Challita, Dalia
(2013)
*Providing College Level Calculus Students with Opportunities to Engage in Theoretical Thinking.*
Masters thesis, Concordia University.

Preview |
Text (application/pdf)
2MBChallita_MTM_F2013.pdf - Accepted Version Available under License Spectrum Terms of Access. |

## Abstract

Previous research has reported a procedural, rather than conceptual, approach in college level Calculus courses. In particular, previous studies have shown that theoretical thinking is not a necessary condition for success. This can be gleaned from the exercises on assignments and assessments which constitute all, or most of, students’ course grades. This approach has been linked with institutional constraints that are often imposed on these courses. Our belief is that theoretical thinking is necessary for learning Calculus, and that students should be provided with opportunities to engage in this type of thinking. In this thesis, we provide empirical evidence that students can be engaged in theoretical thinking in a college level Calculus course, despite the existing institutional constraints. Students enrolled in a Calculus course were presented with optional tasks intended to engage them in theoretical thinking. We analyze collected data from the perspective of Sierpinska, Nnadozie, and Oktac’s (2002) model of theoretical thinking; all students attending class engaged in these optional tasks and our analysis shows that on average, more than half of them engaged in theoretical thinking. We place our study in the context of previous research in the teaching and learning of university introductory (and remedial) level mathematics and of the role that Calculus courses play in the mathematics education of undergraduate students.

Divisions: | Concordia University > Faculty of Arts and Science > Mathematics and Statistics |
---|---|

Item Type: | Thesis (Masters) |

Authors: | Challita, Dalia |

Institution: | Concordia University |

Degree Name: | M.T.M. |

Program: | Teaching of Mathematics |

Date: | 30 June 2013 |

Thesis Supervisor(s): | Hardy, Nadia |

Keywords: | Theoretical thinking, Calculus, Quizzes, Institutional constraints |

ID Code: | 977419 |

Deposited By: | DALIA CHALLITA |

Deposited On: | 26 Nov 2013 17:29 |

Last Modified: | 18 Jan 2018 17:44 |

## References:

Barbé, J., Bosch, M., Espinoza, L., & Gascón, J. (2005). Didactic restrictions on the teacher’s practice: The case of limits of functions in Spanish high schools. In Beyond the apparent banality of the mathematics classroom, 235-268. Springer US.Bobos, G. (2004). The effect of weekly quizzes on the development of students’ theoretical thinking (Master’s thesis, Concordia University).

Boesen, J., Lithner, J., & Palm, T. (2010). The relation between types of assessment tasks and the mathematical reasoning students use. Educational studies in mathematics, 75(1), 89-105.

Guberman, R. (2008). A Framework for Characterizing the Development of Arithmetical Thinking. Proceedings of ICME-11–topic study group 10; research and development in the teaching and learning of number systems and arithmetic, 113-121.

Hardy, N. (2009a). Students’ perceptions of institutional practices: the case of limits of functions in college level Calculus courses. Educational Studies in Mathematics, 72(3), 341-358.

Hardy, N. (2009b). Students’ models of the knowledge to be learned about limits in college level calculus courses. The influence of routine tasks and the role played by institutional norms (Doctoral dissertation, Concordia University).

Hardy, N. (2010). Students’ praxeologies of routine and non-routine limit finding tasks: normal behavior vs. mathematical behavior. In M. Bosch, J. Gascon, A. Ruiz Olarria, et al. (Eds.) An Overview of the ATD:Proceedings of the 3rd International Conference on the Anthropological Theory of the Didactic, Sant Hilari Sacalm, Barcelona, Spain, January 25-29, 2010, 349-366. http://www.crm.cat/Conferences/0910/cdidactic/cdidactic.pdf

Hardy, N., & Challita, D. (2012). Students' perceptions of the role of theory and examples in college level mathematics. Accepted. Proceedings of the Psychology in Mathematics Education North American Chapter, Kalamazoo, Michigan, November 1-4, 2012.

Hewitt, D. (1999). Arbitrary and necessary part 1: A way of viewing the mathematics curriculum. For the Learning of Mathematics, 19(3), 2-9.

Lithner, J. (2000). Mathematical reasoning in task solving. Educational studies in mathematics, 41(2), 165-190.

Lithner, J. (2001). Undergraduate learning difficulties and mathematical reasoning. (Doctoral dissertation, Umeå University).

Lithner, J. (2004). Mathematical reasoning in calculus textbook exercises. The Journal of Mathematical Behavior, 23(4), 405-427.

Love, E., & Pimm. D. (1996). “This is so”: A text on texts. International handbook of mathematics education, 371-410.

Mason, J., Burton, L., & Stacey, K. (2010). Thinking mathematically. 2nd edition. London: Pearson.

Ostrom, E. (2005). Understanding institutional diversity. Princeton, NJ: Princeton University Press.

Schoenfeld, A. H. (1987). What’s All the Fuss About Metacognitlon?. Cognitive science and mathematics education, 189.

Selden, A., Selden, J., Hauk, S., & Mason, A. (1999). Do Calculus students eventually learn to solve non-routine problems. Technical Report: Department of Mathematics (5), Tennessee Technological University.

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), 1-36.

Sierpinska, A., Nnadozie, A., & Oktac, A. (2002). A study of relationships between theoretical thinking and high achievement in Linear Algebra. Unpublished manuscript. Retrieved on May 18th from http://www.annasierpinska.wkrib.com/index.php?page=publications.

Sierpinska, A., Bobos, G., & Knipping, C. (2008). Sources of students’ frustration in pre-university level, prerequisite mathematics courses. Instructional Science, 36(4), 289-320.

Sweet, S. (1998). Practicing radical pedagogy: Balancing ideals with institutional constraints. Teaching Sociology, 100-111.

Tall, D. (1990). Inconsistencies in the learning of calculus and analysis. Focus on Learning Problems in mathematics, 12(3), 49-63.

Tall, D. (1995). Cognitive growth in elementary and advanced mathematical thinking. In PME conference (Vol. 1, pp. 1-61). The program committee of the 18th PME conference.

Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational studies in mathematics, 12(2), 151-169.

Vinner S., & Hershkowitz R. (1980). Concept images and some common cognitive paths in the development of some simple geometric concepts. Proceedings of the fourth PME Conference, 177-184.

Vygotsky, L. S. (1987). The collected works of LS Vygotsky: Problems of general psychology, including the volume Thinking and speech. Rieber RW, Carton AS,(Eds, translated by Minick N), 1.

Repository Staff Only: item control page