An active learning initiative by the First-Year Mathematics Task Force, made up of faculty in the UNL Department of Mathematics and Center for Science, Mathematics and Computer Education (CSMCE) and in place since 2012, has now positioned the department as a nationwide model for how to successfully reform pre-calculus courses and to sustain higher levels of student success.
Recent key strategies include changing pre-calculus to an instructional format that emphasizes active learning; extending the time students have in class; utilizing classrooms that have tables and chairs rather than fixed, auditorium-style seating; supporting graduate students to be successful teachers; and hiring undergraduate learning assistants to help out in pre-calculus courses.
Pre-calculus students have been taking a survey based on attitudes and beliefs toward mathematics for the past year. Nationally, students tend to drop (have lower attitude/beliefs) from the beginning to the end of each semester taking a mathematics class. At UNL, scores remained statistically flat, which is an indicator of success.
Not only are more students passing the pre-calculus courses, but those students now go on to calculus (despite some majors only requiring a pre-calculus course) and succeed at the same rates calculus students did before.
Allan Donsig, vice chair of mathematics and chair of the First Year Mathematics Task Force, is delighted to be able to say that this new iteration of pre-calculus courses, focusing on active learning and student understanding, continues to prepare students effectively to succeed in calculus.
Revisions to the first-year math courses continue, with the pre-calculus courses, Math 100A, 101, 102 and 103, showing greater student success (now consistently around 80 percent), and the work of the task force is turning now to the calculus courses: Math 104, 106 and 107.
Wendy Smith, a member of the task force and faculty in the CSMCE, is leading research into these changes, to help focus and accelerate efforts.
“We studied the research literature both on mathematics reforms and on institutional change, so that we could learn from what others have done. We found many reforms fail because they are too simplistic, lack effective leadership, or ignore relevant contexts and data,” Smith said. “The math department has engaged in data-based, wholesale reform efforts under the leadership of Judy Walker, the First-Year Mathematics Task Force, and Nathan Wakefield, the director of first-year mathematics.”
The initiative also has instituted a Course Readiness Activity (CRA) in Math 101 and 103, similar to the calculus gateway exams, but taken on paper the first week of class and then up to once per day online at the Arts and Sciences Testing Center. It gets students started working early in the semester and ensures that they review and master the background material they need to succeed in the course. A similar CRA for Math 106 is in place this fall, and a CRA for Math 104 will start in Spring 2016.
The task force has found students who do not pass the CRA are much more likely to struggle in the course, compared to students who pass the CRA either on the first day of class or during the first two weeks of class. Using 2014-15 data with a statistical regression model that includes 935 students’ performance in Math 101 or 103, high school rank, ACT mathematics score and performance on the CRA, the task force is able to predict whether students will pass each course with very high accuracy – only 7 percent false positive (students predicted to pass the course but failed) and 19 percent false negatives (predicted to fail the course but passed).
Wakefield and Donsig are working on creating interventions for students who do not pass the CRA. Donsig said, “Knowing that we can identify students at risk for failure puts us in a strong position to better support those students.”
Because of participation in the Association of Public and Land-grant Universities’ Mathematics Teacher Education Partnership, the task force and department are able to turn attention to active learning in calculus courses and collaborate with other institutions focused on calculus reforms, in particular the University of Nebraska at Omaha and the University of Colorado Boulder. In Math 106, beginning in the spring, the department will switch from 50-minute recitations to 75-minute recitations and use the additional time to fully incorporate active learning activities. Wakefield and Bill Rogge will be teaching the lectures for these sections.
In 2016, this work will be shared at a variety of conferences, including the Joint Math Meetings and the Research in Undergraduate Mathematics Education conference.