Dialogic Teaching Model For Ninth Class Students To Conceptualize Inequalities

It is known that difficulties are often experienced in conceptual learning of mathematics, which is an abstract lesson. For this reason, it is difficult for students to conceptually learn inequalities, one of the difficult subjects of mathematics. The aim of this study is to investigate the effect of dialogic teaching to overcome the general mistakes and difficulties of 9th grade students in deepening the conceptual teaching of inequalities. This study was designed as an action research. The answers and solutions given to 7 open-ended questions prepared to determine students’ misconceptions and mistakes were scored between 0 and 2 points. When a detailed analysis of solutions written by the students was done, it was determined that the students had difficulty in establishing the concept of numbers, that they ignored the real numbers in a defined range and only focused on integers, that they ignored zero when finding the square of the inequality in a defined range, and that they had difficulty in understanding the principle of reversing when the inequality was multiplied by a negative number and also had difficulty in the solution of inequalities when two inequalities were combined into a single inequality. According to the results of the research, dialogic teaching played a supporting role for the students to reach the conceptual learning of inequalities. It was also seen that high school students were able to reconstruct the concept of inequality conceptually in the learning process. Keywords: dialogic teaching, inequalities, conceptual teaching, reconstructing

[1]  R. Skemp.  The psychology of learning mathematics , 1979 .

[2]  Lesley R Booth.  Algebra: Children's Strategies and Errors : A Report of the Strategies and Errors in Secondary Mathematics Project , 1984 .

[3]  Derek H. Sleeman,et al.  An Attempt to Understand Students' Understanding of Basic Algebra , 1984, Cogn. Sci..

[4]  Paul Cobb,et al.  Contexts, Goals, Beliefs, and Learning Mathematics. , 1986 .

[5]  J. Hiebert,et al.  Conceptual and Procedural Knowledge in Mathematics: An Introductory Analysis , 1986 .

[6]  W. Whyte.  Advancing scientific knowledge through participatory action research , 1989 .

[7]  J. Lemke.  Talking Science: Language, Learning, and Values , 1990 .

[8]  Stephen J. Payne,et al.  Algebra Mal-Rules and Cognitive Accounts of Error , 1990, Cogn. Sci..

[9]  Carolyn Kieran.  The learning and teaching of school algebra. , 1992 .

[10]  G. Posner,et al.  A revisionist theory of conceptual change , 1992 .

[11]  Nicholas C. Burbules,et al.  Dialogue in Teaching: Theory and Practice , 2000 .

[12]  J. Novak.  How Do We Learn Our Lesson , 1993 .

[13]  David Tall,et al.  Diagnosing Students' Difficulties in Learning Mathematics , 1993 .

[14]  Paul Ernest.  Mathematics Education and Philosophy : An International Perspective , 1994 .

[15]  Celia Hoyles,et al.  Cognition and instruction : special issue processes and products of collaborative problem solving : some interdisciplinary perspectives , 1995 .

[16]  Albert B Bennett,et al.  Mathematics for Elementary Teachers: A Conceptual Approach , 1997 .

[17]  J. Greeno.  On Claims That Answer the Wrong Questions , 1997 .

[18]  E. Forman,et al.  Mathematics Learning in Sociocultural Contexts. , 1998 .

[19]  W. Frawley.  Mind as Action , 1998, Trends in Cognitive Sciences.

[20]  F. Monaghan.  Judging a Word by the Company it Keeps: The Use of Concordancing Software to Explore Aspects of the Mathematics Register , 1999 .

[21]  Anna Sfard,et al.  On Reform Movement and the Limits of Mathematical Discourse , 2000 .

[22]  Howard Tanner,et al.  Becoming a Successful Teacher of Mathematics , 2001 .

[23]  Martin Nystrand,et al.  Questions in Time: Investigating the Structure and Dynamics of Unfolding Classroom Discourse , 2003 .

[24]  Carolyn Kieran,et al.  Cognition as Communication: Rethinking Learning-by-Talking Through Multi-Faceted Analysis of Students' Mathematical Interactions , 2001 .

[25]  J. Fitzgerald,et al.  Dialogic Discussion and the Paideia Seminar , 2002 .

[26]  Carolyn Kieran,et al.  The Mathematical Discourse of 13-Year-Old Partnered Problem Solving and Its Relation to the Mathematics That Emerges , 2002 .

[27]  A. Sfard.  There is more to discourse than meets the ears: Looking at thinking as communicating to learn more about mathematical learning , 2001 .

[28]  Elif Yetkin,et al.  Student Difficulties in Learning Elementary Mathematics. ERIC Digest. , 2003 .

[29]  Yuksel Dede.  The Concept of Variable and Identification its Learning Difficulties , 2004 .

[30]  Yaşar Ersoy,et al.  Kassel Projesi Cebir Testinde Bir Grup Türk Öğrencinin Genel Başarısı ve Öğrenme Güçlükleri , 2005 .

[31]  N. Mercer,et al.  Dialogue and the Development of Children's Thinking: A Sociocultural Approach , 2007 .

[32]  Hakan Şandır,et al.  9. Sınıf Öğrencilerinin Aritmatik İşlemler, Sıralama, Denklem ve Eşitsizlik Çözümlerindeki Hataları , 2007 .

[33]  M. Gregory.  A Framework for Facilitating Classroom Dialogue , 2007 .

[34]  Karen Koellner,et al.  A Framework for Understanding and Cultivating the Transition from Arithmetic to Algebraic Reasoning , 2007 .

[35]  John Airey,et al.  Bilingual Scientific Literacy? The Use of English in , 2008 .

[36]  P. K. Murphy,et al.  What the Discourse Tells Us: Talk and Indicators of High-Level Comprehension. , 2008 .

[37]  S. Lyle.  Dialogic Teaching: Discussing Theoretical Contexts and Reviewing Evidence from Classroom Practice , 2008 .

[38]  Paul Thompson,et al.  Dialogic Education and Technology: Expanding the Space of Learning , 2009, J. Comput. Assist. Learn..

[39]  Richard C. Anderson,et al.  Collaborative reasoning: a dialogic approach to group discussions , 2009 .

[40]  Marion Meiers.  Language in the mathematics classroom , 2010 .

[41]  A. Little.  Essays on pedagogy , 2011 .

[42]  Mansureh Hajhosseiny.  The Effect of Dialogic Teaching on Students’ Critical Thinking Disposition , 2012 .

[43]  J. Díez-Palomar,et al.  Using dialogic talk to teach mathematics: the case of interactive groups , 2015 .

[44]  R. Wegerif,et al.  The importance of dialogic processes to conceptual development in mathematics , 2015 .

[45]  Adalet Kandır,et al.  Yapılandırmacı öğrenme yaklaşımı , 2017 .

[46]  N. Herscovics.  Cognitive Obstacles Encountered in the Learning of Algebra , 2018, Research Issues in the Learning and Teaching of Algebra.