Original Research

Teachers’ reasoning in a repeated sampling context

Helena Wessels, Hercules Nieuwoudt
Pythagoras | Vol 34, No 1 | a169 | DOI: https://doi.org/10.4102/pythagoras.v34i1.169 | © 2013 Helena Wessels, Hercules Nieuwoudt | This work is licensed under CC Attribution 4.0
Submitted: 06 April 2012 | Published: 02 May 2013

About the author(s)

Helena Wessels, Research Unit for Mathematics Education, University of Stellenbosch, South Africa; School of Natural Sciences and Technology Education, North-West University, South Africa
Hercules Nieuwoudt, School of Natural Sciences and Technology Education, North-West University, South Africa

Abstract

The concepts of variability and uncertainty are regarded as cornerstones in statistics. Proportional reasoning plays an important connecting role in reasoning about variability and therefore teachers need to develop students’ statistical reasoning skills about variability, including intuitions for the outcomes of repeated sampling situations. Many teachers however lack the necessary knowledge and skills themselves and need to be exposed to hands-on activities to develop their reasoning skills about variability in a sampling environment. The research reported in this article aimed to determine and develop teachers’ understanding of variability in a repeated sampling context. The research forms part of a larger project that profiled Grade 8–12 teachers’ statistical content and pedagogical content knowledge. As part of this larger research project 14 high school teachers from eight culturally diverse urban schools attended a series of professional development workshops in statistics and completed a number of tasks to determine and develop their understanding of variability in a repeated sampling context. The Candy Bowl Task was used to probe teachers’ notions of variability in such a context. Teachers’ reasoning mainly revealed different types of thinking based on absolute frequencies, relative frequencies and on expectations of proportion and spread. Only one response showed distributional reasoning involving reasoning about centres as well as the variation around the centres. The conclusion was that a greater emphasis on variability and repeated sampling is necessary in statistics education in South African schools. To this end teachers should be supported to develop their own and learners’ statistical reasoning skills in order to help prepare them adequately for citizenship in a knowledge-driven society.

Keywords

variability, repeated sampling; statistical reasoning; proportional reasoning

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