Contributions of a sequence of activities to the conceptual understanding of sampling and its implications for the teaching of statistics by in-service and pre-service teachers

Abstract

Currently, the critical interpretation of statistical data is becoming increasingly necessary. Understanding sampling-related concepts is also relevant, given the prevalence of sample surveys in everyday life. To meet social demands and the requirements of the curricula, teacher education focused on statistical literacy plays a significant role, contributing to conceptual and pedagogical improvement. This article analyzes a sampling activity, part of a formative program conducted with in-service and pre-service teachers, within the context of a validated proposal developed in doctoral research. The objective of this work is to analyze, from a reflective perspective, the contributions of an activity involving erroneous beliefs about sampling to the development of content and pedagogical knowledge necessary for its teaching. Principles of design experiments support the methodological design of the study, whose data-collection instruments included participant protocols, a field diary, and audio recordings from the activity. We used content analysis following a directed approach, with predefined categories based on statistical literacy and knowledge mastery for teaching. The results revealed gaps in statistical and curriculum knowledge, and enabled the identification of erroneous beliefs about sampling, such as insensitivity to sample size and the composition fallacy. The observed strengths relate to contextual and mathematical knowledge, as well as critical questioning. Finally, when addressing issues aimed at improving the observed obstacles, pertinent discussions emerged that highlighted pedagogical knowledge.