Identifying Gaps in Mathematical Ability

In 2002, I initiated educational research into the gaps that existed with the mathematics abilities of undergraduates in the MIT AeroAstro department. We conducted a study to map the "implicit mathematics curriculum", where we made a systematic mapping of the mathematics skills required for the core undergraduate curriculum of AeroAstro and the associated flow of learning provided by required courses in the Department of Mathematics.

In 2004, we conducted a pilot program in 16.06, Principles of Automatic Control, to create explicit links between engineering courses and upstream mathematics courses. We established a process for explicit linking of mathematics courses and other mathematics resources in engineering courses by creating a lecture-by-lecture mapping that details the specific mathematical skills required in each 16.06 lecture and the associated upstream mathematics course where the concept was previously introduced or taught.

The result was a set of supplementary mathematics notes and linkages to provide students with remedial resources for self-study and reference, and modified lecture content to incorporate "flashbacks", specific references to materials used in upstream mathematics courses. We worked with MIT OCW to create an online version of the supplementary mathematics notes that provides direct links to online mathematics resources.