The Heuristics of Statistical Argumentation: Scaffolding at the Postsecondary Level
1 online resource (254 pages) : PDF
University of North Carolina at Charlotte
Language plays a key role in statistics and, by extension, in statistics education. Enculturating students into the practice of statistics requires preparing them to communicate results of data analysis. Statistical argumentation is one way of providing structure to facilitate discourse in the statistics classroom. In this study, a teaching experiment was conducted in which postsecondary students took an introductory statistics course that included formal and informal instruction in statistical argumentation, and a series of tasks designed to support the scaffolding of statistical argumentation. Their work was then analyzed qualitatively to determine how their statistical arguments changed over the course of a semester. Statistical argumentation is not clearly defined in existing literature. Toward filling this gap in the literature, a formal definition and heuristics of statistical argumentation are developed. Statistical argumentation is defined in this dissertation as a process of justifying a claim using evidence based on data, statistical concepts, and reasoning. Abelson’s (1995) five criteria for effective statistical arguments—magnitude, articulation, generality, interestingness, and credibility—are modified to make them appropriate for students at the introductory level. The new criteria consist of three factors: linking to context, articulating results, and making inferences. Students’ progress was monitored according to these three criteria.A constructivist classroom teaching experiment was designed to take into account the institutional curriculum for a first course in statistics at the postsecondary level and special teaching methodology to scaffold statistical argumentation. The teaching experiment was piloted three times to refine the tasks and pedagogy before data was collected for this study in the fourth implementation. A key part of the pedagogy was the development of a classroom culture that supported statistical argumentation. In addition, formal instruction in statistical argumentation took place in four teaching episodes. Each teaching episode followed the same pattern: 1) the teacher-researcher presented a sample argument to the class, 2) students completed arguments in small groups, 3) students completed arguments individually, and 4) students answered reflection questions about their arguments, either in writing or by interview. Students who completed reflections via interview could choose to have the conversation recorded as part of the data collection process. All tasks were the same format: students were asked to answer a research question based on information provided, which consisted of sampling and data collection procedures and results of data analysis in the form of output from a computer software package. The four teaching episodes were based on increasingly advanced statistical content that aligned with the material being covered in class.The individual statistical arguments and interviews of three students were chosen for full analysis as case studies. The three students were chosen to represent a wide variety of characteristics of statistical arguments. Results show the students made little change in linking to context. However, they showed improvement in the individual aspects of articulation of results: center, spread, distribution, and hypothesis testing. They were also able to incorporate increasingly advanced statistical content while maintaining or improving in their discussion of previously included content. Students’ statistical inference improved over time as well, particularly when hypothesis testing was added to the data analysis; this is not surprising since hypothesis testing is inherently inferential. Student feedback solicited at the end of the teaching experiment indicated that students believed the tasks helped support their learning of statistical concepts and prepared them to interact with statistics in the future.
STATISTICAL ARGUMENTATIONSTATISTICAL REASONINGSTATISTICS EDUCATIONTEACHING EXPERIMENT
Curriculum & Instruction
Blitvich, PilarCifarelli, VictorFlowers, Claudia
Thesis (Ph.D.)--University of North Carolina at Charlotte, 2017.
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