The role of mental representations in mathematics and computer science (for teaching or research) is often downplayed or even completely ignored. Using an ongoing work on the subject, we argue for a more systematic study and use of mental representations, to get an intuition of mathematical concepts, and also to understand and build proofs. We…

A summer bridge program for incoming engineering and computer science freshmen has been used at the University of Wisconsin-Milwaukee from 2007 to 2010. The primary purpose of this program has been to improve the mathematics course placement for incoming students who initially place into a course below Calculus I on the math placement examination.…

The notion of equivalence relation is a fundamental concept in mathematics and yet mathematics students often are not given formal exposure to it until midway through their college careers. Not only do they need to become adept at working with equivalence relations but they should also understand the wide applicability of this notion. In this…