Abstract

SILVESTRE CASTRO, Eleazar; SANCHEZ SANCHEZ, Ernesto Alonso  and  INZUNZA CAZARES, Santiago. The reasoning of high school students about repeated sampling and the empirical sampling distribution. Educ. mat. [online]. 2022, vol.34, n.1, pp.100-130.  Epub June 06, 2022. ISSN 2448-8089.  https://doi.org/10.24844/em3401.04.

We present the results of the implementation of a learning trajectory whose purpose was to explore the development of high school students’ reasoning about sampling and empirical sampling distributions (ESD). We designed three tasks related to the estimation of a proportion, which were solved by the students by physically simulating the sampling process and with the support of a software. The answers to the tasks were analyzed and coded with grounded theory techniques. Results indicate that, at first, the adherence to an additive conception of sampling pushes many students to “reconstruct” the population through the unification of samples, but once they build and use an empirical sampling distribution, their reasoning begins to move towards a multiplicative conception, showing signs of assimilating some basic properties of the sampling distribution. Based on the response patterns, three levels of reasoning are proposed: naive, transitional and distributional-multiplicative.

Keywords : Levels of reasoning; additive and multiplicative conception of repeat-ed sampling; empirical sampling distribution; computer simulation; high school.