Abstract
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Artzt, A.F., and Armour-Thomas, E. (1992). Development of a cognitive-metacognitive framework for protocol analysis of mathematical problem solving in small groups. Cognition and Instruction, 9, 137–175.
Artzt, A.F., and Armour-Thomas, E. ( 1996, April). Evaluation of instructional practice in the secondary school mathematics classroom. Paper presented at the annual meeting of the American Educational Research Association, New York.
Artzt, A.F., and Armour-Thomas, E. ( 1993. April). Mathematics teaching as problem solving: A framework for studying the relationship between instructional practice and teachers’ cognitive and metacognitive thoughts and behaviors. Paper presented at the annual meeting of the American Education Research Association, Atlanta.
Ball, D.L. (1991). Research on teaching mathematics: Making subject matter knowledge part of the equation. In 1..E..Brophy (Ed.), Advances in research on teaching Teachers’ subject matter knowledge and classroom instruction (pp. 1–48) (Vol. 2 ). Greenwich, CT: JAI Press.
Borko, H. and Livingston, C. (1989). Cognition and improvisation: Differences in mathematics instruction by expert and novice teachers. American Educational Research Journal, 26 (4), 473–498.
Brown, C.A. and Baird, J. (1993). Inside the teacher: Knowledge, beliefs, and attitudes. In P. S. Wilson (Ed.), Research ideas for the classroom: High school mathematics (pp. 245–259 ).
Carpenter, T.P. (1989). Teaching as problem solving. In R. Charles and Silver (Eds.), The teaching and assessing of mathematical problem solving (pp. 187–202 ). Reston, VA: NCTM.
Clark, C.M. and Elmore, J. L. (1981). Transforming curriculum in mathematics, science and writing: A case study of leacher yearly planning (Research Series 99 ). East Lansing: Michigan State University, Institute for Research on Teaching.
Clark, C.M. and Peterson, P. L. (1981). Stimulated-recall. In B..R.. Joyce, C..C. Brown, and L. Peck (Eds.), Flexibility in teaching: An excursion into the nature of teaching and training New York: Longman
Clark, C.M. and Peterson, P..L. (1986). Teachers’ thought processes. In M. C. Wittrock (Ed.), Handbook of research on teaching (3rd., pp. 255–296 ). New York, NY: Macmillan.
Clark, C.M. and Yinger, R.J. (1979). Teachers’ thinking. In P. L. Peterson and H..A Walberg (Eds.), Research on teaching (pp. 231–263 ). Berkeley, CA: McCutchan.
Cobb, P., Yackel, E., and Wood, T. (1991). Curriculum and teacher development: psychological and anthropological perspectives. In E. Fennema, T. Carpenter, and S. J. Lamon (Eds.), Integrating research on teaching and learning mathematics (pp. 55–82 ). Albany, NY: State University of New York Press.
Dougherty, B.J. (1990). Influence of leacher cognitive/conceptual levels on problem solving instruction. In G. Booker, et al. (Eds.), Proceedings of the fourteenth international conference for the psychology of mathematics education (pp. 119 126 ). Oaxtepec, Mexico: International Group for the Psychology of Mathematics Education.
Ernest, P. ( 1988, July). The impact of beliefs on the teaching of mathematics. Paper prepared for ICME V I, Budapest, Hungary.
Fennema, E., Carpenter, T.P., and Peterson, P. L. (1989). Teachers’ decision making and cognitively guided instruction: A new paradigm for curriculum development. In N.F. Ellerton and M. A. (Ken) Clements (Eds.), School mathematics: The challenge to change (pp. 174–187 ). Geelong, Victoria, Australia: Deakin University Press.
Fennema, E. and Franke, M. L. (1992). Teachers’ knowledge and its impact. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 147164 ). New York: Macmillan Publishing Company.
Fogarty, J., Wang, M., and Creek, R. (1983). A descriptive study of experienced and novice teachers’ interactive instructional thoughts and actions. Journal of Educational Research, 77, 22–32.
Garofalo, J., and Lester, F. K. (1985). Metacognition, cognitive monitoring, and mathematical performance. Journal for Research in Mathematics Education, 16, 163–176.
Hiebert, J., (Ed.). (1986). Conceptual knowledge and procedural knowledge: The case of mathematics. Hillsdale, NJ: Lawrence Erlbaum Associates.
Hiebert, J., and Carpenter, T. P. (1992). Learning and teaching with understanding. in D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 65–97 ). New York, NY: Macmillan.
