Abstract
Current reform-driven mathematics documents stress the need for teachers to provide learning environments in which students will be challenged to engage with mathematics concepts and extend their understandings in meaningful ways (e.g., National Council of Teachers of Mathematics, 2000, Curriculum and evaluation standards for school mathematics. Reston, VA: The Council). The type of rich learning contexts that are envisaged by such reforms are predicated on a number of factors, not the least of which is the quality of teachers’ experience and knowledge in the domain of mathematics. Although the study of teacher knowledge has received considerable attention, there is less information about the teachers’ content knowledge that impacts on classroom practice. Ball (2000, Journal of Teacher Education, 51(3), 241–247) suggested that teachers’ need to ‘deconstruct’ their content knowledge into more visible forms that would help children make connections with their previous understandings and experiences. The documenting of teachers’ content knowledge for teaching has received little attention in debates about teacher knowledge. In particular, there is limited information about how we might go about systematically characterising the key dimensions of quality of teachers’ mathematics knowledge for teaching and connections among these dimensions. In this paper we describe a framework for describing and analysing the quality of teachers’ content knowledge for teaching in one area within the domain of geometry. An example of use of this framework is then developed for the case of two teachers’ knowledge of the concept ‘square’.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.R. Anderson (2000) Cognitive psychology and its implications EditionNumber5 Worth Publishers New York
D.L. Ball (2000) ArticleTitleBridging practices: Intertwining content and pedagogy in teaching learning to teach Journal of Teacher Education 51 IssueID3 241–247
D.L. Ball S.T. Lubienski D.S. Mewborn (2001) Research on teaching mathematics: The unresolved problem of teachers’ mathematical knowledge V. Richardson (Eds) Handbook of research on teaching NumberInSeries4 American Educational Research Association Washington 433–456
Beissner, K.L., Jonassen, D.H. & Grabowski, B.L. (1993). Using and selecting graphic techniques to acquire structural knowledge. ERIC Document No. ED362151
InstitutionalAuthorNameBoard of Studies (2002) K-10 Mathematics Syllabus Department of Education and Training Sydney
J.S. Bruner (1966) Toward a theory of instruction Norton New York
M. Chinnappan (1998a) ArticleTitleSchemas and mental models in geometry problem solving Educational Studies in Mathematics 36 201–217 Occurrence Handle10.1023/A:1003134323371
M. Chinnappan (1998b) ArticleTitleThe accessing of geometry schemas by high school students Mathematics Education Research Journal 10 27–45
C. Clark P.L. Peterson (1986) Teachers’ thought processes M.C. Wittrock (Eds) Handbook of research on teaching Macmillan New York 255–297
Coleman, E. (1993). Inducing a shift from intuitive to scientific knowledge with inquiry training. In M. Polson (Ed.), Proceedings of the fifteenth annual conference of the Cognitive Society (pp. 347–352). Hillsdale: Erlbaum.
S. Feiman-Nemser (1990) Teacher preparation: Structural and conceptual alternatives W.R. Houston M. Haberman J. Sikula (Eds) Handbook of research on teacher education Macmillan New York 212–233
E. Gray M. Pinto D. Pitta D. Tall (1999) ArticleTitleKnowledge construction and divergent thinking in elementary and advanced mathematics Educational Studies in Mathematics 38 111–133 Occurrence Handle10.1023/A:1003640204118
P.L. Grossman (1995) Teachers’ knowledge L.W. Anderson (Eds) International encyclopaedia of teaching and teacher education Elsevier Science Ltd 2 Kidlington Oxford, UK 20–24
D.H. Jonassen K. Beissner M.A. Yacci (1993) Structural knowledge: Techniques for conveying, assessing, and acquiring structural knowledge Lawrence Erlbaum Hillsdale, NJ
M.S. Knapp (1997) ArticleTitleBetween systemic reforms and the maths and science classroom: the dynamics of innovation, implementation, and professional learning Review of Educational Research 67 227–266
Laturno, J. (1994). The validity of concept maps as a research tool in remedial mathematics. In D. Kirshner (Ed.), Proceedings of the sixteenth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 60–66). Baton Rouge: Louisiana State University.
