Which form of the presentation preservice mathematics teachers are more successfull? An Integral Study

Yıl 2015, , 418 - 445, 10.12.2015

Sefa Dündar , Yasemin Yılmaz

https://doi.org/10.16949/turcomat.55314

Öz

In this study, the integral subject in which difficulties mostly seen about learning and understanding in mathematics education has been studied. The aim of this study is to determine that primary (secondary) preservice mathematics teachers’ performance in given tests about the intagral problems’ having same numerical solution but different presentation forms and to find out the causes of the failures in these tests. The mixed method, enriched with regards to quantitative and qualitative datas, has been used. When the preservice teachers’ answers given to the these tests were analyzed, it has been found out their performances differentiate in interclasses and in the same class group. Besides the preservice mathematics teachers have become successfull in tests which have been comprising of symbolic, visual and verbal problems respectively. The preservice teachers have explained their opinions about the reasons of their failures in verbal, visual and symbolic tests, and they have been ciriticised.

Anahtar Kelimeler

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Matematik Öğretmen Adayları Hangi Gösterim Biçiminde Daha Başarılıdır? İntegral Örneği

Öz

Bu çalışmada matematik eğitiminde öğrenme ve anlamada sıkıntıların çokça yaşandığı integral konusu ele alınmıştır. Çalışmanın amacı matematik öğretmen adaylarının integral ile ilgili problemlerin aynı sayısal çözümüne sahip fakat farklı gösterim biçimlerinde verilen testlerdeki performanslarını belirlemek ve farklı gösterim biçimlerinde verilen bu testlerdeki başarısızlıkların nedenlerini ortaya çıkarmaktır. Çalışmada nicel ve nitel veriler bakımından zenginleştirilmiş karma bir yöntem kullanılmıştır. Öğretmen adaylarının farklı gösterimler kullanılarak hazırlanan testlere verdiği cevaplar incelendiğinde sınıflar arası ve aynı sınıf grubu içerisinde performanslarının farklılaştığı bulunmuştur. Öğretmen adayları sırasıyla sembolik, görsel ve sözel problemlerden oluşan testlerde başarılı oldukları ortaya çıkmıştır. Ayrıca öğretmen adayları sözel, görsel ve sembolik testlerdeki başarısızlıklarının arkasında yatan sebepleri ile ilgili görüşlerini açıklayarak değerlendirmelerde bulunulmuştur.

