Students' images and their understanding of definitions of the limit of a sequence

Educational Studies in Mathematics

Volumn 69, Issue 3, 2008, Pages 217-233

  Roh, Kyeong Hah ^a  

^a ARIZONA STATE UNIVERSITY   (United States)

Author keywords

Asymptotes; Cluster points; Images; Limits; Rigorous definitions; Sequences

Indexed keywords

EID: 53849115008     PISSN: 00131954     EISSN: 15730816     Source Type: Journal    
DOI: 10.1007/s10649-008-9128-2     Document Type: Article

References (32)

1. L. Alcock A. Simpson (2004) Convergence of sequences and series: Interactions between visual reasoning and the learner's beliefs about their own role Educational Studies in Mathematics 57 1 32
2. L. Alcock A. Simpson (2005) Convergence of sequences and series 2: Interactions between visual reasoning and the learner's beliefs about their own role Educational Studies in Mathematics 58 77 100
3. Apostol, T. (1974). Mathematical analysis. Reading, MA: Addison-Wesley.
4. J. Bezuidenhout (2001) Limits and continuity: Some conceptions of first-year students International Journal of Mathematical Education in Science and Technology 32 487 500
5. Brackett, J. D. (1991). The association of mathematical context with students' responses to tasks involving infinity. Dissertation, University of Georgia.
6. Brousseau, G. (1997). Theory of didactical situations in mathematics (N. Balacheff, M. Cooper, R. Sutherland, & V. Warfield, Trans.) Dordrecht, The Netherlands: Kluwer Academic.
7. Cornu, B. (1991). Limits. In D. Tall (Ed.), Advanced mathematical thinking (pp. 153-166). Dordrecht, The Netherlands: Kluwer Academic.
8. J. Cottrill E. Dubinsky D. Nichols K. Schwingendorf K. Thomas D. Vidakovic (1996) Understanding the limit concept: Beginning with a coordinated process schema Journal of Mathematical Behavior 15 167 192
9. R. B. Davis S. Vinner (1986) The notion of limit: Some seemingly unavoidable misconception stages Journal of Mathematical Behavior 5 281 303
10. Ferrini-Mundy, J., & Lauten, D. (1993). Teaching and learning calculus. In P. S. Wilson (Ed.), Research ideas for the classroom: High school mathematics (pp. 155-176). New York: Macmillan.
11. Fischbein, E. (1987). Intuition in science and mathematics. Dordrecht, The Netherlands: D. Reidel.
12. Hitt, F., & Lara-Chavez, H. (1999). Limits, continuity and discontinuity of functions from two points of view: That of the teacher and that of the student. In L. Bills (Ed.), Proceeding of the British Society for Research into Learning Mathematics, 19, 49-54.
13. Kawski, M. (1997). How CAS and visualization lead to a complete rethinking of an introduction to vector calculus. In W. Fraunholz (Ed.), Proceeding of the Third International Conference on Technology in Mathematics Teaching. Koblenz, Germany.
14. I. Kidron N. Zehavi (2002) The role of animation in teaching the limit concept The International Journal of Computer Algebra in Mathematics Education 9 205 227
15. J. Mamona-Downs (2001) Letting the intuitive bear on the formal: A didactical approach for the understanding of the limit of a sequence Educational Studies in Mathematics 48 259 288
16. Marsden, J. E., & Hoffman, M. J. (2000). Elementary classical analysis (2nd ed.). New York: Freeman.
17. M. Navarro P. Carreras (2006) Constructing a concept image of convergence of sequences in the van Hiele framework Research in Collegiate Mathematics Education VI 61 98
18. Neuhauser, C. (2004). Calculus for biology and medicine (2nd ed.). Upper Saddle River, New Jersey: Pearson Education.
19. Oehrtman, M. (2002). Collapsing dimensions, physical limitation, and other student metaphors for limit concepts: An instrumentalist investigation into calculus students' spontaneous reasoning. Dissertation, The University of Texas.
20. Piaget, J., & Inhelder, B. (1967). The child's conception of space (F. J. Langdon & J. L. Lunzer., Trans.). New York: The Norton Library.
21. M. Pinto D. Tall (2002) Building formal mathematics on visual imagery: A case study and a theory For the Learning of Mathematics 22 2 10
22. M. Przenioslo (2004) Images of the limit of function formed in the course of mathematical studies at the university Educational Studies in Mathematics 55 103 132
23. Roh, K. (2005). College students' intuitive understanding of the limit of a sequence and their levels of reverse thinking. Dissertation, The Ohio State University.
24. A. Sierpińska (1987) Humanities students and epistemological obstacles related to limits Educational Studies in Mathematics 18 371 397
25. Stewart, J. (2003). Calculus: Early transcendental single variable (5th ed.). Belmont, CA: Brooks/Cole-Thomas Learning.
26. Stroyan, K. D. (1998). Mathematical background: Foundations of infinitesimal calculus. Retrieved from http://www.math.uiowa.edu/~stroyan/ research.htm. (June 8, 2007)
27. J. E. Szydlik (2000) Mathematical beliefs and conceptual understanding of the limit of function Journal for Research in Mathematics Education 31 256 276
28. Taback, S. (1975). The child's concept of limit. In M. F. Rosskopf (Ed.), Children's mathematical concepts (pp. 111-144). New York: Teachers College Press.
29. Tall, D. (1992). The transition to advanced mathematical thinking: functions, limits, infinity, and proof. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 495-511). New York: Macmillan.
30. D. Tall S. Vinner (1981) Concept image and concept definition in mathematics, with particular reference to limits and continuity Educational Studies in Mathematics 12 151 169
31. Vinner, S. (1991). The role of definitions in the teaching and learning of mathematics. In D. Tall (Ed.), Advanced mathematical thinking (pp. 65-81). Dordrecht, The Netherlands: Kluwer Academic.
32. S. Williams (1991) Models of limit held by college calculus students Journal for Research in Mathematics Education 22 219 236