I describe the motivation, structure, implementation, and student feedback of my mastery-based testing (MBT) system with a significant final exam component in Calculus I and II since 2016. Grades for each written assignment, quiz, and exam question were assigned on a Mastery/Progressing/Needs Improvement (M/P/NI) scale. Homework and quizzes could…

A typical mathematics assignment consists of one or two dozen practice problems relating to the same skill or concept, yet empirical evidence suggests that there is little or no long-term benefit from working more than a few problems of the same kind in immediate succession. Alternatively, randomized experiments in the laboratory and classroom…

It is common for freshmen students to enter Calculus I with a wide range of levels of preparation and mastery of background material. In addition, many of the students struggle with the adjustment from high school to college. In an effort to help the students to solidify their understanding of concepts as they progress through the course, as well…

Starting in March 2005, the SAT, taken annually by more than 1.4 million college-bound students, will undergo its most significant change since 1994, when the College Board, which sponsors the test, first allowed calculators into test rooms, added open-ended math questions, and eliminated antonyms and added more critical-reading passages in the…

This article describes a writing activity that is employed after graded exams are handed back to students. Students are asked to reflect on their performance and to demonstrate understanding of mathematics related to the exam and/or unit of instruction. The article provides examples of student writing, scoring rubrics, and suggestions for…