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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

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

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3 Engineering: 2,151 Science: 1,624 Total: 3,775 Total UGs at UTEP: 17,060 Source: CIERP, Fall 2006 Undergraduate Students in Science and Engineering

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4 UTEP Enrollment Trends

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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

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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

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

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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). 8

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Modular Delivery Format for Precalculus I 9 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.

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Modular Delivery Format for Precalculus II 10 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.

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Modular Delivery Format for Precalculus 11

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Grade Distribution (Spring 2008, n=578) 12

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Theory of Validation I 13 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.

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14 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 Theory of Validation II * Rendón, L. I. (1994). Validating culturally diverse students: Toward a new model of learning and student development. Innovative Higher Education. 19 (1),

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Peer-Led Team Learning at UTEP 15 S upported 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 2008 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

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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. 16 PLTL Principles

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

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Contacts 18 Helmut KnaustEmil Schwab Department of Mathematical Sciences The University of Texas at El Paso El Paso TX

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