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Presentation 7F6. Interactive Visualizations of Statistical Relationships: What do We Gain?

Andee Rubin (USA)


Presentation Abstract
Data literacy has become a fundamental skill for living in a democratic society. Data-driven decision making is increasingly at the heart of health care, education, public policy, business, and environmental activities. Many scientific statements construed as "fact" are based on correlations derived through statistical analysis of large amounts of data. As statistics educators, we know that most people are woefully bad at understanding data beyond the simple (and often misleading) pie graphs they see in the newspaper. Each day misguided decisions are being made through lack of understanding of important statistical concepts. However, there is currently some reason for optimism. Two recent developments in statistical education provide the opportunity for significant advances in helping non-statisticians judge statistical claims.

1) Research in statistical thinking has begun to yield models of people's conceptions that are detailed enough to have practical, pedagogical implications;
2) Powerful new software tools designed explicitly for statistical education provide new visualizations with enormous potential for making statistical thinking accessible.

This talk will describe research that involves a collaboration between researchers and software designers which will accelerate the development of both research and software in important ways. The work involves a three-way collaboration among TERC (Andee Rubin), the University of Massachusetts (Cliff Konold) and Key Curriculum Press (Bill Finzer). The research will focus on the effects of interactive visualizations on teachers' and students' reasoning about statistical association. The research questions, in brief, are:

Research Question 1-Examining shapes of univariate distributions: How can technology help students shift their perception from individual data points, or cases of similar value, to seeing an entire group and the characteristics of that group?

Research Question 2-Comparing univariate distributions: Konold argues that instruction should begin with comparisons of datasets, based on characteristics of their distributional shape. He propose one such tool that would make it easy for users to divide a distribution into two if there is a principled reason (e.g., a bimodal distribution of weights among young and old lions in a zoo) and work with these sub-distributions instead of the whole. How would the ability to partition data sets in this way affect the meaning teachers and students attribute to measures of central tendency?

Research Question 3-Bivariate distributions: Both Cobb (1999) and Noss et al. (1999) have found that one way people can understand covariation is by considering a scatterplot as a distribution of univariate distributions, but that students still do not always see the univariate distributions created this way as having shape. What visualization tools would reinforce this idea?

Research Question 4-Role of case information: Most real datasets have more than two variables. Many statistical analysis tools (including both Fathom and Tinkerplots) have the ability for users to see all the information about any case by selecting it on a graph. What are the effects of these features? Can they be used in a way that supports students' developing ideas of covariation or does a focus on the individual interfere with consideration of an entire distribution?


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