List of FAQ
- What should prospective teachers know or be able to do to be prepared to analyze mathematics curriculum?
- What additional resources do you recommend?
What should prospective teachers know or be able to do to be prepared to analyze mathematics curriculum?
The descriptions below are suggested preparation activities for prospective teachers that you might engage in if you have time in your course.
Exploration of Curriculum Materials
It would be helpful if prospective teachers spent some time before this module exploring curriculum materials – the features of different curriculum materials, comparing and contrasting different curriculum series, etc.
Discussion of Features of Good Mathematics Tasks (and discussions of related readings)
We have found it helpful for prospective teachers to consider, read about, and discuss important features of good mathematics tasks, including tasks having multiple entry points, meaningful contexts, and requiring high levels of cognitive demand. We have also found it helpful to have this discussion while simultaneously referring to and introducing the Curriculum Spaces Analysis Table to the prospective teachers.
Cognitive Demand Task Sort [highly recommended]
A useful preparation activity would be the cognitive demand task sort (Smith, Stein, Arbaugh, Brown & Mossgrove, 2004).
Top of page
What additional resources do you recommend?
Arbaugh, F. & Brown, C.A. (2004). What makes a mathematical task worthwhile? Designing a learning tool for high school mathematics teachers. In Rheta N. Rubenstein & George W. Bright (Eds)., Perspectives on the Teaching of Mathematics, Sixty-sixth yearbook (pp. 27-41). Reston, VA: NCTM.
Boston, M.D. & Smith, M.S. (2009). Transforming Secondary Mathematics Teaching: Increasing the Cognitive Demands of Instructional Tasks Used in Teachers’ Classrooms. Journal for Research in Mathematics Education, 40(2), 119-156.
Breyfogle, M.L. & Williams, L.E. (December, 2008). From the classroom: Designing and implementing worthwhile tasks. Teaching Children Mathematics, 15(5), p. 276.
Drake, C., Land, T., Bartell, T.G., Aguirre, J., Foote, M.Q., Roth McDuffie, A. & Turner, E. E. (in press). Three strategies for opening curriculum spaces: building on children’s multiple mathematical knowledge bases while using curriculum materials. Teaching Children Mathematics.
Featherstone et al. (2011) Chapters 5-6. Addressing status issues through lesson design & addressing status issues during the lesson. In Smarter Together!: Collaboration and Equity in the elementary math classroom. Reston, VA: NCTM.
Jackson et al (2012). Launching complex tasks. Mathematics Teaching in the Middle School 18(1) 24-29.
Karp, K. & Howell, P. (2004). Building responsibility for learning in students with special needs. Teaching Children Mathematics. 11(3) 118-126.
Roth McDuffie et al, (2011). Tailoring tasks to meet student needs. Mathematics Teaching in the Middle School. 16(9), 550-555.
Smith, M. (2004). Beyond presenting good problems: how a Japanese teacher implements a mathematics task. In Rheta N. Rubenstein & George W. Bright (Eds)., Perspectives on the Teaching of Mathematics, Sixty-sixth yearbook (pp. 96-106). Reston, VA: NCTM.
Smith, M.S., Bill, V. & Hughes, E.K. (2008). Thinking through a Lesson: Successfully Implementing High-Level Tasks. Mathematics Teaching in the Middle School, 14(3), October 2008.
Smith, M.S., Hughes, E.K., Engle, R.A., & Stein, M.K. (May 2009). Orchestrating Discussions. Mathematics Teaching in the Middle School, 14(9), p. 548.
Stallings, L.L. (2007). See a different mathematics. Mathematics Teaching in the Middle School, 13(4), p. 212.
Stein, M.K., Smith, M.S., Henningsen, M.A., & Silver, E.A. (2000). Implementing Standards-based Mathematics Instruction: A casebook for professional development. Reston, VA: NCTM.