Students’ Guided Reinvention of Definition of Limit of a Sequence With Interactive Technology
article
Alfinio Flores, Jungeun Park, University of Delaware, United States
CITE Journal Volume 16, Number 2, ISSN 1528-5804 Publisher: Society for Information Technology & Teacher Education, Waynesville, NC USA
Abstract
In a course emphasizing interactive technology, 19 students, including 18 mathematics education majors, mostly in their first year, reinvented the definition of limit of a sequence while working in small cooperative groups. The class spent four sessions of 75 minutes each on a cyclical process of guided reinvention of the definition of limit of a sequence for a particular value, L = 5. Tentative definitions were tested systematically against a well-chosen set of examples of sequences that converged, or not, to 5. Students shared their definitions and the problems they were having with their definitions with their peers through whole class presentations and public postings on a course electronic forum. Student presenters received feedback from their peers both in person and through the forum. The approximation, error, error bound framework was used to help structure students’ thinking. The use of interactive examples with epsilon bands and movable N values, in which students could zoom in to adjust the value of epsilon or zoom out to find a value of N, proved especially helpful in the process. The changes in their tentative definitions show the difficulties students had as well as the learning that occurred.
Citation
Flores, A. & Park, J. (2016). Students’ Guided Reinvention of Definition of Limit of a Sequence With Interactive Technology. Contemporary Issues in Technology and Teacher Education, 16(2), 110-126. Waynesville, NC USA: Society for Information Technology & Teacher Education. Retrieved March 19, 2024 from https://www.learntechlib.org/primary/p/151562/.
© 2016 Society for Information Technology & Teacher Education
References
View References & Citations Map- Allen, D.H., Donham, R.S., & Bernhardt, S.A. (2011). Problem-based learning. New Directions for Teaching and Learning, 2011(128), 21-29.
- Ball, D.L., Thames, M.H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389-407.
- Fernandez, E. (2004). The students’ take on the epsilon-delta definition of a limit.PRIMUS, 14(1), 43-54.
- Flores, A. (2014). Integrating computers, science, and mathematics: A course for future mathematics teachers. In S. Zvacek, M.T. Restivo, J. Uhomoibhi, & M. Helfgert (Eds.), Proceedings of the 6th International Conference on Computer Supported Education (Vol. 2, pp. 246-251). Setúbal, Portugal: Scitepress. Doi:
- Heid, M.K., Wilson, P.S., & Blume, G.W. (2015). Mathematical understanding for secondary teaching. Charlotte, NC: Information Age Publishing.
- Hershkowitz, R. (1987). The acquisition of concepts and misconceptions in basic geometry—or when “a little learning is a dangerous thing.” In J.D. Novak (Ed.),Proceedings of the 2nd International Seminar on Misconceptions and Educational Strategies in Science and Mathematics (Vol. 3, pp. 238-251). Ithaca, NY: Cornell
- Medin, D. (1989). Concepts and conceptual structure. American Psychologist, 44(12), 1469-1481.
- Moore, D.S. (1995). Teaching as a craft. MAA Focus, 15(2), 5-8.
- Oehrtman, M. (2008). Layers of abstraction: Theory and design for the instruction of limit concepts. In M.P. Carlson& C. Rasmussen (Eds.), Making the connection: Research and teaching in undergraduate mathematics education (pp. 65-80).
- Oehrtman, M., Swinyard, C., Martin, J., Roh, K., & Hart-Weber, C. (2011, February).From intuition to rigor: Calculus students’ reinvention of the definition of sequence convergence. Paper presented at the 14th annual Conference on Research in Undergraduate Mathematics Education, Portland, OR.
- Park, J., Martin, J., & Oehrtman, M. (2013). Scaling up reinvention: Developing a framework for instructor roles in the classroom. In S. Brown, G. Karakok, K.H. Roh, & M. Oehrtman (Eds.), Proceedings of the 16th Conference on Research in Undergraduate Mathematics Education (Vol. 2, pp. 613-618), Denver, CO.
- Pitta-Pantazi, D., Christou, C., & Zachariades, T. (2007). Secondary school students’ levels of understanding in computing exponents. Journal of Mathematical Behavior,26, 301-311.
- Roh, K.H. (2008). Students’ images and their understanding of definitions of the limit of sequence. Educational Studies in Mathematics, 69, 217-233.
- Rosch, E. & Mervis, C.B. (1975). Family resemblances: Studies in the internal structure of categories. Cognitive Psychology, 7, 578-605.
- Sagor, R. (2000). Guiding school improvement with action research. Alexandria, VA: Association for Supervision and Curriculum Development.
- Sowder, L. (1980). Concept and principle learning. In R.J. Shumway (Ed.), Research in mathematics education (pp. 244-285). Reston, VA: National Council of Teachers of
- Stewart, J. (2012). Calculus: Early transcendentals (7th ed.). Belmont, CA: Brooks/Cole Cengage Learning.
- Swinyard, C. (2011). Reinventing the formal definition of limit: The case of Amy & Mike. Journal of Mathematical Behavior, 30, 93-114.
- Swinyard, C., & Larsen, S. (2012). What does it mean to understand the formal definition of limit?: Insights gained from engaging students in reinvention. Journal for Research in Mathematics Education, 43(4), 465-493.
- Tall, D. (1992). The transition to advanced mathematical thinking: Functions, limits, infinity, and proof. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 495–511). New York, NY: Macmillan.
- Williams, S.R. (1991). Models of limit held by college calculus students. Journal for Research in Mathematics Education, 22(3), 219-236.
These references have been extracted automatically and may have some errors. Signed in users can suggest corrections to these mistakes.
Suggest Corrections to References