Browse > Article
http://dx.doi.org/10.7468/jksmed.2015.19.2.101

Theoretical Discussion on Mathematical Knowledge for Teaching from Constructivists' Perspective  

LEE, Soo Jin (Department of Mathematics Education, Korea National University of Education)
SHIN, Jaehong (Department of Mathematics Education, Korea National University of Education)
Publication Information
Research in Mathematical Education / v.19, no.2, 2015 , pp. 101-115 More about this Journal
Abstract
In the present paper, we argue any research concerning human knowledge construction, components, or types needs to clarify its epistemological stance regarding 'knowledge' in that such viewpoint might have much influence on the nature of knowledge the researcher sees and the way in which evidence for knowledge development is gathered. Thus, we suggest two alternative research groups who conducted their studies on mathematical knowledge for teaching with an explicit epistemological standpoint. We finalize our discussion by reviewing concrete examples in the previous literature on teacher knowledge of fraction conducted by the two groups.
Keywords
mathematical knowledge for teaching (MKT); teacher knowledge; constructivism; fraction;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Thompson, P. W. & Saldanha, L. A. (2003). Fractions and multiplicative reasoning. In: J. Kilpatrick, W. G. Martin & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 95-113). Reston, VA: National Council of Teachers of Mathematics.
2 Tzur, R. (1999a). An integrated study of children's construction of improper fractions and the teacher's role in promoting that learning. J. Res. Math. Educ. 30(4), 390-416.   DOI
3 Tzur, R. (1999b). An integrated research on children's construction of meaningful, symbolic, partitioning-related conceptions, and the teacher's role in fostering that learning. J. Math. Behav. 18(2), 123-147.   DOI
4 Tzur, R. (2003). Teacher and students' joint production of a reversible fraction conception. J. Math. Behav.23(1), 93-114.   DOI
5 Ball, D. L.; Thames, M. H. C. & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education 59(5), 389-407.   DOI
6 Carpenter, T. P.; Fennma, E.; Peterson, P. L.; Chiang, C.-P.; & Loaf, M. (1989). Using knowledge of children's mathematics thinking in classroom teaching: an experimental study. Am. Educ. Res. J. 26(4), 499-531.   DOI
7 Behr, M. J.; Harel, G.; Post, T. R. & Lesh, R. (1994). Units of quantity: a conceptual basis common to additive and multiplicative structures. In: G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics. (pp. 121-176). Albany: NY: State University of New York Press.
8 Behr, M. J.; Khoury, H. A.; Harel, G.; Post, T. & Lesh, R. (1997). Conceptual units analysis of preservice elementary school teachers' strategies on a Rational-Number-as-Operator task. J. Res. Math. Educ. 28(1), 48-69.   DOI
9 Carpenter, T. P.; Fennema, E.; Peterson, P. L. & Carey, D. A. (1988). Teachers' pedagogical content knowledge of students' problem solving in elementary arithmetic. J. Res. Math. Educ. 19(5), 385-401.   DOI
10 Cobb, P. & Steffe, L. P. (1983). The constructivist researcher as teacher and model builder. J. Res. Math. Educ. 14(2), 83-94.   DOI
11 Cobb, P.; Wood, T. & Yackel, E. (1990). Chapter 9: Classrooms as learning environments for teachers and researchers. In: R. B. Davis, C. A. Maher and N. Noddings (Eds.), Constructivist Views on the Teaching and Learning of Mathematics. Ser. Title: J. Res. Math. Educ. Monograph. No. 4 (pp. 125-146 and pp. 195-210). Reston, VA: National Council of Teachers of Mathematics.
12 Cobb, P. & Yackel, E. (1995). Constructivist, emergent, and sociocultural perspectives in the context of developmental research. In: D. T. Owens et al. (Eds.), Proceedings of the 17th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA XVII). Vol. 1. (pp. 3-29).
13 Hill, H. C.; Schilling, S. G. & Ball, D. L. (2004). Developing measures of teachers' mathematics knowledge for teaching. Elementary School Journal 105(1), 11-30.   DOI
14 Confrey, J. (1994). Splitting, similarity, and rate of change: a new approach to multiplication and exponential functions. In: G. Harel & C. J. (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 291-330). Albany, NY: State University of New York Press.
15 Gutstein, E. & Mack, N. K. (1998). Learning about teaching for understanding the study of tutoring. J. Math. Behav. 17(4), 441-465.   DOI
16 Heinz, K.; Kinzel, M.; Simon, M. A. & Tzur, R. (2000). Moving students through steps of mathematical knowing: An account of the practice of an elementary mathematics teacher in transition. J. Math. Behav. 19, 83-107.   DOI
17 Hill, H.; Ball, D. & Schilling, S. (2008). Unpacking pedagogical content knowledge : Conceptualizing and measuring teachers' topic specific knowledge of students. J. Res. Math. Educ. 39(4), 372-400.
