Abstract
We consider how prospective elementary teachers think about multiple mathematical knowledge bases as they consider adapting existing mathematics curriculum materials to meet the needs of culturally, linguistically, and socioeconomically diverse students. Multiple mathematical knowledge bases include both children’s mathematical thinking and the cultural-, home-, and community-based funds of knowledge that children inevitably bring into the classroom. We explored how prospective elementary teachers attended to multiple mathematical knowledge bases as they used a lesson analysis tool, the Curriculum Spaces Table, to evaluate existing curriculum materials and identify spaces for adapting these curriculum materials to more efficiently meet the needs of all students. Our analysis examined 47 written reflections on the analysis of and adaptations for a Grade 3 lesson. Findings showed that prospective teachers paid considerable attention to children’s mathematical thinking and gave some attention to funds of knowledge, but they considered these knowledge bases largely in isolation of each other. Attention to integrating children’s mathematical thinking with funds of knowledge was rare. Nonetheless, prospective teachers overwhelmingly found the Curriculum Spaces Table useful for analyzing an existing lesson and identifying spaces for adaptations to more effectively build on children’s mathematical knowledge bases. Thus, we argue that a lesson analysis tool that draws attention to multiple mathematical knowledge bases offers a promising start for prospective elementary teachers’ development of pedagogical practices that integrate children’s mathematical thinking with diverse cultural-, home-, and community-based funds of knowledge.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Aguirre, J. M., Turner, E. E., Bartell, T. G., Kalinec-Craig, C., Foote, M. Q., Roth McDuffie, A., et al. (2012). Making connections in practice: How prospective elementary teachers connect to children’s mathematical thinking and community funds of knowledge in mathematics instruction. Journal of Teacher Education, 64(2), 178–192.
Aguirre, J. M., Zavala, M., & Katanyoutanant, T. (2012). Developing robust forms of pre-service teachers’ pedagogical content knowledge through culturally responsive mathematics teaching analysis. Mathematics Teacher Education and Development, 14(2), 113–136.
Barton, A. C., & Tan, E. (2009). Funds of knowledge and discourses and hybrid space. Journal of Research in Science Teaching, 46(1), 50–73.
Boaler, J., & Brody, K. (2004). The importance of depth and bredth in the analysis of teaching: A framework for analyzing teacher questions. In D. E. McDougall & J. A. Ross (Eds.), Proceedings of the 26th annual meeting of the North American chapter of teh International Group for the Psychology of Mathematics Education (pp. 773–780). Toronto: Ontario Institute for Studies in Education of the University of Toronto.
Carpenter, T. P., Fennema, E., Peterson, P. L., Chiang, C. P., & Loef, M. (1989). Using knowledge of children’s mathematics thinking in classroom teaching: An experimental study. American Educational Research Journal, 26(4), 499–531.
Civil, M. (2007). Building on community knowledge: An avenue to equity in mathematics education. In N. Nasir & P. Cobb (Eds.), Improving access to mathematics: Diversity and equity in the classroom (pp. 105–117). New York: Teachers College Press.
Drake, C., Land, T. J., Bartell, T. G., Aguirre, J. M., Foote, M. Q., McDuffie, A. R., et al. (2015). Three strategies for opening curriculum spaces. Teaching Children Mathematics, 21(6), 346–353.
Erickson, F. (1986). Qualitative methods in research on teaching. In M. Wittrock (Ed.), Hand-book of research on teaching (3rd ed., pp. 119–161). New York: Macmillan.
Fennema, E., Franke, M. L., Carpenter, T. P., & Carey, D. A. (1993). Using children’s mathematical knowledge in instruction. American Educational Research Journal, 30(3), 555–583.
Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28(5), 524–549.
Howard, T. C. (2001). Telling their side of the story: African-American students’ perceptions of culturally relevant teaching. The Urban Review, 33(2), 131–149.
