AN ANALYSIS OF SEVENTH-GRADE STUDENTS’ MATHEMATICAL REASONING

Year 2015, Volume: 44 Issue: 1, 123 - 142, 19.12.2014

Emrullah Erdem , Ramazan Gürbüz

Abstract

The aim of this study is to determine the seventh-graders’ levels of mathematical reasoning and to reveal their performance. The present study was carried out with 167 seventh-grade students studying at randomly selected three elementary schools that served low and middle socioeconomic areas in a city of Turkey. “Mathematical Reasoning Test (MRT)” was developed and used as data collection tool. In analyzing the data, participants’ scores of the test was computed and which mathematical reasoning level they were in was determined. Sample responses of the some students regarding any question (Q7) in the test were presented directly and discussed. As a result of the analysis, it was found that about half of the students (45.5%) had medium and 27.5% of them had low level of mathematical reasoning. When the results are evaluated, it is probable to say that that most of the students’ mathematical reasoning is at medium or low level in general. On the other hand, it is remarkable that rather than the familiar classical problems, students need to be enabled to deal with the problems that they can do reasoning and thus their mathematical reasoning could be improved.

Keywords

Mathematical reasoning, Sevent-grade students, Problems requiring reasoning

Yedinci Sınıf Öğrencilerinin Matematiksel Muhakemelerinin Bir Analizi

Abstract

Bu çalışmanın amacı, yedinci sınıf öğrencilerinin matematiksel muhakeme düzeylerini belirlemek ve bu yöndeki performanslarını ortaya koymaktır. Çalışma, Türkiye’nin bir ilindeki düşük ve orta sosyo-ekonomik düzeye sahip üç ortaokulunda öğrenim gören 167 yedinci sınıf öğrencisinin katılımıyla gerçekleştirilmiştir. Matematiksel Muhakeme Testi (MMT) geliştirilmiş ve veri toplama aracı olarak kullanılmıştır. Verilerin analizi için katılımcıların test puanları hesaplanmış ve hangi düzeyde oldukları belirlenmiştir. Bazı öğrencilerin testteki örnek bir soruya (Q7) ilişkin bazı cevapları doğrudan aktarılmış ve tartışılmıştır. Yapılan analiz sonucunda, katılımcıların yaklaşık yarısının (%45.5) matematiksel muhakemesinin orta, %27.5’inin ise düşük düzeyde olduğu tespit edilmiştir. Bu sonuçlar göz önüne alındığında, genel olarak öğrencilerin matematiksel muhakemelerinin orta ve düşük düzeyde olduğu söylenebilir. Matematiksel muhakemenin geliştirilebilmesi için öğrencilerin alışılmış klasik problemlerden ziyade muhakame yapmalarını gerektiren problemlerle uğraşmalarına imkân tanınmalıdır

