Open AccessJournal Article
Exploring Students' Conceptions of the Standard Deviation
Robert delMas,Yan Liu +1 more
TLDR
This article investigated introductory statistics students' conceptual understanding of the standard deviation and found that students moved from simple, one-dimensional understandings of standard deviation that did not consider variation about the mean to more mean-centered conceptualizations that coordinated the effects of frequency (density) and deviation from the mean.Abstract:
SUMMARY This study investigated introductory statistics students’ conceptual understanding of the standard deviation. A computer environment was designed to promote students’ ability to coordinate characteristics of variation of values about the mean with the size of the standard deviation as a measure of that variation. Twelve students participated in an interview divided into two primary phases, an exploration phase where students rearranged histogram bars to produce the largest and smallest standard deviation, and a testing phase where students compared the sizes of the standard deviation of two distributions. Analysis of data revealed conceptions and strategies that students used to construct their arrangements and make comparisons. In general, students moved from simple, one-dimensional understandings of the standard deviation that did not consider variation about the mean to more mean-centered conceptualizations that coordinated the effects of frequency (density) and deviation from the mean. Discussions of the results and implications for instruction and further research are presented.read more
Citations
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Journal ArticleDOI
Secondary mathematics teachers’ planned approaches for teaching standard deviation
TL;DR: The authors survey lesson plans designed by in-service and preservice secondary mathematical teachers and report on the accuracy, technology usage, and visual representations in the lesson plans and find that teachers tend to teach in alignment with prior learning experiences, despite professional development.
High school teachers' pedagogical content knowledge of variability
Sylvain Vermette,Linda Gattuso +1 more
TL;DR: This article explored teachers' pedagogical content knowledge of the concept of variability and found that teachers had difficulties and misconceptions related to the concept and that teachers' reactions to some scenarios highlighted the influence of content knowledge on the pedagogy knowledge related to this concept.
Book ChapterDOI
Preservice Teachers’ Difficulties with Statistical Writing
TL;DR: This chapter examined preservice teachers’ difficulties when they wrote about statistical concepts by comparing written responses and interview transcripts of the variance concept task to find the missing information in their written language compared to their verbal language.
Book ChapterDOI
Integrated Reasoning About Statistical Variation: Secondary Teachers’ Development of Foundational Understandings
Abstract: This phenomenological study investigates factors identified by secondary statistics teachers as deepening their understandings of statistical variation. Framed by a perspectives framework for reasoning about variation and transformative learning theory, this study identifies factors for teachers who exhibited integrated reasoning about variation within design, data centric, or modeling perspectives or across perspectives. Analysis revealed factors such as engagement in rational discourse and with tasks and activities that attend to fundamental statistical concepts and principles and distinctions among factors within each perspective. This work contributes to understanding circumstances conducive to developing deep understandings of statistical content.
References
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Journal ArticleDOI
Accommodation of a scientific conception: Toward a theory of conceptual change
TL;DR: In this paper, a general model of conceptual change is proposed, which is largely derived from current philosophy of science, but which they believe can illuminate * This model is partly based on a paper entitled "Learning Special Relativity: A Study of Intellectual Problems Faced by College Students,” presented at the International Conference Celebrating the 100th Anniversary of Albert Einstein, November 8-10, 1979 at Hofstra University.
Journal ArticleDOI
The Role of Anomalous Data in Knowledge Acquisition: A Theoretical Framework and Implications for Science Instruction
Clark A. Chinn,William F. Brewer +1 more
TL;DR: In this article, a detailed analysis of the ways in which scientists and science students respond to anomalous data is presented, giving special attention to the factors that make theory change more likely.