Abstract
This study focuses on a group of practitioners from a school district that adopted reform-oriented curriculum materials but later rejected them, partially due to the inclusion of alternative algorithms in the materials. Metaphors implicit in a conversation among the group were analysed to illuminate their perspectives on instructional issues surrounding alternative algorithms. Several possible sources of resistance to folding alternative algorithms into instruction were found, including the ideas that: successful learning does not involve struggling with mathematics, the teacher’s role in the classroom is primarily to present information, and that mathematics learning progresses according to a fixed sequence of levels.
Similar content being viewed by others
References
Ball, D. L., Lubienski, S. T., & Mewborn, D. S. (2001). Research on teaching mathematics: The unsolved problem of teachers’ mathematical knowledge. In V. Richardson (Ed.),Handbook of research on teaching (4th ed., pp. 433–456). New York: Macmillan.
Australian Association of Mathematics Teachers. (2006).Standards for excellence in teaching mathematics in Australian schools. Retrieved 25 January 2007 from: http://www.aamt.edu.au/standards/intro.html
Bogdan, R. C., & Biklen, S. K. (1992).Qualitative research for education: An introduction to theory and methods. Boston: Allyn & Bacon.
Bullough, R. V. (1991). Exploring personal teaching metaphors in preservice teacher education.Journal of Teacher Education, 42(1), 43–51.
Chapman, O. (1997). Metaphors in the teaching of mathematical problem solving.Educational Studies in Mathematics, 32(3), 201–228.
Collopy, R. (2003). Curriculum materials as a professional development tool: How a mathematics textbook affected two teachers’ learning.Elementary School Journal, 103(3), 287–311.
Carpenter, T. P., Fennema, E., Franke, M. L., Levi, L., & Empson, S. B. (1999).Children’s mathematics: Cognitively Guided Instruction. Portsmouth, NH: Heinemann.
Carpenter, T. P., Franke, M. L., Jacobs, V. R., Fennema, E., & Empson, S. B. (1998). A longitudinal study of invention and understanding in children’s multidigit addition and subtraction.Journal for Research in Mathematics Education, 29(1), 3–20.
Carroll, W. M., & Isaacs, A. (2003). Achievement of students using the University of Chicago School Mathematics Project’s Everyday Mathematics. In S. L. Senk & D. R. Thompson (Eds.),Standards-based school mathematics curricula: What are they? What do students learn? (pp. 79–108). Mahwah, NJ: Lawrence Erlbaum.
Conference Board of the Mathematical Sciences. (2001).The mathematical education of teachers. Providence, RI: American Mathematical Society.
Desire2Learn (2006).Desire2Learn: Innovative teaching technology. Retrieved February 2, 2006 from http://www.desire2learn.com/index.asp.
Dooley, C. (1998). Teaching as a two-way street: Discontinuities among metaphors, images, and classroom realities.Journal of Teacher Education, 49(2), 97–107.
Dysthe, O. (2002). The learning potential of a web-mediated discussion in a university course.Studies in Higher Education, 27(3), 339–352.
Education Development Center. (2005).MathScape: Seeing and thinking mathematically. Retrieved February 2, 2006 from http://www2.edc.org/Mathscape/phil/default.asp.
Erlwanger, S. H. (1973). Benny’s conception of rules and procedures in IPI mathematics.Journal of Children’s Mathematical Behavior, 1(2), 7–26.
Fishel, M., & Ramirez, L. (2005). Evidence-based parent involvement interventions with school-aged children.School Psychology Quarterly, 20(4), 371–402.
Gentner, D., & Holyoak, K. J. (1997). Reasoning and learning by analogy.American Psychologist, 52(1), 32–34.
Glesne, C. (1999).Becoming qualitative researchers: An introduction (2nd ed.). New York: Longman.
Greeno, J. G. (1997). On claims that answer the wrong questions.Educational Researcher, 26(1), 5–17.
Grossman, P. (2005). Research on pedagogical approaches in teacher education. In M. Cochran-Smith & K. M. Zeichner (Eds.),Studying teacher education: The report of the AERA panel on research and teacher education (pp. 425–476). Mahwah, NJ: Erlbaum.
Groth, R. E., & Bergner, J. A. (in press). Building an online discussion group for teachers.Mathematics Teaching in the Middle School.
Harism, L. M. (1990). Online education: An environment for collaboration and intellectual amplification. In L. M. Harism (Ed.),Online education: Perspectives on a new environment (pp. 39–64). New York: Praeger.
Hatfield, M. M., Edwards, N. T., Bitter, G. G., & Morrow, J. (2003).Mathematics methods for elementary and middle school teachers (4th ed.). New York: John Wiley.
Heaton, R. M. (2000).Teaching mathematics to the new standards: Relearning the dance. New York: Teachers College Press.
Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K. C., & Wearne, D. (1997).Making sense: Teaching and learning mathematics with understanding. Portsmouth, NH: Heinemann.
Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement.American Educational Research Journal, 42(2), 371–406.
Hill, H. C., & Ball, D. L. (2004). Learning mathematics for teaching: Results from California’s mathematics professional development institutes.Journal for Research in Mathematics Education, 35(5), 330–351.
Kamii, C. K., & Dominick, A. (1998). The harmful effects of algorithms in grades 1–4. In L. J. Morrow (Ed.),The teaching and learning of algorithms in school mathematics (pp. 130–140). Reston, VA: National Council of Teachers of Mathematics.
Kilpatrick, J., Swafford, J. & Findell, B. (Eds.). (2001).Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.
