metaforlar. 1. Uluslararası Eğitim ve Sosyal Bilimlerde Yeni Ufuklar Kongresi Bildiriler Kitabı, 9-11 Nisan 2018, İstanbul-TÜRKİYE
  • Borromeo Ferri, R. & Blum, W. (2010). Mathematical modelling in teacher education–experiences from a modelling seminar. In Proceedings of the sixth Congress of the European Society for Research in Mathematics Education (pp. 2046-2055).
  • Burton, D. M. (2021). Erken sayı sistemleri ve sembolleri (N. Akal, & Z. E. Özel, çeviri). S. Durmuş (Çeviri Editörü), Matematik Tarihi Giriş (3.baskı) içinde (ss. 1-33). Nobel Yaşam.
  • Chirume, S. (2012). How does the use of mathematical symbols influence understanding of mathematical concepts by secondary school students? International Journal of Social Sciences & Education, 3(1).
  • Chin, K. E., & Pierce, R. (2019). University students’ conceptions of mathematical symbols and expressions. EURASIA Journal of Mathematics, Science and Technology Education, 15(9), em1748.
  • Creswell, J. W. (2021). Nitel Araştırma Yöntemleri, N. A. Mesut Bütün-Selçuk Beşir Demir. çev. Osman Birgin vd. Ankara: Siyasal Kitabevi.
  • De Cruz, H., & De Smedt, J. (2013). Mathematical symbols as epistemic actions. Synthese, 190, 3-19.
  • Douglas, H., Headley, M. G., Hadden, S., & LeFevre, J. A. (2020). Knowledge of mathematical symbols goes beyond numbers. Journal of Numerical Cognition, 6(3), 322-354.
  • Even, R. (1993). Subject-matter knowledge and pedagogical content knowledge: Prospective secondary teachers and the function concept. Journal for Research in Mathematics Education, 24(2), 94-116.
  • Gelman, R. & Gallsitel, C. R. (1978). The Child’s Understanding of Number. Harvard Universtiy Press: Cambridge, Massachusetts, London
  • Gelman, R., & Meck, E. (1983). Preschoolers’ counting: Principles before skill. Cognition, 13 (3), 343-359.
  • Goldin, G. A. (1998). Representational systems, learning, and problem solving in mathematics. The Journal of Mathematical Behavior, 17(2), 137-165.
  • Greenes, C., Schulman, L., & Spungin, R. (1993). Developing sense about numbers. The Arithmetic Teacher, 40(5), 279-284.
  • Hassidov, D., & Ilany, B. S. (2019, February). Between natural language and mathematical symbols (<,>,=): the comprehension of pre-service and preschool teachers’ perspective of “Numbers” and “Quantity”. In Eleventh Congress of the European Society for Research in Mathematics Education (No. 25). Freudenthal Group; Freudenthal Institute; ERME.
  • Hiebert, J. (1988). A theory of developing competence with written mathematical symbols. Educational Studies in Mathematics, 19(3), 333-355.
  • Horzum, T., & Kılıç, Z. N. (2016). Middle school students’ understanding of some geometry symbols. Journal of Research in Education, Science and Technology, 1(2), 113-132.
  • Kaminski, E. (1997). Teacher education students’ number sense: Initial explorations. Mathematics Education Research Journal, 9(2), 225-235.
  • Karaaslan, B. (2015). Doğal sayıların tarihsel gelişimi ve ilköğretim matematik programındaki doğal sayıların öğretimi ile karşılaştırılması (Yüksek Lisans Tezi, Eğitim Bilimleri Enstitüsü).
  • Koellner-Clark, K., & Lesh, R. (2003). A modeling approach to describe teacher knowledge. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 159-174). Lawrence Erlbaum Associates.
  • Lesh, R., & Doerr, H. M. (Eds.). (2003). Beyond constructivism: Models and modeling perspectives on mathematics problem solving learning, and teaching. Lawrence Erlbaum Associates.
  • Lim, S. Y., & Chapman, E. (2010). Using history to enhance student learning and attitudes in Singapore mathematics classrooms. Education Research and Perspectives, (2), 110-132.
  • Merriam, S. B. (1998). Qualitative research and case study applications in education. San Francisco: Jossey-Bass Publishers
  • Miles, M. B., Huberman, A. M., & Saldana, J. (2014), Qualitative data analysis: A Methods Sourcebook (4th ed.). Sage.
  • Ministry of National Education [MNE]. (2018). Matematik dersi öğretim programı. Ankara: MEB.
  • Mutodi, P., & Mosimege, M. (2021). Learning mathematical symbolization: conceptual challenges and instructional strategies in secondary schools. Bolema: Boletim de Educação Matemática, 35, 1180-1199.
  • National Council of Teachers of Mathematics (NCTM) (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
  • Nesher, P., Greeno, J. G., & Riley, M. S. (1982). The development of semantic categories for addition and subtraction. Educational Studies in Mathematics, 13(4), 373-394.
  • Olkun, S., Fidan, E., & Özer, A. B. (2013). 5-7 yaş aralığındaki çocuklarda sayı kavramının gelişimi ve saymanın problem çözmede kullanımı. Eğitim ve Bilim, 38(169), 236-248.
  • Özdemir, A.Ş., & Göktepe Yıldız, S. (2015). Sınıfta matematik tarihinin kullanımına bir örnek: Babil sayma sistemi. Amasya Üniversitesi Eğitim Fakültesi Dergisi, 4(1), 26-49.
