Mathematics Momentum to Community College Calculus Success

PhD Dissertation Defense: Mathematics Education

Michael Bostick

University of Wyoming

November 17, 2025

Overview

Background

Pathways to Community College Calculus

Pathways to Community College Calculus

Traditional CC Pathways to Calculus

  • Strict math placement with test cut-scores.
  • Up to three developmental math courses.
  • Long developmental math course sequences have not proven effective (Xu and Dadgar 2018).
  • Efficacy of math placement test scores are questioned, holistic placement is recommended (Ngo, Chi, and Park 2018).
  • HS GPA has been found to be a better predictor of success than ACT Math scores (Bahr et al. 2019), but its impact decreases with time since HS (Hayward 2020).

Pathways to Community College Calculus

Contemporary CC Pathways to Calculus

  • Math placement with test cut-scores
  • Holistic placement options with HS GPA/Transcript for some students
  • Up to two developmental math courses
  • Options to bypass developmental math classes by taking corequisite College Algebra
  • Have these changes influenced calculus success for students at CCs?

Methods

Theoretical Framework

  • Academic momentum conceptualizes continued academic achievement as a result of past course taking behaviors and academic achievements (Adelman 2006).

  • This framework has been extended to momentum for CC student success (Wang 2017) and STEM academic momentum Wang (2015).

  • Does students’ mathematical momentum influence their calculus success in a rural CC system?

  • This study investigated if students’ academic preparation by their enrollment pathways (RQ1), and student characteristics by learning contexts (RQ2) can predict success in CC calculus.

Research Questions

RQ1 - To what extent does student academic preparation (measured by HS GPA and ACT Math) predict success in CC calculus, and how are these effects moderated by time since high school graduation or participation in concurrent enrollment courses?

RQ2 - To what extent do student-level factors including demographics (biological sex and URM group status) and prior coursework (precalculus course completions) predict success in CC calculus, and how are these effects moderated by the availability of corequisite courses or by mean HS GPA within a course section?

Research Questions

RQ1 - To what extent does student academic preparation (measured by HS GPA and ACT Math) predict success in CC calculus, and how are these effects moderated by time since high school graduation or participation in concurrent enrollment courses?

RQ2 - To what extent do student-level factors including demographics (biological sex and URM group status) and prior coursework (precalculus course completions) predict success in CC calculus, and how are these effects moderated by the availability of corequisite courses or by mean HS GPA within a course section?

RQ1 Model Terms

  • HS GPA (cwc)
  • years since HS (cwc)
  • HS GPA (cwc) × years since HS (cwc)
  • ACT Math (cwc)
  • concurrent prerequisite (cwc)
  • ACT Math (cwc) × concurrent prerequisite (cwc)

Research Questions

RQ1 - To what extent does student academic preparation (measured by HS GPA and ACT Math) predict success in CC calculus, and how are these effects moderated by time since high school graduation or participation in concurrent enrollment courses?

RQ2 - To what extent do student-level factors including demographics (biological sex and URM group status) and prior coursework (precalculus course completions) predict success in CC calculus, and how are these effects moderated by the availability of corequisite courses or by mean HS GPA within a course section?

RQ2 Model Terms

  • mathematics prerequisites (cwc)
  • Corequisite college
  • mathematics prerequisites (cwc) × corequisite college
  • female
  • URM
  • HS GPA (gmc)
  • URM × HS GPA (gmc)

Data Set

Geographical Comparison of all Wyoming CC Calculus Sections and Those Used in the Analysis.

Model

Note. Bold & italic font = grand mean centered (gmc), bold font = section mean centered (cwc)

Model

\[\scriptsize {\begin{aligned} &\quad \log\left(\frac{P(Y_{ij} = \text{Pass})}{P(Y_{ij} = \text{Fail})}\right) = \gamma_{00} \\ &\quad + \gamma_{01}(\text{HSGPA})_{gmc} \\ &\quad + \gamma_{02}(\text{Coreq College}) \\ &\quad + \gamma_{10}(\text{HSGPA})_{cwc} \\ &\quad + \gamma_{20}(\text{ACTMath})_{cwc} \\ &\quad + \gamma_{30}(\text{YearsCalc})_{cwc} \\ &\quad + \gamma_{40}(\text{MathPrereqs})_{cwc} \\ &\quad + \gamma_{41}(\text{MathPrereqs})_{cwc} \times (\text{CoreqCollege}) \\ &\quad + \gamma_{50}(\text{Female}) \\ &\quad + \gamma_{60}(\text{ConcurrentPrereq})_{cwc} \\ &\quad + \gamma_{70}(\text{URM}) \\ &\quad + \gamma_{71}(\text{URM}) \times (\text{HSGPA})_{gmc} \\ &\quad + \gamma_{80}(\text{HSGPA})_{cwc} \times (\text{YearsCalc})_{cwc} \\ &\quad + \gamma_{90}(\text{ConcurrentPrereq})_{cwc} \times (\text{ACTMath})_{cwc} \\ &\quad + u_{0j} \end{aligned}}\]