Klein, P.D. (1997). Multiplying the problems of intelligence by eight: A critique of Gardner’s theory.Canadian Journal of Education, 22(4), 377–394.
Lakoff, G., & Johnson, M. (1980).Metaphors we live by. Chicago: University of Chicago Press.
Lampert, M. (2001).Teaching problems and the problems of teaching. New Haven: Yale University Press.
Lewis, C., & Ketter, J. (2004). Learning as social interaction: Interdiscursivity in a teacher and researcher study group. In R. Rogers (Ed.),Introduction to critical discourse analysis in education (pp. 117–146). Mahwah, NJ: Lawrence Erlbaum.
Lloyd, G. M. (1999). Two teachers’ conceptions of a reform-oriented curriculum: Implications for mathematics teacher development.Journal of Mathematics Teacher Education, 2(3), 227–252.
Lloyd, G. M., & Behm, S. L. (2005). Preservice elementary teachers’ analysis of mathematics instructional materials.Action in Teacher Education, 26(4), 48–62.
Ma, L. (1999).Knowing and teaching elementary mathematics. Mahwah, NJ: Lawrence Erlbaum.
Mack, N. K. (1990). Learning fractions with understanding: Building on informal knowledge.Journal for Research in Mathematics Education, 21(1), 16–32.
Matusov, E. (1996). Intersubjectivity without agreement.Mind, Culture, and Activity, 3(1), 25–45.
Matusov, E., Hayes, R., & Pluta, M. J. (2005). Using discussion webs to develop an academic community of learners.Educational Technology & Society, 8(2), 16–39.
Miles, M. B., & Huberman, A. M. (1994).Qualitative data analysis: An expanded sourcebook (2nd ed.). Thousand Oaks, CA: Sage.
Mish, F. C. (Ed.). (1991).Webster’s ninth new collegiate dictionary. Springfield, MA: Merriam-Webster.
Muhr, T. (2004).User’s Manual for ATLAS.ti 5.0. Berlin: ATLAS.ti Scientific Software Development.
Newell, G., Wilsman, M., Langenfeld, M., & McIntosh, A. (2002). Online professional development: Sustained learning with friends.Teaching Children Mathematics, 8(9), 505–508.
Nieto, S. (1992).Affirming diversity: The sociopolitical context of multicultural education. White Plains, NY: Longman.
Ogawa, R. T. (1998). Organising parent-teacher relations around the work of teaching.Peabody Journal of Education, 73(1), 6–14.
Petrie, H. (1980). Metaphor and learning. In A. Ortony (Ed.),Metaphor and thought (pp. 438–461). Cambridge: Cambridge University Press.
Philipp, R. A. (1996). Multicultural mathematics and alternative algorithms.Teaching Children Mathematics, 3(3), 128–133.
Piaget, J. (1983). Piaget’s theory. In P. Mussen (Ed.),Handbook of child psychology (pp. 103–128). New York: John Wiley.
Presmeg, N. C. (1992). Prototypes, metaphors, metonymies and imaginative rationality in high school mathematics.Educational Studies in Mathematics, 23(6), 595–610.
Presmeg, N. C. (1998). Metaphoric and metonymic signification in mathematics.Journal of Mathematical Behavior, 17(1), 25–32.
Putnam, R. T., & Borko, H. (2000). What do new views of knowledge and thinking have to say about research on teacher learning?Educational Researcher, 29(1), 4–15.
Randolph, T. D., & Sherman, H. J. (2001). Alternative algorithms: Increasing options, reducing errors.Teaching Children Mathematics, 7(8), 480–484.
Raymond, A. M. (1997). Inconsistency between a beginning elementary school teacher’s mathematics beliefs and teaching practice.Journal for Research in Mathematics Education, 28(5), 550–576.
Remillard, J. T., & Bryans, M. B. (2004). Teachers’ orientations toward mathematics curriculum materials: Implications for teacher learning.Journal for Research in Mathematics Education, 35(5), 352–388.
Remillard, J. T., & Jackson, K. (2006). Old math, new math: Parents’ experiences with standards-based reform.Mathematical Thinking and Learning, 8(3), 231–259.
Romberg, T. A., & Shafer, M. C. (2003).Mathematics in context — Preliminary evidence about student outcomes. In S. L. Senk & D. R. Thompson (Eds.),Standards-based school mathematics curricula: What are they? What do students learn? (pp. 225–250). Mahwah, NJ: Erlbaum.
Salmon, G. (2004).E-Moderating: The key to teaching and learning online. London: Routledge/Falmer.
Shotsberger, P. G. (1999). The INSTRUCT Project: Web professional development for mathematics teachers.Journal of Computers in Mathematics and Science Teaching, 18(1), 49–60.
Stake, R. E., & Trumbull, D. J. (1982). Naturalistic generalizations.Review Journal of Philosophy and Social Science, 7(1–2), 1–12.
Stein, M. K., Grover, B. W., & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms.American Educational Research Journal, 33(2), 455–488.
Stigler, J. W., & Hiebert, J. (1999).The teaching gap. New York: The Free Press.
Wickstom, C. D. (2003). A funny thing happened on the way to the forum.Journal of Adult and Adolescent Literacy, 46(5), 414–423.
Zaslavsky, O. (2005). Seizing the opportunity to create uncertainty in learning mathematics.Educational Studies in Mathematics, 60(3), 297–321.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Groth, R. Understanding teachers’ resistance to the curricular inclusion of alternative algorithms. Math Ed Res J 19, 3–28 (2007). https://doi.org/10.1007/BF03217447
Issue Date:
DOI: https://doi.org/10.1007/BF03217447