Lawson, M.J. (1994). Concept mapping. In T. Husén & T.N. Postlethwaite (Eds.), The international encyclopedia of education (2nd ed., Vol. 2, pp. 1026–1031). Oxford: Elsevier Science.
M.J. Lawson M. Chinnappan (1994) ArticleTitleGenerative activity during geometry problem solving: Comparison of the performance of high-achieving and low-achieving students Cognition and Instruction 12 61–93
G. Leinhardt (1987) ArticleTitleThe development of an expert explanation: An analysis of a sequence of subtraction lessons Cognition and Instruction 4 225–282
K.M. Markman J.J. Mintzes M.G. Jones (1994) ArticleTitleThe concept map as a research and evaluation tool: Further evidence of validity Journal of Research in Science Teaching 31 91–101
R.E. Mayer (1975) ArticleTitleInformation processing variables in learning to solve problems Review of Research in Education 45 525–541
M. McKeown I. Beck (1990) ArticleTitleThe assessment and characterisation of young learners knowledge of a topic in history American Educational Research Journal 27 688–726
H. Munby T. Russell A.K. Martin (2001) Teachers’ knowledge and how it develops V. Richardson (Eds) Handbook of research on teaching NumberInSeries4 American Educational Research Association Washington, DC 877–904
InstitutionalAuthorNameNational Council of Teachers of Mathematics. (1989) Curriculum and evaluation standards for school mathematics The Council Reston, VA
InstitutionalAuthorNameNational Council of Teachers of Mathematics. (2000) Curriculum and evaluation standards for school mathematics The Council Reston, VA
J. Novak (1990) ArticleTitleConcept mapping: A useful device for science education Journal of Research in Science Education 27 937–949
J. Novak D.B. Gowin (1984) Learning how to learn Cambridge University Press New York
L.R. Novick S.M. Hurley (2001) ArticleTitleTo matrix, network or hierarchy: That is the question Cognitive Psychology 42 158–216 Occurrence Handle10.1006/cogp.2000.0746 Occurrence Handle11259107
D.N. Perkins R. Simmons (1988) ArticleTitlePatterns of misunderstanding: An integrative model for science, math and programming Review of Educational Research 58 303–326
Robinson, N., Even, R. & Tirosh, D. (1992). Connectedness in teaching algebra: A novice-expert contrast. In W. Geeslin & K. Graham (Eds), Proceedings of the psychology of mathematics education conference, PME-XVI (pp. 258–265). Durham, New Hampshire: PME.
A.H. Schoenfeld (1988) ArticleTitleWhen good teaching leads to bad results: The disasters of ‘well taught’ mathematics classes Educational Psychologist 23 145–166
A.H. Schoenfeld (1992) Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics Grouws A. Douglas (Eds) Handbook of research on mathematics teaching and learning Macmillan New York 334–370
Shavelson, R.J., Lang, H. & Lewin, B. (1993). On concept maps as potential ‘authentic’ assessments in science: Indirect approaches to knowledge representation of high school science. ERIC Document, No. ED367691.
L.S. Shulman (1986) Paradigms and research programs in the study of teaching M.C. Wittrock (Eds) Handbook on research in teaching NumberInSeries3 MacMillan New York 3–36
S. Vinner T. Dreyfus (1989) ArticleTitleImages and definitions for the concept of function Journal for Research for Mathematics Education 20 356–366
K.L. Watson M.J. Lawson (1995) ArticleTitleImproving access to knowledge: The effect of strategy training for question answering in high school geography British Journal of Educational Psychology 65 97–111
C.G. Williams (1998) ArticleTitleUsing concept maps to assess conceptual knowledge of function Journal for Research in Mathematics Education 29 414–421
M.C. Wittrock (1990) ArticleTitleGenerative processes of comprehension Educational Psychologist 24 345–376
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chinnappan, M., Lawson, M.J. A Framework for Analysis of Teachers’ Geometric Content Knowledge and Geometric Knowledge for Teaching. J Math Teacher Educ 8, 197–221 (2005). https://doi.org/10.1007/s10857-005-0852-6
Issue Date:
DOI: https://doi.org/10.1007/s10857-005-0852-6