A collective case study of the influence of teachers' beliefs and knowledge on error-handling practices during class discussion of Mathematics

This collective case study examines the influence of 4 third-grade teachers’ beliefs and knowledge on their error-handling practices during class discussion of mathematics. Across cases, 3 dimensions of teachers’ error-handling practices are identified and discussed in relation to teacher beliefs and knowledge: (a) intentional focus on flawed solutions in class discussion, (b) promotion of conceptual understanding through discussion of errors, and (c) mobilization of a community of learners to address errors. Study findings suggest that, although teachers’ ways of handling student errors during class discussion of mathematics are clearly linked to both teacher beliefs and teacher knowledge, some aspects of teacher response are more strongly linked to knowledge and others are influenced more by beliefs.

[1]  유창조 Naturalistic Inquiry , 2022, The SAGE Encyclopedia of Research Design.

[2]  Malcolm Correll,et al.  A+ for Teaching , 1962 .

[3]  Sudhir Gupta,et al.  Case Studies , 2013, Journal of Clinical Immunology.

[4]  P. Cobb,et al.  Reflections on Learning and Teaching Mathematics in Elementary School , 2012 .

[5]  Ernst von Glasersfeld,et al.  A Constructivist Approach to Teaching , 2012 .

[6]  Deborah J. Stipek,et al.  Promoting Conceptual Thinking in Four Upper-Elementary Mathematics Classrooms , 2009 .

[7]  Margaret S. Smith,et al.  Orchestrating Productive Mathematical Discussions: Five Practices for Helping Teachers Move Beyond Show and Tell , 2008 .

[8]  W. Bray A Study of Teacher Transitions to a Reform-Based Mathematics Curriculum in an Urban School: The Interaction of Beliefs, Knowledge, and Classroom Practices , 2007 .

[9]  Lieven Verschaffel,et al.  A Teaching Experiment , 2007 .

[10]  P. Cobb,et al.  Reflective Discourse and Collective Reflection , 1997 .

[11]  Keith R. Leatham Viewing Mathematics Teachers’ Beliefs as Sensible Systems* , 2006 .

[12]  Gaye Williams,et al.  Children's Mathematical Thinking in Different Classroom Cultures , 2006 .

[13]  R. Santagata Practices and beliefs in mistake-handling activities: A video study of Italian and US mathematics lessons , 2005 .

[14]  The Extent and Consequences of Risk in U.S. Education , 2005 .

[15]  Michael D. Steele,et al.  Seeing the Complexity of Standing to the Side: Instructional Dialogues , 2005 .

[16]  Edward A. Silver,et al.  Moving from rhetoric to praxis: Issues faced by teachers in having students consider multiple solutions for problems in the mathematics classroom , 2005 .

[17]  L. Lippman Urban Schools: The Challenge Of Location And Poverty , 2004 .

[18]  Debra L. Junk,et al.  Teachers' Knowledge of Children's Mathematics after Implementing a Student-Centered Curriculum , 2004 .

[19]  A Web-Based Survey to Assess Prospective Elementary School Teachers' Beliefs about Mathematics and Mathematics Learning: An Alternative to Likert Scales. , 2003 .

[20]  James P. Spillane Challenging Instruction for "All Students": Policy, Practitioners, and Practice , 2002 .

[21]  Sam Stringfield,et al.  Educating at-risk students , 2002 .

[22]  R. Mistretta,et al.  "Principles and Standards for School Mathematics" in the Classroom. , 2001 .

[23]  Susan H. Fuhrman From the capitol to the classroom : standards-based reform in the states , 2001 .

[24]  Susan Empson Equal Sharing and the Roots of Fraction Equivalence. , 2001 .

[25]  A. Su,et al.  The National Council of Teachers of Mathematics , 1932, The Mathematical Gazette.

[26]  E. Fennema,et al.  Teaching and Learning Mathematics With Understanding , 1999 .

[27]  K. Fuson,et al.  Advancing children's mathematical thinking in everyday mathematics classrooms , 1999 .

[28]  Alan H. Schoenfeld,et al.  Models of the Teaching Process , 1999 .

[29]  Natasha M. Speer,et al.  Examining the Relationship Between Beliefs and Goals in Teacher Practice , 1999 .

[30]  Geoffrey B. Saxe,et al.  The Value (and Convergence) of Practices Suggested by Motivation Research and Promoted by Mathematics Education Reformers. , 1998 .

[31]  Thomas J. Cooney,et al.  Conceptualizing Belief Structures of Preservice Secondary Mathematics Teachers. , 1998 .

[32]  S. Merriam Qualitative Research and Case Study Applications in Education: Revised and Expanded from Case Study Research in Education , 1998 .

[33]  Alan H. Schoenfeld,et al.  Toward a theory of teaching-in-context , 1998 .

[34]  Susan B. Empson,et al.  A Longitudinal Study of Learning to Use Children's Thinking in Mathematics Instruction , 1996, Journal for Research in Mathematics Education.

[35]  Michael S. Knapp,et al.  Teaching for Meaning in High-Poverty Classrooms , 1995 .

[36]  N. Denzin,et al.  Handbook of Qualitative Research , 1994 .

[37]  Raffaělla Borasi Capitalizing on Errors as "Springboards for Inquiry": A Teaching Experiment. , 1994 .

[38]  Arthur F. Coxford,et al.  Professional Development for Teachers of Mathematics. 1994 Yearbook. , 1994 .

[39]  Randolph A. Philipp,et al.  Calculational and Conceptual Orientations in Teaching Mathematics , 1994 .

[40]  Mary M. Kennedy,et al.  A Study Package for Examining and Tracking Changes in Teachers' Knowledge. NCRTL Technical Series 93-1. , 1993 .

[41]  Mm Kennedy,et al.  A study package for examining and tracking changes in teachers' knowledge (Technical Series ). East The National Center for Research on Teacher Education. , 1993 .

[42]  M. Pajares,et al.  Teachers’ Beliefs and Educational Research: Cleaning Up a Messy Construct , 1992 .

[43]  A. Thompson Teachers' beliefs and conceptions: A synthesis of the research. , 1992 .

[44]  M. Franke,et al.  Teachers' knowledge and its impact. , 1992 .

[45]  Douglas A. Grouws,et al.  Handbook of research on mathematics teaching and learning , 1992 .

[46]  Sharan B. Merriam,et al.  Case Study Research in Education : A Qualitative Approach , 1991 .

[47]  E. Guba,et al.  Fourth Generation Evaluation , 1989 .

[48]  P. Grossman The Making of a Teacher: Teacher Knowledge and Teacher Education , 1990 .

[49]  H. Borko,et al.  Cognition and Improvisation: Differences in Mathematics Instruction by Expert and Novice Teachers , 1989 .

[50]  C. Hirsch Curriculum and Evaluation Standards for School Mathematics , 1988 .

[51]  L. Shulman Those Who Understand: Knowledge Growth in Teaching , 1986 .

[52]  M. Wittrock Handbook of research on teaching , 1986 .

[53]  R. Yin Case Study Research: Design and Methods , 1984 .

[54]  Stephen Lerman Problem‐solving or knowledge‐centred: the influence of philosophy on mathematics teaching , 1983 .

[55]  R. Glaser Advances in Instructional Psychology , 1978 .

[56]  J. Stenton,et al.  Learning how to teach. , 1973, Nursing mirror and midwives journal.

[57]  A. Strauss,et al.  The discovery of grounded theory: strategies for qualitative research aldine de gruyter , 1968 .