Addressing Cognitive and Situational Complexity in the Instruction and Assessment of Statistical Reasoning (original) (raw)
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Three paradigms in developing students' statistical reasoning
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This article is a reflection on more-than-a-decade research in the area of statistics education in upper primary school (grades 4-6, 10-12 years old). The goal of these studies was to better understand young students' statistical reasoning as they were involved in authentic data investigations and simulations in a technology-enhanced learning environment entitled Connections. The article describes three main paradigms that guided our educational and academic efforts: EDA, ISI, and Modeling. The first, EDA, refers to Exploratory Data Analysis-children investigate sample data they collected without making explicit inferences to a larger population. The second, ISI, refers to Informal Statistical Inference-children make inferences informally about a larger population than the sample they have at hand. The third, Modeling-children use computerized tools to model the phenomenon they study, and simulate many random samples from that model to study statistical ideas. In each of these three paradigms, we provide a short rationale, an example of students' products, and learned lessons. To conclude, current challenges in statistics education are discussed in light of these paradigms. Statistical reasoning Although statistics is now viewed as a unique discipline, statistical content is most often taught worldwide in the mathematics curriculum (K-12) and in departments of mathematics (college level). This has led to exhortations by leading statisticians, such as Moore (1998), about the differences between statistics and mathematics. These arguments challenge statisticians and statistics educators to carefully define the unique characteristics of statistics 13
2014
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Journal of Statistics Education, 2019
The purpose of this study was to study the impact of conformity to Statistical Reasoning Learning Environment (SRLE) principles on students' statistical reasoning in Advanced Placement statistics courses. A quasi-experimental design was used to compare teachers' levels of conformity to SRLE principles through a matching process used to mitigate the effects of nonrandom assignment. This matching process resulted in five pairs of similar teachers and schools who differed in self-reported beliefs in the effectiveness and application of SRLE principles. Increases in students' statistical reasoning were found at varying levels in both high and low conformity classrooms. Improvements among teachers with low conformity to SRLE principles were less varied and consistent with national averages for improvement by college students. Improvements in classes with high conformity to SRLE principles were more varied. Students of two teachers with high levels of conformity to SRLE principles showed large levels of improvement in statistical reasoning in comparison to national results. While the comparison between classrooms conformity to SRLE principles revealed no statistically significant differences in students' statistical reasoning ability, deeper analysis suggests that beliefs and practices aligned with SRLE principles have potential to increase students' statistical reasoning at rates above national averages.
Technological advances in developing statistical reasoning at the school level.
Biehler, R., Ben-Zvi, D., Bakker, A., & Makar, K. (2013). Technology for enhancing statistical reasoning at the school level. In M. A. Clement, A. J. Bishop, C. Keitel, J. Kilpatrick, J., & A. Y. L. Leung, (Eds.). Third International Handbook on Mathematics Education (pp. 643-689). New York: Springer. The purpose of this chapter is to provide an updated overview of digital technologies relevant to statistics education, and to summarize what is currently known about how these new technologies can support the development of students’ statistical reasoning at the school level. A brief literature review of trends in statistics education is followed by a section on the history of technologies in statistics and statistics education. Next, an overview of various types of technological tools highlights their benefits, purposes and limitations for developing students’ statistical reasoning. We further discuss different learning environments that capitalize on these tools with examples from research and practice. Dynamic data analysis software applications for secondary students such as Fathom and TinkerPlots are discussed in detail, . Examples are provided to illustrate innovative uses of technology. In the future, these uses may also be supported by a wider range of new tools still to be developed. To summarize some of the findings, the role of digital technologies in statistical reasoning is metaphorically compared with travelling between data and conclusions, where these tools represent fast modes of transport. Finally, we suggest future directions for technology in research and practice of developing students’ statistical reasoning in technology-enhanced learning environments.
Applying Cognitive Theory to Statistics Instruction
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