Keywords

Matematiksel muhakeme, Yedinci sınıf öğrencileri, Muhakeme gerektiren problemler

References

• Amir, G. & Williams, J. (1999). Cultural influences on children’s probabilistic thinking. Journal of Mathematical Behavior, 18, 85-107.
• Baker, W. & Czarnocha, B. (2002). Written meta-cognition and procedural knowledge. Proceedings of the 2nd International Conference on the Teaching of Mathematics. University of Crete, Hersonissos Crete, Greece, 1-6 July 2002.
• Baki, A. (1998). Matematik öğretiminde işlemsel ve kavramsal bilginin dengelenmesi. Atatürk Üniversitesi 40. Kuruluş Yıldönümü Matematik Sempozyumu, Erzurum.
• Batanero, C. & Serrano, L. (1999). The meaning of randomness for secondary school students. Journal for Research in Mathematics Education, 30(5), 558-567.
• Camacho, J. E. D. (2002). Comparing declarative and procedural learning strategies under a problem based learning approach. Unpublished doctoral dissertation, United States International University, San Diego.
• Cohen, L., Manion, L., & Morrison, K. (2000). Research methods in education. London: Routledge Falmer.
• Curtis, J. (2004). A comparative analysis of walled lake consolidated schools’ mathematics assessment program and the state of Michigan’s educational assessment program. Unpublished master’s thesis, Wayne State University.
• Çalıkoğlu-Bali, G. (2003). Matematik öğretmen adaylarının matematik öğretiminde dile ilişkin görüşleri. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 25, 19-25.
• Çimen, E. E. (2008). Matematik öğretiminde, bireye “Matematiksel Güç” kazandırmaya yönelik ortam tasarımı ve buna uygun öğretmen etkinlikleri geliştirilmesi. Unpublished doctoral dissertation, Dokuz Eylül Üniversitesi, Eğitim Bilimleri Enstitüsü, İzmir.
• Diezmann, C. & English, L. D. (2001). Developing young children’s mathematical power. Roeper Review, 24(1), 11-13.
• English, L. D. (1998). Reasoning by analogy in solving comparison problems, Mathematical Cognition, 4(2), 125-146.
• Fischbein, E., Nello, M. S., & Marino, M. S. (1991). Factors affecting probabilistic judgments in children and adolescents. Educational Studies in Mathematics, 22, 523-549.
• Fischbein, E. & Schnarch, D. (1997). The evolution with age of probabilistic, intuitively based misconceptions. Journal of Research in Science Teaching, 28(1), 96-105.
• Francisco, J. M. & Maher, C. A. (2005). Conditions for promoting reasoning in problem solving: Insights from a longitudinal study. Journal of Mathematical Behavior, 24, 361–372.
• Frederiksen, N. (1984). Implications of cognitive theory for instruction in problem solving. Review of Educational Research, 54, 363-407.
• Gibbs, W. & Orton, J. (1994). Language and mathematics. In A. Orton & G. Wain (Eds.), Issues in teaching mathematics (pp. 95-116). London: Cassell.
• Gürbüz, R. (2010). The effect of activity based instruction on conceptual development of seventh grade students in probability. International Journal of Mathematical Education in Science and Technology, 41(6), 743-767.
• Gürbüz, R. & Birgin, O. (2012). The effect of computer-assisted teaching on remedying misconceptions: The case of the subject “probability”. Computers and Education, 58(3), 931-941.
• Gürbüz, R. & Erdem, E. (2014). Matematiksel ve olasılıksal muhakeme arasındaki ilişkinin incelenmesi: 7. sınıf örneği. Adıyaman Üniversitesi Sosyal Bilimler Enstitüsü Dergisi, 7(16), 205-230.
• Henningsen, M. & Stein, M. K. (1997). Mathematical tasks and student cognition: classroom based factors that support and ınhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28(5), 524-549.
• İşleyen, T. & Işık, A. (2003). Conceptual and procedural learning inmathematics. Journal of The Korea Society of Mathematical Education SeriesD: Research in Mathematical Education, 7(2), 91–99.
• Kramarski, B. A., Mevarech, Z. R., & Lieberman A. (2001). Effects of multilevel versus unilevel metacognitive training on mathematical reasoning. Journal of Educational Research, 94(5), 292-300.
