Abstract
The chapter deals with language in the mathematics classrooms, especially with mathematics remedial classrooms. It presents an unusual example of integrating two independent theories, the Sfard (1991) theory of reification and Shepard (1993)/Shuell (1990) integrated theory of cognitive development and writing categories. In the first cycle it’s the TR Design Type A, from Practice; it uses problem types designed through practice and supports itself by a standard yet simple statistical analysis.
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
Preview
Unable to display preview. Download preview PDF.
References
Aspinweil, L., & Miller, D. (1997). Students’ positive reliance on writing as a process to learn first semester calculus. Journal of Instructional Psychology, 24, 253–261.
Baker, W., & Czarnocha, B. (2002). Written metacognition and procedural knowledge. Proceedings of the 2nd International Conference on the Teaching of Mathematics, University of Crete, Hersonissos Crete, Greece. Retrieved from
Baker, W., & Czarnocha, B. (2008). Procedural knowledge and written thought in pre-algebraic mathematics. Mathematics Teaching-Research Journal Online, 2(2), 28–47. Retrieved from http://wf01.bcc.cuny.edu/~vrundaprabhu/TRJ/site/archivesnews.htm
Bell, E., & Bell, R. (1985). Writing and mathematical problem solving: Arguments in favor of synthesis. School Science and Mathematics, 85(3), 210–221.
Bessé, M., & Faulconer, J. (2008). Learning and assessing mathematics through reading and writing. School Science and Mathematics, 108(1), 8–19.
Bicer, A., Capraro, R., & Capraro M. (2013) Integrating writing into mathematics classroom to increase students’ problem solving skills. International Online Journal of Educational Sciences, 5(2), 361–369.
Britton, J., Burgess, T., Martin, N., McLeod, A., & Rosen, H. (1975). The development of writing abilities (pp. 11–18). London: MacMilliam.
Davis, G., Gray, E., Simpson, A., Tall, D., & Thomas, M. (2000). What is the object of the encapsulation of a process? Journal of Mathematical Behaviour, 18(2), 223–241.
Dubinsky, E. (1991). Reflective abstraction in advanced mathematical thinking. In D. Tall (Ed.), Advanced mathematical thinking (pp. 95–123) Dordrecht, Netherlands: Kluwer. Retrieved from http://www.math.uoc.gr/~ictm2/Proceedings/ICTM2_Presentations_by_Author.html#B
Meier, J., & Rishel, T. (1998). Writing in the teaching and learning of mathematics (MAA, 48). Washington, DC: The Mathematical Association of America.
Porter, M., & Masingila, J. (2000). Examining the effects of writing on conceptual and procedural knowledge in calculus. Educational Studies in Mathematics, 42, 165–177.
Powell A., & López, J. (1989) Writing as a vehicle to learn mathematics: A case study. In P. Connolly & T. Vilardi (Eds.), Writing to learn mathematics and science (pp. 147–156). New York, NY: Teachers College Press.
Pugalee, D. (2001). Writing, mathematics, and metacognition: Looking for connections through students’ work in mathematical problem solving. School Science and Mathematics, 101(5), 236–245.
Pugalee, D. K. (2004). A comparison of verbal and written descriptions of students’ problem solving processes. Educational Studies in Mathematics, 55(1/3), 27–47.
Sfard, A. (1991). On the dual nature of mathematical conceptions: reflection 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 notions and the quandary of reification: The case of functions. In E. Dubinsky & G. Harel (Eds.), The concept of functions: Aspects of epistemology and pedagogy (MAA Notes, 25, 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.
Shepard, R. S. (1993). Writing for conceptual development in mathematics. Journal of Mathematical Behaviour, 12, 287–293.
Shield, M., & Galbraith, P. (1998). The analysis of students expository writing. Educational Studies in Mathematics, 36, 29–52.
Shuell, T. (1990). Phases of meaningful learning. Review of Educational Research, 60(4), 531–547.
Vygotsky, L. (1997). Thought and language (10th printing). Cambridge, MA: MIT Press.
Whalberg, M. (1998). The effects of writing assignments on second-semester calculus students’ understanding of the limit concept. Paper Presented at 3Rd RUMEC International Conference in Advanced Mathematical Thinking.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Sense Publishers
About this chapter
Cite this chapter
Baker, W., Czarnocha, B. (2016). From Arithmetic to Algebra. 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_32
Download citation
DOI: https://doi.org/10.1007/978-94-6300-549-4_32
Publisher Name: SensePublishers, Rotterdam
Online ISBN: 978-94-6300-549-4
eBook Packages: EducationEducation (R0)