Mathematical Justification Studies in Mathematics Education: An Evaluation of Studies between 2007 and 2016

Yasemin YILMAZ, Ülkü AYVAZ, Nazan MERSİN, Soner DURMUŞ, Hakan YAMAN

Abstract


In this study, it was aimed to evaluate the mathematical justification studies in mathematics education between 2007 and 2016. In the study, 31 theses and articles about mathematical justification in mathematics education were analyzed by means of determined databases. In the literature review, the studies were classified according to the method, the study group, the mathematics subject, and the time frame of ten years. As a result of study, mathematical justification studies in mathematics education were carried out mostly in 2009, 2010 and 2016. As a study group, examined studies are composed mostly of students. As a method, qualitative method was used mostly. The tasks related to justification at three different levels of education were included. According to primary, middle and high school levels, the most common areas of learning for which mathematical justification tasks take place are numbers and operations, algebra and numbers and algebra, respectively.


Keywords


Justification; Mathematical Justification; Mathematics Education

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Acevedo Nistal, A., Van Dooren, W., & Verschaffel, L. (2013). Students’ reported justifications for their representational choices in linear function problems: an interview study. Educational Studies, 39(1), 104-117.

Bieda, K. N. (2010). Enacting proof-related tasks in middle school mathematics: Challenges and opportunities. Journal for Research in Mathematics Education, 41(4), 351-382.

Bostic, J. D. (2016). Fostering Justification: A Case Study of Preservice Teachers, Proof-Related Tasks, and Manipulatives. Journal of Mathematics Education at Teachers College, 7(1), 35-43.

Brodie, K. (2010). Pressing dilemmas: meaning‐making and justification in mathematics teaching. Journal of Curriculum Studies, 42(1), 27-50.

Ceylan, T. (2012). GeoGebra yazılım ortamında ilköğretim matematik öğretmen adaylarının geometrik ispat biçimlerinin incelenmesi. (Yayımlanmamış Yüksek Lisans Tezi). Ankara Üniversitesi Eğitim Bilimleri Enstitüsü, Ankara.

Çiltaş, A., Güler, G., & Sözbilir, M. (2012). Mathematics Education Research in Turkey: A Content Analysis Study. Educational Sciences: Theory and Practice, 12(1), 574-580.

Dixon, J. K., Egendoerfer, L. A., & Clements, T. (2009). Do they really need to raise their hands? Challenging a traditional social norm in a second grade mathematics classroom. Teaching and Teacher Education, 25(8), 1067-1076.

Dolev, S. ve Even, R. (2013). Justifications and Explanations In Israeli 7th Grade Math Textbooks. International Journal of Science and Mathematics Education, May 2015, 13(Suppl 2), 309-327.

Ellis, A. B. (2007). Connections between generalizing and justifying: Students' reasoning with linear relationships. Journal for Research in Mathematics Education, 38(3), 194-229.

Flegas, K., & Charalampos, L. (2013). Exploring logical reasoning and mathematical proof in grade 6 elementary school students. Canadian Journal of Science, Mathematics and Technology Education, 13(1), 70-89.

Guven, B., Cekmez, E., & Karatas, I. (2010). Using empirical evidence in the process of proving: the case of Dynamic Geometry. Teaching Mathematics and its Applications: An International Journal of the IMA, 29(4), 193-207.

Hauk, S., & Isom, M. A. (2009). Fostering college students’ autonomy in written mathematical justification. Investigations in Mathematics Learning, 2(1), 49-78.

Henningsen, M. ve Stein, M. K. (1997). Mathematical Taks and Student Cognition: Classroom- Based Factors That Support and Inhibit High-Level Mathematical Thinking and Reasoning. Journal for Research Mathematics Education, 28(5), 524-549.

Hershkowitz, R. (2014). Shape and Space – Geometry Teaching and Learning. Stephen Lerman (Ed.), Encyclopedia of Mathematics Education (pp. 542-547). Springer.

Karsenty, R., Arcavi, A., & Hadas, N. (2007). Exploring informal mathematical products of low achievers at the secondary school level. The Journal of Mathematical Behavior, 26(2), 156-177.

Kidron, I. & Dreyfus, T. (2010). Justification enlightenment and combining constructions of knowledge. Educational Studies in Mathematics 74(1), 75-93.

Kosyvas, G. (2016). Levels of arithmetic reasoning in solving an open-ended problem. International Journal of Mathematical Education in Science and Technology, 47(3), 356-372.

Lau, P. N. K., Singh, P., & Hwa, T. Y. (2009). Constructing mathematics in an interactive classroom context. Educational Studies in Mathematics, 72(3), 307-324.

Leach, G., Hunter, R., & Hunter, J. (2014). Teachers Repositioning Culturally Diverse Students as Doers and Thinkers of Mathematics. Mathematics Education Research Group of Australasia, 381-388.

Liu, Y., & Manouchehri, A. (2013). Middle school children’s mathematical reasoning and proving schemes. Investigations in Mathematics Learning, 6(1), 18-40.

Lo, J. J., Grant, T. J., & Flowers, J. (2008). Challenges in deepening prospective teachers’ understanding of multiplication through justification. Journal of Mathematics Teacher Education, 11(1), 5-22.

Löfström, E., & Pursiainen, T. (2015). Knowledge and knowing in mathematics and pedagogy: a case study of mathematics student teachers’ epistemological beliefs. Teachers and Teaching, 21(5), 527-542.

Maher, C. A., Palius, M. F., Maher, J. A., Hmelo-Silver, C. E., & Sigley, R. (2014). Teachers can learn to attend to students' reasoning using videos as a tool. Issues in Teacher Education, 23(1), 31-47.

