# İLKÖĞRETİM DÜZEYİNDE MATEMATİK YETERLİLİĞİ İÇİN GEREKLİ DÖRT TEMEL PRENSİPTEN BİRİSİ “TERSİNE ÇEVİRME PRENSİBİ” NEDİR? NEDEN ÖNEMLİDİR? STRATEJİLERİ NELERDİR?

Bu makalede matematiği anlama, işlem pratiğinde kullanma ve günlük hayata uyarlamada oldukça önemli olan matematik yeterliliğinin dört temel prensibinden biri olan “Tersine Çevirme” prensibinin ne olduğu, önemi ve kullanımı ile ilgili durumlara dikkat çekilmiştir. Çalışma, bu konuda öne sürülen kuramsal bilgilerin ve bu konuda yapılan deneysel çalışmaların taranması, derlenmesi ve yorumlanmasıyla oluşturulmuştur
Anahtar Kelimeler:

# What Is “Inversion Principle”, Which Is One Of Four Basic Principles Of Mathematical Proficiency In Elementary School Level? Why Is It Important? What Are The Strategies In Relation To The Principle?

This article points out that understanding of “inversion principle”- one of four principles of mathematical proficiency-is important for comprehending math, using it in procedure, adapting it to daily life, and understanding the significance of principle. The study includes some theoretical information and empirical researches about the topic acquired by scanning, compiling and discussing the related studies
Keywords:

## Inversion principle, inversion strategy, arithmetic, elementary school math,

#### ___

Baroody, A. J., Torbeyns, J. & Verschaffel, L. (2009). Young children’s understanding and application of subtraction-related principles. Mathematical Thinking and Learning, 11, 2-9.

Baroody, A. J., Lai, M., Li, X & Baroody, E. (2009). Preschoolers’ understanding of subtraction-related principles. Mathematical Thinking and Learning, 11, 41-60.

Bisanz, J., ve LeFevre, J. (1990). Strategic and nonstrategic processing in the development of mathematical cognition. In D. F. Bjorklund (Eds.), Children’s strategies: Contemporary views of cognitive development. Hillsdale, NJ: Lawrence Erlbaum, 213–244.

Bisanz, J., Watchorn, R. P. D., Piatt, C. (2009). On ‘understanding’ children’s developing use of inversion. Mathematical Thinking and Learning, 11, 10-24. Bryant, P., Christie, C., Rendu, A. (1999). Children’s understanding of the relation between addition and subtraction: Inversion, identity, and decomposition. Journal of Experimental Child Psychology, 74, 194-212.

Carr, M. ve Hettinger, H. (2003). Perspectives on mathematics strategy development. In J. M. Royer (Eds.), Mathematical cognition (pp.33–69). USA: Information Age Publishing Inc.

Dowker, A. (2005). Individual differences in arithmetic: Implications for psychology, neuroscience and education (pp. 123–148). New York: Psychology Press.

Geary, D. C. (2006). Development of mathematical understanding. In D. Kuhl & R. S. Siegler (Eds.) Cognition, perception, and language, Vol. 2 (pp. 777– 810). W. Damon (Gen. Ed.), Handbook of child psychology (sixth edition). New York: John Wiley & Sons

Gilmore, C. K. & Spelke, E. S. (2008). Children’s understanding of the relationship between addition and subtraction. Cognition, 107, 932-945.

Gordon, P. (2008). Look ma, no fingers Are children numerical solipsists? Behavioral and Brain Sciences, 31, 654-655. Doi: 10.1017/ S0140525X08005712.

Klein, J. S. & Bisanz, J. (2000). Preschoolers doing arithmetic: The concepts are willing but the working memory is weak. Canadian Journal Experimental Psychology, 54, 105-114.

Lester, F.K. (2007). Second handbook of research on mathematics teaching and learning: A project of the national council of teachers of mathematics. National Council of Teachers of Mathematics (NCTM). USA: Information Age Publishing Inc.

MEB (2005), İlköğretim Matematik Programı 1-5. Sınıflar. Ankara: MEB Yayınları.

Nunes, T., Bryant, P., Hallett, D., Bell, D. & Evans, D. (2009). Teaching children about the inverse relation between addition and subtraction. Mathematical Thinking And Learning, 11, 61-78.

Nunes, T., Schliemann, A. L. & Carraher, D. (1993). Street mathematics and school mathematics. New York: Cambridge Univ. Press.

Olkun S., Toluk Z. (2007). İlköğretimde etkinlik temelli matematik öğretimi (Genişletilmiş 3. baskı).Ankara: Maya Akademi Yayıncılık.

Piaget, J. & Moreau, A. (2001). The inversion of arithmetic operations. In J. Piaget (Ed.), Studies in reflecting abstraction (R.L. Campbell, Trans., pp.69-86). Hove, UK: Psychology Press (Original work published 1977).

Piaget, J. (1952). The child’s conception of number. London: Routledge ve Kegan Paul.

Rasmussen, C., Ho, E. & Bisanz, J. (2003). Use of the mathematical principle of inversion in young children. Journal of Experimental Child Psychology, 85, 89-102.

Robinson, K. M., Arbuthnott, K. D., Rose, D. McCarron, M.C., Globa, C. A. & Phonexay, S. D. (2006). Stability and change in children’s division strategies. Journal of Experimental Child Psychology, 93, 224-238.

Robinson, K. M., Ninowski, E.J. & Gray L.M. (2006). Children’s understanding of the arithmetic concepts of inversion and associativity. Journal of Experimental Child Psychology, 94, 346-362.

Royer, J. M. Sherman, J., Bisanz, J. (2007). Evidence for Use of Mathematical Inversion By Three-Year-Old Children. Journal of Cognition and Development, 8, 3, 333-344.

Schneider,M. & Stern,E. (2009). The inverse relation of addition and subtraction: A knowledge integration perspective. Mathematical Thinking and Learning, 11, 92-101.

Sherman, J., & Bisanz, J. (2007). Evidence for use of mathematical inversion by three-year-old children. Journal of Cognition and Development, 8, 333- 344.

Stern, E. (1992). Spontaneous use of conceptual mathematical knowledge in elementary school children. Contemporary Educational Psychology, 17, 266- 277.

Vilette, B. (2002). Do young children grasp the inverse relationship between addition and subtraction? Evidence against early arithmetic. Cognitive Development, 1, 365-383.

#### ___

 APA Acar, E . (2013). İLKÖĞRETİM DÜZEYİNDE MATEMATİK YETERLİLİĞİ İÇİN GEREKLİ DÖRT TEMEL PRENSİPTEN BİRİSİ “TERSİNE ÇEVİRME PRENSİBİ” NEDİR? NEDEN ÖNEMLİDİR? STRATEJİLERİ NELERDİR? . Balıkesir Üniversitesi Sosyal Bilimler Enstitüsü Dergisi , 16 (30) , 65-87 .
• ISSN: 1301-5265
• Yayın Aralığı: Yılda 2 Sayı
• Yayıncı: Balıkesir Üniversitesi

82.2b36.4b

Sayıdaki Diğer Makaleler