Investigation of Gifted Students’ Problem Posing Abilities Requiring Arithmetical Operations with Natural Numbers

Year 2018, Volume: 19 Issue: 3, 531 - 546, 30.12.2018

Fatma Erdoğan , Tuba Erben

https://doi.org/10.17679/inuefd.486674

Cited By: 2

Abstract

This study aimed to investigate gifted
students’ problem posing abilities requiring arithmetical operations with
natural numbers. In the present
study, the descriptive research model has been used which is one of the
quantitative research methods. The research sample was composed of 25
fourth grade primary school students. All of the students were studying in
science and arts center located in a province in the Eastern Anatolia region of
Turkey. In the study, Problem Posing Form, consisting of six items for arithmetical operations with natural numbers
was used as data collection tool. The problems posed were analyzed according to
the semantic structures. According to the findings, it was determined
that gifted students posed problems using different semantic structures that
requiring arithmetical operations with natural numbers. However, it was
determined that some semantic structures were used more frequently in problems.
Accordingly to this, it has emerged as most frequently used semantic structures
in problems, join for addition, separation for subtraction, repeated addition
for multiply and sharing for division operations. Also, it was determined that
some gifted students experienced problems such as using different arithmetical
operation, writing the exercises, not responding, and making logical mistakes.
In the light of findings, it has recommended that problem posing activities
involving different semantic structures should be included in differentiated
mathematics curriculum to be developed for gifted students. It is suggested to
investigate gifted students’ problem posing abilities in the context of
creativity in later studies.

Keywords

Gifted students, mathematically giftedness, problem posing, mathematics education.

Özel Yetenekli Öğrencilerin Doğal Sayılarla Dört İşlem Gerektiren Problem Kurma Becerilerinin İncelenmesi

Abstract

Bu araştırmada özel yetenekli öğrencilerin doğal sayılarla dört işlem gerektiren problem kurma becerilerinin incelenmesi amaçlanmıştır. Araştırmada, nicel araştırma yöntemlerinden betimsel araştırma modeli kullanılmıştır. Araştırmanın örneklemini, Türkiye’nin Doğu Anadolu Bölgesindeki bir ilde bulunan, bilim ve sanat merkezinde öğrenim görmekte olan 25 ilkokul dördüncü sınıf öğrencisi oluşturmuştur. Araştırmada veri toplama aracı olarak, doğal sayılarla dört işleme yönelik altı maddeden oluşan Problem Kurma Formu kullanılmıştır. Öğrencilerin kurdukları problemler, anlamsal yapılarına göre analiz edilmiştir. Araştırma bulgularına göre, özel yetenekli öğrencilerin doğal sayılarla dört işlem gerektiren farklı anlamsal yapılara sahip problemler kurdukları görülmüştür. Ancak, doğal sayılarla dört işlem türüne göre problemlerde bazı anlamsal yapıların daha sık kullanıldığı belirlenmiştir. Buna göre, özel yetenekli öğrencilerin kurdukları problemlerde, toplamanın birleştirme, çıkarmanın ayırma, çarpmanın tekrarlı toplama, bölmenin ise paylaşma anlamının en sık kullanılan anlamsal yapılar olduğu saptanmıştır. Ayrıca, bazı öğrencilerin problem kurma durumlarında istenilen dört işlemin dışında diğer işlemlere yönelik problem kurma, alıştırma yazma, yanıt verememe, mantık hataları yapma gibi sorunlar yaşadıkları belirlenmiştir. Araştırma bulguları ışığında, özel yetenekli öğrenciler için geliştirilecek farklılaştırılmış matematik dersi öğretim programlarında farklı anlamsal yapılar içeren problem kurma etkinliklerine yer verilmesi önerilmektedir. Daha sonra yapılacak araştırmalarda özel yetenekli öğrencilerin problem kurma becerilerinin yaratıcılık bağlamında incelenmesi önerilmektedir.