• Lansdell, J. M. (1999). Introducing young children to mathematical concepts: Problems with new terminology. Educational Studies, 25(3), 327-333.
• Lithner, J. (2000). Mathematical reasoning in task solving. Educational Studies in Mathematics, 41, 165- 190.
• Lecoutre, M. P. (1992). Cognitive models and problem spaces in “purely random” situations. Educational Studies in Mathematics, 23, 557-568.
• Lithner, J. (2008). A research framework for creative and imitative reasoning. Educational Studies in Mathematics, 67, 255-276.
• Mandacı-Şahin, S. (2007). 8. Sınıf öğrencilerinin matematik gücünün belirlenmesi. Unpublished doctoral dissertation Karadeniz Teknik Üniversitesi, Fen Bilimleri Enstitüsü, Trabzon.
• MEB (2009). İlköğretim matematik dersi 1-5. sınıflar öğretim programı. T.C. Milli Eğitim Bakanlığı. Talim ve Terbiye Kurulu Başkanlığı, Ankara.
• MEB (2013). Ortaokul matematik dersi (5, 6, 7 ve 8. Sınıflar) öğretim programı. T.C. Milli Eğitim Bakanlığı. Talim ve Terbiye Kurulu Başkanlığı, Ankara.
• Moore, R. C. (1994). Making the transition to formal proof. Educational Studies in Mathematics, 27, 249- National Council of Teachers of Mathematics [NCTM] (1989). Curriculum and evaluation standards for school mathematics. Reston: Virginia.
• National Council of Teachers of Mathematics [NCTM] (2000). Principles and standards for school mathematics. Reston, VA.
• Nilsson, P. (2007). Different ways in which students handle chance encounters in the explorative setting of a dice game. Educational Studies in Mathematics, 66, 293-315.
• Nilsson. P. (2009). Conceptual variation and coordination in probability reasoning. Journal of Mathematical Behavior, 28, 247-261.
• Orton, A. & Frobisher, L. (1996). Insights into teaching mathematics. London: Cassell.
• Pilten, P. (2008). Üstbiliş stratejileri öğretiminin ilköğretim beşinci sınıf öğrencilerinin matematiksel muhakeme becerilerine etkisi. Unpublished doctoral dissertation Gazi Üniversitesi, Eğitim Bilimleri Enstitüsü, Ankara.
• Pratt, D. (1998). The construction of meanings in and for a stochastic domain of abstraction. Unpublished doctoral dissertation, Institue of Education, University of London.
• Raiker, A. (2002). Spoken language and mathematics. Cambridge Journal of Education, 32(1),45- 60.
• Rittle-Johnson, B. & Koedinger, K. R. (2002). Comparing instructional strategies for integrating conceptual and procedural knowledge. In D. S. Mewborn, P. Sztajin, D. Y. White, H. G. Wiegel, R. L.
• Bryant, & K. Nooney (Eds.), Proceedings of the 24th Annual Meeting of the North American Chapters of the International Group for the Psychology of Mathematics Education (pp. 969-978). Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.
• Russell, S. J. (1999). Mathematical reasoning in the middle grades. In L. V. Stiff and F. R. Curcio (Eds.), Developing mathematical reasoning in grades K-12 (pp. 1–12). Reston, VA: National Council of Teachers of Mathematics.
• Schoenfeld, A. H. (1985). Mathematical problem solving. Orlando: Academic Press.
• Schroeder, T. L. (1993). Mathematical connections: two cases from an evaluation of students’ mathematical problem solving, Annual Meeting of NCTM, Seattle, Mart.
• Soylu, Y. & Soylu, C. (2006). Matematik derslerinde başarıya giden yolda problem çözmenin rolü. İnönü Üniversitesi Eğitim Fakültesi Dergisi, 7(11), 97-111.
• Sparkes, J. J. (1999). NCTM’s vision of mathematics assessment in the secondary school: Issues and challenges. Unpublished Master’s Thesis. Memorial University of Newfoundland.
• Toulmin, S., Rieke, R., & Janik, A. (1984). An introduction to reasoning (Second Edition). Macmillan Publishing Co., Inc. New York.
• Umay, A. (2003). Matematiksel muhakeme yeteneği. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 24, 234-243.
• Umay, A. & Kaf, Y. (2005). Matematikte kusurlu akıl yürütme üzerine bir çalışma. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 28, 188-195.
• White, C. S., Alexander, P. A., & Daugherty, M. (1998). The relationship between young children’s analogical reasoning and mathematical learning. Mathematical Cognition, 4(2), 103-123.