VIEWS OF TEACHERS AND 7TH GRADERS ON AN ENRICHED LEARNING ENVIRONMENT DESIGNED FOR IMPROVING MATHEMATICAL REASONING

Emrullah Erdem, Yasin Soylu

Abstract


The purpose of the present study is to reveal the views of middle school mathematics teachers and students regarding a learning environment designed around different methods for improving Mathematical Reasoning (MR). The study was conducted with 27 seventh grade students studying at a randomly selected state school in a city center in Turkey, the teacher who instructs these students’ mathematics courses, and another mathematics teacher employed at the school. For eight weeks (32 class hours in total), the students were instructed on the subjects of fractions and integers through educational games, concrete materials, cartoons, computer-assisted applications, association with daily life, and collaborative group argumentation. Data for the study were collected through interviews conducted with participants, observations of the teachers, and diaries kept by the students throughout the implementation process. The data were analyzed using a content analysis technique. Evidence was found that this environment improved the MR of students, provided effective and permanent learning, and increased attendance at lessons, but the teachers and the students also agreed that it had different effects in terms of classroom management such as noise, control over the classroom, lack of exam marks, not taking notes, time problems, and effects on students’ success in their central exams. It is also possible to say that, with the help of open-ended high-level problems, students tried to provide solutions instead of focusing on choices for answers, and thus they used more MR skill.

Article visualizations:

Hit counter


Keywords


design of learning environment, mathematical reasoning, open-ended problems, views of middle school mathematics teachers and seventh-graders

Full Text:

PDF

References


Akkuzu, N. (2014). The role of different types of feedback in the reciprocal interaction of teaching performance and self-efficacy belief. Australian Journal of Teacher Education, 39(3), 36-66.

Artzt, A. & Yaloz-Femia, S. (1999). Mathematical reasoning during small-group problem-solving. In L. Stiff and F. Curio (eds.), Developing Mathematical Reasoning in Grades K-12: 1999 Yearbook (pp. 115–126), National Council of Teachers of Mathematics, Reston, VA.

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.

Bergqvist, T., & Lithner, J. (2012). Mathematical reasoning in teachers’ presentations. The Journal of Mathematical Behavior, 31(2), 252-269.

Black, P. & Wiliam, D. (1998). Assessment and classroom learning. Assessment in Education, 5(1), 7-74.

Booker, G. (2000). The maths game: using instructional games to teach mathematics. Wellington, NZ: New Zealand Council for Educational Research.

Bragg, L. (2007). Students’ conflicting attitudes towards games as a vehicle for learning mathematics: A methodological dilemma. Mathematics Education Research Journal, 19(1), 29–44.

Bragg, L. A., Herbert, S., Loong, E. Y. K., Vale, C., & Widjaja, W. (2016). Primary teachers notice the impact of language on children’s mathematical reasoning. Mathematics Education Research Journal, 28(4), 523-544.

Briscoe, C. & Stout, D. (2001). Prospective elementary teachers’ use of mathematical reasoning in solving a lever mechanics problem. School Science and Mathematics, 101(5), 228-235.

Castro, C. S. (1998). Teaching probability for conceptual change. Educational Studies in Mathematics, 35, 233-254.

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

Crook, T. J. (1988). The impact of classroom evaluation practice on student. Review of Educational Research, 58(4), 438-481.

Çilenti, K. (1988). Eğitim teknolojisi ve öğretim. Ankara: Kadıoğlu Matbaası.

Diezmann, C. & English, L. D. (2001). Developing young children’s mathematical power. Roeper Review, 24(1), 11-13.

Ellis, A., Özgür, Z. & Reiten, L. (2018). Teacher moves for supporting student reasoning. Mathematics Education Research Journal, https://doi.org/10.1007/s13394-018-0246-6

English, L. D. (1998). Reasoning by analogy in solving comparison problems. Mathematical Cognition, 4(2), 125-146.

Erdem, E. (2011). An investigation of the seventh grade students’ mathematical and probabilistic reasoning skills (MA Thesis). Adıyaman University, Adıyaman, Turkey.

Erdem, E., Gürbüz, R., & Duran, H. (2011). An investigation of mathematics used in daily life from past to present: theory out practice in. Turkish Journal of Computer and Mathematics Education, 2, 232–246.

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

Erdem, E. (2015). The effect of enriched learning environment on mathematical reasoning and attitude (Doctoral dissertation). Ataturk University, Erzurum, Turkey.

Erdem, E., Fırat, T., & Gürbüz, R. (2019). Improving mathematical reasoning and mathematics attitude of disadvantaged children in rural regions. Journal of Computer and Education Research, 7(14), 673-697.

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

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.

Gardner, H. (1997). Multiple intelligences as a partner in school improvement. Educational Leadership, 55(1), 20-21.

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(2), 401-431.

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.

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

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

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

Kezar, A. (2001). Theory of multiple intelligences: implications for higher education, Innovative Higher Education, 26(2), 141-154.

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.

Kuhn, D., Shaw, V., & Felton, M. (1997). Effects of dyadic interaction on argumentative reasoning. Cognition and Instruction, 15, 287–315.

Kumar, R. & Lightner, R. (2007). Games as an interactive classroom technique: perceptions of corporate trainers, college instructors and students. International Journal of Teaching and Learning in Higher Education, 19(1), 53–63.

