EVALUATION OF THE MATHEMATICAL THINKING PROCESSES OF A GIFTED AND 4TH GRADE STUDENT ON GEOMETRY

Abstract

In this study, the mathematical thinking processes of a gifted 4th grade student regarding geometry were examined. Based on the thought that the geometric thinking level of the student will affect his mathematical thinking skills, it was determined that his geometric thinking level is the second level. While studying mathematical thinking processes, the theoretical framework of the three worlds of mathematics was used. According to this theoretical framework, mathematical thinking is divided into three levels: the conceptual embodied world, the perceptual symbolic world and the axiomatic formal world. While examining the mathematical thinking processes of this student named Alp, two semi-structured interviews were conducted. In the first, his prior knowledge of geometry was questioned and a verbal expression of triangle inequality was presented. In the second interview, an activity that is expected to create knowledge structures about triangle inequality was presented. As a result of the research, it was seen that Alp was able to carry out a thinking process towards proof processes, even at a simple level. His thinking skills are generally limited to the conceptual embodied world dimension.

Keywords: Gifted student, mathematical thinking, three worlds of mathematics

REFERENCES  

Açıl, E. (2015). Ortaokul 3. sınıf öğrencilerin denklem kavramına yönelik soyutlama süreçlerinin incelenmesi: Apos teorisi [Investigation of middle school 7rd graders abstraction processes of the concept of equation: APOS theory] Unpublished Doctorate Thesis. Ataturk University, Institute of Education Sciences, Erzurum.

Akarsu Yakar, E. (2019). Ortaokul öğrencilerinin matematiksel düşünme süreçlerinin ve matematiksel dil becerilerinin matematiğin üç dünyası kuramsal çerçevesi açısından incelenmesi [Examining the mathematical thinking processes and mathematical language skills of secondary school students in terms of the theoretical framework of the three worlds of mathematics]. Unpublished Doctorate Thesis, Dokuz Eylul University, Institute of Educational Sciences, İzmir.

Alyeşil, D. (2005). Kavram haritaları destekli ve problem çözme merkezli geometri öğretimi 7. sınıf öğrencilerinin geometrik düşünme düzeyleri üzerindeki etkileri [The effect of geometry learning with the method of conception charts supported problem solving to the 7th class students' geometry thinking level] Unpublished Master's Thesis. Dokuz Eylul University, Institute of Education Sciences, İzmir.

Bağdat O., & Saban P. (2014). İlköğretim 8. sınıf öğrencilerinin cebirsel düşünme becerilerinin Solo taksonomisi ile incelenmesi [Investigation of the 8th grade students’ algebraic thinking skills with solo taxonomy]. International Journal of Social Science, 26 (2), 473-496.

Bobango, J. C. (1988). Van Hiele levels of geometric thought and student achievement in standard content and proof writing: The effect of phase-based instruction. Dissertation Abstract Index, 48 (10).

Breen, J. J. (2000). Achievement of Van Hiele level two in geometry thinking by eight grade students through the use of geometry computer-based guided instruction. Dissertation Abstract Index, 60 (07).

Creswell, J. W. (2003). Research design: Qualitative, quantitative and mixed methods approaches. California: Sage Publications.

Davis, G. A., & Rimm, S. B. (2004). Education of the gifted and talented. Boston, MA: Pearson Education Press.

Doğan, M., & Güner, P. (2012). İlköğretim matematik öğretmen adaylarının matematik dilini anlama ve kullanma becerilerinin incelenmesi [Examination of pre-service primary school mathematics teachers' skills of understanding and using mathematics language]. Paper presented at the X. National Science and Mathematics Education Congress, Niğde University, Niğde.

Fidan, Y. (2009). İlköğretim 5. sınıf öğrencilerinin geometrik düşünme düzeyleri ve buluş yoluyla geometri öğretiminin öğrencilerin geometrik düşünme düzeylerine etkisi [The geometric thinking levels of primary grade 5 students and the effect of geometry teaching with discovery learning on geometric thinking levels of students]. Unpublished Doctorate Thesis. Dokuz Eylul University, Institute of Education Sciences, İzmir.

Fuys, D., (1985). Van Hiele levels of thinking in geometry. Education and Urban Society, 17(4), 447-462.

Gardner, H. (1993). Frames of mind: The theory of multiple intelligences. New York: Basic.

Guilford, J. P. (1967). The nature of human intelligence. New York: Mcgraw-Hill.

Gündoğdu Alaylı, F. (2012). Geometride şekil oluşturma ve şekli parçalarına ayırma çalışmalarında ilköğretim 6. 7. ve 8. sınıf öğrencilerinin düşünme süreçlerinin incelenmesi ve bu süreçteki düzeylerinin belirlenmesi [The investigation of thinking process of primary 6th ,7th and 8th grade students in the studies of composing and decomposing shapes in geometry and determination of their levels in this process]. Unpublished Doctorate Thesis. Dokuz Eylul University, Institute of Education Sciences, İzmir.

