Advertisement

From Arithmetic to Algebra

A Sequence of Theory-Based Tasks
  • William Baker
  • Bronislaw Czarnocha
Chapter

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.

Keywords

Conceptual Knowledge Mathematics Classroom Final Exam Procedural Knowledge Instructional Sequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 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.Google Scholar
  2. 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 fromGoogle Scholar
  3. 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.htmGoogle Scholar
  4. Bell, E., & Bell, R. (1985). Writing and mathematical problem solving: Arguments in favor of synthesis. School Science and Mathematics, 85(3), 210–221.CrossRefGoogle Scholar
  5. Bessé, M., & Faulconer, J. (2008). Learning and assessing mathematics through reading and writing. School Science and Mathematics, 108(1), 8–19.CrossRefGoogle Scholar
  6. 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.Google Scholar
  7. Britton, J., Burgess, T., Martin, N., McLeod, A., & Rosen, H. (1975). The development of writing abilities (pp. 11–18). London: MacMilliam.Google Scholar
  8. 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.Google Scholar
  9. 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#BGoogle Scholar
  10. Meier, J., & Rishel, T. (1998). Writing in the teaching and learning of mathematics (MAA, 48). Washington, DC: The Mathematical Association of America.Google Scholar
  11. Porter, M., & Masingila, J. (2000). Examining the effects of writing on conceptual and procedural knowledge in calculus. Educational Studies in Mathematics, 42, 165–177.CrossRefGoogle Scholar
  12. 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.Google Scholar
  13. 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.CrossRefGoogle Scholar
  14. 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.CrossRefGoogle Scholar
  15. 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.CrossRefGoogle Scholar
  16. 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.Google Scholar
  17. Sfard, A., & Linchevski, L. (1994). The gains and the pitfalls of Reification – The case of algebra. Educational Studies in Mathematics, 26, 191–228.CrossRefGoogle Scholar
  18. Shepard, R. S. (1993). Writing for conceptual development in mathematics. Journal of Mathematical Behaviour, 12, 287–293.Google Scholar
  19. Shield, M., & Galbraith, P. (1998). The analysis of students expository writing. Educational Studies in Mathematics, 36, 29–52.CrossRefGoogle Scholar
  20. Shuell, T. (1990). Phases of meaningful learning. Review of Educational Research, 60(4), 531–547.CrossRefGoogle Scholar
  21. Vygotsky, L. (1997). Thought and language (10th printing). Cambridge, MA: MIT Press.Google Scholar
  22. 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.Google Scholar

Copyright information

© Sense Publishers 2016

Authors and Affiliations

  • William Baker
    • 1
    • 2
  • Bronislaw Czarnocha
    • 3
    • 4
  1. 1.Mathematics DepartmentEugenio Maria de Hostos Community CollegeUSA
  2. 2.City University of New YorkUSA
  3. 3.Mathematics DepartmentEugenio Maria de Hostos Community CollegeUSA
  4. 4.City University of New YorkUSA

Personalised recommendations