Modeling Engineering Degree Attainment Using High School and College Physics and Calculus Coursetaking and Achievement

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    Journal of Engineering EducationOctober 2011, Vol. 100, No. 4, pp. 760777

    2011 ASEE.

    Modeling Engineering Degree AttainmentUsing High School and College

    Physics and Calculus Coursetaking and Achievement

    WILL TYSONUniversity of South Florida

    BACKGROUNDModels of engineering retention use high school GPA and mathematics standardized test scores tomeasure pre-college characteristics and first year of college GPA to measure academic integration incollege. This study uses high school and college physics and calculus coursetaking and achievementto predict engineering degree attainment among students on-track for an engineering degree.

    PURPOSE (HYPOTHESIS)This study predicts that high school accelerated physics and calculus coursetaking and grades influencesgrades earned in college physics and calculus and both sets of factors influence engineering degree attainment.

    DESIGN/METHODMultinomial logistic regression analyses determine the effects of high or low achievement in high schoolon high and low achievement in college physics and calculus courses and the effects of both on earning anengineering degree.

    RESULTSPre-college characteristics and academic integration were not consistently related to the destination ofengineering migrants. Community college enrollment was not related to attrition. High school calculusachievement is the strongest predictor of grades in college physics and calculus courses, accounting for thepositive effects of accelerated physics and calculus coursetaking.

    CONCLUSIONSEngineering degree attainment models should include coursetaking and particularly achievement in highschool and college physics and calculus courses. Attrition outcomes should include the destination majorin order to capture achievement effects on migration to business and non-STEM fields compared tomigration to other STEM fields that require quantitative skills acquired in physics and calculus courses.

    KEYWORDSdegree attainment, precollege coursetaking, retention


    Models of college student retention integrate psychological, social, and organizationalexplanations for college attrition. Given the amount of preparation necessary to earn anengineering degree and the stability of engineering college and career pathways, attritionrepresents a major change in academic and career goals. Engineering majors typically

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    100 (October 2011) 4 Journal of Engineering Education

    begin their preparation by taking high level science and mathematics courses in highschool where they acquire what Adelman (1998) calls curricular momentum. Tintos(1993) interactionalist theory of student departure focuses on this high school academicachievement and other pre-college characteristics that help prepare students for collegesuch as family background and skills and abilities. Students matriculate into college andtheir academic and social experiences determine the likelihood of retention. Academic in-tegration includes academic achievement in early college courses whereas social integra-tion includes how students adapt to the new environment. Engineering majors differ littlefrom other students in characteristics that impact retention such as commitment to col-lege, financial need, and parents education or expectations for the student (Ohland,Sheppard, Lichtenstein, Eris, Chachra & Layton, 2008; Veenstra, Dey, & Herrin, 2009).Unlike most non-engineering majors, engineering majors have stronger science andmathematics skills and abilities and higher confidence in those skills (Veenstra, Dey, &Herrin, 2008). In order to account for these differences, models of engineering retentionand degree attainment must also include rigorous high school science and mathematicscourses and rigorous college first year science and mathematics courses that make path-ways to engineering retention different from overall retention.

    Figure 1 illustrates the conceptual framework for this study. This study extends Tintos (1993) model of student departure and Veenstra et al.s (2009) model of engi-neering retention by including measures that are absent from much of the engineeringeducation literature:

    A. Pre-college characteristics include high school science and mathematics courses andgrades earned in physics and calculus, including accelerated courses along with highschool GPA, the commonly used measure.

    B. Academic integration is measured by grades earned in college physics and calculusengineering prerequisite courses instead of college GPA.

    C. Social integration measures include community college enrollment in order to ac-count for ways in which community college transfers are integrated into engineeringdifferently than native university students.

    D. Retention includes engineering degree attainment compared to switching out of en-gineering to earn a degree in computer science, science, technology, or mathematics(STM), business, or other non-STEM field.

    This study also builds upon the work of Adelman (1998) by using a similar sample ofstudents who completed college prerequisite courses and are on-track to earn an engineer-ing degree.