Lach, T. & Sakshaug, L. (2004). The role of playing games in developing algebraic reasoning, spatial sense and problem-solving. Focus on Learning Problems in Mathematics, 26(1), 34-42.

Lee, M. Y. (2017). Pre-service teachers’ flexibility with referent units in solving a fraction division problem. Educational Studies in Mathematics, 96(3), 327-348.

Lithner, J. (2003). Students’ mathematical reasoning in university textbook exercises. Educational Studies in Mathematics, 52, 29–55.

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

Lithner, J. (2017). Principles for designing mathematical tasks that enhance imitative and creative reasoning. ZDM, 49(6), 937-949.

Ma, L. (1999). Knowing and teaching elementary mathematics: teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Erlbaum.

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

Mata-Pereira, J., & da Ponte, J. P. (2017). Enhancing students’ mathematical reasoning in the classroom: teacher actions facilitating generalization and justification. Educational Studies in Mathematics, 96(2), 169-186.

McCoy, L. P. (1996). Computer-based mathematics learning. Journal of Research Computing in Education, 28(4), 438-460.

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

Ministry of National Education (MNE). (2009). Middle school mathematics 6–8. classes teaching program. Ankara, Turkey: Head Council of Education and Morality.

Ministry of National Education (MNE). (2013). Middle school mathematics 5–8. classes teaching program. Ankara, Turkey: Head Council of Education and Morality.

Miles, M. B. & Huberman, A. M. (1994). An expanded sourcebook: qualitative data analysis (2nd Editon). Thousand Oaks, CA: Sage.

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

Moyer, P. S., Bolyard, J. J., & Spikell, M. M. (2002). What are virtual manipulatives? Teaching Children Mathematics, 8, 372-377.

Mueller, M. and Yankelewitz, D. (2014). Fallacious argumentation in student reasoning: Are there benefits? European Journal of Science and Mathematics Education, 2(1), 27-38.

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.

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

Özdemir, E. M., Duru, A., & Akgün, L. (2005). Two or three dimensional thinking: visualization of some identities with two and three dimensional geometrical figures. Kastamonu Education Journal, 13(2), 527-540.

Özpolat, V. (2013). The place of student-centered approach in teachers’ occupational priorities. National Education Journal, 200, 5-27.

Pape, S. J., Bell. C. V., & Yetkin, I. E. (2003). Developing mathematical thinking and self-regulated learning: A teaching experiment in a seventh-grade mathematics classroom. Educational Studies in Mathematics 53, 179-202.

Pijls, M., Dekker, R., & Van Hout-Wolters, B. (2007). Reconstruction of a collaborative mathematical learning process. Educational Studies in Mathematics, 65, 309-329.

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 learning. 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, P. A. & Braden, J. P. (1991). The effects of token reinforcement versus cognitive behavior modification on learning‐disabled students’ math skills. Psychology in the Schools, 28(3), 247-256.

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

Schoenfeld, A. H. (1985). Mathematical problem-solving. Orlando: Academic Press.

Slavin, R. E. (1987). Cooperative learning and cooperative school. Educational Leadership, 45, 7–13.

Suzuki, K. (1997). Cognitive constructs measured in word problems: A comparison of students’ responses in performance-based tasks and multiple-choice tasks for reasoning. Paper presented at the Annual Meeting of the American Educational Research Association, Chicago

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

Şengül, S. & Dereli, M. (2013). The effects of teaching integers using cartoons on 7th grade students’ achievements and retention levels. 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.

Tirosh, D. (2000). Enhancing prospective teachers’ knowledge of children’s conceptions: the case of division of fractions. Journal for Research in Mathematics Education, 31(1), 5-25.

Umay, A. (2003). Mathematical reasoning ability. Hacettepe University Journal of Education, 24, 234-243.

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

Yackel, E. Cobb, P., & Wood, T. (1999). The interactive constitution of mathematical meaning in one second grade classroom: An illustrative example. Journal of Mathematical Behavior, 17(4), 469-488.

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

Yaman, H. (2009). Teachers’ views on the applicability of the Turkish course curriculum in crowded primary classrooms. Educational Sciences: Theory & Practice, 9(1), 349-359.

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

Yin, R. K. (2011). Qualitative research from start to finish. New York: The Guilford Press.




DOI: http://dx.doi.org/10.46827/ejes.v7i11.3335

Refbacks

  • There are currently no refbacks.


Copyright (c) 2020 Emrullah Erdem, Yasin Soylu

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Copyright © 2015-2023. European Journal of Education Studies (ISSN 2501 - 1111) is a registered trademark of Open Access Publishing Group. All rights reserved.

This journal is a serial publication uniquely identified by an International Standard Serial Number (ISSN) serial number certificate issued by Romanian National Library (Biblioteca Nationala a Romaniei). All the research works are uniquely identified by a CrossRef DOI digital object identifier supplied by indexing and repository platforms. All authors who send their manuscripts to this journal and whose articles are published on this journal retain full copyright of their articles. All the research works published on this journal are meeting the Open Access Publishing requirements and can be freely accessed, shared, modified, distributed and used in educational, commercial and non-commercial purposes under a Creative Commons Attribution 4.0 International License (CC BY 4.0).