Collaborative Research: Tutoring to Apply Conceptual Understanding of Ordinary Differential Equations, Analysis for Cognitive and Computable Patterns

Principal Investigator: 
Co-Investigator: 
Project Overview
Background & Purpose: 

This project extends two threads of current research. One thread is how to tutor and assess conceptual understanding of differential equations (DE) solution methods. One area of conceptual understanding might be whether or not the student can explain qualitatively what the solution might look like, or why a particular solution procedure is appropriate. The other thread is dialogue-based computerized tutoring, where we are capturing human dialogues and building a program to provide assistance to human tutors of differential equations.

Setting: 

The students in this study are STEM undergraduates at several universities in Indiana and North Carolina.

Research Design: 

The research design for this project is descriptive [observational]. Mathematics professors, grad student teachers, and undergraduate students are observed. This project includes a tutoring intervention.

The project is developing assessments of student relational understanding of several DE solution techniques. These involve multiple choice, short-answer, and longer written or sketched answers questions administered pencil-and-paper or electronically.

The transcripts of tutoring are manually analyzed for tutorial goal structures and linguistic phenomena. Tutoring pre-tests and post-tests are analyzed for learning gains using simple statistics. Interviews with professors are analyzed manually. Assessments are tested for validity and reliability both internally and against other measures.

This project has plans to make originally collected data available to others. Other researchers may examine the repositories of tutorial dialogues.

Findings: 

To date, this project has not yet generated findings.

Other Products: 

This project expects to generate: 1) assessments for relational understanding of a few differential equation solution techniques; 2) software for assisting tutoring of ODE solution techniques; and 3) published descriptions of relational understanding, how to teach and assess it, and phenomena that are useful for computerization.