At the college level, it can be difficult to engage students outside the classroom through the use of effective homework assignments. Although it is straightforward to create assignments that test the ability to carry out computations as discussed in class, it is more challenging to create assignments that encourage students to think more…

In this note, we report on an implementation of discovery-oriented problems in courses on Real Analysis and Differential Equations. We explain a type of task design that gives students the opportunity to conjecture, refute and prove. What is new is that the complexity in our problems is limited and thus the tasks can also be used in homework…

Addressed toward course coordinators and departmental leaders interested in redesigning an undergraduate mathematics course, we highlight the steps our team at the University of Maryland, College Park has taken in bringing active learning to our Precalculus course. We provide examples of ways in which we have coordinated active learning across…

Like many math educators, I have spent much of my career bound to traditional methods of instruction and assessment. In recent years, motivated by a growing understanding that such approaches may not result in equitable or inclusive classroom environments, my teaching philosophy has shifted radically. In this article, I describe how I transformed…

My goal in crafting homework in calculus is twofold: to provide scaffolding for students to develop a theoretical understanding of calculus concepts and to incorporate good mathematical exposition, including justification and proof when appropriate. I achieve these goals by creating weekly homework sets that students work on in groups of three or…

This paper describes an innovative way of randomly collecting handwritten homework in calculus classes with approximately 50 students using a standard deck of cards, which does not place an excessive burden on faculty with regard to grading. In addition to the increased awareness students develop in structuring a mathematical solution, the…

This paper describes and assesses the implementation of online homework in a first-semester calculus course. Comparing sections of the course before implementation to those after, we find statistically significant improvements in retention rates, measures of student engagement, and participation on homework. We do not, however, find statistically…

A significant amount of attention has been given to the predictors of academic achievement in higher education. However, the vast majority of articles have centred on entrance criteria and the learning approaches or personal habits of students. Investigations into how achievement depends on student efforts, being almost invariably based on…

It is generally agreed that the ability to read mathematics is an important skill--one that few of our students possess. A number of people have published some suggestions for helping students learn to read their mathematics textbooks. What these have in common is suggestions for getting students more active while reading. Using these resources as…