Resumen

MONTORO, Virginia; SCHEUER, Nora  y  PEREZ ECHEVERRIA, Ma. del Puy. How Abundant are the Sets of Numbers? Students Comparing Infinite Sets of Numbers. Educ. mat. [online]. 2016, vol.28, n.3, pp.145-174.  Epub 08-Abr-2022. ISSN 2448-8089.  https://doi.org/10.24844/em2803.06.

We studied how students with different mathematical background conceive infinite cardinality of number sets. We analyzed a task in which high school and college students were requested to compare infinite number sets. Students were classified according to their ideas on infinity. Using this classification together with the students' level of math education, we performed a correspondence factorial analysis. A gradient was found in the depth of students' ideas. At one end we found what we called horror infiniti, based students propensity avoid infinity and instead construe it as something undefined. These views were associated with students with less mathematical education. In an intermediate zone, the finitist conception was placed. It was the most frequent way of thinking among the participants of the study, with three versions: tacitly infinitist, explicitly finitist, or taking the integers as model of inclusion. At the other end, the infinitist conception was placed. It was present among students with college mathematical education, according to two types: thinking of the cardinality of number sets as a unique infinite quantity; or conceiving different infinite cardinals. The latter was found only in advanced mathematics students.

Palabras llave : comparison; number sets; cardinal infinity; mathematics education.

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