Heid, M. K. (1983). Characteristics and special needs of the gifted student in mathematics. Mathematics Teacher, 76, 221– 226.

Henderson, P. (2002). Materials development in support of mathematical thinking. ACM SIGCSE Bulletin, 35(2), 185-190. Erişim adresi: http://Blue.Butler.Edu/Phenders/İticse2002wg.Rtf

Jukić, L., & Brückler, F.M. (2014). What Do Croatian Pre-Service Teachers Remember from Their Calculus Course?. Issues in the undergraduate mathematics preparation of school teachers, 1,1-15.

Karakarçayıldız, R. Ü. (2016). 7. Sınıf öğrencilerinin geometrik düşünme düzeyleri ile çokgenleri sınıflama becerileri ve aralarındaki ilişki [Geometrical thinking levels and polygons classification skills of 7 th grade students and relationship between them]. Unpublished Master's Thesis. Eskisehir Osmangazi University, Institute of Education Sciences, Eskişehir.

Kashefi, H., Ismail, Z., & Yusof, Y. M. (2010). Obstacles in the learning of two-variable functions through mathematical thinking approach. Pocedia Social and Behavioral Sciences, 173-180.

Kirk, S. A. & Gallagher, J. J. (1989). Educating exceptional children. Boston, MA: Houghton Mifflin

Köse, O. (2018). Üst düzey uzamsal yeteneğe sahip matematik öğretmen adaylarının düşünme yapılarına göre SOLO taksonomisi düzeylerinin belirlenmesi [Determination of SOLO taxonomy levels of mathematics teacher candidates with high level spatial ability according to thinking structures] Unpublished Master's Thesis. Selcuk University, Institute of Education Sciences, Konya.

Krutetskii, V. A. (1976). The psychology of mathematical abilities in school children. Chicago, IL: University of Chicago Press

Milli Eğitim Bakanlığı (2019). Matematik dersi öğretim programı [Mathematics lesson curriculum]. Ankara: Talim ve Terbiye Kurulu.

Mudrikah, A. (2016). Problem-based learning associated by action-process-object-schema (APOS) theory to enhance students’ high order mathematical thinking ability. International Journal of Research in Education and Science (IJRES), 2(1), 125- 135.

Olkun, S., Toluk, Z., & Durmuş, S. (2002, Eylül). Sınıf öğretmenliği ve matematik öğretmenliği öğrencilerinin geometrik düşünme düzeyleri [Geometric thinking levels of primary school and mathematics teaching students]. Paper presented at the 5th National Science and Mathematics Education Congress, ODTÜ, Ankara.

Özcan, B. N. (2012). İlköğretim öğrencilerinin geometrik düşünme düzeylerinin geliştirilmesinde bilgiyi oluşturma süreçlerinin incelenmesi [The investigation of knowledge construction process of primary school students while developing geometric thinking levels]. Unpublished Doctorate Thesis. Dokuz Eylul University, Institute of Education Sciences, İzmir.

Renzulli, J. S. (2003). Conception of giftedness and its relationship to the development of social capital. N. Colangelo ve G. A. Davis (Editörler.) Handbook of gifted education (75–87). Boston MA: Allyn and Bacon, Inc

Sheffield, L. J. (1994). The development of gifted and talented mathematics students and the National Council of Teachers of Mathematics Standards (No. 9404). DIANE Publishing.

Sternberg, R. J. (2003). Giftedness according to theory of successful intelligence. N. Colangelo ve G. A. Davis (Editörler) Handbook of gifted education (88-99). Boston MA: Allyn and Bacon, Inc.

Tall, D. (2007). Developing a theory of mathematical growth. Zdm Mathematics Education, 39, 145-154.

Tall, D., Lima, R. N., & Healy, L. (2014). Evolving a three-world framework for solving algebraic equations in the light of what a student has met before. The Journal of Mathematical Behavior, 34, 1-13.

Türnüklü, E., & Özcan, B. (2014). Öğrencilerin geometride RBC teorisine göre bilgiyi oluşturma süreçleri ile Van Hiele geometrik düşünme düzeyleri arasındaki ilişki: Örnek olay çalışması [The relationship between students' construction of geometric knowledge process based on rbc theory and van hiele geometric thinking levels: case study]. Mustafa Kemal University Journal of Graduate School of Social Sciences, 11 (27), 295-316.

Usiskin, Z. (1982). Van Hiele levels and achievement in secondary school geometry, Final Report, Cognitive Development And Achievement in Secondary School Geometry Project. Chicago: University Of Chicago.

Vandebrouck, F. (2010). Students conceptions of functions at the transition between secondary school and university. Proceedings of the Conference CERME 7, University of Rzeszow, Poland.

Van Hiele, P. M. (1986). Structure and insight: A theory of mathematics education. Academic Pr.