Figural and Conceptual Aspects in Defining and Identifying Polygons

Ustun, Isil; UBUZ, BEHİYE

Figural and Conceptual Aspects in Defining and Identifying Polygons

Behiye UBUZ, (Boş)

Işıl ÜSTÜN (Boş)

Eurasian Journal of Educational Research

10 0

Yıl: 2004 Cilt: 0 Sayı: 16 Sayfa Aralığı: 15 - 26 Metin Dili: Türkçe İndeks Tarihi: 29-07-2022

Figural and Conceptual Aspects in Defining and Identifying Polygons

Öz:

Bu çalışmada matematik de ‘ortalamanın üstünde’, ‘ortalama’ ve ‘ortalamanın altında’ başarıya sahip öğrenciler üzerinde çalışılmıştır. Yüz yüze görüşme ile çokgenlerin belirlenmesinde şekilsel ve kavramsal boyutların etkileşimi gözlenmiştir. Şonuçların analizi göstermiştir ki (a) öğrenciler sıklıkla esas model (ilk örnek) şekilleri kullanıyorlar fakat onların özel (ayrıcalıklı) olduklarını düşünmüyorlar, ve (b) bir kavramın şekilde verilen kritik olmayan özelliği kavramlarla ilgili örnekleri belirlerken zorluklara neden oluyor. Yukarıda belirtilen sonuçların hepsi çokgenlerin öğrenilmesinde üç düzey öğrencide de yaygın olduğu gözlenmiştir. We studied three eighth-grade students identified by their mathematics teacher as having ‘above average,’ ‘average’ and ‘below average’ achievers in mathematics. We sought to observe, using face to face interview, the process of interaction between figural and conceptual aspects in identifying and defining process of polygons, squares, rectangles, and parallelograms. Analysis of the results revealed that (a) students often use prototypic figures but do not consider them as exclusive, (b) noncritical attributes of a concept given in a figure leads to difficulties in identifying concept examples, and (c) students’ own definitions include noncritical attributes of the concepts as well as their critical attributes. All these mentioned above are quite prevalent among all levels of students in concept learning.

Anahtar Kelime: şekilsel matematik eğitimi kavram anlama kavramsal anlama seviyesi geometri çokgenler

Konular: Eğitim, Eğitim Araştırmaları

Çokgenlerin Belirlenmesinde ve Tanımlanmasında Şekilsel ve Kavramsal Boyutlar

Öz:

We studied three eighth-grade students identified by their mathematics teacher as having ‘above average,’ ‘average’ and ‘below average’ achievers in mathematics. We sought to observe, using face to face interview, the process of interaction between figural and conceptual aspects in identifying and defining process of polygons, squares, rectangles, and parallelograms. Analysis of the results revealed that (a) students often use prototypic figures but do not consider them as exclusive, (b) noncritical attributes of a concept given in a figure leads to difficulties in identifying concept examples, and (c) students’ own definitions include noncritical attributes of the concepts as well as their critical attributes. All these mentioned above are quite prevalent among all levels of students in concept learning.

Anahtar Kelime: understanding conceptual understanding level geometry polygons figural mathematics education concept

