A FRAMEWORK FOR TEACHING AND ASSESSING REASONING ABOUT VARIABILITY

SUMMARY This article is a discussion of and reaction to two collections of papers on research on Reasoning about Variation: Five papers appeared in November 2004 in a Special Issue 3(2) of the Statistics Education Research Journal (by Hammerman and Rubin, Ben-Zvi, Bakker, Reading, and Gould), and three papers appear in a Special Section on the same topic in the present issue (by Makar and Confrey, delMas and Liu, and Pfannkuch). These papers show that understanding of variability is much more complex and difficult to achieve than prior literature has led us to believe. Based on these papers and other pertinent literature, the present paper, written by the Guest Editors, outlines seven components that are part of a comprehensive epistemological model of the ideas that comprise a deep understanding of variability: Developing intuitive ideas of variability, describing and representing variability, using variability to make comparisons, recognizing variability in special types of distributions, identifying patterns of variability in fitting models, using variability to predict random samples or outcomes, and considering variability as part of statistical thinking. With regard to each component, possible instructional goals as well as types of assessment tasks that can be used in research and teaching contexts are illustrated. The conceptual model presented can inform the design and alignment of teaching and assessment, as well as help in planning research and in organizing results from prior and future research on reasoning about variability.

[1]  Yan Liu,et al.  EXPLORING STUDENTS’ CONCEPTIONS OF THE STANDARD DEVIATION , 2005 .

[2]  G. Wiggins,et al.  Understanding by Design , 1998 .

[3]  Jere Confrey,et al.  “VARIATION-TALK”: ARTICULATING MEANING IN STATISTICS , 2005 .

[4]  Maxine Pfannkuch.  Thinking Tools and Variation. , 2005 .

[5]  Dani Ben-Zvi,et al.  Research on Statistical Literacy, Reasoning, and Thinking: Issues, Challenges, and Implications , 2004 .

[6]  Maxine Pfannkuch,et al.  TOWARDS AN UNDERSTANDING OF STATISTICAL THINKING , 2004 .

[7]  Refractor.  Uncertainty , 2001, The Lancet.

[8]  C. Wild,et al.  Statistical Thinking in Empirical Enquiry , 1999 .

[9]  Andee Rubin,et al.  STRATEGIES FOR MANAGING STATISTICAL COMPLEXITY WITH NEW SOFTWARE TOOLS , 2004 .

[10]  Christine M. Anderson-Cook.  The Challenge of Developing Statistical Literacy, Reasoning and Thinking , 2006 .

[11]  D. S. Moore,et al.  New Pedagogy and New Content: The Case of Statistics , 1997 .

[12]  Robert G. Gould,et al.  VARIABILITY: ONE STATISTICIAN'S VIEW , 2004, STATISTICS EDUCATION RESEARCH JOURNAL.

[13]  D. A. Cowan.  Rhythms of Learning , 1995 .

[14]  Lynn Arthur Steen,et al.  On the shoulders of giants: new approaches to numeracy , 1990 .

[15]  R. Skemp.  Relational Understanding and Instrumental Understanding. , 2006 .

[16]  Joan Garfield,et al.  The challenge of developing statistical literacy, reasoning and thinking , 2004 .

[17]  T. M. F. Smith.  [Statistical Thinking in Empirical Enquiry]: Discussion , 1999 .

[18]  Dani Ben-Zvi,et al.  REASONING ABOUT VARIABILITY IN COMPARING DISTRIBUTIONS 4 , 2004 .

[19]  Chris Reading.  Student Description of Variation while Working with Weather Data. , 2004 .

[20]  Jerome S. Bruner,et al.  Going Beyond the Information Given , 2006 .

[21]  Jane Watson,et al.  School Mathematics Students' Acknowledgement of Statistical Variation , 1999 .

[22]  Arthur Bakker,et al.  REASONING ABOUT SHAPE AS A PATTERN IN VARIABILITY , 2004, STATISTICS EDUCATION RESEARCH JOURNAL.

[23]  Sheldon P. Gordon,et al.  Statistics for the Twenty-First Century , 1992 .

[24]  D. Ben-Zvi.  Toward Understanding the Role of Technological Tools in Statistical Learning , 2000 .

[25]  Maxine Pfannkuch,et al.  Statistical Thinking: One Statistician's Perspective , 1997 .