Unlocking the gate to calculus success: Pre-calculus for engineers - An assertive approach to readying underprepared students

Abstract

In general, underrepresented engineering students who enter the college underprepared in mathematics lack the basic skills necessary to succeed in calculus. Numerous factors contribute to these issues, including high school mathematics instruction deficiencies such as the absence of qualified teacher resources, poor instruction, and low student interest in higher-level math. The Engineering GoldShirt Program at the College of Engineering and Applied Science at the University of Colorado Boulder is piloting a well-supported new pre-calculus for engineers course in the college with the aim to adequately prepare these students for success in calculus, so as to not lose them at the gateway of the engineering education pathway. In previous semesters in an effort to gain pre-calculus mastery, these GoldShirt students took math courses outside of the college in order to prepare to take the calculus sequence in the engineering curriculum. A subsequent review of these students' results in calculus I showed less than stellar performance. Of the students who took math courses outside of engineering, 64% earned less than a B- And 33% received Ds or Fs in calculus I. In response to this failure at the important mathematics juncture to success in engineering, a new pre-calculus for engineers course was developed in collaboration with the Applied Math Program to prepare students with a deeper understanding of mathematical concepts beyond what they previously received and prepare them for calculus success. A pilot class of 16 took the course in spring 2012, of which many moved on to calculus I in fall 2012 (pilot 1). A description and modifications to the precalculus for engineers course are presented in the paper, including the adoption of the ALEKS Learning System to assess and teach student math skills. Students are expected to take ownership of their learning and progress through modules to attain concept proficiency while meeting the lecture and recitation expectations for the course. Student performance in ALEKS contributes substantially to final course grades. In fall 2012, pilot 2 of the class enrolled 29 students of which 22 were GoldShirt students, and 7 GoldShirt students enrolled in the course in the spring 2013. Two sections of pre-calculus for engineers will be offered in the fall 2013 semester (pilot 3). Other first-year students in the college placed below the threshold for calculus I readiness, based on placement scores from ALEKS, and are not included in the new course (about 100 additional students or 14% of the new first-year class). Recommendations made to the college to expand the pre-calculus for engineers course have not yet been adopted. This paper examines the performance results of the pre-calculus for engineers course and compares them to students' subsequent calculus I performance, uncovering the keys to proficiency in math and calculus success for engineering students with high potential who are underprepared in mathematics. To gauge student understanding and mastery of foundational mathematical concepts necessary for calculus success, the results of course assessment via postsurvey, focus group and case study are described. ©American Society for Engineering Education, 2013.