### The Effect of a Learning Environment Designed Using Different Teaching Methods on Mathematical Reasoning and Mathematics Attitude

#### Abstract

The purpose of this research is to determine the effect of a learning environment enriched by using different teaching methods on mathematical reasoning and mathematics attitude. The study was carried out with the participation of 27 seventh-grade students who study at a state middle school randomly selected from a provincial center in Turkey. Instruction of fractions and integers was performed in the designed learning environment for 8 weeks (32 lesson hours in total) by using educational games, concrete materials, cartoons, computer-aided applications, and associating with daily life and discussing in cooperative heterogeneous groups. The data were obtained from students’ responses to the Mathematical Reasoning Test (MRT) and the Mathematical Attitude Scale (MAS) on pretest and posttest. Responses to MRT and MAS were analyzed using the Wilcoxon Signed Ranks Test. Analyzes have shown that the intervention in this environment improves students’ mathematical reasoning significantly and improves their attitudes towards mathematics to a significant degree. It has been observed that through open-ended problems presented in cooperative groups, instead of focusing on the answer options, students tried to provide a solution, explaining the solution, discussing it with their group friends, developing different strategies and thus they were found to have more mathematical reasoning. This result underscores the need to use open-ended problems in determining, evaluating, and improving mathematical reasoning.

#### Keywords

#### Full Text:

PDF (Türkçe)#### References

Aşkar, P. (1986). Matematik dersine yönelik tutumu ölçen likert tipi bir ölçeğin geliştirilmesi. Eğitim ve Bilim, 11(62), 31-36.

Ball, D., & Bass, H. (2003). Making mathematics reasonable in school. In J. Kilpatrick,W. Martin, & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 27–44). Reston, VA: NCTM.

Behr, M. J., Lesh, R., Post, T., & Silver, E. A. (1983). Rational number concepts. In R. Lesh, & M. Landau (Eds.), Acqui-sitions of mathematics concepts and processes (pp. 92–126). New York: Academic Press.

Clements, D. H. (2000). 'Concrete' manipulatives, concrete ideas. Contemporary Issues in Early Childhood, 1(1), 45-60.

Cobb, P., Yackel, E., & Wood, T. (1992). Interaction and learning in mathematics classroom situations. Educational Studies in Mathematics, 23, 99 -122.

Erdem, E. (2011). İlköğretim 7. sınıf öğrencilerinin matematiksel ve olasılıksal muhakeme becerilerinin incelenmesi. Yüksek Lisans Tezi, Adıyaman Üniversitesi Fen Bilimleri Enstitüsü, Adıyaman.

Erdem, E. & Gürbüz, R. (2015). An analysis of seventh-grade students’ mathematical reasoning. Çukurova University Faculty of Education Journal, 45(1), 123-142.

Fischbein, E. (1987). Intuition in science and mathematics: An educational approach. Dordrecht: Reidel.

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 lon-gitudinal study. Journal of Mathematical Behavior, 24, 361–372.

Frederiksen, N. (1984). Implications of cognitive theory for instruction in problem solving. Review of Educational Re-search, 54, 363-407.

Gürbüz, R., Erdem, E. & Uluat, B (2014). Reflections from the process of game-based teaching of probability. Croatian Journal of Education, 16(Sp. Ed. 3), 109-131.

Hartman, H. J. (2001). Developing students’ meta-cognitive knowledge and skills. In H. J. Hartman (Ed.), Metacogni-tion in learning and instruction (pp. 33–68). Dordrecht, The Netherlands: Kluwer Academic.

Hativa, N. & Cohen, D. (1995). Self learning of negative number concepts by lower division elementary students thro-ugh solving computer-provided numerical problems. Educational Studies in Mathematics, 28(2), 401-431.

Henningsen, M. & Stein, M. K. (1997). Mathematical tasks and student cognition: classroom based factors that sup-port and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28(5), 524-549.

Howell, T. H. & Wilson, P. H. (2014). The role of teachers’ questions in support of students’ articulation of their mat-hematical reasoning. Paper presented in proceedings of the 41the Annual Meeting of the Research Council on Mat-hematics Learning (pp. 105-112).

Inoue, N. (2008). Minimalism as a guiding principle: Linking mathematical learning to everyday knowledge. Mathem-matical Thinking and Learning, 10(1), 36-67.

Kamii, C. & Rummelsburg, J. (2008). Arithmetic for first graders lacking number concepts. Teaching Children Mathe-matics, 14(7), 389–394.

Kramarski, B. & Zeichner, O. (2001). Using technology to enhance mathematical reasoning: Effects of feedback and self-regulation learning. Educational Media International, 38(2-3), 77-82.

Kramarski, B. & Zoldan, S. (2008). Using errors as springboards for enhancing mathematical reasoning with three me-tacognitive approaches. The Journal of Educational Research, 102(2), 137-151.

Leighton, J. P. (2003). Defining and describing reasoning. In J. P. Leighton and R. J. Sternberg (Eds.), The nature of rea-soning. New York, NY: Cambridge.

Lithner, J. (2008). A research framework for creative and imitative reasoning. Educational Studies in Mathematics, 67, 255-276.

