Research Article
BibTex RIS Cite

PROSPECTIVE MATHEMATICS TEACHERS' MAKING SENSE OF THE DECIMAL REPRESENTATION OF REAL NUMBERS AS RATIONAL NUMBER SEQUENCES THROUGH QUANTITATIVE REASONING

Year 2017, Volume: 6 , 38 - 42, 04.08.2017

Abstract

Previous studies have revealed that students have
misconceptions on numbers specifically on real numbers (Tall &
Schwarzenberger, 1978; Ely, 2010). In order to eliminate the misconceptions,
Voskoglou (2013) suggested that teaching should emphasize the use of multiple
representations of real numbers and flexible transformations among the
representations. In the current study, we conducted classroom teaching
experiments (Cobb, 2000) with 19 prospective mathematics teachers in an
English-medium university in İstanbul about the decimal representation of real
numbers with the emphasis of quantitative reasoning (Thompson, 2011;
Karagöz-Akar, 2016). The ongoing and retrospective data analysis was done
through line by line analysis of the transcriptions of the video records and
the written artifacts. Results showed that thinking through quantities depicted
in diagrams, once prospective teachers related long division with multiple
representations of rational numbers such as fractions, equivalent fractions and
decimals through the mental actions of equal partitioning, grouping and
counting, they were able to deduce that all these representations corresponded
to the same number and squeezing the decimal representation of both rational
and irrational numbers, prospective teachers were able to deduce that real
numbers could be represented by the limits of rational number sequences.
Results might contribute to the mathematics education field by providing task
sequences showing how difficulties regarding the real numbers could be
eliminated via focusing on quantities. 

References

  • Cobb, P. (2000). Conducting teaching experiments in collaboration with teachers. In A. E. Kelly, R. A. Lesh (Eds), Handbook of Research Design in Mathematics and Science Education, pp. 307–333. Lawrence Erlbaum Associates. Ely, R. (2010). Nonstandard student conceptions about infinitesimals. Journal for Research in Mathematics Education, 41(2), 117–146. Heinz, K. A. (2000). Conceptions of ratio in a class of pre-service and practicing teachers. Ph.D. Thesis, The Pennsylvania State University. Karagoz Akar, G. (2016). Nicel muhakeme ve nicel muhakeme yoluyla kesirler üzerinden gerçek sayıların inşaası. In E. Bingölbali, S. Arslan, & İ. Ö., Zembat (Eds.), Matematik Eğitimi Teorileri (pp.117–133). Ankara: Pegem Akademi. Simon, M. A. and Tzur, R. (1999). Explicating the teacher’s perspective from the re- searchers’ perspectives: Generating accounts of mathematics teachers’ practice. Journal for Research in Mathematics Education, 30(3), 252–264. Steffe, L. P. and Thompson, P. W. (2000). Teaching experiment methodology: Underlying principles and essential elements. Handbook of research design in mathematics and science education, pp. 267–306. Tall, D., & Schwarzenberger, R. L. (1978). Conflicts in the learning of real numbers and limits. Mathematics Teaching, 82, 44–49. Thompson, P.W. (2011). Quantitative reasoning and mathematical modeling. In S. Chamberlin, L.L. Hatfield, & S. Belbase (Eds.), New perspectives and directions for collaborative research in mathematics education: Papers from a planning conference for WISDOM (pp. 33-57). Laramie: WY: University of Wyoming. Usiskin, Z., Peressini, A., Marchisotto, E. A. & Stanley, D. (2003). Mathematics for high school teachers. Prentice Hall: Upper Saddle River, New Jersey. Voskoglou, M. and Kosyvas, G.D. (2012). Analyzing students’ difficulties in understanding real numbers. Journal of Research in Mathematics Education, 1(3), 301–336. Voskoglou, M. G. (2013). An application of the APOS/ACE approach in teaching the irrational numbers. Journal of Mathematical Sciences and Mathematics Education, 8(1), 30–47.
Year 2017, Volume: 6 , 38 - 42, 04.08.2017

Abstract

References

  • Cobb, P. (2000). Conducting teaching experiments in collaboration with teachers. In A. E. Kelly, R. A. Lesh (Eds), Handbook of Research Design in Mathematics and Science Education, pp. 307–333. Lawrence Erlbaum Associates. Ely, R. (2010). Nonstandard student conceptions about infinitesimals. Journal for Research in Mathematics Education, 41(2), 117–146. Heinz, K. A. (2000). Conceptions of ratio in a class of pre-service and practicing teachers. Ph.D. Thesis, The Pennsylvania State University. Karagoz Akar, G. (2016). Nicel muhakeme ve nicel muhakeme yoluyla kesirler üzerinden gerçek sayıların inşaası. In E. Bingölbali, S. Arslan, & İ. Ö., Zembat (Eds.), Matematik Eğitimi Teorileri (pp.117–133). Ankara: Pegem Akademi. Simon, M. A. and Tzur, R. (1999). Explicating the teacher’s perspective from the re- searchers’ perspectives: Generating accounts of mathematics teachers’ practice. Journal for Research in Mathematics Education, 30(3), 252–264. Steffe, L. P. and Thompson, P. W. (2000). Teaching experiment methodology: Underlying principles and essential elements. Handbook of research design in mathematics and science education, pp. 267–306. Tall, D., & Schwarzenberger, R. L. (1978). Conflicts in the learning of real numbers and limits. Mathematics Teaching, 82, 44–49. Thompson, P.W. (2011). Quantitative reasoning and mathematical modeling. In S. Chamberlin, L.L. Hatfield, & S. Belbase (Eds.), New perspectives and directions for collaborative research in mathematics education: Papers from a planning conference for WISDOM (pp. 33-57). Laramie: WY: University of Wyoming. Usiskin, Z., Peressini, A., Marchisotto, E. A. & Stanley, D. (2003). Mathematics for high school teachers. Prentice Hall: Upper Saddle River, New Jersey. Voskoglou, M. and Kosyvas, G.D. (2012). Analyzing students’ difficulties in understanding real numbers. Journal of Research in Mathematics Education, 1(3), 301–336. Voskoglou, M. G. (2013). An application of the APOS/ACE approach in teaching the irrational numbers. Journal of Mathematical Sciences and Mathematics Education, 8(1), 30–47.
There are 1 citations in total.

Details

Journal Section Articles
Authors

Mervenur Belin This is me

Gulseren Karagoz Akar This is me

Publication Date August 4, 2017
Published in Issue Year 2017 Volume: 6

Cite

APA Belin, M., & Karagoz Akar, G. (2017). PROSPECTIVE MATHEMATICS TEACHERS’ MAKING SENSE OF THE DECIMAL REPRESENTATION OF REAL NUMBERS AS RATIONAL NUMBER SEQUENCES THROUGH QUANTITATIVE REASONING. The Eurasia Proceedings of Educational and Social Sciences, 6, 38-42.