Informed by theory and research in inquiry-based mathematics, this study examined how classroom practices create a press for conceptual learning. Using videotapes of a lesson on the addition of fractions in 4 primarily low-income classrooms from 3 schools, we analyzed conversations that create a high or lower press for conceptual thinking. We use examples of interactions from these fourth-and fifth-grade lessons to propose that a high press for conceptual thinking is characterized by the following sociomathematical norms: (a) an explanation consists of a mathematical argument, not simply a procedural description; (b) mathematical thinking involves understanding relations among multiple strategies; (c) errors provide opportunities to reconceptualize a problem, explore contradictions in solutions, and pursue alternative strategies; and (d) collaborative work involves individual accountability and reaching consensus through mathematical argumentation.
Get full access to this article
View all access options for this article.
References
1.
BallD. L. (1993). With an eye toward the mathematical horizon: Dilemmas of teaching elementary school mathematics. Elementary School Journal, 93, 373–397.
2.
BallD. L., & BassH. (2000). Making believe: The collective construction of public mathematical knowledge in the elementary classroom. In PhillipsD. (Ed.), Yearbook of the National Society for the Study of Education: Constructivism in education (pp. 193–224). Chicago: University of Chicago Press.
3.
BlumenfeldP. C., PuroP., & MergendollerJ. R. (1992). Translating motivation into thoughtfulness. In MarshallH. H. (Ed.), Redefining student learning: Roots of educational change (pp. 207–239). Norwood, NJ: Ablex.
4.
California State Department of Education., (1992). Mathematics framework for California public schools: Kindergarten through grade twelve.Sacramento, CA: Author.
5.
ChazanD., & BallD. (1995). Beyond exhortations not to tell: The teacher's role in discussion-intensive mathematics classes (Craft Paper 95– 2). East Lansing: Michigan State University, National Center for Research on Teacher Learning.
6.
CobbP., WoodT., & YackelE. (1993). Discourse, mathematical thinking, and classroom practice. In FormanE. A., MinickN., & StoneC. A. (Eds.), Contexts for learning: Sociocultural dynamics in children's development (pp. 91–119). New York: Oxford University Press.
7.
CobbP., WoodT., YackelE., & McNealE. (1993). Mathematics as procedural instructions and mathematics as meaningful activity: The reality of teaching for understanding. In DavisR., & MaherC. (Eds.), Schools, mathematics, and the world of reality (pp. 119–133). Boston: Allyn & Bacon.
8.
CobbP., & YackelE. (1996). Constructivist, emergent, and sociocultural perspectives in the context of developmental research. Educational Psychologist, 31, 175–190.
9.
CohenD. K. (1990). A revolution in one classroom: The case of Mrs. Oublier. Educational Evaluation and Policy Analysis, 12, 311–329.
10.
CohenD. K., & BallD. L. (1990). Relations between policy and practice: A commentary. Educational Evaluation and Policy Analysis, 12, 311–338.
11.
CorwinR. B., RussellS. J., & TierneyC. C. (1990). Seeing fractions: Representations of wholes and parts. A unit for the upper-elementary grades.Sacramento, CA: California Department of Education.
12.
FennemaE., CarpenterT., FrankeM., & CareyD. (1993). Learning to use children's mathematical thinking: A case study. In DavisR., & MaherC. (Eds.), Schools, mathematics, and the world of reality (pp. 93–117). Boston: Allyn & Bacon.
13.
FennemaE., CarpenterT. P., FrankeM. L., LeviL., JacobsV. R., & EmpsonS. B. (1996). A longitudinal study of learning to use children's thinking in mathematics instruction. Journal for Research in Mathematics Education, 27, 403–434.
14.
FormanE. A., MinickN., & StoneC. A. (Eds.). (1993). Contexts for learning: Sociocultural dynamics in children's development.New York: Oxford University Press.
15.
FrankeM. L., CarpenterT., FennemaE., AnsellE., & BehrendJ. (1998). Understanding teachers' self-sustaining, generative change in the context of professional development. Teaching and Teacher Education, 14, 67–80.
16.
FullanM. G. (1991). The new meaning of educational change.New York: Teachers College Press.
17.
GearhartM., SaxeG., SeltzerM., SchlackmanJ., FallR., ChingC., NasirN., BennettT., RhineS., & SloanT. (1999). When can educational reforms make a difference? Opportunities to learn fractions in elementary mathematics classrooms. Journal for Research in Mathematics Education, 30, 286–315.
18.
HeatonR (1993). Who is minding the mathematics content? A case study of a fifth-grade teacher. Elementary School Journal, 93, 153–162.
19.
HiebertJ., & CarpenterT. P. (1992). Learning and teaching with understanding. In GrouwsD. A. (Ed.), Handbook of research on mathematics teaching and learning (pp. 65–97). New York: Macmillan.
20.
LampertM (1991). Connecting mathematical teaching and learning. In FennemaE., CarpenterT. P., & LamonS. J. (Eds.), Integrating research on teaching and learning mathematics (pp. 121–152). Albany, NY: SUNY Press.
21.
MollL. (Ed.). (1990). Vygotsky and education: Instructional implications and applications of sociohistorical psychology.New York: Cambridge University Press.
22.
National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics.Reston, VA: Author.
23.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics.Reston, VA: Author.
24.
PrawatR. S. (1992). Are changes in views about mathematics teaching sufficient? The case of a fifth-grade teacher. Elementary School Journal, 93, 195–211.
25.
RogoffB (1994). Developing understanding of the idea of communities of learners. Mind, Culture, and Activity, 1, 209–229.
26.
RogoffB (1997). Evaluating development in the process of participation: Theory, methods, and practice building on each other. In AmselE., & RenningerA. (Eds.), Change and development: Issues of theory, application, and method (pp. 265–285). Hillsdale, NJ: Erlbaum.
27.
SaxeG., GearhartM., & SeltzerM. (1999). Relations between classroom practices and student learning in the domain of fractions. Cognition and Instruction, 17, 1–24.
28.
StipekD., GivvinK., SalmonJ., & MacGyversV. (1998). Can a teacher intervention improve classroom practices and student motivation in mathematics?Journal of Experimental Education, 66, 319–337.
29.
StipekD., SalmonJ., GivvinK., KazemiE., SaxeG., & MacGyversV. (1998). The value (and convergence) of practices suggested by motivation researchers and mathematics education reformers. Journal for Research in Mathematics Education, 29, 465–488.
30.
StoneJ. M. (1989). Cooperative learning and language arts: A multi-structured approach.San Juan Capistrano, CA: Resources for Teachers.
31.
VygotskyL. S. (1978). Mind in society: The development of higher psychological processes.Cambridge, MA: Harvard University Press.
32.
WilliamsS. R., & BaxterJ. A. (1996). Dilemmas of discourse-oriented teaching in one middle school mathematics classroom. Elementary School Journal, 97, 21–38.
33.
WoodT., CobbP., & YackelE. (1991). Change in teaching mathematics: A case study. American Educational Research Journal, 28, 587–616.
34.
YackelE., & CobbP. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27, 458–477.
