Math

Characteristics of Successful Programs in College Calculus - Phase II

Principal Investigator:

David Bressoud

Co-Investigator:

Chris Rasmussen

Linda Braddy

Sean Larsen

Project Overview

Background & Purpose:

This project has enabled us to identify what works in college calculus instruction, to understand why it works, and to disseminate this information to improve student success in calculus throughout the United States. Phase I of the study was a large-scale survey based on a stratified random sample of calculus programs; Phase II involved in-depth case study analysis of eighteen highly successful programs in a variety of types of colleges.

Setting:

The survey was conducted as a stratified random sample consisting of over 400 colleges and universities across the United States. The case study visits were to 18 colleges and universities that including rural and urban 2-year colleges, undergraduate colleges, comprehensive universities, and large research universities, representing all regions of the United States and both public and private institutions.

Research Design:

The project uses a cross-sectional and comparative research design and will generate evidence that is descriptive [case study, observational] and associative correlational [statistical modeling based on survey data]. Original data are being collected on students taking mainstream Calculus I drawn from a stratified random sample chosen from all 2- and 4-year colleges in the United States using school records, observation [personal], and survey research [self-completion questionnaire, structured interviewer-administered questionnaire, semi-structured or informal interviews, and focus groups]. Specifically, Phase I employed four online surveys: an instructor survey before class begins, a student survey in the second week of class, a student survey in the last week of the term, and an instructor survey immediately after the term ends. Phase II developed protocols for classroom observations and gathering of consistent data from faculty and administrators.

For the Phase I survey, data were mapped to metrics so that multiple linear regression and its variants could be applied. Propensity matching was employed to even out the differences between, for example, those who did and those who did not study AP Calculus in high school. For Phase II, we will employ pattern matching to compare rival hypotheses regarding explanations of the observations, explanation building through iterative construction of a narrative that explains student success, and cross-case synthesis, comparing narratives across different institutions. Survey data has been made anonymous and is now available by request at maa.org/cspcc.

Findings:

A hierarchical linear model that enabled us to study the effect of classroom experience on shifts in student attitudes showed three factors that explained most of the variation attributable to classroom experience: "use of technology," which had little effect except when use by graduate teaching assistants when it had a strong negative effect; "good teaching," which had a strong positive effect that was most pronounced for the students entering with poor attitudes; and "progressive pedagogies," which had a negative effect but which interacted very strongly with "good teaching," producing a positive effect when combined with high "good teaching" and a negative effect when combined with low "good teaching."

We also identified seven characteristics of successful programs:

Regular use of local data to guide curricular and structural modifications.
Attention to the effectiveness of placement procedures.
Coordination of instruction, including the building of communities of practice.
Construction of challenging and engaging courses.
Use of student-centered pedagogies and active-learning strategies.
Effective training of graduate teaching assistants.
Proactive student support services, including the fostering of student academic and social integration.

Publications & Presentations:

Links to all publications and presentations are available at maa.org/cspcc.

Other Products:

Protocols for classroom observation.

On the Web:

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