Konular: Eğitim, Eğitim Araştırmaları

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Bibliyografik

Banks, J. H., & Bannister, R. L., & Posamentier, A. S. (1972). Geometry: Its elements and structure. McGraw- Hill Book Company.
Bruner, J.S., Goodnow, J. J., & Austin, G. A. (1956). A study of thinking. New York: Wiley.
Burger, W. F., & Shaughnessy, J. M. (1986). Characterizing the van Hiele levels of development in geometry. Journal for Research in Mathematics Education, 17, 31-48.
De Villers, M. (1994). The role and function of a hierarchical classification of quadrilaterals. For the Learning of Mathematics, 14(1), 11-18.
De Villers, M. (1998). To teach definitions in geometry or teach to define?. Proceedings of Psychology of Mathematics Education 22 (Vol. 2, pp. 249-255), Stellenbosch: South Africa.
Fischbein, E. (1993). The theory of figural concepts. Educational Studies in Mathematics, 24, 139-162.
Furinghetti, F., & Paola, D. (1999). Exploring students’ images and definitions of area. Proceedings of Psychology of Mathematics Education 23(Vol.2,pp.345-352), Israel.
Hershkowitz, R. ( 1989). Visualization in geometry: Two sides of the coin. Focus on Learning problems in Mathematics, 11(1&2) , 61-75.
Hershkowitz, R. ( 1990). Pschological aspects of learning geometry. In P. Nesher and J. Kilpatrick (eds.), Mathematics and Cognition (70-95), Cambridge University Pres: Cambridge
Hershkowitz, R., & Vinner, S. (1983). The role of critical and non-critical attributes in the conceptimage of geometrical concepts. Proceedings of Psychology of Mathematics Education 7 (pp.223-228), Israel.
Hershkowitz, R., Vinner, S., & Bruckheimer, M. (1987). Activities with teachers based on cognitive research. In M. M. Lindquist & A. P.Shulte (Eds.), Learning and teaching geometry K-12 (pp. 222-235). National Council of Teachers of Mathematics: Reston.
Hoffer, A. (1983). Van Hiele based research. In R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts and process (pp. 205-227). NewYork: Academic Press.
Matsua, N. (2000). States of understanding relations among concepts of geometric figures: Considered from the aspect of concept image and concept definition. Proceedings of Psychology of Mathematics Education 24 (Vol.3, pp. 271-278), Japan.
Musser, G. L., & Trimple, L. E. (1994). College geometry: A problem solving approach with applications. New Jersey: Prentice-Hall.
Prevost, F. J. (1985). Geometry in the junior high school. Mathematics Teacher, 411-418.
Schwarz, B. B., & Hershkowitz, R. (1999). Prototypes: Brakes or levers in learning the function concept? The role of computer tools. Journal for Research in Mathematics Education, 30(4), 363-387.
Shir, K., & Zaslavsky, O. (2001). What constitues a (good) definition? The case of a square. Proceedings of Psychology of Mathematics Education 25 (Vol. 4, pp. 161-168), Netherland.
Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12, 151-169.
Tsamir, P., Tirosh, D., & Stavy, R. (1998). Do equilateral polygons have equal angles?. Proceedings of Psychology of Mathematics Education 22 (Vol. 4, pp. 137-144), Stellenbosch: South Africa.
Ubuz, B. (1999). 10th and 11th grade students errors and misconceptions on basic geometric concepts. Hacettepe University Journal of Education, 16-17, 95-104.
Usiskin, Z. (1982). Van Hiele Levels and Achievement in Secondary School Geometry. (CDASSG Project). Chicago: Chicago University.
Vinner, S. (1983). Concept definition, concept image and the notion of function. International Journal of Mathematics Education in Science and Technology,14, 239-305.
Vinner, S. (1991). The role of definitions in the teaching and learning of mathematics. In D. Tall (Ed.), Advanced Mathematical Thinking (65-81), Kluwer Academic Publishers: Netherlands.
Wilson, P. S. (1983). Use of negative instances in identifying geometric features. Proceedings of Psychology of Mathematics Education 5 (Vol. 1, pp.326-332), Monteal: Canada.

APA	UBUZ B, Ustun I (2004). Figural and Conceptual Aspects in Defining and Identifying Polygons. , 15 - 26.
Chicago	UBUZ BEHİYE,Ustun Isil Figural and Conceptual Aspects in Defining and Identifying Polygons. (2004): 15 - 26.
MLA	UBUZ BEHİYE,Ustun Isil Figural and Conceptual Aspects in Defining and Identifying Polygons. , 2004, ss.15 - 26.
AMA	UBUZ B,Ustun I Figural and Conceptual Aspects in Defining and Identifying Polygons. . 2004; 15 - 26.
Vancouver	UBUZ B,Ustun I Figural and Conceptual Aspects in Defining and Identifying Polygons. . 2004; 15 - 26.
IEEE	UBUZ B,Ustun I "Figural and Conceptual Aspects in Defining and Identifying Polygons." , ss.15 - 26, 2004.
ISNAD	UBUZ, BEHİYE - Ustun, Isil. "Figural and Conceptual Aspects in Defining and Identifying Polygons". (2004), 15-26.

APA	UBUZ B, Ustun I (2004). Figural and Conceptual Aspects in Defining and Identifying Polygons. Eurasian Journal of Educational Research, 0(16), 15 - 26.
Chicago	UBUZ BEHİYE,Ustun Isil Figural and Conceptual Aspects in Defining and Identifying Polygons. Eurasian Journal of Educational Research 0, no.16 (2004): 15 - 26.
MLA	UBUZ BEHİYE,Ustun Isil Figural and Conceptual Aspects in Defining and Identifying Polygons. Eurasian Journal of Educational Research, vol.0, no.16, 2004, ss.15 - 26.
AMA	UBUZ B,Ustun I Figural and Conceptual Aspects in Defining and Identifying Polygons. Eurasian Journal of Educational Research. 2004; 0(16): 15 - 26.
Vancouver	UBUZ B,Ustun I Figural and Conceptual Aspects in Defining and Identifying Polygons. Eurasian Journal of Educational Research. 2004; 0(16): 15 - 26.
IEEE	UBUZ B,Ustun I "Figural and Conceptual Aspects in Defining and Identifying Polygons." Eurasian Journal of Educational Research, 0, ss.15 - 26, 2004.
ISNAD	UBUZ, BEHİYE - Ustun, Isil. "Figural and Conceptual Aspects in Defining and Identifying Polygons". Eurasian Journal of Educational Research 16 (2004), 15-26.