Keywords

problem kurma, matematik eğitimi, Özel yetenekli öğrenciler, matematiksel özel yeteneklilik, matematik eğitimi

References

• Baltacı, S., Yıldız, G., & Güven, B. (2014). Knowledge types used by eighth grade gifted students while solving problems. Bolema, Rio Claro (SP), 28 (50), 1032-1055.
• Brown, S. I., & Walter, M. I. (1990). The art of problem posing. New Jersey: Lawrence Erlbaum Associates, Inc., Publishers.
• Burton, L. (1999). The practices of mathematicians: What do they tell us about coming to know mathematics? Educational Studies in Mathematics, 37(2), 121-143.
• Chang, N. (2007). Responsibilities of a teacher in a harmonic cycle of problem solving and problem posing. Early Child hood Education Journal, 34(4), 265-271.
• Christou, C., Mousoulides, N., Pittalis, M., Pitta-Pantazi, D., & Sriraman, B. (2005). An empirical taxonomy of problem posing processes. ZDM, 37(3), 149-158.
• Cross, T. L., & Coleman, L. J. (2005). School-based conception of giftedness. Conceptions of giftedness, 2, 52-63.
• Çetinkaya, A., & Soybaş, D. (2018). İlköğretim 8. sınıf öğrencilerinin problem kurma becerilerinin incelenmesi. Kuramsal Eğitimbilim Dergisi, 11(1), 169-200.
• Diezmann, C. M. (2005). Challenging mathematically gifted primary students. Australasian Journal of Gifted Education, 14(1), 50-57.
• Ellerton, N. (1986). Children’s made up mathematics problems: A new perspective on talented mathematicians. Educational Studies in Mathematics, 17(3), 261-271.
• Espinoza, J., Lupiáñez J. L. & Segovia, I. (2013). Características del talento matemático asociadas a la invención de problemas. Revista Científica, número especial octubre 2013, 190-195.
• Espinoza, J., Lupiáñez, J. L., & Segovia, I. (2016). The posing of arithmetic problems by mathematically talented students. Electronic Journal of Research in Educational Psychology, 14(2), 368-392.
• Freiman, V. (2006). Problems to discover and to boost mathematical talent in early grades: A challenging situations approach. The Montana Mathematics Enthusiast, 3(1), 51-75.
• Gagné, F. (2005). From gifts to talents: The DMGT as a developmental model. In R. J. Sternberg & J. E. Davidson (Eds.), Conceptions of giftedness (pp. 98–120). Cambridge, UK: Cambridge University Press.
• Guvercin, S., & Verbovskiy, V. (2014). The effect of problem posing tasks used in mathematics instruction to mathematics academic achievement and attitudes toward mathematics. International Online Journal of Primary Education, 3(2), 59-65.
• Holmes, E. E. (1995). New directions in elementary school mathematics: Interactive teaching and learning. Englewood Cliffs, N.J. : Merrill.
• Johnson, D. T. (2000). Teaching Mathematics to Gifted Students in a Mixed-ability Classroom. (Report No. EDO-EC-00-3). Reston, VA: ERIC Clearinghouse on Disabilities and Gifted Education. (ERIC Document Reproduction Service No. ED441302).
• Keşan, C., Kaya, D., & Güvercin, S. (2010). The effect of problem posing approach to the gifted student’s mathematical abilities. International Online Journal of Educational Sciences, 2(3), 677-687.
• Krutetskii, V. A. (1976). The Psychology of Mathematical Abilities in Schoolchildren. University of Chicago Press.
• Lavy, I., & Shriki, A. (2007). Problem posing as a means for developing mathematical knowledge of prospective teachers. Proceedings of the 31st conference of the International Group for the Psychology of Mathematics Education, vol.3, pp. 129- 136.Seoul: PME.
• Levenberg, I., & Shaham, C. (2014). Formulation of word problems in geometry by gifted pupils. Journal for the Education of the Young Scientist and Giftedness, 2(2), 28-40.
• Miles, B., M., & Huberman, A., M. (1994). Qualitative data analysis (21nd ed.). London: Sage Publication.
• Miller, R. C. (1990). Discovering mathematical talent. Reston, VA: Eric Clearinghouse on Handicapped and Gifted Children.
• Milli Eğitim Bakanlığı. (2018). Matematik dersi öğretim programı (İlkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar). Ankara: MEB Yayınları.
• National Council of Teachers of Mathematics (2000). Principals and standards for school mathematics. Reston, Va: National council of Teachers of Mathematics Publication.
