Before moving further, I recommend you take a look at Bowman Dickson’s thoughts on alternative forms of assessment. There are a few principles that will guide this project’s implementation in the classroom, though the majority of content for this page will be added later as different strategies are implemented. With that said, here are a few guiding principles:

  1. This course is not about tests. The goal is to introduce students to the art of asking interesting mathematical questions, pursuing them to their logical ends, and finding ways to get unstuck, which could mean reading, asking peers, reaching out to mathematicians, and/or watching videos. With this in mind, I am advocating for a portfolio style assessment model, where students are assessed based on a body of work, reflections on process, and presentation of results.
  2. Communication is critical. Research is irrelevant if it cannot be communicated and audience matters. Whereas most quizzes/tests are based on producing answers for a teacher, the world beyond school requires learning to communicate with audiences that could include fellow mathematicians, math enthusiasts, scientists, science fiction novelists, coworkers, children, the general public (whatever that is), etc. This means understanding one’s work so well that they can adapt it based on the background of their audience. To do this, students should have the chance to communicate to a non-faculty/student audience.
  3. Technology is influencing mathematics. Although there are mixed feelings in the mathematics community about using computers for proof, they have become an essential part of applied mathematics. Because of this, students should be allowed to use appropriate technology, but must also justify its need. Additionally, there is a growing community of math communicators, including some who make a living off YouTube videos (see 3Blue1Brown). Because of this, student presentation of work does not have to mean standing in front of an audience, but can be entirely digital.
  4. Encourage revision. Mathematical research is not perfect on the first try, therefore peer review and revision are essential parts of the process. To make the student research authentic, this same process should be employed with peers and with professionals from the local community. This will help to overcome the emphasis on the solution rather than the process and communication aspects of mathematics.

These are simply guiding principles, but I will actively update this page with actual examples from the classroom as time goes on.