Jackson, C., Appelgate, M., Seiler, G., Sheth, M., & Nadolny, L. (2016). Using virtual environment to uncover biases, assumptions, and beliefs and implications for mathematics teaching. In M. B. Wood, E. E. Turner, M. Civil, & J. A. Eli (Eds.), Proceedings of the 38th annual meeting of the North American chapter of the International Group for the Psychology of Mathematics Education (pp. 1333–1336). Tucson, AZ: The University of Arizona.
Kisker, E. E., Lipka, J., Adams, B. L., Rickard, A., Andrew-Ihrke, D., Yanez, E. E., & Millard, (2012). The potential of a culturally based supplemental mathematics curriculum to improve the mathematics performance of Alaska Native and other students. Journal for Research in Mathematics Education, 43(1), 75–113.
Ladson-Billings, G. (2009). The dreamkeepers: Successful teachers of African American children. San Francisco: Wiley.
Martin, D. B. (2003). Hidden assumptions and unaddressed questions in “Mathematics for All” rhetoric. The Mathematics Educator, 13(2), 7–21.
McDonald, M. A. (2005). The integration of social justice in teacher education: Dimensions of prospective teachers’ opportunities to learn. Journal of Teacher Education, 56(5), 418–435.
Moll, L. C., Amanti, C., Neff, D., & Gonzalez, N. (1992). Funds of knowledge for teaching: Using a qualitative approach to connect homes and classrooms. Theory Into Practice, 31(2), 132–141.
Sleeter, C. E., & Milner, H. R. (2011). Researching successful efforts in teacher education to diversify teachers. In A. F. Ball & C. A. Tyson (Eds.), Studying diversity in teacher education (pp. 81–103). New York: Rowman & Littlefield Publishers.
Smith, M. S., & Stein, M. K. (2011). 5 practices for orchestrating productive mathematics discussions. Reston, VA: National Council of Teachers of Mathematics.
TERC. (2008). Investigations in number, data, and space. Grade 3. Glenview: Pearson Scott Foresman.
Turner, E., Celedón-Pattichis, S., & Marshall, M. E. (2008). Cultural and linguistic resources to promote problem solving and mathematical discourse among Hispanic kindergarten students. In R. S. Kitchen & E. Silver (Eds.), Promoting high participation and success in mathematics by Hispanic students: Examining opportunities and probing promising practices (pp. 19–42). Tempe, AZ: TODOS: Mathematics for All.
Turner, E. E., Drake, C., Roth McDuffie, A., Aguirre, J., Bartell, T. G., & Foote, M. Q. (2011). Promoting equity in mathematics teacher preparation: A framework for advancing teacher learning of children’s multiple mathematics knowledge bases. Journal of Mathematics Teacher Education, 15(1), 67–82.
Villaseñor, A., & Kepner, H. S. (1993). Arithmetic from a problem-solving perspective: An urban implementation. Journal for Research in Mathematics Education, 24(1), 62–69.
White, D. Y., Murray, E. C., & Brunaud-Vega, V. (2012). Discovering multicultural mathematics dispositions. Journal of Urban Mathematics Education, 5(1), 31–43.
Zevenbergen, R. (2001). Language, social class and underachievement in school mathematics. In P. Gates (Ed.), Issues in mathematics teaching (pp. 38–50). New York: Routledge.
Acknowledgments
The research reported in this chapter was supported with funding from the National Science Foundation (NSF, Award #1228034). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the NSF.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Harper, F.K., Drake, C., Bartell, T.G., Najarro, E. (2018). “How I Want to Teach the Lesson”: Framing Children’s Multiple Mathematical Knowledge Bases in the Analysis and Adaptation of Existing Curriculum Materials. In: Bartell, T. (eds) Toward Equity and Social Justice in Mathematics Education. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-92907-1_15
Download citation
DOI: https://doi.org/10.1007/978-3-319-92907-1_15
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-92906-4
Online ISBN: 978-3-319-92907-1
eBook Packages: EducationEducation (R0)