• Renzulli, J. S. (1986) The three ring conception of giftedness: A developmental model of creative productivity. Sternberg, R. J., & Davidson, J. E. (Eds.), Conceptions of giftedness (pp. 53-92). New York: Cambridge University Press.
• Reys, R. E., Suydam, M. N., Lindquist, M. M., & Smith, N. L. (1998). Helping children learn mathematics. Needham Heights: Allyn & Bacon.Rosli, R., Capraro, M. M., & Capraro, R. M. (2014). The effects of problem posing on student mathematical learning: A Meta-Analysis. International Education Studies, 7 (13), 227-241.
• Saygılı, G., & Atahan, R. (2014). Üstün zekâlı çocukların problem çözmeye yönelik yansıtıcı düşünme becerilerinin çeşitli değişkenler bakımından incelenmesi. Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Sosyal Bilimler Dergisi, 31, 181-192.
• Sheffield, L. J. (1994). The development of gifted and talented mathematics students and the National Council of Teachers of Mathematics Standards ( Re p o rt No. RBDM 9404). Storrs: National Research Center on the Gifted and Talented, University of Connecticut. (ERIC Document Reproduction Service No. ED388011).
• Simonton, D. K. (2005). Genetics of giftedness: The implications of an emergenic-epigenetic model. In Sternberg, R. J., & Davidson, J. E. (Eds.), Conceptions of giftedness (pp. 312-326). NY: Cambridge University Press.
• Singer, F. M., Ellerton, N., & Cai, J. F. (2013). Problem-posing research in mathematics education: New questions and directions. Educational Studies in Mathematics, 83(1), 1–7.
• Silver E. A., & Cai, J. (1996). An analysis of arithmetic problem posing by middle school. Journal for Research in Mathematics Education, 27(5), 521-539.
• Souviney, R. J. (1994). Learning to teach mathematics (2nd Ed.). Englewood Cliffs: Macmillan Publishing Company.
• Sriraman, B. (2005). Are giftedness and creativity synonyms in mathematics. The Journal of Secondary Education, 17(1), 20–36.
• Sriraman, B., Haavold, P., & Lee, K. (2013). Mathematical creativity and giftedness: a commentary on and review of theory, new operational views, and ways forward. Zdm, 45(2), 215-225.
• Sternberg, R. J., & Zhang, L. (1995). What Do We Mean by Giftedness? A Pentagonal Implicit Theory. Gifted Child Quarterly, 39(2), 88-94.
• Stoyanova, E. (2000). Empowering students’ problem solving via problem posing: The art of framing good‛ questions. Australian-Mathematics-Teacher, 56(1), 33-37.
• Stoyanova, E. (2003). Extending students’ understanding of mathematics via problem posing. The Australian Mathematics Teacher, 59(2), 32–40.
• Uçar, F.M., Uçar, M.B., & Çalışkan, M. (2017). Investigation of gifted students' problem-solving skills. Journal for the Education of Gifted Young Scientists, 5(3), 15-28.
• Van de Walle, J. A., Karp, K. S., & Williams, J. M. B. (2016). Elementary and middle school mathematics. Teaching developmentally. Boston: Pearson.
• Van Harpen, X. Y., & Presmeg, N. C. (2013). An investigation of relationships between students’ mathematical problem-posing abilities and their mathematical content knowledge. Educational Studies in Mathematics, 83(1), 117–132.
• Van Tassel-Baska, J. (1998). Excellence in educating gifted & talented learners (3rd. ed.). Denver: Love.
• Wagner, H., & Zimmermann, B. (1986). Identification and fostering of mathematically gifted students. In A. Cropley, K. Urban, H. Wagner, and W. Wieczerkowski (Eds.) Giftedness: A continuing world-wide challenge (pp.273-287). New York: Trillium Pres.
• Wieczerkowski, W., Cropley, A. J., & Prado, T. M. (2000). Nurturing talents/gifts in mathematics. In K. A. Heller, F. J. Monks, R. J. Sternberg, and R. F. Subotnik (Eds.), International handbook of giftedness and talent education (pp. 413- 425). Oxford, United Kingdom: Pergamon.
• Yazgan-Sağ, G., & Argün, Z. (2016). The motivational forethoughts of gifted students in mathematical problem solving situations. Kastamonu Education Journal, 24(3), 1165-1182.
• Yıldız, A., Baltacı, S., Kurak, Y., & Güven, B. (2012). Üstün yetenekli ve üstün yetenekli olmayan 8. Sınıf öğrencilerinin problem çözme stratejilerini kullanma durumlarının incelenmesi. Uludağ Üniversitesi Eğitim Fakültesi Dergisi, 25(1), 123-143.
• Yildiz, A., Baltaci, S., & Güven, B. (2011). Metacognitive behaviours of the eighth grade gifted students in problem solving process. The New Educational Review, 26 (4), 248-260.