# Intuitive Development of the Concept of Integers among Primary School Students

## Main Article Content

## Abstract

This paper investigated the intuitive development of the concept of integers among primary school students. In order to reveal if primary school students had an intuitive sense of integers, an assessment consisting of five questions was prepared and applied to a total 100 4^{th} grade students. A variety of integer concepts were utilized in the assessment including; integer ordering, less-than greater-than relations, as well as, integer addition and subtraction. In order to analyze the assessment data a coding system was utilized. Two researchers separately coded the students’ answer responses, and later met with a third researcher to resolve any differences of rater reliability. According to the findings from this research, the 4^{th} grade students investigated did exhibit an intuitive understanding of integers. In order to build upon students understanding of integers, examples from daily life as well as cardinal and ordinal meanings of numbers should be utilized in future instruction.

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## Article Details

**International Electronic Journal of Elementary Education**, [S.l.], v. 11, n. 2, p. 191-199, jan. 2019. ISSN 1307-9298. Available at: <https://iejee.com/index.php/IEJEE/article/view/648>. Date accessed: 23 may 2019.

## References

Altun, M. (2008). İlkögretim ikinci kademe (6, 7 ve 8. sınıflarda) matematik ögretimi, 6. Baskı, Bursa: Aktüel Yayınları.

Ball, D. L. (1993). With an eye on the mathematical horizon: Dilemmas of teaching elementary school mathematics. The Elementary School Journal, 93(4), 373-397.

Behrend, J. L., & Mohs, L. C. (2006). From simple questions to powerful connections: A two-year conversation about negative numbers. Teaching Children Mathematics, 12(5), 260-264.

Beswick, K. (2011). Positives experiences with negative numbers: Building on students’ in and out of school experiences. Australian Mathematics Teachers, 67(2), 31-40.

Bishop, J. P., Lamb, L. L. C., Philipp, R. A., Schapelle, B. P., & Whitacre, I. (2011). First graders outwit a famous mathematician. Teaching Children Mathematics, 17(6), 350–358.

Bishop, J., Lamb, L., Philipp, R., Whitacre, I., & Schappelle, B. (2014). Using order to reason about negative numbers: The case of Violet. Educational Studies in Mathematics, 86(1), 39-59.

Bofferding, L. (2014). Negative integer understanding: Characterizing first graders’ mental models. Journal for Research in Mathematics Education, 45(2), 194-245.

Büyüköztürk, Ş., Çakmak, E. K., Akgün, Ö. E., Karadeniz, Ş., & Demirel, F. (2012). Bilimsel araştırma yöntemleri. Pegem A.

Carson, C. L., & Day, J. (1995). Annual report on promising practices: How the algebra project eliminates the" game of signs" with negative numbers. Southwest Regional Laboratory.

Cathcart, W. G., Pothier, Y. M., Vance, J. H., & Bezuk, N. S. (2003). Learning mathematics in elementary and middle schools (Third Edition.). Upper Saddle River, NJ: Prentice.

Crowley, M. L., & Dunn, K. A. (1985). On multiplying negative numbers. The Mathematics Teacher, 78(4), 252-256.

Fischbein, H. (1987). Intuition in science and mathematics: An educational approach (Vol. 5). Springer Science & Business Media.

Galbraith, M. J. (1974). Negative numbers. International Journal of Mathematical Education in Science and Technology, 5, 83-84-90.

Gelman, R., & Gallistel, C. R. (1986). The child's understanding of number. Harvard University Press.

Goldin, G., & Shteingold, N. (2001). Systems of representations and the development of mathematical concepts. The Roles Of Representation In School Mathematics, 1-23.

Hativa, N., & Cohen, D. (1995). Self-learning of negative number concepts by lower division elementary students through solving computer-provided numerical problems. Educational Studies in Mathematics, 28(4), 401-431.

Işıksal Bostan, M. (2009). Negatif sayılara ilişkin zorluklar, kavram yanılgıları ve bu yanılgıların giderilmesine yönelik öneriler. İlköğretimde karşılaşılan matematiksel zorluklar ve çözüm önerileri, Ankara: Pegem Akademi Yayınları.

Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics (National Research Council. Mathematics Learning Study Committee). Washington: National Academy Press.

Kümbetoğlu, B. (2008). Sosyolojide ve antropolojide niteliksel yöntem ve araştırma. Bağlam Yayıncılık.

Linchevski, L. & Williams, J. (1999). Using intuition from everyday life in 'filling' the gap in children's extension of their number concept to include the negative numbers. Educational Studies in Mathematics, 39(1), 131-147.

Milli Eğitim Bakanlığı. (2013). Ortaokul matematik dersi (5, 6, 7, 8. sınıflar) öğretim programı [Secondary school mathematics curriculum]. Ankara: Talim ve Terbiye Kurulu Başkanlığı.

Milli Eğitim Bakanlığı. (2017). Matematik dersi öğretim programı [Mathematics curriculum]. Ankara: MEB.

Murray, J. C. (1985). Children’s informal conceptions of integer arithmetic. In proceedings of the ninth international conference for the psychology of mathematics education (Vol. 1, pp. 147-155). Utrecht, the Netherlands: The State University of Utrecht.

National Council of Teachers of Mathematics (1989). Curriculum and evaluation standards for school mathematics. Washington, DC: Author.

National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: Author.

Otten, S. (2009). Down and to the left: Students’ movement toward negative numbers. Michigan State University, SME 840.

Streefland, L. (1996). Negative numbers: Reflections of a learning researcher. The Journal of Mathematical Behavior, 15(1), 57-77.

Van de Walle, J. A., Karp, K. S., & Williams, J. M. B. (2007). Elementary and middle school mathematics. Teaching development. Boston: Pearson.

Vlassis, J. (2008). The role of mathematical symbols in the development of number conceptualization: The case of the minus sign. Philosophical Psychology, 21(4), 555-570.

Whitacre, I., Bishop, J., Lamb, L., Phillipp, R., Schappelle, B. P., & Lewis, M. (2012a). Happy and sad thoughts. Journal of Mathematical Behavior, 31(3).

Whitacre, I., Bishop, J., Lamb, L., Philipp, R, Schappelle, B. P., & Lewis, M. (2012b). What sense do children make of negative dollars? In L. Van Zoest, J. Lo., & J. Kratky (Eds.), Proceeding of the 34th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 958-964).

Wilcox, V. B. (2008). Questioning zero and negative numbers. Teaching children mathematics, 15(4), 202-206.