    Pre-College Quantitative and Analytic SkillsStudies of engineering retention generally focus on high school GPA, SAT Math, and

    ACT Math as key predictors of engineering retention and graduation (i.e., Astin & Astin,1992; Lotkowski, Robbins, & Noeth, 2004; Veenstra & Herrin, 2006; Zhang, Anderson,Ohland, Carter & Thorndyke, 2004). Students who enter an engineering college withmore quantitative knowledge in areas such as trigonometry, calculus, and physical sciencesare most likely to succeed in engineering (Veenstra et al., 2009). Grades earned in high

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    Journal of Engineering Education 100 (October 2011) 4

    school mathematics and science courses are measures of pre-college quantitative skills andshould be included in effect models of engineering retention.

    Physics and calculus high school course-taking are the strongest indicators of futurecollege enrollment and subsequent completion of a STEM degree (Riley, 1997; Tyson,Lee, Borman, & Hanson, 2007). Physics coursetakers have the largest increases in scienceproficiency in high school (Madigan, 1997). Calculus is a prerequisite for most STEMcollege courses and is a critical gatekeeper to college and STEM success (Oakes, 1990).Recent trends show that college-bound students lack calculus training (Ma, 2006) eventhough almost all students completed algebra and geometry. Advanced Placement (AP)physics and calculus coursetaking (Suresh, 2006) and AP calculus exam scores (Mesa, Jaquette, & Finelli, 2009) predict grades earned in college physics, calculus, and engineeringcourses. This study tests two hypotheses about the effects of pre-college characteristics ongrades earned in college physics and calculus courses and engineering degree attainment.

    H1a: Students who took Advanced Placement, International Baccalaureate, andother accelerated physics and calculus courses in high school have a) higherachievement in college prerequisite physics and calculus courses and b) lower ratesof switching out of engineering compared to students who completed lower levelscience and mathematics courses.

    H1b: Students who earned high grades in high school physics and calculus courseshave a) higher achievement in college prerequisite physics and calculus courses andb) lower rates of switching out of engineering compared to lower achieving students.

    Academic IntegrationTinto (1993) describes academic integration as doing well in courses. Because of the

    significance of quantitative skills, academic integration may be more important than social

    FIGURE 1. Model of engineering degree attainment.

  • integration upon entering college. Students with a C average or less have a high probabilityof leaving engineering (Veenstra et al., 2009; Zhang, Min, Ohland, & Anderson, 2006).Many studies measure academic integration using first year GPA without specifically ex-amining grades earned in engineering prerequisite courses commonly referred to as gate-keeper courses.

    All universities included in this sample require that students complete a physics and cal-culus sequence to earn an engineering degree. For the cohort in this study, the flagship uni-versity recommended that engineering students in most programs start taking prerequisitecourses before taking their first engineering course and complete Physics II and/or Calcu-lus III during the same semester as the first engineering course (University of Florida1999-2000 course catalog, 1999).

    Suresh (2006) found that a majority of engineering majors earned a B- or below orwithdrew from Physics I, Physics II, Calculus I, Calculus II, in effect, weeding many ofthem out of engineering. High achievement in introductory physics and calculus courses(i.e., Physics I and Calculus I) predicts high achievement in later prerequisite courses (i.e.,Physics II and Calculus II), achievement in engineering courses, and engineering degreeattainment (Levin & Wyckoff, 1990; Suresh, 2006).

    Additional research concludes academic integration has little impact on retention andengineering degree attainment. Despite finding specific effects of achievement in prerequi-site courses, Suresh (2006) also found that highly motivated students persist despite lowachievement. Many students leave engineering with passing GPAs, even with a B averageor above (Ohland, Zhang, Thorndyke, & Anderson, 2004). Adelman (1998) finds thatonly 8.5% of students who start engineering coursework earn low grades and switch out ofengineering. These findings differ primarily because Adelman (1998) used a sample of stu-dents who had completed prerequisite courses as opposed to students who drop out of en-gineering before completing prerequisites. This study uses achievement in Physics I,Physics II, Calculus I, Calculus II, and Calculus III as measures of academic integrationthat may influence engineering degree attainment even among students who have com-pleted these prerequisite requirements. Hypothesis 2 represents the impact of academic in-tegration in current models.