Matteson, S., Capraro, M. M., Capraro, R. M., & Lincoln, Y. S. (2012). Extricating Justification Scheme Theory in Middle School Mathematical Problem Solving. Investigations in Mathematics Learning, 5(1), 38-62.

Mueller, M. F. (2009). The co-construction of arguments by middle-school students. The Journal of Mathematical Behavior, 28(2-3), 138-149.

National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Reston, VA: NCTM Publications.

Özcan, B. N. (2012). İlköğretim Öğrencilerinin Geometrik Düşünme Düzeylerinin Geliştirilmesinde Bilgiyi Oluşturma Süreçlerinin İncelenmesi. (Yayımlanmamış Doktora Tezi). Dokuz Eylül Üniversitesi Eğitim Bilimleri Enstitüsü, İzmir.

Polat, M. (2015). İlköğretim 7. Sınıf Matematik Ders ve Çalışma Kitaplarındaki Açıklama ve Gerekçelendirme Gerektiren Görevlerin Öğrenme Alanlarına Göre İncelenmesi. (Yayımlanmamış Yüksek Lisans Tezi). Gaziantep Üniversitesi Eğitim Bilimleri Enstitüsü, Gaziantep.

Rott, B., & Leuders, T. (2016). Inductive and Deductive Justification of Knowledge: Flexible Judgments Underneath Stable Beliefs in Teacher Education. Mathematical Thinking and Learning, 18(4), 271-286.

Sidenvall, J., Lithner, J., & Jäder, J. (2015). Students’ reasoning in mathematics textbook task-solving. International Journal of Mathematical Education in Science and Technology, 46(4), 533-552.

Simon, M. A. & Blume, G. W. (1996). Justification in the mathematics classroom: A study of prospective elementary teachers. The Journal of Mathematical Behavior, 15(1), 3-31.

Sönmez, N. (2016). Üç boyutlu sanal öğrenme ortamlarında sosyal ve sosyomatematiksel normların belirlenmesi: Mathlife Örneği. (Yayımlanmamış Yüksek Lisans Tezi). Karadeniz Teknik Üniversitesi Eğitim Bilimleri Enstitüsü, Trabzon.

Staples, M. E., Bartlo, J., & Thanheiser, E. (2012). Justification as a teaching and learning practice: Its (potential) multifacted role in middle grades mathematics classrooms. The Journal of Mathematical Behavior, 31(4), 447-462.

Stylianou, D. A. (2013). An Examination of Connections in Mathematical Processes in Students' Problem Solving: Connections between Representing and Justifying. Journal of Education and Learning, 2(2), 23-35.

Tabach, M., Barkai, R., Tsamir, P., Tirosh, D., Dreyfus, T., & Levenson, E. (2010). Verbal justifcation—Is it a proof? secondary school teachers’ perceptions. International Journal of Science and Mathematics Education, 8(6), 1071-1090.

Tabach, M., Levenson, E., Barkai, R., Tirosh, D., Tsamir, P., & Dreyfus, T. (2010). Secondary school teachers' awareness of numerical examples as proof. Research in Mathematics Education, 12(2), 117-131.

Tymoczko, T. (1986). Making room for mathematicians in the philosophy of mathematics. The Mathematical Intelligencer, 8(3), 44-50.

Tsamir, P., Tirosh, D., Dreyfus, T., Barkai, R., & Tabach, M. (2009). Should proof be minimal? Ms T's evaluation of secondary school students’ proofs. The Journal of Mathematical Behavior, 28(1), 58-67.

Ulutaş, F. & Ubuz, B. (2008). Matematik Eğitiminde Araştırmalar ve Eğilimler: 2000 ile 2006 Yılları Arası. İlköğretim Online, 7(3), 614-626.

Valero, P. (2014). Political Perspectives in Mathematics Education. Stephen Lerman (Ed.), Encyclopedia of Mathematics Education (pp. 484-487). Springer.

Widjaja, W. (2014, January). Year 3/4 children's forms of justification. In MERGA 2014: Curriculum in focus: research guided practice: Proceedings of the Mathematics Education Research Group of Australasia 2014 annual conference (pp. 694-697). Mathematics Education Research Group of Australasia.

Yalçınkaya, Y., & Özkan, H. H. (2012). 2000-2011 Yılları Arasında Eğitim Fakülteleri Dergilerinde Yayımlanan Matematik Öğretimi Alternatif Yöntemleri İle İlgili Makalelerin İçerik Analizi. Süleyman Demirel Üniversitesi Sosyal Bilimler Enstitüsü Dergisi, 2(16), 31-45.

Yaşar, Ş. & Papatğa, E. (2015). İlkokul Matematik Derslerine Yönelik Yapılan Lisansüstü Tezlerin İncelenmesi. Trakya Üniversitesi Eğitim Fakültesi Dergisi, 5(2), 113-124.

Yenilmez, K. & Sölpük, N. (2014). Matematik Dersi Öğretim Programı İle İlgili Tezlerin İncelenmesi (2004-2013). Eğitim ve Öğretim Araştırmaları Dergisi, 3(2), 33-42.

Yıldırım, A. & Şimşek, H. (2013). Sosyal Bilimlerde Nitel Araştırma Yöntemleri. Ankara: Seçkin Yayıncılık.

Zeybek, Z. (2016). Pre-Service Elementary Teachers’ Proof and Counterexample Conceptions. International Journal for Mathematics Teaching and Learning, 17(2).




DOI: https://doi.org/10.29103/mjml.v2i2.2129

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