1. The Westfield Model for Undergraduate Mathematics Education Karin Vorwerk, Ph.D., Professor and Chair, Department of Mathematics Westfield State University, kvorwerk@westfield.ma.edu

2. Who We Are 6000+ total students 5000 day school undergraduates Enrollment in Math core classes 2663 (AY15-16) Karin Vorwerk, Ph.D., Professor and Chair, Department of Mathematics, Westfield State University, kvorwerk@westfield.ma.edu

3. Background No non-credit bearing developmental Mathematics course at WSU for a long time Process of creating different pathways and co- requisites started at WSU in the early 2000’s Initiated by Dr. John Judge (chair 2002 – 2012) Studies showed little correlation between ACCUplacer scores and success in first college level math class Karin Vorwerk, Ph.D., Professor and Chair, Department of Mathematics, Westfield State University, kvorwerk@westfield.ma.edu

4. Our Approach Different major aligned courses Teaching methods and pedagogy Co-requisites when appropriate and possible Flexible placement Karin Vorwerk, Ph.D., Professor and Chair, Department of Mathematics Westfield State University, kvorwerk@westfield.ma.edu

5. Teaching Method The Common Vision report * released earlier this year states: “failure rates under traditional lecture are 55 percent higher than the rates observed under more active approaches to instruction.” * Common Vision for Undergraduate Mathematical Sciences Programs in 2025 The Common Vision project is organized by the MAA and supported by the National Science Foundation. The leadership team includes representation from all five of the professional organizations who focus on undergraduate mathematical sciences programs as an integral part of their mission (AMATYC, AMS, ASA, MAA and SIAM) Karin Vorwerk, Ph.D., Professor and Chair, Department of Mathematics, Westfield State University, kvorwerk@westfield.ma.edu

6. At WSU, we have: Almost all our classes in active learning classrooms All Math courses capped at 30 or less Freedom to experiment Karin Vorwerk, Ph.D., Professor and Chair, Department of Mathematics, Westfield State University, kvorwerk@westfield.ma.edu

7. Placement Used to rely exclusively on ACCUplacer Study of 1180 students (2002-2003) showed little correlation between ACCUplacer scores and success in first college level math class Females tend to perform weakest on the SAT, better on the ACCUPLACER, and best in a classroom setting. Males have better standardized test scores than females, but perform weaker than females in the classroom Repeat study in 2012 of 3000 student records confirmed findings Karin Vorwerk, Ph.D., Professor and Chair, Department of Mathematics, Westfield State University, kvorwerk@westfield.ma.edu

8. Combination of SAT(Math) and high school GPA seems to work best Strength of correlation varies with type of class General consensus on campus about ACCUplacer Currently using GPA (2.7) pilot, but collecting ACCUplacer for some students Working on building better placement tools incorporating high school (Math) GPA and other measures Karin Vorwerk, Ph.D., Professor and Chair, Department of Mathematics, Westfield State University, kvorwerk@westfield.ma.edu

9. “Appropriate placement in entry-level courses is an ongoing challenge in higher education. Despite the tremendous amount of effort and resources devoted to establishing effective placement mechanisms, many agree that our community has not solved the problem of placing students in appropriate entry-level courses.” * * Common Vision for Undergraduate Mathematical Sciences Programs in 2025 Karin Vorwerk, Ph.D., Professor and Chair, Department of Mathematics, Westfield State University, kvorwerk@westfield.ma.edu

10. Extended Time Sections Idea: Place every student in a credit bearing mathematics class right away Place students that need remediation (as determined by ACCUplacer) in class sections that meet an extra hour per week Allows for the right remediation at the right time In 2005: 12 ET sections for 1180 incoming students (30%) Karin Vorwerk, Ph.D., Professor and Chair, Department of Mathematics, Westfield State University, kvorwerk@westfield.ma.edu

11. Example 1: BUSM BUSM requires two math classes – Math for Business and Statistics Course has a substantial computational/algebra component Dr. Judge redesigned course in cooperation with the BUSM department to satisfy both content and accreditation requirements Went from lecture format to group work / board work format Used ACCUplacer for placement Karin Vorwerk, Ph.D., Professor and Chair, Department of Mathematics, Westfield State University, kvorwerk@westfield.ma.edu

12. Results for First Year Students Students that failed ACCUplacer, placed in regular class: 33% withdrew, 11% stayed and failed, average grade 1.78 (on a 4 point scale) Students that failed ACCUplacer, placed in extended time sections: 6% withdrew, 3% stayed and failed, average grade 2.63 Students that passed ACCUplacer: 0% withdrew, 98% pass rate, average grade 2.97 First year students have a 10% – 18% higher pass rate than upper class students Karin Vorwerk, Ph.D., Professor and Chair, Department of Mathematics, Westfield State University, kvorwerk@westfield.ma.edu

13. Example 2: BIOL - ENVS Developed at the request of the Biology department in 2003 Topics ranging from pre-calculus to elements of calculus, statistics, experiment design Originally lecture – lab format Placement by advising Problem: different background of students Went to self-paced approach Now offered as hybrid course Success rate: 93% Karin Vorwerk, Ph.D., Professor and Chair, Department of Mathematics, Westfield State University, kvorwerk@westfield.ma.edu

14. Example 3: Calculus track Placement by transcript analysis and SAT(Math) for incoming students, by advising thereafter Problem: No consensus about high school course content Option to switch between pre-Calculus, Calculus 1, and Calculus 2 for an extended period of time Just started re-examining content and emphasis Karin Vorwerk, Ph.D., Professor and Chair, Department of Mathematics, Westfield State University, kvorwerk@westfield.ma.edu

15. Example 4: Liberal Arts Have two designated courses for students without math requirement tied to major Data shows ET sections are not effective Placement tests not good predictors Work started in early 2000’s by Julian Fleron Now a group of four faculty: Julian Fleron, Phil Hotchkiss, Volker Ecke, Christine von Renesse Work has been NSF grant supported since 2009 – 2020, ≈ $980,000 Karin Vorwerk, Ph.D., Professor and Chair, Department of Mathematics, Westfield State University, kvorwerk@westfield.ma.edu

16. Started by analyzing the audience – students with “mixed” experience in Mathematics, but strengths in writing, arts, and the humanities Leverage these strengths to help students discover what Mathematics can and should be Focus on sense making, not memorizing procedures More information on “Discover the Arts of Mathematics” can be found online at http://artofmathematics.org Pass rates are between 85% and 95% Karin Vorwerk, Ph.D., Professor and Chair, Department of Mathematics, Westfield State University, kvorwerk@westfield.ma.edu

17. What we learned One size does not fit all, need major specific solutions Different courses Different remediation models Different teaching methods Different placement methods and standards Compromise between the ideal and the possible Active learning makes a huge difference Karin Vorwerk, Ph.D., Professor and Chair, Department of Mathematics, Westfield State University, kvorwerk@westfield.ma.edu

18. Challenges Funding - sustainability Active learning style vs large lecture Reflective writing assignments vs Scantron tests Transcript analysis and advising vs testing Scaling up Improved placement and data collection Changing student population Changing major requirements Karin Vorwerk, Ph.D., Professor and Chair, Department of Mathematics, Westfield State University, kvorwerk@westfield.ma.edu

19. We’d love to learn from our sister institutions Karin Vorwerk, Ph.D., Professor and Chair, Department of Mathematics, Westfield State University, kvorwerk@westfield.ma.edu