Review
Year 2021,
, 44 - 58, 08.03.2021
Abstract
Öğrenciler tamsayılar ve tamsayılarla işlemler yapma konusunda çeşitli öğrenme güçlükleri yaşamaktadırlar. Bu zorlukların üstesinden gelebilmek için alanyazında tamsayılar konusunun öğretiminde çeşitli bağlamların, yöntemlerin veya modellerin kullanılması tavsiye edilmektedir. Bu çalışmada tamsayılarla toplama, çıkarma, çarpma ve bölme işlemlerinin sayma pulları ve sayı doğrusu modelleri ile yapılışı açıklanmıştır. Tamsayılarla bölme işlemlerinin yapılışında sayı doğrusu kullanımının; negatif bir tamsayı ile pozitif bir tamsayının çarpılması ve pozitif bir tamsayının negatif bir tamsayıya bölünmesi işlemlerinde sayma pullarının kullanılmasının zor ve karmaşık olduğu görülmüştür. Bu sebeple tamsayılarla çarpma işlemlerinde kullanılabilecek “örüntü arama” ve bölme işlemlerinde kullanılabilecek “çarpma işlemi ile ilişkilendirme” stratejilerine yer verilmiştir. Çalışmanın tamsayılarla temel işlemlerin sayı doğrusu ve sayma pulları modelleriyle yapılışı hakkında öğrencilere ve matematik öğretmeni adaylarına önemli katkılar sağlayacağı düşünülmektedir.
References
- Battista, M. T. (1983). A complete model for operations on integers. The Arithmetic Teacher, 30(9), 26-31.
- Billstein, R., Libeskind, S., & Lott, J. (2016). A problem solving approach to mathematics for elementary school teachers (12th ed.). Pearson Education, Inc
- Bosse, M. J., Lynch-Davis, K., Adu-Gyamfi, K., & Chandler, K. (2016). Using integer manipulatives: Representational determinism. International Journal for Mathematics Teaching and Learning, 17(3)
- Cemen, P. B (1993). Adding and subtracting integers on the number line. Arithmetic Teacher, 40(7), 388-389, URL: https://www.jstor.org/stable/pdf/41195814.pdf
- Cunningham AW. (2009). Using the number line to teach signed numbers for remedial community college mathematics. Math Teaching Res J Online, 3(4):1–40
- Fischbein, E. (1987). Intuition in Science and Mathematics: An Educational Approach (D.Reidel Publishing Co., Dordrecht), pp. 97-102.
- Hativa, N., ve 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(2), 401–431.
- Janvier C. (1983). The understanding of directed numbers. Seventh International Conference for the Psychology of Mathematics Education; Jerusalem, Israel; p. 295–301.
- Peled I, Mukhopadahyay S, ve Resnick LB. (1989). Formal and informal sources of mental models for negative numbers. 13th InternationalConference for the Psychology ofMathematics Education; Paris, France; p. 106–110.
- Van de Walle, A. J., Karp, S.K. ve Bay-Williams, M.J. (2012). Elementary and Middle School Mathematics, (Çeviri Ed. Soner Durmuş, (2012). İlkokul ve Ortaokul Matematiği, Nobel Akademik Yayıncılık, Ankara
- Vlassis, J. (2004). Making sense of the minus sign or becoming flexible in ‘negativity’, Learning and Instruction 14, 469–484, doi:10.1016/j.learninstruc.2004.06.012
Year 2021,
, 44 - 58, 08.03.2021
Abstract
Students have various learning difficulties in doing operations with integers and integers. In order to overcome these difficulties, it is recommended to use various contexts, methods or models in teaching the subject of integers in the literature. This study explains the use of counters and number line models when carrying out addition, subtraction, multiplication and division operations with integers. Some operations, such as multiplying a negative number with a positive number, and dividing a negative integer with a positive integer, were found to be difficult and complicated using counters and a number line, and so the strategies of “searching for a pattern” and “relating to multiplication” were included for use in integer multiplication and division operations, respectively. The present study is expected to support students and prospective mathematics teachers in the use of counters and number line models when carrying out basic operations with integers.
References
- Battista, M. T. (1983). A complete model for operations on integers. The Arithmetic Teacher, 30(9), 26-31.
- Billstein, R., Libeskind, S., & Lott, J. (2016). A problem solving approach to mathematics for elementary school teachers (12th ed.). Pearson Education, Inc
- Bosse, M. J., Lynch-Davis, K., Adu-Gyamfi, K., & Chandler, K. (2016). Using integer manipulatives: Representational determinism. International Journal for Mathematics Teaching and Learning, 17(3)
- Cemen, P. B (1993). Adding and subtracting integers on the number line. Arithmetic Teacher, 40(7), 388-389, URL: https://www.jstor.org/stable/pdf/41195814.pdf
- Cunningham AW. (2009). Using the number line to teach signed numbers for remedial community college mathematics. Math Teaching Res J Online, 3(4):1–40
- Fischbein, E. (1987). Intuition in Science and Mathematics: An Educational Approach (D.Reidel Publishing Co., Dordrecht), pp. 97-102.
- Hativa, N., ve 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(2), 401–431.
- Janvier C. (1983). The understanding of directed numbers. Seventh International Conference for the Psychology of Mathematics Education; Jerusalem, Israel; p. 295–301.
- Peled I, Mukhopadahyay S, ve Resnick LB. (1989). Formal and informal sources of mental models for negative numbers. 13th InternationalConference for the Psychology ofMathematics Education; Paris, France; p. 106–110.
- Van de Walle, A. J., Karp, S.K. ve Bay-Williams, M.J. (2012). Elementary and Middle School Mathematics, (Çeviri Ed. Soner Durmuş, (2012). İlkokul ve Ortaokul Matematiği, Nobel Akademik Yayıncılık, Ankara
- Vlassis, J. (2004). Making sense of the minus sign or becoming flexible in ‘negativity’, Learning and Instruction 14, 469–484, doi:10.1016/j.learninstruc.2004.06.012
There are 11 citations in total.
Details
| Primary Language | Turkish |
|---|---|
| Subjects | Other Fields of Education |
| Journal Section | Research Article |
| Authors | |
| Publication Date | March 8, 2021 |
| Published in Issue | Year 2021 |