Teachers’ reasoning in a repeated sampling context
Date
2013-05-02
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
AOSIS Publishing
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.
Description
Please cite as follows:
Wessels, H., & Nieuwoudt, H. 2013. Teachers’ reasoning in a repeated sampling context. Pythagoras, 34(1):1-11 (Art. #169), doi:10.4102/pythagoras.v34i1.169.
The original publication is available at http://www.pythagoras.org.za
Wessels, H., & Nieuwoudt, H. 2013. Teachers’ reasoning in a repeated sampling context. Pythagoras, 34(1):1-11 (Art. #169), doi:10.4102/pythagoras.v34i1.169.
The original publication is available at http://www.pythagoras.org.za
Keywords
Mathematical statistics -- Study and teaching, Educational statistics
Citation
Wessels, H., & Nieuwoudt, H. 2013. Teachers’ reasoning in a repeated sampling context. Pythagoras,
34(1):1-11 (Art. #169), doi:10.4102/pythagoras.v34i1.169.