Model

Effect Parameter Level Centering
Intercept \(\gamma_{00}\) – –
HSGPA (gmc) \(\gamma_{01}\) Section gmc
Coreq College \(\gamma_{02}\) Section none
HSGPA (cwc) \(\gamma_{10}\) Student cwc
ACT Math (cwc) \(\gamma_{20}\) Student cwc
Years since HS (cwc) \(\gamma_{30}\) Student cwc
Math Courses (cwc) \(\gamma_{40}\) Student cwc
Female \(\gamma_{50}\) Student None
Concurrent Prereq (cwc) \(\gamma_{60}\) Student cwc
URM \(\gamma_{70}\) Student None
Math Courses (cwc) × Coreq College \(\gamma_{41}\) Cross-Level –
URM × HSGPA (gmc) \(\gamma_{71}\) Cross-Level –
HSGPA (cwc) × Years since HS (cwc) \(\gamma_{80}\) Student-Level –
Concurrent Prereq (cwc) × ACT Math (cwc) \(\gamma_{90}\) Student-level –

Results

Research Question 1

RQ1 - To what extent does student academic preparation (measured by HS GPA and ACT Math) predict success in CC calculus, and how are these effects moderated by time since high school graduation or participation in concurrent enrollment courses?

  • The student level variable HS GPA were statistically significant.

  • The student-level interaction variables HS GPA × Years Since HS and Concurrent Enrollment Prerequisite × ACT Math were statistically significant.

Research Question 1

RQ1: Academic preparation (HS GPA, ACT Math) moderated by enrollment pathway (years since HS, concurrent prerequisite) on CC calculus success.

Significant Terms for RQ1:

  • HS GPA (cwc) \(\scriptsize{(γ_{10}=1.608,p<0.001)}\)
  • HS GPA (cwc) x years since HS (cwc) \(\scriptsize{(γ_{80}=-0.798,p<0.001)}\)
  • ACT Math (cwc) x concurrent prerequisite (cwc) \(\scriptsize{(γ_{90}=0.203,p<0.05)}\)

RQ1 - HS GPA (cwc)

RQ1 - HS GPA (cwc)

  • HS GPA was a statistically significant predictor of success with a large positive effect size.
  • ACT Math was not a statistically significant predictor of success.
  • The positive effect of HS GPA was moderated by the number of years since HS

RQ1 - HS GPA (cwc) x years since HS (cwc)

RQ1 - HS GPA (cwc) x years since HS (cwc)

  • The student-level interaction term HS GPA and years since HS was statistically significant with a negative effect.
  • For each additional year past high school, the positive predictive benefit of a high HS GPA decreases by a multiplicative factor of 0.450
  • The number of years since HS was not stastically significant alone

RQ1 - ACT Math (cwc) x concurrent enrollment prereq (cwc)

RQ1 - ACT Math (cwc) x concurrent enrollment prereq (cwc)

  • While the main effects of ACT Math and concurrent enrollment prerequisites were not statistically significant, their interaction was with a positive effect.
  • Students who took concurrent enrollment courses receive a positive benefit of a higher ACT Math score in predicting calculus success

Research Question 2

RQ2 - To what extent do student-level factors including demographics (biological sex and URM group status) and prior coursework (precalculus course completions) predict success in CC calculus, and how are these effects moderated by the availability of corequisite courses or by mean HS GPA within a course section?

  • The student-level variable precalculus course completions was found to be statistically significant.

  • The section-level variable section mean HS GPA was found to be statistically significant.

  • The cross-level interaction variables Corequisite Availability × Number of Math Prerequisites and URM × Section Mean HS GPA were also statistically significant.

Research Question 2

RQ2: Student characteristics (Bio. Sex, URM, Math Prereqs) moderated by learning contexts (section mean HS GPA, corequisite course availability) on CC calculus success.

Significant Terms for RQ2:

  • number of math prerequisites (cwc) \(\scriptsize{(γ_{40}=0.3053,p<0.05)}\)
  • number of math prerequisites (cwc) × corequisite availability \(\scriptsize{(γ_{41}=-0.5524,p<0.01)}\)
  • section mean HS GPA (gmc) \(\scriptsize{(γ_{01}=2.9118,p<0.001)}\)
  • section mean HS GPA (gmc) × URM \(\scriptsize{(γ_{71}=-2.7377,p<0.05)}\)

RQ2 - Number of Math Prerequisites (cwc)

RQ2 - Number of Math Prerequisites (cwc)

  • The number of math prerequisite courses completed was statistically significant with a positive effect.
  • The number of math prerequisite courses completed was moderated by the availability of corequisite courses.
  • Neither Biological sex or URM were statistically significant.

RQ2 - Math Prerequisites (cwc) x Corequsite Availability

RQ2 - Math Prerequisites (cwc) x Corequsite Availability

  • The college-level context variable corequisite availability was not statistically significant alone, but it had a negative moderating effect on the number of prerequisite math courses.
  • The positive effect from number of prerequisite math courses was negated for students who attended colleges where corequsite math courses were available.

RQ2 - Section Mean HS GPA (gmc)

RQ2 - Section Mean HS GPA (gmc)

  • Section Mean HS GPA was statistically significant with a large positive effect.
  • Students who enroll in course sections with high mean HS GPA have increased odds of passing calculus.
  • The positive effect from section mean HS GPA was moderated for students who were URM.

RQ2 - HS GPA (gmc) x URM

RQ2 - HS GPA (gmc) x URM

  • The cross-level interaction variable GPA (gmc) x URM was statistically significant with a negative effect.
  • Students who are URM did not share in the positive effect from attending a calculus section with a higher mean HS GPA.
  • URM status was not a statistically significant predictor of success alone.

Discussion

Questions?

References

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Appendix

For summary statistics for the dataset used in the model, model result details, model diagnostics, and model assumption testing visit:

Multilevel Logistic Regression Model Dashboard