AN INVESTIGATION ON RELATIONSHIP BETWEEN MATHEMATICAL AND PROBABILISTIC REASONING: THE CASE OF SEVENTH GRADE

Year 2014, Issue: 16, 205 - 230, 01.04.2014

Ramazan Gürbüz Emrullah Erdem

https://doi.org/10.14520/adyusbd.748

Cited By: 3

Abstract

The current study aims at determining the relationship between seventh graders’ mathematical and probabilistic reasoning. The study was carried out with 167 seventh-grade students. As data collection tool, “Mathematical Reasoning Test (MRT)” and “Probabilistic Reasoning Test (PRT)” were developed and used. In analysing the data, Pearson's correlation coefficient (r) between participants’ scores of each test was computed. Some sample responses of the students regarding some questions in the test were also presented directly. Analysis shows that there is a significant correlation between seventh graders’ mathematical reasoning and probabilistic reasoning.

Keywords

Mathematical reasoning, probabilistic reasoning, mathematical reasoning-probabilistic reasoning rela

MATEMATİKSEL VE OLASILIKSAL MUHAKEME ARASINDAKİ İLİŞKİNİN İNCELENMESİ: 7. SINIF ÖRNEĞİ

Abstract

Bu çalışmanın amacı, 7. sınıf öğrencilerinin matematiksel ve olasılıksal muhakemeleri arasındaki ilişkiyi belirlemektir. Çalışma, 167 yedinci sınıf öğrencisinin katılımıyla gerçekleştirilmiştir. Veri toplamak amacıyla iki test [Matematiksel Muhakeme Testi (MMT), Olasılıksal Muhakeme Testi (OMT)] geliştirilmiş ve kullanılmıştır. Öğrencilerin her bir testten aldıkları puanlar arasındaki ilişkiyi belirlemek için Pearson korelasyon katsayısı (r) hesaplanmıştır. Ayrıca her bir testteki bazı sorulara ilişkin örnek öğrenci cevapları doğrudan aktarılarak tartışılmıştır. Yapılan analizler sonucunda, 7. sınıf öğrencilerinin matematiksel muhakemeleriyle olasılıksal muhakemeleri arasında doğru bir ilişki olduğu saptanmıştır.

Keywords

Matematiksel muhakeme, olasılıksal muhakeme, matematiksel muhakeme-olasılıksal muhakeme ilişkisi, yedinci sınıf öğrencileri

