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Abstract
This study compares students at a North Carolina community college taking a course-based developmental mathematics sequence to students taking a new, module-based emporium method developmental mathematics sequence using a Markov chain model to compare their effectiveness in progressing students toward completion of their first college-level mathematics course. Preliminary analysis to determine if the data satisfied the Markov property found that students completing previous developmental coursework had comparable pass rates, however, students attempting a course for the second or subsequent time had lower pass rates than students attempting the course for the first time. These lower rates persisted through subsequent courses even after the original course was passed. The Markov chain model was modified to account for these pass rate changes. Students under the new sequence has slightly lower, but comparable, first college-level mathematics course completion rates than those under the old sequence, however, individual course progression rates were higher under the new sequence, suggesting that other factors, such as choice of college-level mathematics course, may be affecting these results. Female and African-American students were more likely to be placed lower under both sequences, and African-American students had lower progression rates under both sequences. Students placed directly into college-level mathematics based on high school GPA and high school courses taken, instead of placement test results, were found to have slightly lower, but comparable, pass rates to traditionally placed students in college-level mathematics courses, except for those courses requiring the most rigorous mathematics prerequisites.