McNeil, N. M. & Jarvin, L. (2007). When theories don’t add up: Disentangling the manipulatives debate. Theory into Practice, 46(4), 309-316.

Maher, C. A. & Davis, R. B. (1995). Children's explorations leading to proof. In C. Hoyles and L. Healy (Eds.), Justif-ying and proving in school mathematics (pp. 87-105). Mathematical Sciences Group, Institute of Education, Uni-versity of London, London.

Mason, J. (2001). Questions about mathematical reasoning and proof in schools. Opening address to QCA Conferen-ce, UK.

Mata-Pereira, J. & da Ponte, J. P. (2017). Enhancing students’ mathematical reasoning in the classroom: teacher acti-ons facilitating generalization and justification. Educational Studies in Mathematics, 96, 169-186.

MEB (2013). Ortaokul matematik dersi (5, 6, 7 ve 8. Sınıflar) öğretim programı. T.C. Milli Eğitim Bakanlığı. Talim ve Terbiye Kurulu Başkanlığı, Ankara.

Moss, J. & Case, R. (1999). Developing children’s understanding of the rational numbers: a new model and experimen-tal curriculum. Journal for Research in Mathematics Education, 30(2), 122 – 147.

Moyer, P. S. (2001). Are we having fun yet? How teachers use manipulatives to teach mathematics. Educational Stu-dies in Mathematics, 47, 175-197.

Nahiley, J., Stephens, J., & Sutherland, J. (1982). Cartoons: When they are effective. Journal of Extansion. 3-4, 531-540.

National Council of Teachers of Mathematics [NCTM] (1989). Curriculum and evaluation standards for school mat-hematics. Reston: Virginia.

National Council of Teachers of Mathematics [NCTM] (2000). Principles and standards for school mathematics. Res-ton, VA.

Nisbet, S. (2006). Mathematics without attitude. Keynote address to the Annual Conference of the Queensland Asso-ciation of Mathematics Teachers, Brisbane.

Olson, J. (2007). Developing students’ mathematical reasoning through games. Teaching Children Mathematics, 13(9), 464-471.

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.

Pratt, D. (2000). Making sense of the total of two dice. Journal for Research in Mathematics Education, 31(5), 602-625.

Prensky, M. (2001). Fun, play and games: what makes games engaging. In M. Prensky (Ed.), Digital game-based lear-ning. New York: McGraw-Hill

Ragasa, C. Y. (2008). A comparison of computer-assisted instruction and the traditional method of teaching basic statistics. Journal of Statistics Education, 16(1), 1-10.

Raphael, D. & Wahlstrom, M. (1989). The influence of instructional aids on mathematics achievement. Journal for Research in Mathematics Education, 20, 173–190.

Ross, K. A. (1998). Doing and proving: The place of algorithms and proofs in school mathematics. The American Mat-hematical Monthly, 105(3), 252-255.

Schliemann, A. D. & Carraher, D. W. (2002). The evolution of mathematical reasoning: Everyday versus idealized understandings. Developmental Review, 22(2), 242-266.

Stafylidou, S. & Vosniadou, S. (2004). The development of students’ understanding of the numerical value of fracti-ons. Learning and Instruction, 14, 503-518.

Swan, M. (2011). Improving reasoning: analysing alternative approaches. Retrieved from http://nrich.maths.org/7812/index

Şengül, S. & Dereli, M. (2013). Karikatürle öğretimin 7. sınıf öğrencilerinin tam sayılar konusundaki başarılarına ve kalıcılık düzeylerine etkisi. The Journal of Academic Social Science Studies, 6(7), 973-1003.

Thompson, P. W. (1992). Notations, conventions and constraints: Contributions to effective uses of concrete materials in elementary mathematics. Journal for Research in Mathematics Education, 23(2), 123-147.

Toulmin, S., Rieke, R., & Janik, A. (1984). An introduction to reasoning (Second Edition). New York: Macmillan Pub-lishing Co.

Uğurel, I. & Moralı, S. (2006). Karikatürler ve matematik öğretiminde kullanımı. Milli Eğitim Dergisi, 170, 32-47.

Umay, A. (2003). Matematiksel muhakeme yeteneği. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 24, 234-243.

Vygotsky, L. S. (1978). Mind and society: The development of higher mental processes. Cambridge, MA: Harvard University Press.

Williams, C. K. & Kamii, C. (1986). How do children learn by handling objects? Young Children, 42(1), 23–46.

Yackel, E. & Hanna, G. (2003). Reasoning and proof. In J. Kilpatrick, G. Martin and D. Schifter (Eds.), A research com-panion to principles and standards for school mathematics (pp. 227–236). Reston, VA: National Council of Teac-hers of Mathematics.

Yankelewitz, D., Mueller, M., & Maher, C. A. (2010). A task that elicits reasoning: A dual analysis. The Journal of Mat-hematical Behavior, 29, 76-85.

DOI: https://doi.org/10.24106/kefdergi.3056

### Refbacks

- There are currently no refbacks.

indexed by TR-DİZİN, DOAJ, SOBİAD

Kastamonu Eğitim'de yayınlanan tüm içerik ve makaleler "Creative Commons Alıntı 4.0 Uluslararası Lisansı" ile lisanslanmıştır.