Abstract
This chapter has a special aim and organization. It presents the comparative study of three different approaches to the same theme of proportional reasoning, in particular of the concept of the rate. The idea for the study is related to the Chinese Keli lesson study method (Huang & Bao, 2006), whose one of the approaches is the observation of two classes taught by different instructors and presenting different approaches to the same theme (CTRAS 5, 2013) followed by the discussion comparing the instructional approaches.
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
Adi, H., & Pulos, S. (1980). Individual differences and formal operational performance of college students. Journal for Research in Mathematics Education, 11(2), 150–156.
Anderson, J. R. (1990). Cognitive psychology and its implications. New York, NY: WH Freeman/Times Books/Henry Holt & Co.
Arnon, I., Cottrill, J., Dubinsky, E., Oktaç, A., Fuentes, S. R., Trigueros, M., & Weller, K. (2013). APOS theory: A framework for research and curriculum development in mathematics education. Berlin: Springer Science & Business Media.
Berk, D., Taber, S. B., Gorowara, C. C., & Poetzl, C. (2009). Developing prospective elementary teachers’ flexibility in the domain of proportional reasoning. Mathematical Thinking and Learning, 11(3), 113–135.
Bailin, S. (1987). Critical and creative thinking. Informal logic, 9(1).
Caddle, M. C., & Brizuela, B. M. (2011). Fifth graders’ additive and multiplicative reasoning: Establishing connections across conceptual fields using a graph. The Journal of Mathematical Behavior, 30(3), 224–234.
Christou, C., & Philippou, G. (2001). Mapping and development of intuitive proportional thinking. The Journal of Mathematical Behavior, 20(3), 321–336.
Cifarelli, V. V. (1998). The development of mental representations as a problem solving activity. The Journal of Mathematical Behavior, 17(2), 239–264.
Cobb, P. (2011) Chapter 2 Introduction: Part I Radical constructivism. In E. Yackel, K. Gravemeijer, & A. Sfard (Eds.), A journey in mathematics education research: insights from the work of Paul Cobb, Mathematics education library 48 (pp. 9–17). Dordrecht, Heidelberg, London, & New York, NY: Springer Verlag.
Cobb, P., & Steffe, L. P. (2010). The constructivist researcher as teacher and model builder. In A journey in mathematics education research (pp. 19–30). Netherlands: Springer.
CTRAS 5. (Conference of Teaching-Research for All Students, 2013), Fujiow, China
Czarnocha, B., Dubinsky, E., Prabhu, V., & Vidakovic, D. (1999). One theoretical perspective in undergraduate mathematics education research. In Proceedings PME Conference, Vol. 1 (pp. 1–95).
Dubinsky, E. (1991). Reflective abstraction in advanced mathematical thinking. In D. Tall (Ed.), Advanced mathematical thinking (pp. 95–126). Dordrecht: Kluwer Academic Publishers.
Fernandez, C., Llinares, S., Modestou, M., & Gagatsis, A. (2010). Proportional reasoning: How task variables influence the development of students’ strategies from primary to secondary school. Acta Didactica Universitatis Comenianae Mathematics, ADUC, 10, 1–18.
Glasersfeld, E. V. (1998, September). Scheme theory as a key to the learning paradox. Paper presented at the 15th Advanced Course, Archives Jean Piaget, Geneva, Switzerland.
Goodson-Espy, T. (1998). The roles of reification and reflective abstraction in the development of abstract thought: Transitions from arithmetic to algebra. Educational studies in mathematics, 36(3), 219–245.
Huang, R., & Bao, J. (2006). Towards a model for teacher professional development in China: Introducing KELI. Journal of Mathematics Teacher Education, 9, 279–298.
Inhelder, B., & Piaget, J. (1958). The growth of logical thinking from childhood to adolescence. New York, NY: Basic Books.
Kuhn, D. (1999). A developmental model of critical thinking. Educational Researcher, 28(2), 16–25.
Lamon, S. (2007). Rational numbers and proportional reasoning: Towards a theoretical framework for research. In F. K. Lester, Jr. (Ed.), Second handbook of research on mathematics teaching and learning. Greenwich CT; Information Age Publishing.
Lo, J. J., & Watanabe, T. (1997). Developing ratio and proportion schemes: A story of a fifth grader. Journal for Research in Mathematics Education, 28(2), 216–236.
Mariotti, M., A. (2009) Artifacts and signs after a Vygotskian perspective: the role of the teacher. ZDM Mathematics Education, 41, 427–440.
Norton, A., & D’Ambrosio, B. S. (2008). ZPC and ZPD zones of teaching and learning. Journal of Research in Mathematics Education, 39(3), 220–246.
Paul, R., & Elder, L. (2008). Critical and creative thinking. Dillon Beach, CA: The Foundation for Critical Thinking Press. Retrieved January 2015, www.criticalthinking.org
Piaget, J., & Garcia, R. (1991). Toward a logic of meaning (Trans.). Hillsdale, NJ: Lawrence Erlbaum Associates. (Original work published 1987)
Presmeg, N. (2003). Creativity, mathematizing, and didactizing: Leen Streefland’s work continues. Educational Studies in Mathematics, 54(1), 127–137.
Richardson, V. (2003). Constructivist pedagogy. Teachers College Record, 105(9), 1623–1640.
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. The Concept of Function: Aspects of Epistemology and Pedagogy, 25, 59–84.
Sfard, A., & Linchevski, L. (1994). The gains and pitfalls of reification: The case of algebra. Educational Studies in Mathematics, 26, 191–228.
Simon, M. A., Tzur, R., Heinz, K., & Kinzel, M. (2004). Explicating a mechanism for conceptual learning: Elaborating the construct of reflective abstraction. Journal for Research in Mathematics Education, 35, 305–329.
Singh, P. (2000). Understanding the concepts of proportion and ratio constructed by two grade six students. Educational Studies in Mathematics, 43, 271–292.
Steffe, L. P., & Thompson, P. W. (2000). Teaching experiment methodology: Underlying principles and essential elements. In R. Lesh & A. E. Kelly (Eds.), Research design in mathematics and science education (pp. 267–307). Hillsdale, NJ: Erlbaum.
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.
Treffinger, D. J. (1995). Creative problem solving: Overview and educational implications. Educational Psychology Review, 7(3), 301–312.
Vergnaud, G. (1983). Multiplicative structures. In R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts and processes (pp. 127–174). New York, NY: Academic Press.
Vergnaud, G. (1994). Multiplicative conceptual field: what and why. In G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 41–59). Albany, NY: State University of New York Press.
Vygotsky, L. S. (1997). Thought and language – Revised edition (10th ed.). Cambridge MA: 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
Dias, O., Baker, W., Czarnocha, B. (2016). Comparative Study of Three Approaches to Teaching Rates. 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_24
Download citation
DOI: https://doi.org/10.1007/978-94-6300-549-4_24
Publisher Name: SensePublishers, Rotterdam
Online ISBN: 978-94-6300-549-4
eBook Packages: EducationEducation (R0)