Learning and teaching of calculus: performance analysis in a unified system

This work presents an evaluation of a unified Calculus 1 course in a large Brazilian federal university. By course unification we mean having all the sections following the same weekly schedule, under the same syllabus and common assessment. We analyse two sets of data: pass rates relative to the 9 semesters prior to the unification and to the following 12 semesters; results of objective tests based on the item response theory, taken by the students during the period following unification. Data analysis gives us the average students' performances grouped by programme for which Calculus 1 is compulsory and shows us no difference in pass rates over the two periods. These two results help us to point out the problems in the implementation of our unification. We also explain traditional low pass rates for some sections and why our Calculus 1 may not be adequate to some of the programmes for which it is compulsory. More importantly, we show that among the students' abilities assessed by the objective tests, two seem to be necessary for the learning of Calculus and proficiency in Calculus 1 appears to be related to seven of these abilities.