References

• Ashline, G. & Frantz, M. (2009). “Proportional reasoning and probability”. Synergy Learning, Nov/Dec: 8-10.
• Batanero, C., Serrano, L., & Garfield, J. (1996). Heuristics and biases in secondary school students’ reasoning about probability. In the Proceedings of the International Meeting of the Psychology of Mathematics Education Meeting, Valencia, Spain.
• Clarke, D. (1998). Assessment alternatives in mathematics. Mathematics Curriculum and Teaching Project, Canberra, Australia.
• Çakan, M. (2004). “Öğretmenlerin ölçme-değerlendirme uygulamaları ve yeterlik düzeyleri: ilk ve ortaöğretim”. Ankara Üniversitesi Eğitim Bilimleri Fakültesi Dergisi, 37(2): 99-114.
• Demir, S. & Bozkurt, A. (2011). “İlköğretim matematik öğretmenlerinin teknoloji entegrasyonundaki öğretmen yeterliklerine ilişkin görüşleri”. İlköğretim Online, 10(3): 850-860.
• Diezmann, C., & English, L. D. (2001). “Developing young children’s mathematical power”. Roeper Review, 24(1): 11-13.
• Dursun, Ş. & Dede Y. (2004). Öğrencilerin matematikte başarısını etkileyen faktörler: Matematik öğretmenlerinin görüşleri bakımından. Gazi Eğitim Fakültesi Dergisi, 24(2), 217-230.
• English, L. D. (1998). “Reasoning by analogy in solving comparison problems”. Mathematical Cognition, 4(2): 125-146.
• Erdem, E. & Soylu, Y. (2013). “Öğretmen adaylarının KPSS ve alan sınavına ilişkin görüşleri”. Çankırı Karatekin Üniversitesi Sosyal Bilimler Enstitüsü Dergisi, 4(1): 223-2
• Fischbein, E. (1975). The intuitive sources of probabilistic thinking in children. Dordrecht, The Netherlands: Reidel.
• Fischbein, E., & Schnarch, D. (1997). “The evolution with age of probabilistic, intuitively based misconceptions”. Journal of Research in Science Teaching, 28(1): 9610
• Fraenkel, J. R., Wallen, N. E., & Hyun, H. H. (2012). How to design and evaluate research in education (8th ed.). New York: McGraw Hill.
• Gal, I. & Baron, J. (1996). “Understanding repeated simple choices”. Thinking and Reasoning, 2(1): 1-18.
• Garfield, J. & delMas, R. (1989). Reasoning about chance events: Assessing and changing students' conceptions of probability. Proceedings of the 11th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Volume 2, pp. 189-195). Rutgers University Press.
• Garfield, J. & Ben-Zvi, D. (2007). “How students learn statistics revisited: a current review of research on teaching and learning statistics”. International Statistical Review, 75(3): 372–396.
• Graham, A. (1994). Statistics: An introduction. London: Hodder & Stoughton.
• Greer, B. (2001). “Understanding probabilistic thinking: The legacy of Efrahim Fischbein”. Educational Studies in Mathematics, 45: 15-33.
• 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., Çatlıoğlu, H. Birgin, O., & Erdem, E. (2010). “An investigation of fifth grade students’ conceptual development of probability through activity based instruction: A quasi-experimental study”. Educational Sciences: Theory & Practice, 10(2): 1021–1069.
• 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. & Gülburnu, M. (2013). “Sınıf öğretmenlerinin matematik yeterliklerini etkileyen faktörlerin incelenmesi”. Ahi Evran Üniversitesi Kırşehir Eğitim Fakültesi Dergisi (KEFAD), 14(2): 255-272.
• Gürbüz, R., Erdem, E., & Fırat, S. (2014). “The Effect of activity-based teaching on remedying the probability-related misconceptions: A cross-age comparison”. Creative Education, 5(1): 18-30.
• Hacıömeroğlu, G. & Şahin, Ç. (2011). “Sınıf öğretmeni adaylarının uygulama öğretmenleri hakkındaki özel alan yeterlikleri algısı”. Mustafa Kemal Üniversitesi Sosyal Bilimler Enstitüsü Dergisi, 8(15): 473-486.
• Henningsen, M. & Stein, M. K. (1997). “Mathematical tasks and student cognition: classroom based factors that support and inhibit high-level mathematical thinking and reasoning”. Journal for Research in Mathematics Education, 28(5): 524-549.
• Holyoak, K. J. & Morrison, R. G. (2005). Thinking and reasoning: A reader’s guide. In K. J. Holyoak & R. G. Morrison (Eds.), The Cambridge handbook of thinking and reasoning (pp. 1–9). New York, NY: Cambridge University Press.
• Jones, G. A., Thornton, C. A., Langrall, C. W., & Tarr, J. E. (1999). “Understanding students' probabilistic reasoning”. Developing mathematical reasoning in grades K-12, 61: 146.
• Kahneman, D. & Tversky, A. (1972). “Subjective probability: A judgment of representativeness”. Cognitive Psychology, 3: 430-454.
• Korkmaz, A. (2005). “Olasılık kuramının doğuşu”. Ankara Üniversitesi SBF Dergisi, 60(2): 171-19
• 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.
• Lithner, J. (2000). “Mathematical reasoning in task solving”. Educational Studies in Mathematics, 41: 165-190.
• 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.
• Memnun, D. S. (2008). “Olasılık kavramlarının öğrenilmesinde karşılaşılan zorluklar, bu kavramların öğrenilememe nedenleri ve çözüm önerileri”. İnönü Üniversitesi Eğitim Fakültesi Dergisi, 9(15): 89–101.
• 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.
• Nickerson, R. S. (2004). Cognition and chance: the psychology of probabilistic reasoning. Lawrence Erlbaum Associates, Publishers Mahwah, New Jersey, London.
• Peresini, D. & Webb, N. (1999). Analyzing mathematical reasoning in students’ responses across multiple performance assessment tasks. Developing Mathematical Reasoning in Grades K-12 / Lee V. Stiff, 1999 Yearbook Editor, National Council Of Teachers Of Mathematics, Reston, Virginia.
• Polaki, M. V. (2002). “Using instruction to identify key features of Basotho elementary students’ growth in probabilistic thinking”. Mathematical Thinking and Learning, 4(4): 285-313.
• Rosenholtz, S. J. (1985). “Political myth about education reform: Lessons from research on teaching”. PhiDelta Kappan, 66(5): 349-355.
• Schoenfeld, A. H. (1985). Mathematical problem solving. Orlando: Academic Press. Shaughnessy, J. M. (1992). Research in probability and statistics: Reflections and directions. In, D.A. Grouws (Ed.) Handbook on research on mathematics teaching and learning (pp. 465-494). New York: Macmillan.
• Suzuki, K. (1997). Cognitive constructs measured in word problems: a comparison of students’ responses in performance-based tasks and multiple choice tasks for reasoning. Annual Meeting of the American Educational Research Association, Chicago, Mart.
• Umay, A. (2003). “Matematiksel muhakeme yeteneği”. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 24: 234-243.
• 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.