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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
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.
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.
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.
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.
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.
Bruner, J. S. (1977). The process of education. Cambridge: Harvard University Press.
Charalambous, C. Y., & Pitta-Pantazi, D. (2007). Drawing a theoretical model to study students’ understanding of fractions. Educational Studies in Mathematics, 64, 293–316.
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.
Dubinsky, E. (1991). Reflective abstraction in advanced mathematical thinking. In D. Tall (Ed.), Advanced mathematical thinking (pp. 95–126). Dordrecht: Kluwer Academic Publishers.
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.
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.
Filloy, E., & Rojano, T. (1989). Solving equations: The transition from arithmetic to algebra. For the Learning of Mathematics, 9(2), 19–25.
Glasersfeld, E. V. (1989). Cognition, construction of knowledge, and teaching. Synthese, 80(1), 121–140.
Glasersfeld, E. V. (1995). Radical constructivism: A way of knowing and learning. London: Falmer Press.
Haapasalo, L., & Kadijevich, D. (2000). Two types of mathematical knowledge and their relation. Journal für Mathematik-Didaktik, 21(2), 139–157.
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.
Koestler, A. (1964). The act of creation. London: Hutchinson and Co.
Piaget, J., & Garcia, R. (1989). Psychogenesis and the history of science (H. Feider, Trans.). New York, NY: Columbia University Press. (Original work published 1983)
Piaget, J., & Garcia, R. (1991). Toward a logic of meaning (Trans.) Hillsdale, NJ: Lawrence Erlbaum Associates. (Original work published 1987)
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.
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.
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.
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.
Sfard, A., & Linchevski, L. (1994). The gains and the pitfalls of Reification – The case of algebra. Educational Studies in Mathematics, 26, 191–228.
Shuell, T. J. (1990). Phases of meaningful learning. Review of Educational Research, 60, 531–547.
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.
Vygotsky, L. S. (1986). Thought and language (A. Kozulin, Trans.). Cambridge, MA: The MIT Press.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights 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)