As math graduate students, we often get teaching assignments from our departments, some of us tutor independently for financial reasons, and some volunteer to teach at local schools or libraries. Teaching is an inseparable part of our job/life. But that is where the consensus ends and we enter this wild jungle of ideas about (and debates over) math pedagogy, inquiry-based learning, proofs in math education, technology in math education, and so on. In this short note, I will not touch on any of these issues but rather share with you my own experience with reflecting on my teaching habits and trying to improve on them.

I was lucky to be an English teacher back home, before coming to US as a graduate student. The English teaching community is much more self-aware of teaching methodologies. For example, to become an English teacher, even if you are a native speaker, you must attend Teachers’ Training Courses (TTC) and get a certificate. This forced me to read about both theoretical and practical aspects of teaching. In what follows I will share some practical advice I have benefited immensely from in my own classrooms.

Set SMART Goals

Let’s say you have been assigned a Calculus I course to teach for this coming Fall. What are your goals, your objectives for this course? “To teach students calculus,” is not a SMART goal. A SMART goal must be (according to

  • Specific (simple, sensible, significant)
  • Measurable (meaningful, motivating)
  • Achievable (agreed, attainable)
  • Relevant (reasonable, realistic and resourced, results-based)
  • Time bound (time-based, time limited, time/cost limited, timely, time-sensitive)

“To teach calculus,” is not a measurable target. “My students will be able to differentiate quotients of elementary functions,” is specific, measurable, achievable, relevant (to the whole structure of the course), and time-based (once we get that it will be covered on quiz 3). “I want to get a B in this course,” is in fact quite a SMART goal for a student you tutor.

Having SMART goals agreed to by your student(s) is especially important when individuals pay you directly—you need some proof of what you helped them attain in case you need to.

Having such documents in your teaching portfolio will give a potential employer an impression of a solid organized teacher.

SMART goals will help with writing fair and on-point exams and quizzes. One complaint I received from my students in the teaching survey last year was that my “exams were not consistent.” And they were right: one time I would test concepts, the other time I would rely on computations.

Finally, having set SMART goals helps decide what material to focus on and what material can receive a lighter weight. This semester, for instance, I realized that spending a whole 1.5 hour session on delineating Riemann Sums does not really fit into the overall objectives of a Business Calculus course—at least the objectives I had set for that course. Instead, I was able to allocate that time to Gini Index and Consumers’ Surplus.

To help write SMART goals, start with “students will be able to + action verbs.” Avoid “Students will appreciate…” Appreciation is not easily measurable. Action verbs from Bloom’s Taxonomy is a great way of synching your expectations with the students’ skills. Choose the appropriate column from the taxonomy according to the complexity level of the course, and use verbs from that column in setting goals. These verbs can also be used in phrasing exam questions in a clear and non-confusing way.

Setting SMART goals makes your life easier—you have a mission, you are focused, the students are focused, and your success is measurable, quantifiable. The time that it saves you later is  significant (when writing exams, for example) and the confidence you and your students have in the efficiency of the teaching is boosted. Let me finish by this excerpt from my Business Calculus course:


  1. SMART goals can be applied to any context other than teaching. I have found that when I set my goals more thoughtfully I am more likely achieve them. I write them on a piece of paper, and draw little squares next to them. I check each one that I accomplish!
  2. I may follow this article by one on “Components of Class Activities.”


About Behnam Esmayli

I started PhD in Mathematics at Pitt in Fall 2015. I have come to grow a passion for metric spaces -- a set and a distance function that satisfies the triangle inequality -- simple and beautiful! These spaces when equipped with other structures, such as a measure, becomes extremely fun to play with!
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