Title

A Deeply Digital Instructional Unit on Binomial Distributions and Statistical Inference: A Design Experiment

Date of Award

6-2014

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Dr. Christian R. Hirsch

Second Advisor

Dr. Steven W. Ziebarth

Third Advisor

Dr. Christine A. Browning

Fourth Advisor

Dr. Brin A. Keller

Abstract

Mathematics curriculum materials and the nature of their tasks strongly influence what mathematics students have the opportunity to learn and how they learn it. Flexible, highly interactive digital instructional resources offer a promising, but thus far underdeveloped, alternative to conventional print materials.

A design experiment that involved iterative cycles of (re)design, development, and testing of a “deeply digital” problem-based instructional unit on binomial distributions and statistical inference, intended for students in a fourth-year high school mathematics course, had four foci:

(1) explicate how the design features and learning progressions of a print binomial distributions unit were transformed into deeply digital versions through iterative cycles of (re)design, development, and testing; (2) examine the enactment of the deeply digital instructional unit and explicate the differences revealed between the intended and observed learning progressions; (3) assess the efficacy of the deeply digital instructional unit in promoting understanding of key concepts and methods related to binomial distributions and statistical inference; and (4) interpret the implications of the findings for practitioners.

Data from classroom observations and digital artifacts, student and teacher interviews, and student surveys and assessments were collected, analyzed, and interpreted. Research methodology, results, and implications are elaborated in two research papers. A third paper interpreted the research in terms of classroom practice.

Paper 1: A Study of the Iterative Development and Efficacy of a Deeply Digital Instructional Unit on Binomial Distributions and Statistical Inference Paper 2: A Didactical Analysis of Learning Progressions for Print and Deeply Digital Delivery of a Binomial Distributions Unit Paper 3: Delving Deeper into Digitally Based Lessons: How Design Features Can Transform Problem-Based Instruction

Design features of the digital unit included mathematical and statistical software tools, accessibility features, learner-controlled scaffolding, embedded audio and video clips, and digital collaborative notebooks. Results indicated that students generally accessed the open-ended problems without use of the learner-controlled scaffolding. When students selected to use the scaffolding, they solved problems without evidencing any statistical or mathematical errors in their final work. Results also indicated that students showed growth in their understanding of key concepts and methods related to binomial distributions and statistical inference.

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