SRTL-4 (2005)

Date: July 2-7 2005
Venue: University of Auckland, Auckland, New Zealand
Theme: Reasoning about Distribution
Focus: Reasoning about Distribution
Forum Coordinator: Maxine Pfannkuch
Mathematics Education Unit
Department of Mathematics
The University of Auckland
Private Bag 92019
New Zealand
Phone: +64 9 373 7599 ext 88794
Fax: +64 9 373 7018

Presentations from SRTL4

How do Primary School Students Begin to Reason about Distributions?
Dani Ben-Zvi & Yael Sharett-Amir, University of Haifa (Israel).
This study explores the emergence of second graders’ informal reasoning about distribution in a carefully planned learning environment that includes extended encounters with open-ended Exploratory Data Analysis (EDA) activities. The current case study is offered as a contribution to understanding the process of constructing meanings, language, representations and appreciation for distributions at an early age of schooling. It concentrates on the detailed qualitative analysis of the ways by which three second grade students (age 7) started to develop views (and tools to support them) of distributions in investigating real data, inventing and using various informal data ideas and representations. In the light of the analysis, a description of what it may mean to begin reasoning about distribution by young students is proposed, and implications to teaching, curriculum and research are drawn.

Using Assessment Items To Study Students’ Difficulty Reading and Interpreting Graphical Representations Of Distributions
Robert Delmas, Joan Garfield & Ann Ooms, University of Minnesota (USA)
This paper describes the analysis of assessment items used in a large scale class testing of high school and college students to learn how students reason about graphical representations of distribution. We focus on the use of items that reveal some consistent errors and misconceptions students exhibit when presented with graphical representations of data. We find that perhaps because of students’ early exposure to bar graphs and time plots, they tend to confuse bar graphs and time plots with histograms. In addition, students have difficulty correctly reading information from histograms and identifying what the horizontal and vertical scales represent. We offer some reasons for why it is important for students to be able to correctly read and interpret histograms, and offer suggestions for how to help develop this type of reasoning.

Using Distributions as Statistical Evidence In Well-Structured and Ill-Structured Problems
Katie Makar & Jere Confrey, University of Queensland (Australia) & Washington University in St. Louis (USA)
Research has suggested that understanding in well-structured settings often does not transfer to the everyday, less-structured problems encountered outside of school. Little is known, beyond anecdotal evidence, about how teachers’ consideration of distributions as evidence in well-structured settings compares with their use in ill-structured problem contexts. A qualitative study of preservice secondary teachers examined their use of distributions as evidence in four tasks of varying complexity and ill-structuredness. Results suggest that teachers’ incorporation of distributions in well-structured settings does not imply that they will be incorporated in less structured problems (and vice-versa). Implications for research and teaching are discussed.

The Evolution of Teachers’ Understandings of Statistical Data Analysis: A Focus on Distribution
Kay McClain (2005), Vanderbilt University (USA).

Informal Inferential Reasoning: A Case Study (No Video)
Maxine Pfannkuch, The University of Auckland (New Zealand).
In this paper a secondary teacher’s reasoning from the comparison of box plot distributions during the teaching of a Year 11 (15-year-old) class is analyzed. Her purpose is to draw evidencebased conclusions from the data using informal statistical inference. A perspectives model, incorporating eight views moderated by two other views, is established to describe her reasoning. The nature of the box plot representation, the methods of instruction, and the difficulties and richness of verbalizing from the comparison of box plot distributions are discussed. Implications for research, educational practice, and assessment are drawn.

The Emergence of Distribution From Causal Roots
David Pratt & Theodosia Prodromou, Centre for New Technologies Research in Education, University of Warwick (UK).
Our premise, in line with a constructivist approach, is that thinking about distribution and stochastic phenomena in general, must develop from resources already established. Our prior research has suggested that, given appropriate tools to think with, meanings for distribution might emerge out of knowledge about causality. In this study, based on the second author’s ongoing doctoral research, we consider the relationship between the design of a microworld, in which students can control attempts to throw a ball into a basket, and the emergence of meanings for distribution. We suggest that the notion of statistical error or noise is a rich idea for helping students to bridge their deterministic and stochastic worlds.

Reasoning About Variation: A Key to Unlocking the Mystery of Distributions
Chris Reading & Jackie Reid, SiMERR National Centre & School of Mathematics, Statistics and Computer Science, University of New England (Australia).
Reasoning about variation and distribution are closely linked by researchers and much of the recent research into reasoning about variation refers specifically to notions of distribution that emerge as students reason. The research being reported here aimed to determine what aspects of students’ reasoning about variation provided a foundation for reasoning about distribution. Students in an introductory tertiary statistics course completed minute papers and tutorial questions. Those minute papers coded as demonstrating either weak or developing reasoning about variation were then reanalyzed to disclose any reasoning about distribution. In a case study approach, two pairs of students were videotaped discussing their tutorial questions to allow a more in-depth analysis of their reasoning. Key aspects of students’ progression from just describing key elements of distribution to being able to use them in comparisons and inference are discussed. The results provide educators with important considerations to inform the planning and implementing of a curriculum rich in experiences with variation, and provide researchers with some clues to better understand students’ reasoning about distribution.

The Effect of Distributional Shape on Group Comparison Strategies
Andee Rubin, Jim Hammerman, Camilla Cambell & Gilly Puttick, TERC (USA) & Massachusetts Institute of Technology (USA).
Representational tools can influence the models one builds of distributions, including methods for making group comparisons. Research has begun to explore what differences the use of such tools might make, and our work extends that research in substantial ways. In addition, this study examines how different distributional shapes might influence teachers’ analytic strategies when they are using a visualization tool. This research involved clinical interviews with teachers who had been using the visualization tool TinkerPlots™ for a year in a professional development/research seminar. The interviews included two group comparison tasks: one surrounding a symmetrical distribution and one surrounding a skewed distribution. We examine the comparison strategies teachers used in the light of the characteristics of TinkerPlots™ and the shape of the distribution they were analyzing.

Developing an Awareness of Distribution
Jane Watson, University of Tasmania (Australia)
This paper is an informal account of observations about students’ developing awareness of distribution as exhibited in responses to tasks used in Tasmanian research over the past decade. The paper attempts a synthesis of individual studies, most of which have been published task by task to illustrate detailed student performance. Themes are drawn from the collection of tasks to build an understanding of how intuitions develop before formal ideas of distribution are introduced in the school curriculum. Graphical representations produced by students are the basis of exploring the development over the years of schooling.


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Posters from SRTL4

Answers Needed
Bill Finzer, Key Curriculum Press, USA
Development of educational software requires making a great many decisions about how the software should behave and how learners should interact with it. Grappling with the decisions raises a multitude of questions about learning in general and statistical thinking in particular.

Correlation is not Causation: Instructor Perceptions of Student Understanding & Misconceptions in Bivariate Data
Andrew Zieffler, Department of Educational Psychology, University of Minnesota
This survey study of introductory statistics instructors examines instructor perceptions about students’ understanding of bivariate data. The survey asked the instructors about their current instructional and assessment practices, as well as their perceptions of student misconceptions in that unit. Differences in instructor responses are examined

Understanding p-value Survey
Sharon Lane-Getaz, University of Minnesota , USA
A P-value survey was developed based on proper conceptions and 13 misconceptions identified in the research literature. Students in first and second courses in statistics (N=333) responded to the 17 items in fall 2004. Results are reported by course.

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