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

Mervenur Belin Gulseren Karagoz Akar

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. 

Keywords

Real numbers, quantitative reasoning, decimal representation, prospective teachers

References

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