Developing a local instruction theory for informal statistical estimation in middle schools
DOI:
https://doi.org/10.52041/serj.891Keywords:
Informal statistical estimation; Confidence interval; Realistic mathematics education; Local instruction theory; Conceptual fieldAbstract
This study aimed to develop a Local Instruction Theory for Informal Statistical Estimation (ISE). Although Informal Statistical Inference (ISI) has been addressed in prior studies, ISE—defined as the cognitive process of making conjectures about the likely range of a population parameter based on random sampling outcomes and expressing the uncertainty of such conjectures using probabilistic language—has received limited attention. We conceptualized ISE as situated within the broader ISI framework but distinct in its focus on interval estimation. Grounded in design heuristics of Realistic Mathematics Education, we conducted a teaching experiment with ninth-grade students to explore how they developed informal reasoning about sampling distributions. Students engaged in a series of activities designed to foster a shift from intuitive reasoning to the development of models of and for statistical estimation. Data sources included student artifacts, classroom discourse, and simulation outputs. Using Vergnaud’s conceptual field theory, we analyzed students’ emergent modeling processes by identifying concepts-in-action and theorems-in-action. Findings illustrate how instructional design can support students in understanding variability, uncertainty, and the meaning of confidence levels.
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