Full topic list
This is a session of Topic 6: Innovation and reform in teaching probability within statistics


(Wednesday 16th, 10:55-12:25)

Modeling distributions to connect chance processes, data production, and data distributions


Organizer


Abstract

The concept of distribution is central in statistics. Reasoning, formally or informally, in statistical tasks engages students in making a cycle of connections between data distributions of samples and populations, and theoretical probability distributions. Recent approaches in research and curricula engage students primarily in one direction of this cycle, making a predictive model for a given stochastic situation. This involves careful interpretations of a context and constructing a representation, explanation, or description that can be used to generate data whose distributions are well predictive of real world samples. However, another piece of the cycle comes when a student examines output from an unknown stochastic or sampling process and has to build a model of the processes that may explain the outputs. Engaging in multidirectional modeling can help students make stronger, more useful connections between real contexts and data, and probability distributions, and thus, deeper intuitions in statistical reasoning. This session will explore several different approaches to modeling with an emphasis on the tools, tasks, and metaphors used.

Papers in the session may address one or more of the following ideas:

  • What types of tasks and tools are used to engage students in modeling processes? What may be the potential benefits or drawbacks to these tasks and tools?

  • How do students reason about the use of random processes when modeling complex real world systems?

  • How do students and teachers reconcile different modeling approaches to the same problem? Are they able to justify similarities and differences in how the models may produce similar or different data?

  • When given data from a context, can students infer a model of the distribution and/or processes that produced the data? How do they introduce levels of confidence?

  • What metaphors used in modeling distributions may assist students in developing robust understandings about connections between data distributions and theoretical distributions?

Papers

PaperTitlePresenter / Co-author(s)
6E1Model-based informal inferenceRichard Lehrer (United States)
Min-Joung Kim (United States)
Ryan Seth Jones (United States)
6E2Visual representations of empirical probability distributions when using the granular density metaphorJ Todd Lee (United States)
Hollylynne Stohl Lee (United States)
6E3Multidirectional modelling for fostering students’ connections between real contexts and data, and probability distributionsTheodosia Prodromou (Australia)