Redesigning 18.01 (Calculus) around authentic problems and downstream connections

18.01 (Calculus) is a GIR taken every fall by about 200 students – the first-year students with the least math background. It has an important role in educational equity, making mathematically intensive work in science and engineering available to all students. The students have difficulty translating between mathematics and real-world situations, doing problems like setting up an integral based on a real-world scenario. With support from ACF in 2020, we have been restructuring the course around real-world problems that teach these skills. We are applying for a renewal to continue this work. In particular, we want to keep improving students' ability to set up integrals. We aim to do so through cognitive-task analysis of this ability – identifying the expert steps of the process and subskills that students need to carry it out. We will develop new recitation materials and MITx "finger exercises," and incorporate mastery learning.