Hinsley, D.A., Hayes, J. R. and Simon, H. A. (1977). From words to equation: Meaning and representation in algebra word problems. In M.A. Just and P. A. Carpenter (Eds.), Cognitive processes in comprehension (pp. 89–106 ). Hillsdale, NJ: Lawrence Erlbaum.
Jackson, P. W. (1968). Life in classrooms. New York: Holt, Rinehart and Winston.
Kagan, D. M. (1992). Implications of research on teacher belief. Educational Psychologist, 27 (1), 6590.
Lampert, M. L. (1985). How teachers teach. Harvard Educational Review, 55, 229–246.
Leinhardt, G. (1989). Math lessons: A contrast of novice and expert competence. Journal for Research in Mathematics Education, 20 (1), 52–75.
Leinhardt, G., Putnam, R..T, Stein, M.. K., and Baxter, J. (1991). Where subject knowledge matters. In J. EW. Brophy (Ed.), Advances in research on teaching: Teachers’ subject matter knowledge and classroom instruction. (Vol. 2,. pp. 87–113 ). Greenwich, CT: JAI Press.
Livingston, C. and Borko, H. (1990). High school mathematics review lessons: Expert-novice distinction. Journal for Research in Mathematics Education, 21, 372–387.
National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: The Council.
National Council of Teachers of Mathematics. (1991). Professional standards for teaching mathematics. Reston, VA: The Council.
Pajares, F. (1992). Teacher’s beliefs and educational research: Cleaning up a messy concept. Review in Educational Research, 62: 307–332.
Peterson, P. L. (1988). Teachers’ and students’ cognitional knowledge for classroom teaching and learning. Educational Researcher, 17 (5), 5–14.
Peterson, P. L., Fennema, E., Carpenter, T. P., and Loef, M. (1989). Teachers’ pedagogical content beliefs In mathematics. Cognition and Instruction, 6, 1–40.
Polya, G. (1945). How to solve it. Garden City, NY: Doubleday.
Richardson, V., Anders, P., Tidwell, D. and Lloyd, C. (1991). The relationship between teachers’ beliefs and practices in reading comprehension instruction. American Educational Research Journal, 28 (3), 559–586.
Ross, D. D. (1989). First steps in developing a reflective approach. Journal of Teacher Education, 40 (2), 22–30.
Schoenfeld, A. H (1987). What’s all the fuss about metacognition? In A. H. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 189–215). Hillsdale, NJ: Lawrence Erlbaum Associates.
Shavelson, R. J. (1986). Interactive decision making: Some thoughts on teacher cognition. invited address, I. Congreso Intemacional, “Pensamientos de los Profesores Y Toma de Decisions,” Seville, Spain.
Shavelson, R. J. and Stem, P. (1981). Research on teachers’ pedagogical thoughts, judgments, decisions and beliefs. Review of Educational Research, 51, 455–498.
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15, 4–14.
Silver, E. A. (1987), Foundations of cognitive theory and research for mathematics problem-solving instruction. In A. H. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 33–60 ). Hillsdale, NJ: Lawrence Erlbaum Associates, inc.
Silver, E. A. (1986). Using conceptual and procedural knowledge: A focus on relationships. In J. Hebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 181–198 ). Hillsdale, NJ: Lawrence Erlbaum Associates.
Simmons, J. M., Sparks, G. M., Starko, A., Pasch, M., Colton, A., and Grinberg, J. ( 1989 March). Exploring the structure of reflective pedagogical thinking in novice and expert teachers: The birth of a developmental taxonomy. Paper presented at the annual meeting of the American Educational Research Association, San Francisco.
Thompson, A. G. (1992). Teachers beliefs and conceptions: A synthesis of the research. In D. Grouws (Ed.), Handbook on research on teaching mathematics and learning (pp. 127–146 ). New York: Macmillan Publishing Company.
Wilson, S. M., Shulman, L. S., and Richert, A. E. (1987). 150 different ways of knowing: Representations of knowledge in teaching. In J. Calderhead (Ed.), Exploring teachers’ thinking (pp. 1044 2 4 ). London: Cassell Educational Limited.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Artzt, A.F., Armour-Thomas, E. (2001). Mathematics Teaching as Problem Solving: A Framework for Studying Teacher Metacognition Underlying Instructional Practice in Mathematics. In: Hartman, H.J. (eds) Metacognition in Learning and Instruction. Neuropsychology and Cognition, vol 19. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2243-8_7
Download citation
DOI: https://doi.org/10.1007/978-94-017-2243-8_7
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5661-0
Online ISBN: 978-94-017-2243-8
eBook Packages: Springer Book Archive