Dani Ben-Zvi, University of Haifa
Statistics education, Statistical reasoning,
In this presentation, I reflect on several research projects––conducted during the past 13 years with colleagues and graduate students––on learning to reason statistically. I summarize what I learned regarding the content of these studies and offer some general lessons learned. I also suggest several research challenges that are of current interest to the statistics education community. Statistical reasoning may be defined as,
"… The way people reason with statistical ideas and make sense of statistical information (Garfield and Gal 1999). This involves making interpretations based on sets of data, graphical representations, and statistical summaries. Much of statistical reasoning combines ideas about data and chance, which leads to making inferences and interpreting statistical results. Underlying this reasoning is a conceptual understanding of important ideas, such as distribution, center, spread, association, uncertainty, randomness, and sampling." (Garfield, 2002)
These are important skills and ideas that all citizens should have and understand, and that should therefore be a standard ingredient of every student's education.
In these research projects, I study students' statistical learning and the development of their statistical reasoning at different age levels and settings. I pursue these themes in classroom studies that emphasize inquiry, reasoning, communication and collaboration, and the use of notations and technological tools. These are mostly design experiments that have both a pragmatic aspect—“engineering” particular forms of learning—and a theoretical orientation—developing domain-specific theories by systematically studying those forms of learning and the means of supporting them.
These research projects are structured around some of the core concepts of statistics––data, distribution, center, variability, comparing groups, samples and sampling, and (informal) inference––and the interrelations among them. These studies use powerful visualization tools, such as TinkerPlots, that are designed to help students develop statistical reasoning by actually constructing their own graphs and discussing them to answer their own questions. This research is systematically planned by age level, starting from lower grades in primary school through middle school.
The primary school research program focuses on the origins and emergence of statistical discourse of younger students (grades 2–6). For example, a naïve conception of “flat distribution” was identified as a precursor to the more complex empirical distribution in a study of second graders’ emerging statistical reasoning (Ben-Zvi & Amir, 2004). Students in grade 6 were able to sensibly produce, discuss, and evaluate data-based claims with respect to the sampling methods and the context of the statistical problem (Ben-Zvi, Gil, & Apel, 2007)
In the middle school, I investigate students’ development of reasoning about data, distribution, variability, and comparing groups. The results explain how they analyze data, begin to build concepts and apply representations (e.g., Ben-Zvi, 2004; Ben-Zvi & Arcavi, 2001). Practical issues are also considered, such as design principles and trajectories of instructional activities that promote student’s reasoning about these concepts, alternative assessment framework, as well as the role of technological tools in these classes (Ben-Zvi, 2006; Ben-Zvi & Garfield, 2004; Garfield & Ben-Zvi, in press).
There are many challenging questions in describing what it means for students to understand and reason about statistical concepts, and suggesting pedagogical methods for developing understanding and reasoning. In particular, the following research activities seem crucial:
1. Developing and testing empirically a theoretical framework for informal inferential reasoning––a fundamental element of statistical thinking––and the role of argumentation in inferential processes.
2. Mapping statistical reasoning as it occurs in the social context of the classroom: Expanding the studies on the development of students’ statistical reasoning about key statistical concepts (e.g., modeling and sampling), including its psychological, social, pedagogical and epistemological dimensions.
3. Focusing on learning difficulties in order to advance the understanding of the challenges in learning and teaching statistics to inspire improved instructional methods and materials, enhanced technology and alternative assessment methods.