## Distribution of Advanced Mathematics Achievement

At the end of upper secondary school, the population of students becomes increasingly select. First, varying proportions of the age cohort may no longer be in school, because students either completed programs with an earlier exit point, or they have dropped out of school. Second, and very relevant for this study, there is a range of program and curricular choices available to students who continue in school so that typically not all students at this level study all subjects, or at least not at the same intensity.

Considering all of the students in an age cohort that possibly could have been enrolled in advanced mathematics courses, the percentages of students actually surviving the pipeline and having studied this complex content can vary substantially from country to country. Students will have remained in school and studied challenging content in mathematics all through their school careers.

The TIMSS Advanced coverage index quantifies the variation in the proportion of students taking advanced mathematics courses in the final year of secondary school. It may be helpful to consider this index as a fraction expressed as a percentage. First, TIMSS used census data to estimate the size of the entire national population of students that could have been assessed, if all of the students in the age cohort were still in school and taking advanced courses in their final year of school. That is the denominator. Then, as the numerator, TIMSS used the results of the study to estimate the size of the population of students who actually studied advanced mathematics and physics.