I distribute this handout to all classes where students will present solutions of computational problems to the class at the board. In particular, this includes Calculus 1, Calculus 2, Calculus 3, and Linear Algebra. I believe that by giving specific criteria for what constitutes a "good" presentation, students will convey information  more effectively and feel more at ease because expectations are clear. To evaluate students' presentations, I use the same checklist, giving one point for each action accomplished by a student during a presentation.

These handouts correspond to units in a course. They contain simple questions that require students to scan (or “preview”) a section of the course text before the corresponding material is discussed in class, an important habit to acquire as early as possible. Each handout also contains a list of vocabulary terms that students will be expected to know, goals for comprehension, and lists of exercises (to attempt after the lecture) corresponding to each goal. (With the increased difficulty of mid-level courses, student expectations need to be clear, and these handouts are helpful in this process.)

Having read the handout prior to class (to complete the “preview” questions), students will have encountered the main points and goals before the lecture begins, enabling them to identify key ideas more quickly, thus allowing the lecture to flow more smoothly.

In upper-level or independent study courses, where students are largely responsible for their own learning, I provide them a framework to help them get started: a series of questions that concern basic details and an overview – the “big picture”. Students are expected to be able to discuss the answers in class; thus, the lecture can then be used to develop a deeper and more complete understanding of the concepts. These guides are similar to the “Preview Question” handouts mentioned previously, but require a much greater level of effort and understanding (prior to the lecture) on the part of the student.

In some courses I start each class with a “warm-up” problem: a single, simple question meant to be solved in a few minutes – mental calisthenics before diving into new material. The problem is typically based on the previous lesson or on some fundamental concept. Having to answer questions daily motivates students to keep up with the material and gives them a measure to self-monitor their progress and the effectiveness of their preparation for class.

Towards the middle or end of class I frequently pose a “mix-up” problem: in randomly arranged groups, students work on an in-depth question based on that day's lesson. The “mix-up” solidifies the material as students use the concepts and explain them to each other as they work together to find a solution. Students who have not yet internalized the material benefit from hearing their peers' explanations in addition to my own; students who already understand the material benefit from the process of explaining to others. This “mix-up” helps all students identify potential gaps in their understanding immediately, rather than later on in the day or week when they start their homework.

In the handout, the playing-card notation refers to the deck of cards that I use to randomly choose groups -- each student is given a card from Ace to Nine, all cards with the same rank form a group, and each group will have a corresponding problem on the handout.

Periodically throughout the semester, I will take an entire day to conduct a review. This may consist of students spending an entire class working on exercises in groups, or a writing workshop in more advanced courses.

The Introduction to Proofs course serves as a transition from the more elementary and computational courses to the more difficult theoretical and applied courses. To facilitate this mental transition, I surveyed the students on the final day of the first offering of the course and solicited general advice for the subsequent group of students. This advice was compiled in a handout for future students taking this course; the “student testimonials” can help them realize what habits are necessary and what mistakes to avoid in a timely manner