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Improving Performance in Trigonometry and Pre-Calculus by Incorporating Adaptive Learning Technology into Blended Models on Campus

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2016 ASEE Annual Conference & Exposition


New Orleans, Louisiana

Publication Date

June 26, 2016

Start Date

June 26, 2016

End Date

August 28, 2016





Conference Session

Mathematics Division Technical Session 4

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Paper Authors


Jennifer B. Daines Colorado Technical University

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Jennifer Daines received a B.S. in English from the U.S. Air Force Academy in 1998 and subsequently spent eight and a half years as a Personnel Officer in the Air Force, serving most of that time in the Air Force’s education and training command. In 2005, she went back to school, earning an M.A. in English from the University of Texas at San Antonio.

In 2007, Jennifer separated from the Air Force and moved to Colorado Springs, where she currently resides. She began teaching English courses at CTU in the summer of 2010 as an Adjunct Professor and moved into her current role as Program Chair for General Education in the Spring of 2012. In this capacity, she leads the General Education team across CTU’s Colorado campuses and is responsible for all General Education courses, which includes all Mathematics and Science courses. She is currently pursuing a Doctorate in Education in Higher Education and Organizational Change through Benedictine University in Lisle, Illinois, and is expected to complete in 2016.

When she is not working or studying, Jennifer enjoys spending time with her husband and seven children who range in age from 3-16 years. Her other interests include reading, photography, cooking, sewing, and various writing projects.

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Tonya Troka Colorado Technical University

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Tonya Troka, with more than 10 years of experience working with online students, has been a leader of the adaptive learning implementation project since its initial launch in October 2012. As the University Program Director for General Education/Psychology, she works directly with the general education curriculum that was used to integrate the adaptive learning technology into the classroom. Troka has also provided insight into using the technology in the classroom and how success should be measured.

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John M. Santiago Jr. Colorado Technical University

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Professor John Santiago has been a technical engineer, manager, and executive with more than 26 years of leadership positions in technical program management, acquisition development and operation research support while in the United States Air Force. He currently has over 15 years of teaching experience at the university level and taught over 40 different courses in electrical engineering, systems engineering, physics and mathematics. He has over 30 published papers and/or technical presentations while spearheading over 40 international scientific and engineering conferences/workshops as a steering committee member while assigned in Europe. Professor Santiago has experience in many engineering disciplines and missions including: control and modeling of large flexible space structures, communications system, electro-optics, high-energy lasers, missile seekers/sensors for precision guided munitions, image processing/recognition, information technologies, space, air and missile warning, missile defense, and homeland defense.

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Improving Performance in Trigonometry and Pre-calculus by Incorporating Adaptive Learning Technology into Blended Models on Campus

Trigonometry and Pre-calculus are courses in which students have historically struggled at Colorado Technical University (CTU). These courses are often a student’s first experience with math beyond what they learned in high school. They provide critical prerequisite skills for both Engineering and Computer Science students, and for many, they represent a barrier to success in those programs. In January of 2014, half of all students enrolled in Pre-calculus failed the course, and throughout 2014, students in Trigonometry did not fare much better, with 50% of students failing or withdrawing from the course in July of that year. It was necessary to take proactive steps to improve performance in both courses in order to support our Engineering and Computer Science students. Because CTU had experienced success in implementing our proprietary adaptive learning technology, Intellipath, in the prerequisite College Algebra online, we determined that using a similar approach might positively impact student success in the follow-on Trigonometry and Pre-calculus courses.

From October 2012 to October 2014, CTU conducted a study involving 2,000 students taking College Algebra courses that included an adaptive learning component. The results of that study were positive and supported previous research on the benefits of adaptive learning (Brusilovsky & Millán, 2007). Over the two year study period, the failure rate for College Algebra decreased from 30% to 18%, and the withdraw rate dropped from 32% to 8%. Based on these results, we were hopeful that the same technology would produce similar results when implemented in Trigonometry and Pre-calculus. In addition, because these two courses have historically been offered only on campus in a traditional face to face setting, implementing adaptive learning technology would provide campus-based students with the known benefits of blended learning (US Department of Education, 2010).

In April of 2015, a pilot study was launched to integrate Intellipath into campus-based sections of Trigonometry and Pre-calculus. A total of three sections were offered for two consecutive terms. These classes, which were taught using a blended learning model, included traditional lecture, active demonstration, and guided examples, and they also included computer-based instructions and practice utilizing Intellipath. The software is unique from other “adaptive” models because it does more than just assess student knowledge on the front end and assign problems base on that assessment; it continues to assess students as they complete personalized learning maps designed to drive mastery of course objectives.

While the number of students involved in the study was relatively small (approximately 100 students), early results are promising. Since the inclusion of the Intellipath component into the campus-based classes, average pass rates in Trigonometry have increased from 76% to 98%, and Pre-calculus showed even better results with average pass rates increasing from 66% to 98%. Withdraw rates for both courses have been similarly impacted, as the average withdraw rates in Trigonometry have decreased from 36% to 10%, and the average withdraw rates in Pre-calculus have decreased from 45% to 9%. Although there is limited research on adaptive learning, it is almost exclusively relegated to online learning. This paper includes one pilot study of adaptive learning applied to campus-based courses and will cover a year of data that preliminarily indicates positive results for student success.

Original empirical data to support the above abstract:

Pre-calculus: Term Beginning Pass Rate Completion Rate Withdraw Rate January, 2014 50% 46% 54% April, 2014 61% 58% 42% July, 2014 84% 59% 41% October, 2014 67% 53% 47% January, 2015 67% 60% 40% April, 2015 96% 83% 17% July, 2015 100% 100% 0% October, 2015 85% 79% 21%


Term Beginning Pass Rate Completion Rate Withdraw Rate January, 2014 79% 63% 37% April, 2014 82% 64% 36% July, 2014 60% 50% 50% October, 2014 67% 67% 33% January, 2015 90% 75% 25% April, 2015 100% 93% 7% July, 2015 96% 88% 12% October, 2015 86% 67% 33%

Daines, J. B., & Troka, T., & Santiago, J. M. (2016, June), Improving Performance in Trigonometry and Pre-Calculus by Incorporating Adaptive Learning Technology into Blended Models on Campus Paper presented at 2016 ASEE Annual Conference & Exposition, New Orleans, Louisiana. 10.18260/p.25624

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