Redesigning trigonometry to give students what they need to succeed in calculus



“What is the sine of pi….?” This was a question that I would routinely ask my calculus students at the beginning of each semester. Are you surprised to hear that this question was usually followed up by a classroom of collective silence and roaming eyes trying ever so hard to not make eye contact with me?

For years our calculus instructors would spend two to three class periods “re-teaching” the basic fundamentals of trigonometry at the beginning of the semester to ensure that our students had the basics necessary to handle the new concepts of limits and derivatives involving trigonometric functions.

It had always been “required” for students to have had a trigonometry course prior to taking the first semester of engineering calculus. However, this prerequisite “rule” was never enforced.

Our department had always had a self-paced trigonometry course on the books for students who felt that it was necessary. In other words, trigonometry at the University of Idaho was optional. If you have been around the world of course redesign for the last 15 years or so, you have most likely heard the phrase, “freshman don’t do optional!” As it turns out, neither do sophomores, juniors, or seniors. Consequently, the annual enrollment for this trigonometry course was approximately::__IHACKLOG_REMOTE_IMAGE_AUTODOWN_BLOCK__::1.

In the spring of 2012 the faculty at the University of Idaho decided to enforce the prerequisite of trigonometry for all students enrolled in first semester calculus. Only the students who scored sufficiently high on the Compass trig sub-score could bypass this requirement. As you might expect, the enrollment in our trigonometry course exploded to roughly 400 students per year.

I was left with the task of redesigning our trigonometry course for the following fall 2012 semester. There were certain redesign goals for the course that we wanted to accomplish. These goals included the following:

  • Design a 15-week course, but design it in such a way so that students could accelerate through the course material as fast as they would like
  • Design a course that could be taken as a corequisite to calculus
  • Design a course that would introduce the necessary topics early enough so that the students would be ready when trigonometric functions are introduced in calculus
  • Design a hybrid course that would rely heavily on interactive technology
  • Design a course with solid exercises that require more than just calculator entry or multiple choice graphs to choose from

After five years, our fall trigonometry ABC rate is 84.7%. Dozens of students have finished the course early. The record time for finishing the course is five days! Calculus instructors no longer take the time out of the busy class schedule to “re-teach” trigonometry. Consequently, there is more class time for calculus.

In my ICTCM Friday session at 10:30 AM, I will detail how we redesigned our trigonometry course. I will show you excerpts of the interactive eText, sample notebook pages, and give you an opportunity to work through some fun step-by-step trigonometry exercises.


Professor Trigsted will be speaking at ICTCM 2017. Register today and join your colleagues either in Chicago or virtually to discuss many mathematics topics.

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