PROSPECTIVE MATHEMATICS TEACHERS' MAKING SENSE OF THE DECIMAL REPRESENTATION OF REAL NUMBERS AS RATIONAL NUMBER SEQUENCES THROUGH QUANTITATIVE REASONING
| Autor: | BELİN, Mervenur, KARAGOZ AKAR, Gulseren |
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| Rok vydání: | 2017 |
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| Zdroj: | Volume: 6, Issue: 38-42 The Eurasia Proceedings of Educational and Social Sciences |
| ISSN: | 2587-1730 |
| Popis: | Previous studies have revealed that students havemisconceptions 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 multiplerepresentations of real numbers and flexible transformations among therepresentations. In the current study, we conducted classroom teachingexperiments (Cobb, 2000) with 19 prospective mathematics teachers in anEnglish-medium university in İstanbul about the decimal representation of realnumbers with the emphasis of quantitative reasoning (Thompson, 2011;Karagöz-Akar, 2016). The ongoing and retrospective data analysis was donethrough line by line analysis of the transcriptions of the video records andthe written artifacts. Results showed that thinking through quantities depictedin diagrams, once prospective teachers related long division with multiplerepresentations of rational numbers such as fractions, equivalent fractions anddecimals through the mental actions of equal partitioning, grouping andcounting, they were able to deduce that all these representations correspondedto the same number and squeezing the decimal representation of both rationaland irrational numbers, prospective teachers were able to deduce that realnumbers could be represented by the limits of rational number sequences.Results might contribute to the mathematics education field by providing tasksequences showing how difficulties regarding the real numbers could beeliminated via focusing on quantities. |
| Databáze: | OpenAIRE |
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