1. Modular Delivery and Peer-Led Team-Learning for Precalculus
Helmut Knaust
Emil Schwab
Department of Mathematical Sciences
The University of Texas at El Paso
January 5, 2009

2. Overview UTEP Profile Summer Activities: Accuplacer
Modular Precalculus
Theory of Validation
Peer-Led Team Learning in Precalculus
UTEP Campus

3. Undergraduate Students in Science and Engineering
Total: 3,775
Total UGs at UTEP: ,060
Source: CIERP, Fall 2006

4. UTEP Enrollment Trends

5. UTEP Student Population Profile
24 years of age (undergraduate average)
74% Hispanic
55% female
81% from El Paso County commuting daily
84% employed
50% first generation university students

6. UTEP’s Main Challenges
Incoming students are not well-prepared for studying STEM disciplines
Low retention rates
Low graduation rates
Long time to graduation

7. Summer Invention: Math Review for STEM Students
Before After
Math Review
2001(n=359)
Before After
Math Review
2002 (n=386)

8. Precalculus Setup I
UTEP has no College Algebra course.
Non-Stem majors take the Mathematics for Social Science course or the terminal course Mathematics in the Modern World.
STEM majors take a 5-hour Precalculus course.
The course is a combination of College Algebra and Trigonometry.
The Precalculcus course (and the Calculus I course) is offered in a modular format in classes of about 50 students.
Since Fall 2008 the Precalculus course incorporates Peer-Led Team Learning (PLTL).

9. Modular Delivery Format for Precalculus I
Designed by long-time course coordinator Nancy Marcus
The semester is divided in three time segments. The course is divided into three modules.
When students complete a module in a time segment successfully, they move on to the next module (or Calculus I).
When students successfully complete all three modules, they pass the course. The course grade is the average of the grade in each of the three successfully completed modules.

10. Modular Delivery Format for Precalculus II
Students can attempt each module three times. When they fail a particular module for the third time, they fail the course.
The last module is also offered in a “minimester” after the regular semester.
Students who do not complete the course in one semester, must register for the course again next semester to complete the remaining module(s). They are assigned an “in-progress” grade (P) for the past semester.

11. Modular Delivery Format for Precalculus

12. Grade Distribution (Spring 2008, n=578)

13. Theory of Validation I Laura Rendón’ s Theory of Validation is based
on her own experience as a college student and
her extensive work with minority students at
community colleges and universities.

14. Theory of Validation II
Validation, shown through encouragement and affirmation, can be the factor that determines success or failure, particularly for on‑traditional Students. Laura Rendón* defines validation as “an enabling,
confirming, and supportive process initiated by in- and out-of-class agents that fosters academic and interpersonal development” . Academic validation results when Faculty and Staff reach out to
Students in ways that help individuals “trust their innate capacity to learn and to acquire confidence in being a college student”.
Adapted from UTEP’s Quality Enhancement Plan
* Rendón, L. I. (1994). Validating culturally diverse students:
Toward a new model of learning and student development.
Innovative Higher Education. 19 (1),

15. Peer-Led Team Learning at UTEP
Supported by an NSF-STEP Grant* and a MSEIP Grant from the Department of Education**
Used in all introductory Chemistry, Physics and Mathematics classes
Delivery format in Precalculus since Fall changed to four hours of lecture and two hours of PLTL sessions per week
PLTL sessions (3 sessions per course, students per session) led by an advanced undergraduate student
* PI: Benjamin Flores, Co-PIs: James Becvar, Helmut Knaust, Jorge Lopez, and Josefina Tinajero
** PI: Emil Schwab, Co-PIs: Nancy Marcus, Helmut Knaust

16. PLTL Principles PLTL leaders have successfully completed the course.
PLTL leaders work closely with the instructor of the course.
PLTL leaders are trained and supervised before and during the semester.
The PLTL sessions are integral
to the course, cover
challenging problems,
strive to develop student
thinking and encourage
active student learning.

17. All Questions Answered, All Answers Questioned*
* Borrowed from Donald Knuth

18. Contacts Helmut Knaust Emil Schwab hknaust@utep.edu eschwab@utep.edu
Department of Mathematical Sciences
The University of Texas at El Paso
El Paso TX