Bridging Secondary Mathematics to Post-Secondary Calculus: A Summer Bridge Program

Abstract

The purpose of this study was to determine the effectiveness of early diagnosis and a summer program to strengthen precalculus skills before students enrolled in Engineering Calculus I. A meta-synthesis of interventions to increase success in college calculus was conducted, with a meta-analysis of studies that contained sufficient quantitative data to calculate Hedge's g effect sizes. Content validity for a mathematics placement exam was confirmed by an expert panel, and internal consistency of scores from 2008-2011 was verified using Cronbach's alpha. Effectiveness of a summer program to strengthen precalculus skills was measured by Hedge's g effect size. Results of content analysis of surveys given to tutors and students in the summer program were presented. ANOVA was used to compare mean GPA's of participants and nonparticipants of the summer program.

The meta-synthesis revealed that numerous strategies, some in precalculus and some in calculus, were successful for increasing success in college calculus. For the studies in the meta-analysis, the highest effect sizes were found in studies that used a more comprehensive approach (e.g., collaborative groups and projects) rather than a single strategy (e.g., computer skills practice).

An expert panel determined that the exam was a good measure of requisite knowledge for calculus. One question was considered unnecessary for calculus and was not of a type addressed in precalculus and was eliminated from further analysis. Cronbach's alpha was consistently above .8 for each year's scores 2008-2011 and for each subset of scores by gender, ethnicity, and selected majors for 2008-2011. The 122 students who participated in the summer program increased the average score by 6.45 points (total of 33), with 81% of the students raising their scores above the cut score to take Engineering Calculus I.

Results of ANOVA to compare mean GPA's for students in the summer program and students who did not participate, both with placement exam scores in the range 16 to 21, inclusive, showed no significant difference. The summer program was successful in allowing some students the opportunity to strengthen their precalculus skills and take Engineering Calculus I a semester earlier than the control group.