  • Pape, S. J., & Tchoshanov, M. A. (2001). The role of representation (s) in developing mathematical understanding. Theory into practice, 40(2), 118-127.
  • Postlewait, K. B., Adams, M. R., & Shih, J. C. (2003). Promoting meaningful mastery of addition and subtraction. Teaching Children Mathematics, 9(6), 354-357.
  • Powell, S. R. (2015). The influence of symbols and equations on understanding mathematical equivalence. Intervention in School and Clinic, 50(5), 266-272.
  • Savizi, B. (2007). Applicable Problems in the History of Mathematics: Practical Examples for the Classroom. Teaching Mathematics and Its Applications: An International Journal of the IMA, 26(1), 45-50.
  • Schleppegrell, M. J. (2007). The linguistic challenges of mathematics teaching and learning: A research review. Reading & Writing Quarterly, 23(2), 139-159.
  • Schorr, R., & Lesh, R. (2003). A modeling approach for providing teacher development. Beyond constructivism: A models and modeling perspective. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 141-158). Lawrence Erlbaum Associates.
  • Seggie, F. N., & Bayyurt, Y. (Eds.). (2017). Nitel araştırma: Yöntem, teknik, analiz ve yaklaşımları. Anı Yayıncılık.
  • Sevinc, S., & Ay, B. (2021). Integration of mathematics history into model-eliciting activities for making sense of negative integers. In D. Olanoff, K. Johnson, & S. Spitzer (Eds.), Proceedings of the Forty-Third Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA 43) (pp. 235-244). Philadelphia, PA, October 14-17.
  • Sevinc, S., & Brady, C. (2019). Kindergarteners’ and first graders’ development of numbers representing length and area: Stories of measurement. In K. Robinson, H. Osana, & D. Kotsopoulos (Eds), (pp. 115–137). Springer. https://doi.org/10.1007/978-3-030-12895-1_8
  • Shulman, L. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1–22.
  • Sullivan, P., Clarke, D., & Clarke, B. (Eds.). (2012). Teaching with tasks for effective mathematics learning. Springer. https://doi.org/10.1007/978-1-4614-4681-1
  • Steiner, C. J. (2009). A Study of pre-service elementary teachers’ conceptual understanding of integers (Unpublished doctoral dissertation). Kent State University, Kent.
  • Steinke, D. (2008). Using part-whole thinking in math. Focus on Basics Connecting Research & Practice. 9(A), 1-7.
  • Thanheiser, E., & Rhoads, K. (2009). Exploring preservice teachers’ conceptions of numbers via the Mayan number system. Proceedings of the North American Chapter of the International Group for the Psychology of Mathematics Education, 1220-1227.
  • Treacy, K., & Willis, S. G. (2003). A model of early number development. In Annual conference of the Mathematics Education Research Group of Australasia 2003 (pp. 674-681). Deakin University.
  • Tsamir, P., Tirosh, D., Levenson, E., Tabach, M., & Barkai, R. (2015). Analyzing number composition and decomposition activities in kindergarten from a numeracy perspective. ZDM, 47, 639-651.
  • Yağcı, Z. N. (2018). Ortaokul öğrencilerinin bazı geometri sembollerine geometri problemleri içerisinde yükledikleri anlamlar. (Yayınlanmamış Yüksek Lisans Tezi). Necmettin Erbakan Üniversitesi, Konya.
  • Yang, D. C., Reys, R. E., & Reys, B. J. (2009). Number sense strategies used by pre-service teachers in Taiwan. International Journal of Science and Mathematics Education, 7, 383-403.
  • Young-Loveridge, J. (2001). Helping children move beyond counting to part-whole strategies. Teachers and Curriculum, 5, 72-78.
  • Wessman-Enzinger, N. M., & Tobias, J. M. (2020). The dimensions of prospective elementary and middle school teachers’ problem posing for integer addition and subtraction. Journal of Mathematics Teacher Education, 25, 1-33. https://doi.org/10.1007/s10857-020-09477-x
  • Zawojewski, J., Lesh, R., & English, L. (2003). A models and modeling perspective on the role of small group learning activities. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: A models and modelling perspective on mathematics problem solving; learning and teaching (pp. 337–358). Lawrence Erlbaum Associates.
There are 57 citations in total.

Details

Primary Language Turkish
Subjects Other Fields of Education
Journal Section Research Articles
Authors

Mesture Kayhan Altay 0000-0002-1917-2430

Şerife Sevinç 0000-0002-4561-9742

Publication Date July 31, 2023
Published in Issue Year 2023 Volume: 10 Issue: 2

Cite

APA Kayhan Altay, M., & Sevinç, Ş. (2023). İlköğretim Matematik Öğretmen Adaylarının Sayıları ve İşlemleri Gösterimler Yoluyla Anlamlandırması. Baskent University Journal of Education, 10(2), 193-207.
 Download Cover Image

Başkent Univesity Journal of Education has been published in Dergipark (https://dergipark.org.tr/en/pub/bujoe) since volume 10 and issue 2, 2023. 

For previous issues, the institutional web site (https://buje.baskent.edu.tr) was used.