Fig. 1.
Horizontal and Vertical Course Repetitions in Mathematics. Figure shows names and course numbers for 12 types of college-level math offered at public institutions of higher education in Texas. Horizontal repetition occurs when students complete an introductory math course and then enroll in a different introductory math course (i.e., it only occurs among introductory coursework). Vertical repetition occurs when students repeat a math course in the same sequence (repeating the same specific course or one earlier in the same sequence).