Teaching through whole-classroom discussions as an efficient tool for improving mathematical reasoning abilities of students

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Research Paper 01/03/2015
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Teaching through whole-classroom discussions as an efficient tool for improving mathematical reasoning abilities of students

Golamali Ahmady, Neda Nakhostin-Ruhi
J. Bio. Env. Sci.6( 3), 522-529, March 2015.
Certificate: JBES 2015 [Generate Certificate]

Abstract

Our purpose of conducting this research is to study the impact of promoting whole-class discussions among students on their mathematical reasoning abilities. In this manuscript, we report an experiment within teaching through whole-class discussions by using open-ended problems in classroom provided an efficient tool for improving students’ reasoning abilities. A school was randomly selected among high schools and two classes were randomly selected among grade 8th classes of this school. These classes were assigned into one of two teaching methods: whole-class discussion (the experimental group, 27 students) and traditional instruction (the control group, 30 students). Students in both groups were instructed same topics and learning (materials formal booklet of 8th grade) by the same experienced teacher. Analysis of covariance showed a significant interactive and positive effect of experimental method on improving students reasoning abilities.

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Ball DL. 1993. With an eye on the mathematical horizon: Dilemmas of teaching elementary school mathematics. Elementary School Journal 93(4), 373–397.

Berkowitz M, Gibbs J, Broughton J. 1980. The relation of moral judgment state disparity to developmental effects of peer dialogues. Merrill-Palmer Quarterly 26, 341–357.

Blanton ML, Stylianou DA. 2014. Understanding the role of transactive reasoning in classroom discourse as students learn to construct proofs. Journal of Mathematical Behavior 34, 76–98.

Brandt B, Tatsis K. 2009. Using Goffman’s concepts to explore collaborative interaction processes in elementary school mathematics. Research in Mathematics Education 11(1), 39-56.

Brantlinger A. 2014. Critical mathematics discourse in a high school classroom: examining patterns of student engagement and resistance. Educational Studies in Mathematics 85, 201–220.

Cazden CB. 2001. Classroom discourse: The language of teaching and learning (2nd ed.). Portsmouth, NH: Heinemann.

Chapin SH, O’Connor C, Anderson NC. 2003. Classroom discussions: Using math talk to help students learn. Math Solutions Publications, Sausalito, CA.

Clark KK, Jacobs J, Pittman ME, Borko H. 2005. Strategies for building mathematical communication in the middle school classroom: Modeled in professional development, Implemented in the classroom. Current Issues in Middle Level Education 11(2), 1-12.

Johnston I. 2002. Essays and Arguments. British Colombia, Malaspina.

Kilpatrick J, Swafford J, Findell B. 2001. Adding it up: Helping children learn mathematics. Washington, National Academy Press 115-155.

Knuth E, Peressini D. 2001. Unpacking the nature of discourse in mathematics classrooms. The Mathe-matics Teacher 6, 320–325.

Kruger AC. 1993. Peer collaboration: Conflict, cooperation or both? Social Development 2, 165–182.

Lampert M. 2001. Teaching problems and the problems of teaching. New Haven, Yale University Press.

Leikin R, Dinur S. 2007. Teacher flexibility in mathematical discussion. Journal of Mathematical Behavior 26, 328–347.

Manoucheri A, St John S. 2006. From classroom discussions to group discourse. Mathematics Teacher 99(8), 544-552.

Martin WG, Kasmer L. 2009. Reasoning and sense making In teaching children mathematics, NCTM 16(5), 284.

Miyazaki M. 2000. Levels of proof in lower secondary school mathematics. Educational Studies in Mathematics 41, 47–68.

Muller M, Maher C. 2009. Learning to reason in an informal Math After-School Program. Mathematics Education Research Journal 21(3), 109-119.

NCTM. 2000. Principles and Standards for School Mathematics. The National Council of Teachers of Mathematics, Inc., Reston, USA.

Nicol C. 1999. Learning to teach mathematics: questioning, listening, and responding. Educational Studies in Mathematics 37, 45-66.

Osana H, Lacroix G, Tucker BJ, Desrosiers C. 2006. The role of content knowledge and problem features on preservice teachers’ appraisal of elementary tasks. Journal of Mathematics Teacher Education 9(4), 347-380

Selden A, Selden J. 2003. Validations of proofs considered as texts: Can undergraduates tell whether an argument proves a theorem? Journal for Research in Mathematics Education 34(1), 4-33.

Stein MK, Engle RA, Smith MS, Hughes EK. 2008. Orchestrating productive mathematical discussions: Five practices for helping teachers move beyond show and tell. Mathematical Thinking and Learning 10, 313-340.

Stein MK, Grover BW, Henningsen MA. 1996. Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Educational Research Journal 33(4), 455-488.

Thompson DR, Chappell MF. 2007. Communica-tion and representation as elements in mathematical literacy.Reading & Writing Quarterly 23(2), 179-196.

Tsay JJ, Judd AB, Hauk S, Davis MK. 2011. Case study of a college mathematics instructor: patterns of classroom discourse. Educational Studies in Mathematics 78, 205–229.

Viseu F, Oliveira IB. 2012. Open-ended tasks in the promotion of classroom communication in mathematics. International Electronic Journal of Elementary Education 4(2), 287-300.

Yackel E, Hanna G. 2003. Reasoning and proof. In Kilpatrick, J Martin, WG Schifter, D (Eds.), A research companion to principles and standards for school mathematics 227-236. Reston, VA: NCTM.

Yankelewitz D, Mueller M, Maher C. 2010. A task that elicits reasoning: A dual analysis. The Journal of Mathematical Behavior 29(2), 76-85.

Yopp DA. 2010. From inductive reasoning to proof. Mathematics Teaching in the Middle School 15(5), 286- 291.