Anahtar Kelimeler

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Kaynakça

• Altun, M. (2000). İlköğretimde problem çözme öğretimi. Milli Eğitim Dergisi, 147, 27-33.
• Alamolhodaei, H. (1996). A study in higher education calculus and students' learning styles (Doctoral dissertation). University of Glasgow, England.
• Baki, A. (2006). Kuramdan uygulamaya matematik eğitimi. Trabzon: Derya Yayınları.
• Baykul, Y. (1999). Primary mathematics education. Ankara: Ani Printing Press.
• Castro, E., Morcillo, N., & Castro, E. (2001). Representations produced by secondary education pupils in mathematical problem solving. Procedings of the Twenty First Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, 2, 547-558.
• Creswell, J. W., & Plano-Clark, V. L. (2007). Designing and conducting mixed methods research. Thousand Oaks, CA: Sage.
• Çelik, D. ve Sağlam Arslan, A. (2012). Öğretmen adaylarının çoklu gösterimleri kullanma becerilerinin analizi. İlköğretim Online, 11(1), 239-250.
• Delice, A. (2004). Trigonometri sözel problemlerinde görselleştirme ve diyagram oluşturma. VI. Ulusal Fen ve Matematik Eğitimi Kongresi’nde sunulan bildiri, Marmara Üniversitesi, İstanbul.
• Delice, A. ve Sevimli, E. (2010). Matematik öğretmeni adaylarının belirli integral konusunda kullanılan temsiller ile işlemsel ve kavramsal bilgi düzeyleri. Gaziantep Üniversitesi Sosyal Bilimler Dergisi, 9(3), 581-605.
• Delice, A. ve Sevimli, E. (2012). Analiz dersi öğrencilerinin integral hacim hesabı problemlerindeki çözüm süreçlerinin düşünme yapısı farklılıkları bağlamında değerlendirilmesi. M. Ü. Atatürk Eğitim Fakültesi Eğitim Bilimleri Dergisi, 36, 95-113.
• Durmuş, S. (2004). A diagnostic study to determine learning difficulties in mathematics. Gazi University Kastamonu Education Journal, 12(1), 125-128.
• Dündar, S. (2014). The investigation of spatial skills of prospective teachers with different cognitive. Bartın University Journal of Faculty of Education, 3(1). doi:10.14686/BUEFAD.201416209
• Dündar, S. (2015a). An analysis on the pattern generalizations of the Turkish pre-service Mathematics teachers that are presented in a different structure and presentation. Educational Research and Review, 10(2), 210-224. doi: 10.5897/ERR2014.2057.
• Dündar, S. (2015b). Mathematics Teacher-Candidates’ Performance in Solving Problems with Different Representation Styles: The Trigonometry Example. Eurasia Journal of Mathematics, Science & Technology Education, 11(6), 1379-1397. doi: 10.12973/eurasia.2015.1396a
• Feifei, Y. (2005). Diagnostic assessment of urban middle school student learning of prealgebra patterns (Doctoral dissertation). Ohio State University, USA.
• Fraenkel, J. R., & Wallen, N. E. (2006). How to design and evaluate research in education. Newyork: McGraw-Hill.
• Ghazali, M., Abdullah, S.A.S, İsmail, Z., & İdris, I. (2005). Dominant representation in the understanding of basic integrals among post secondary students. The Mathematics Education into the 21st Century Project Universiti Teknologi Malaysia Reform, Revolution and Paradigm Shifts in Mathematics Education Johor Bahru, Malaysia.
• Goldin, G. A., & Kaput, J. J. (1996). A joint perspective on the idea of representation in learning and doing mathematics. In L. P. Steffe, P. Nesher, P. Cobb, G. A. Goldin & B. Greer (Eds.), Theories of mathematical learning, pp.397-430. Mahwah, NJ: Lawrence Erlbaum Associates.
• Goldin, G. A. (2004). Representations in school mathematics: A unifying research perspectives. In J. Kilpatrick, W. G. Martin and D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 275-285). Reston, VA: NCTM.
• Greeno, J. G., & Hall, R. P. (1997). Practicing representation: Learning with and about representational forms. Phi Delta Kappan, 78: 361–67.
• Haapasalo, L., & Kadijevich, Dj. (2000). Two types of mathematical knowledge and their relation. Journal für Mathematik-Didaktik, 21(2), 139-157.
• Kieren, T. E. (1976). On the mathematical, cognitive, and ınstructional foundations of rational numbers. In R. A. Lesh (Ed.), Number and Measurement (pp. 101-144). Columbus, Oh: Ohio State University, EEIC, SMEAC.
• Landis, J. R., & Koch, G. G. (1977). An application of hierrachical kappa-type statistics in the assessment of majority agreement among multiple observes. Biometrics, 33, 363-374.
• Lesh, R., Post, T., & Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp.33-40). New Jersey: Lawrence Erlbaum Associates.
• McMillian, J. H. (2000). Educational research: Fundamentals for the consumer (3. Edition). New York: Longman.
• Milli Eğitim Bakanlığı [MEB]. (2013). Ortaokul matematik dersi 5-8. sınıflar öğretim programı. Ankara: Devlet Kitapları Müdürlüğü Basımevi.
• National Council of Teachers o Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Reston, VA: NCTM Publications.
• Polya, G. (1957). How to solve it: a new aspect of mathematical method. Princeton: Princeton University Press.
• Rasslan, S., & Tall, D. (2002). Definitions and images for the definite integral concept. In A. Cockburn & E. Nardi (Eds.), Proceedings of the 26th Conference of the International Group for the Psychology of Mathematics Education, (Vol. 4, pp. 89-96). Norwich: England.
• Reed, S. K., Ernest, G. W., & Banerji, R. (1974). The role of analogy in transfer between similar problem states. Cognitive Psychology, 6, 436-450.
• Sam, L. C., Lourdusamy, A., & Ghazali, M. (2001). Factors affecting students' abilities to solve operational and word problems in mathematics. Education, 76, 853-860.
• Sevimli, E., & Delice, A. (2012). May mathematical thinking type be a reason to decide what representations to use in definite integral problems? Proceedings of the British Society for Research into Learning Mathematics 32(2), 76-81.
• Sevimli, E. (2009). Consideration of pre-services mathematics teachers’ preferences of representation in terms of definite integral within the context of certain spatial abilities and academic achievement (Master’s thesis). Marmara University, İstanbul.
• Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.
• Simon, H. A., & Hayes, J. R. (1976). The understanding process: Problem isomorphs, Cognitive Psychology, 8, 165-190.
• Soylu, Y. ve Soylu, C. 2006. Matematik derslerinde başarıya giden yolda problem çözmenin rolü. İnönü Üniversitesi Eğitim Fakültesi Dergisi, 7(11), 97-111.
• Stoessiger, R., & Ernest, P. (1992). Mathematics and national curriculum: primary teacher attitudes. The International Journal for Technology in Mathematics Education, 23(1), 65-74. doi: 10.1080/0020739920230107.
• Tatar, E., Okur, M. ve Tuna, A. (2008). A study to determine learning difficulties in secondary mathematics education. Kastamonu Education Journal, 16(2), 507-516.
• Thompson, P. W., & Silverman, J. (2007). The concept of accumulation in calculus. In M. Carlson & C. Rasmussen (Eds.), Making the connection: Research and teaching in undergraduate mathematics (pp. 117-131). Washington, DC: Mathematical Association of America.
• Umay, A., Akkuş, O., & Duatepe-Paksu, A. (2006). An investigation of 1-5 grades mathematics curriculum by considering NCTM principles and standards, Journal of Hacettepe University Education Faculty, 31, 198-211.
• Villegas, J. L., Castro, E., & Gutierrez, E. (2009). Representations in problem solving: a case study with optimization problems. Electronic Journal of Research in Educational Psychology, 7(1), 279-308.
• Yaman, H. (2010). A study on the elementary students’ perceptions of connections in mathematical patterns (Unpublishing doctoral dissertation). Hacettepe University, Ankara, Turkey.
• Yan, Z., & Lianghuo, F. (2006). Focus on the representation of problem types in intended curriculum: A comparison of selected Mathematics textbooks from mainland China and the United States. International Journal of Science and Mathematics Education, 4(4), 609-626.
• Yıldırım, A. ve Şimşek, H. (2006). Sosyal bilimlerde nitel araştırma yöntemleri. Ankara: Seçkin Yayınevi.