Why it is important for in-service elementary mathematics teachers to understand the equality .999...=1

Journal of Mathematical Behavior

Volumn 30, Issue 4, 2011, Pages 304-318

  Yopp, David A ^a   Burroughs, Elizabeth A ^a   Lindaman, Brian J ^a  

^a MONTANA STATE UNIVERSITY   (United States)

Author keywords

Cognitive disequilibrium; Elementary teaching; In service teachers; Repeating decimals

Indexed keywords

EID: 80054683032     PISSN: 07323123     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmathb.2011.07.007     Document Type: Article

References (18)

1. Asiala M., Brown A., Devries D., Dubinsky E., Mathews D., Thomas K. A framework for research and curriculum development in undergraduate mathematics education. Research in collegiate mathematics education II 1996, 1-32. American Mathematical Society, Providence, RI. J. Kaput, A. Schoenfeld, E. Dubinsky (Eds.).
2. Burroughs E.A., Yopp D. Prospective elementary mathematics teachers' conceptions of decimals with single repeating digits. Investigations in Mathematics Learning 2010, 3(1):23-42.
3. Behr M., Harel G. Students' errors, misconceptions, and conflict in application of procedures. Focus on Learning Problems in Mathematics 1995, 12:75-84.
4. Corbin J., Strauss A. Basics of qualitative research 3e 2008, Sage Publications, Thousand Oaks.
5. Dewey J. How we think: A restatement of the relation of reflective thinking to the educative process 1933, D.C. Heath and Co, Boston.
6. Dubinsky E., Weller K., McDonald M.A., Brown A. Some historical issues and paradoxes regarding the concept of infinity: An APOS analysis: Part 2. Educational Studies in Mathematics 2005, 60:253-266.
7. Festinger L. A theory of cognitive dissonance 1957, Stanford University Press, Stanford, CA.
8. Flavell J. Cognitive development 1977, Prentice Hall, Engelwood Cliffs, NJ.
9. Hadas N., Hershkowitz R., Schwarz B. The role of contradiction and uncertainty in promoting the need to prove in dynamic geometry environments. Educational Studies in Mathematics 2000, 44:127-150.
10. Leikin R., Levav-Waynberg A. Exploring mathematics teacher knowledge to explain the gap between theory-based recommendations and school practice in the use of connecting tasks. Educational Studies in Mathematics 2007, 66(3):349-371.
11. Piaget J. The equilibration of cognitive structures 1985, University of Chicago Press, Chicago, (Original work published 1975).
12. Richman F. Is 0.999=1?. Mathematics Magazine 1999, 72(5):396-400.
13. Sierpinska A. Humanities students and epistemological obstacles related to limits. Educational Studies in Mathematics 1987, 18:371-397.
14. Tall D.O. Cognitive difficulties in learning analysis. Report on the teaching of analysis 1994, 34-44. TaLUM Committee of the Mathematical Association. A. Barnard (Ed.).
15. Tall D.O., Schwarzenberger R.L.E. Conflicts in the learning of real numbers and limits. Mathematics Teaching 1978, 82:44-49.
16. Tirosh D., Graeber A. Evoking cognitive conflict to explore preservice teachers' thinking about division. Journal for Research in Mathematics Education 1990, 21:98-108.
17. Weller K., Arnon I., Dubinsky E. Preservice teachers' understanding of the relation between a fraction or integer and its decimal expansion. Canadian Journal of Science, Mathematics, and Technology Education 2009, 9(1):5-28.
18. Zaslavsky O. Seizing the opportunity to create uncertainty in learning mathematics. Educational Studies in Mathematics 2005, 60:297-321.