
06403524
j
2015b.00467
Voskoglou, Michael Gr.
Kosyvas, Georgios D.
Analyzing students' difficulties in understanding real numbers.
REDIMAT, J. Res. Math. Educ. 1, No. 3, 301336, electronic only (2012).
2012
Hipatia Press, Barcelona
EN
D74
F54
real numbers
rational numbers
irrational numbers
algebraic numbers
transcendental numbers
fractions
decimals
representations of real numbers
ME 1998d.02785
ME 2012b.00597
doi:10.4471/redimat.2012.16
Summary: This article reports on a study of highschool and of technologist students (prospective engineers and economists) understanding of real numbers. Our study was based on written response to a properly designed questionnaire and on interviews taken from students. The quantitative results of our experiment showed an almost complete failure of the technologist students to deal with processes connected to geometric constructions of incommensurable magnitudes. The results of our experiment suggest that the ability to transfer in comfort among several representations of real numbers helps students in obtaining a better understanding of them. A theoretical explanation about this is obtained through the adoption of the conceptual framework of dimensions of knowledge, introduced by {\it D. Tirosh} et al. [Educ. Stud. Math. 35, No. 1, 5164 (1998; ME 1998d.02785)] for studying the comprehension of rational numbers. Following in part the idea of generic decomposition of the APOS analysis [{\it K. Weller} et al., Can. J. Sci. Math. Technol. Educ. 9, No. 1, 528 (2009; ME 2012b.00597)] we suggest a possible order for development of understanding the real numbers by students when teaching them at school. Some questions open to further research are also mentioned at the end of the paper.