Relating the construction of sample spaces and proportional reasoning in Costa Rican students

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Luis A. Hernández-Solís
Universidad Estatal a Distancia, Costa Rica
https://orcid.org/0000-0003-2956-8102
Carmen Batanero
Universidad de Granada, España
https://orcid.org/0000-0002-4189-7139
María M. Gea
Universidad de Granada, España
https://orcid.org/0000-0002-5229-0121

Abstract

The objective of this study was to analyze the relationship between the level of proportional reasoning and the construction of the sample space in Costa Rican students. For this purpose, two questionnaires were used, each with three ratio comparison items, which together consider six different levels of proportional reasoning. In addition, both questionnaires included two identical items on the construction of the sample space compatible with a certain, equiprobable and impossible event. In the responses of 292 students in grades 6-10 (11-15 years old) to these questionnaires we analyze the proportional reasoning shown and the type of event that would occur according to the constructed sample space. The results indicate that few students reach the highest level of proportional reasoning, although the proportion that reaches it increases with the course. The construction of sample spaces associated with the impossible and certain event was difficult and a direct relationship with the level of proportional reasoning is observed, confirmed by the correlation between the level of proportional reasoning and the number of correctly constructed sample spaces.

Item information
Published: Jul 30, 2024
Issue: Vol. 3 (2024): Revista de Educación Estadística
Section: Investigación
DOI: https://doi.org/10.29035/redes.3.1.1
Keywords: Probability, Reasoning, Assessment

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