Skip to main content
  • 835 Accesses

Abstract

The teaching experiment Integrated Course of Arithmetic and Algebra has been designed in response to the challenges that freshmen community college students experience while learning algebra. As the recent New York Times article “Is Algebra Necessary?” (July 28, 2012) demonstrates, the seriousness of the challenges is formidable, both at CUNY and nationwide.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Akst, G. (2005). Performance in selected mathematics courses at the City University of New York: Implication for retention. New York, NY: Office of Institutional Research and Assessment, CUNY.

    Google Scholar 

  • Baker, W., & Czarnocha, B. (2012). Learning trajectories from the arithmetic/algebra divide. Poster Presentation. Proceedings of the 2012 Annual Meeting of the North American Chapter of the Psychology of Mathematics Education, Kalamazoo, MI.

    Google Scholar 

  • Baker, W., Czarnocha, B., Dias, O., Doyle, K., & Prabhu, V. (2009). A study of adult students learning fractions at a community college. Annals of Polish Mathematical Society, 5th Series: Didactica Mathematicae, 32, 5–41.

    Google Scholar 

  • Baker, W., Czarnocha, B., Dias, O., Doyle, K., Kennis, J., & Prabhu, V. (2012). Procedural and conceptual knowledge: Adults reviewing fractions. ALM International Journal, 7(2), 39–65.

    Google Scholar 

  • Behr, M. J., Lesh, R., Post, T. R., & Silver, E. A. (1983). Rational number concepts. In R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts and processes (pp. 91–126). New York, NY: Academic Press.

    Google Scholar 

  • Bruner, J. S. (1977). The process of education. Cambridge: Harvard University Press.

    Google Scholar 

  • Charalambous, C. Y., & Pitta-Pantazi, D. (2007). Drawing a theoretical model to study students’ understanding of fractions. Educational Studies in Mathematics, 64, 293–316.

    Article  Google Scholar 

  • Doyle, K., Dias, O., Kennis, J. R., Czarnocha, B., Baker, W., & V. Prabhu. (2014). The rational number sub-constructs as a foundation for problem solving. ALM International Journal,11(1), 21–42.

    Google Scholar 

  • Dubinsky, E. (1991). Reflective abstraction in advanced mathematical thinking. In D. Tall (Ed.), Advanced mathematical thinking (pp. 95–126). Dordrecht: Kluwer Academic Publishers.

    Google Scholar 

  • Dubinsky, E., & McDonald, M. A. (2001). APOS: A constructivist theory of learning in undergraduate mathematics education research. The teaching and learning of mathematics at university level: An ICMI study (pp. 273–280). Dordrecht, The Netherlands: Kluwer.

    Google Scholar 

  • Duval, R. (2000). Basic issues for research in mathematics education. In T. Nakahara & M. Koyama (Eds.), Proceedings of the 24th Conference of PME, 1 (pp. 55–69). Hiroshima: Nishiki Print Co. Ltd.

    Google Scholar 

  • Filloy, E., & Rojano, T. (1989). Solving equations: The transition from arithmetic to algebra. For the Learning of Mathematics, 9(2), 19–25.

    Google Scholar 

  • Glasersfeld, E. V. (1989). Cognition, construction of knowledge, and teaching. Synthese, 80(1), 121–140.

    Article  Google Scholar 

  • Glasersfeld, E. V. (1995). Radical constructivism: A way of knowing and learning. London: Falmer Press.

    Book  Google Scholar 

  • Haapasalo, L., & Kadijevich, D. (2000). Two types of mathematical knowledge and their relation. Journal für Mathematik-Didaktik, 21(2), 139–157.

    Article  Google Scholar 

  • Kieren, T. E. (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.

    Google Scholar 

  • Koestler, A. (1964). The act of creation. London: Hutchinson and Co.

    Google Scholar 

  • Piaget, J., & Garcia, R. (1989). Psychogenesis and the history of science (H. Feider, Trans.). New York, NY: Columbia University Press. (Original work published 1983)

    Google Scholar 

  • Piaget, J., & Garcia, R. (1991). Toward a logic of meaning (Trans.) Hillsdale, NJ: Lawrence Erlbaum Associates. (Original work published 1987)

    Google Scholar 

  • Rojano, T. (1985). Developing algebraic aspects of problem solving within a spreadsheet environment. In N. Bednarz, C. Kieran, & L. Lee (Eds.) Approaches to algebra (pp. 137–145). Dordrecht, The Netherlands: Springer.

    Google Scholar 

  • Schmittau, J., & Morris, A. (2004). The development of algebra in the elementary mathematics curriculum of V.V. Davydov. The Mathematics Educator, 8(1), 60–87.

    Google Scholar 

  • Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22, 1–36.

    Article  Google Scholar 

  • Sfard, A. (1992). Operational origins of mathematical objects and the quandary of reification-the case of function. In G. Harel & E. Dubinsky (Eds.), The concept of function: Aspects of epistemology and pedagogy (25th ed., pp. 59–84). Washington, DC: Mathematical Association of America.

    Google Scholar 

  • Sfard, A., & Linchevski, L. (1994). The gains and the pitfalls of Reification – The case of algebra. Educational Studies in Mathematics, 26, 191–228.

    Article  Google Scholar 

  • Shuell, T. J. (1990). Phases of meaningful learning. Review of Educational Research, 60, 531–547.

    Article  Google Scholar 

  • Tall, D., Thomas, M., Davis, G., Gray, E., & Simpson, A. (2000). What is the object of the encapsulation of a process? Journal of Mathematical Behaviour, 18(2), 1–19.

    Google Scholar 

  • Vygotsky, L. S. (1986). Thought and language (A. Kozulin, Trans.). Cambridge, MA: The MIT Press.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Sense Publishers

About this chapter

Cite this chapter

Czarnocha, B. (2016). Rate Teaching Sequence. In: Czarnocha, B., Baker, W., Dias, O., Prabhu, V. (eds) The Creative Enterprise of Mathematics Teaching Research. SensePublishers, Rotterdam. https://doi.org/10.1007/978-94-6300-549-4_27

Download citation

  • DOI: https://doi.org/10.1007/978-94-6300-549-4_27

  • Publisher Name: SensePublishers, Rotterdam

  • Online ISBN: 978-94-6300-549-4

  • eBook Packages: EducationEducation (R0)

Publish with us

Policies and ethics