    H2: Students who earned high grades in college physics and calculus courses havelower rates of switching out of engineering compared to lower achieving students.

    Social IntegrationBased on Tintos work, students who transfer into university engineering programs are

    at a disadvantage compared to first time in college students who begin at a university andhave time to develop meaningful social relationships with fellow students and faculty. Dueto the limitations of state tracking data, this study does not examine common elements ofsocial integration such as student involvement in clubs and organizations and social inter-action with fellow students and faculty. Instead, this study examines community collegeenrollment, a key element of academic and social integration that is unaccounted for inmost studies of engineering retention. Many first year students initially enroll in communi-ty college in order to complete general education requirements. For example, over 40% ofall undergraduate engineering majors nationally attended community colleges at somepoint in their academic careers (Tsapogas, 2004) even though engineering attracts highachievers in science and mathematics. Community college transfers complete engineeringdegrees at the same rates as four-year college students (Adelman, 1998).


    100 (October 2011) 4 Journal of Engineering Education

  • Even though more high school graduates are choosing to attend community collegesto fulfill curriculum requirements (Adelman, 2005), research on engineering and com-munity colleges has not examined the impact of taking prerequisite courses at a commu-nity college as opposed to a university. Many studies that do examine first year GPA orprerequisite coursetaking and achievement use institutional data from one engineeringprogram and/or surveys of engineering students and lack information about communitycollege degree attainment or coursetaking (i.e., Mesa, Jaquette, & Finelli, 2009; Suresh,2006; Veenstra, Dey, Herrin, 2008). Veenstra et al. (2009) omit community college at-tendance in their model of freshman engineering retention. This study takes advantageof the unique articulation agreements in the state of Florida that allow students to takeprerequisite courses at community colleges for full credit at four-year universities(Venezia & Finney, 2006). Using state tracking data, this study can effectively includecommunity college degree attainment and coursetaking as measures of social integrationthat provide context for grades earned in engineering prerequisite courses taken at com-munity colleges or universities.

    H3: Community college transfers and students who completed collegeprerequisites at community colleges have higher rates of switching out ofengineering compared to students who never attended community college andstudents who completed prerequisites at a university.

    RetentionEven though the primary goal of retention is eventual degree attainment, many studies

    of engineering retention are limited to the short-term and longer-term positive effects ofcollege GPA on retention from the first semester through eight semesters (Budny,LeBold, & Bjedov, 1998; Burtner, 2004; French, Immekus, & Oakes, 2005; Zhang et al.,2006). Adelmans (1998) work, using a sample of engineering thresholders, distinguishesbetween migrant students who took one or more engineering course(s), but switched outof engineering to another major or dropped out of college altogether and completers whoearned engineering degrees. This study examines degree attainment among engineeringthresholders who did graduate from college, meaning that migrants successfully changedmajors and graduated in a different field.

    There is some evidence that factors that lead to retention defined as long-term enroll-ment in engineering do not lead to graduation with an engineering degree. Zhang, Anderson, Ohland, Carter and Thorndyke (2004) conclude the emphasis on this defini-tion of retention is a drawback because variables that appear to be significant in the short-run (i.e., before graduation) may not, in fact, be significant in the final analysis (p. 9). Stu-dents who migrate out of engineering primarily enter majors that require quantitative skillsattained in high school and college such as computer science, business, and physical sci-ences (Adelman, 1998). The destinations of engineering migrants are not uniformly relat-ed to college GPA. Migrants with higher GPAs tend to switch into physical sciences. Migrants with lower GPAs are more likely to switch to business. There is no specific cor-relation between GPA and migration into other popular non-STEM fields such as socialsciences and education (Ohland et al., 2004b).

    H4a: Migrants with lower grades in college calculus and physics courses willmigrate to business at a higher rate than students with average grades.


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