18 Izsak, A. (2008). Mathematical knowledge for teaching fraction multiplication. Cogn. Instr. 26(1), 95-143.   DOI
19 Izsak, A.; Tillema, E. & Tunc-Pekkan, Z. (2008). Teaching and learning fraction addition on number lines. J. Res. Math. Educ. 39(1), 33-62.
20 Kieran, T. (1976). On the mathematical, cognitive, and instructional foundations of rational numbers. In: R. Lesh (Ed.), Number and measurement: Papers from a research workshop (pp. 101-144), Columbus, OH: ERIC/SMEAC.
21 Lehrer, R. & Franke, M. L. (1992). Applying personal construct psychology to the study of teachers' knowledge of fractions. J. Res. Math. Educ. 23(3), 223-241.   DOI
22 Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. In: D. Grouws (Ed.), Handbook for Research on Mathematics Teaching and Learning (pp. 334-370). New York, NY: MacMillan. ME1993f.01809
23 Maturana, H. R. (1988). Reality: the search for objectivity or the quest for a compelling argument. Irish Journal of Psychology 9(1), 25-82.   DOI
24 Olive, J. & Steffe, L. P. (2001). The construction of an iterative fractional scheme: the case of Joe. J. Math. Behav. 20(4), 413-437.   DOI
25 Post, T.; Harel, G.; Behr, M. & Lesh, R. (1991). Intermediate teachers' knowledge of rational number concepts. In: E. Fennema, T. Carpenter, S. Lamon (Eds.), Integrating research on teaching and learning mathematics (pp. 177-198). New York, NY: State University of New York Press.
26 Schoenfeld, A. H. (1998). Toward a theory of teaching-in-context. Issues in Education 4(1), 1-94.   DOI
27 Shulman, L. S. (1986). Those who understand: knowledge growth in teaching. Educational Researcher 15(2), 4-14.   DOI
28 Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. J. Res. Math. Educ. 26(2), 114-145.   DOI
29 Simon, M. A. (2000). Chapter 14: Constructivism, mathematics teacher education, and research in mathematics teacher development. In: L. P. Steffe & P. W. Thompson (Eds.), Radical constructivism in action: Building on the pioneering work of Ernst von Glasersfeld (pp. 213-230). New York: Routledge.
30 Smith, J. P.; diSessa, A. A. & Rocschelle, J. (1993). Misconception reconceived: a constructivist analysis of knowledge in transition. Journal of the Learning Sciences 3(2), 115-163.   DOI
31 Steffe, L. P. (1994). Children's multiplying schemes. In: G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics. New York, NY: State University of New York Press. ME 1994f.02496
32 Steffe, L. P. (1988). Children's construction of number sequences and multiplying schemes. In: J. Hiebert & M. Behr (Eds.), Number concepts and operations in the middle grades. Vol. 2 (pp. 119-140). Hillsdale, NJ: Lawrence Erlbaum Associates.
33 Steffe, L. P. (1990). On the knowledge of mathematics teachers. In: R. B. Davis, C. A. Maher and N. Noddings (Eds.), Constructivist Views on the Teaching and Learning of Mathematics. Ser. Title: J. Res. Math. Educ. Monograph. No. 4 (pp. 167-184 and pp. 195-210). Reston, VA: National Council of Teachers of Mathematics.
34 Steffe, L. P. (1992). Schemes and action and operation involving composite units. Learning and Individual Differences 4(3), 259-309.   DOI
35 Steffe, L. P. & Olive, J. (2010). Children's fractional knowledge. New York: Springer.
36 Steffe, L. P. & Thompson, P. W. (2000). Teaching experiment methodology: Underlying principles and essential elements. In: R. Lesh & A. E. Kelly (Eds.), Handbook of research design in mathematics and science education (pp. 267-307). Mahwah, NJ: Erlbaum.
37 Steffe, L. P. & Wiegel. (1992). On reforming practice in mathematics education. Educ. Stud. Math. 23(5), 445-465.   DOI
38 Thompson, A. G. & Thompson, P. W. (1994). Talking about rates conceptually, Part I: A teacher's struggle. J. Res. Math. Educ. 25(3), 279-303.   DOI
39 Thompson, A. G. & Thompson, P. W. (1996). Talking about rates conceptually, Part II: mathematical knowledge for teaching. J. Res. Math. Educ. 27(1), 2-24.   DOI