Mathematics teaching as problem solving: A framework for studying teacher metacognition underlying instructional practice in mathematics

The purpose of this exploratory study was to use a “teaching as problem solving” perspective to examine the components of metacognition underlying the instructional practice of seven experienced and seven beginning teachers of secondary school mathematics. A metacognitive framework was developed to examine the thoughts of teachers before, during and after lesson enactments. Data were obtained through observations, lesson plans, videotapes, and audiotapes of structured interviews during the course of one semester. Data analysis suggests that the metacognition of teachers plays a well-defined role in classroom practice. These findings provide useful insights for researchers and teacher educators in their preservice and inservice mathematics programs.

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

[2]  Joe Garofalo,et al.  Metacognition, Cognitive Monitoring, and Mathematical Performance. , 1985 .

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

[4]  Penelope L. Peterson,et al.  Teachers' Pedagogical Content Beliefs in Mathematics , 1989 .

[5]  P. Jackson.  Life in Classrooms , 1968 .

[6]  D. Ball.  Research on Teaching Mathematics: Making Subject Matter Knowledge Part of the Equation. , 1988 .

[7]  J. Hiebert.  Conceptual and procedural knowledge : the case of mathematics , 1987 .

[8]  A. Schoenfeld.  Cognitive Science and Mathematics Education , 1987 .

[9]  M. Lampert.  How Do Teachers Manage to Teach? Perspectives on Problems in Practice , 1985 .

[10]  Penelope L. Peterson,et al.  Teachers' and Students' Cognitional Knowledge for Classroom Teaching and Learning , 1988 .

[11]  M. Just,et al.  Cognitive processes in comprehension , 1977 .

[12]  Marjorie Powell,et al.  Research on Teaching , 1978 .

[13]  Richard J. Shavelson,et al.  Research on Teachers’ Pedagogical Thoughts, Judgments, Decisions, and Behavior , 1981 .

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

[15]  G. Leinhardt.  Math Lessons: A Contrast of Novice and Expert Competence. , 1989 .

[16]  Gilah C. Leder,et al.  School Mathematics: The Challenge to Change , 1989 .

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

[18]  Carol V. Lloyd,et al.  The Relationship Between Teachers’ Beliefs and Practices in Reading Comprehension Instruction , 1991 .

[19]  Edward A. Silver,et al.  The teaching and assessing of mathematical problem solving , 1988 .

[20]  Hilda Borko,et al.  High school mathematics review lessons: Expert-novice distinctions. , 1990 .

[21]  Susan J. Lamon,et al.  Integrating research on teaching and learning mathematics , 1988 .

[22]  Teaching as Problem Solving , 1964 .

[23]  J. Greeno,et al.  The cognitive skill of teaching. , 1986 .

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

[25]  Ed Brinksma.  Invited Address I , 1995 .

[26]  Edward A. Silver,et al.  Foundations of cognitive theory and research for mathematics problem-solving instruction. , 1987 .

[27]  T. P. Carpenter,et al.  Learning and teaching with understanding. , 1992 .

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

[29]  D. Kagan.  Implication of Research on Teacher Belief , 1992 .

[30]  Alice F. Artz,et al.  Development of a Cognitive-Metacognitive Framework for Protocol Analysis of Mathematical Problem Solving in Small Groups , 1992 .

[31]  D. Ross.  First Steps in Developing A Reflective Approach , 1989 .

[32]  Roy J. Creek,et al.  A Descriptive Study of Experienced and Novice Teachers’ Interactive Instructional Thoughts and Actions , 1983 .

[33]  Christopher M. Clark,et al.  Transforming Curriculum in Mathematics, Science, and Writing: A Case Study of Teacher Yearly Planning. , 1981 .

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

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