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

Principal 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 solution methods, for example can the student explain qualitatively what the solution might look like, or why a particular solution procedure is appropriate. The other thread is dialogue-based computized tutoring, where we are capturing human dialogues and building a program to provide assistance to human tutors of differential equations.


Students are STEM undergraduates at several universities in Indiana and North Carolina.

Research Design: 

The research design for this project is descriptive [observational: observing mathematics professors, grad student teachers, and undergraduate students], and includes tutoring as an intervention. This project collects original data using assessments of learning, achievement tests, observation [personal observation, videography, web logs], and survey research [paper and pencil, self-completion questionnaires, and face-to-face semi-structured/informal interviews].

This 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.

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


To date this project hasn’t generated any findings.

Other Products: 

Assessments for relational understanding of a few differential equation solution techniques, software for assisting tutoring of ODE solution techniques, published descriptions of relational understanding, how to teach and assess it, and phenomena that are useful for computerization.