for the
Thirteenth Special Interest Group of the Mathematical Association of America

on Research in
Undergraduate Mathematics Education

Conference on Research
in
Undergraduate Mathematics Education

Marriott Raleigh City
Center - Raleigh, North Carolina

February 25 –
February 28, 2010

**The Student-Centered Active Learning Environment
for Undergraduate Programs (SCALE-UP) Project**

Robert J. Beichner, Alumni Distinguished
Professor of Physics

North Carolina State University

How do you keep a classroom of 100 undergraduates actively learning?
Can students practice communication and teamwork skills in a large class? How
do you boost the performance of underrepresented groups? The SCALE-UP Project
has addressed these concerns. The room design and pedagogy have been adopted at
more than 100 leading institutions across the country. Physics, chemistry,
math, astronomy, biology, engineering, earth sciences, and even literature
classes are currently being taught this way.

Hundreds of hours of classroom video and audio recordings, transcripts
of numerous interviews and focus groups, data from conceptual learning
assessments (using widely-recognized instruments in a pretest/posttest
protocol), and collected portfolios of student work are part of our rigorous
assessment effort.

In this talk I will briefly discuss the classroom environment,
describe some of the activities, and review the findings of studies of learning
in various SCALE-UP settings.

This project has
been generously supported by the U.S. Department of EducationŐs FIPSE program
and the National Science FoundationŐs CCLI program.

**Researching the Practical Rationality of
Mathematics Teaching**

Pat Herbst

University of Michigan

I outline theory
and methods of a program of research on teacher thinking founded on the notion
of practical rationality—the set of dispositions that enable teachers of
a particular course of studies to handle the demands of instructional
exchanges. Using as an example the situation that we call Ňinstalling a
theoremÓ in high school geometry, I show how we go about creating conditions
for empirical data collection by way of developing and using animations of
classroom scenarios. These animations show scenarios that are out of the
ordinary and thus compel practitioners to comment on them. I show examples of
what teachers say in response to one of our animations, and how we use tools
from argumentation and linguistic analysis to discover teachersŐ dispositions
toward particular actions and the categories of appreciation they use to judge
those actions.

**Trajectory
Errors in Advanced Mathematical Thinking**

Adrian Simpson

Josephine Butler College, Durham University, UK

In this talk, I will examine the notion of a learning trajectory in
undergraduate mathematics education. While this is a useful notion, introduced
to allow teachers to think about the kinds of task they might use to support
the development of their students' mathematical concepts, I will argue that it
is all too easy to oversimplify a learning trajectory. Illustrated by examples
of research undertaken with various co-authors, or shamelessly stolen from
people much brighter than I am, the talk will examine a number of 'trajectory
errors,' which can cause us (or our students) to miss the conceptual outcomes
at which we aim. I would like to also talk about how to solve the 'trajectory
error' problems, but annoyingly I really don't have an answer.