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Calculus Enhancements

The past few years I've been actively working to improve calculus courses.  I first developed online Calculus I and Calculus II courses which currently utilized OER.  I then developed Active Calculus classroom courses capitalizing on active learning strategies.  The extensive Canvas sites built for both have been shared with other instructors for use in their teaching.  


Details of these two courses are below.

Problem-Motivated Online Calculus

After students completed my online Trigonometry course and did very well, many of them requested an online calculus course.  Since I'd built online Intermediate Algebra, College Algebra and Trigonometry, this was the next logical step.  When the department chair stated that we needed an online calculus class I jumped at the chance.  


I met with the director of E-Learning to discuss this and was told that they had just decided on a direction for future online courses.  The direction was problem-based learning.  I whole-heartedly embraced this idea and met many times with an e-learning team to brain-storm and figure out a plan for building such a course.  E-learning surveyed the current calculus classes asking these questions:


  1. What’s your Major or Field of Study? 

  2. Briefly, what areas/avenues in your field are you interested in?  

  3. Why are you taking Calculus 1210? 

  4. What are your hobbies or other interests?  

  5. Do you have a dream project, or something you’re looking forward to doing someday in your field of study?  Perhaps a project you’d like to work on or a problem you’d like to solve? What is it?


With the results of their survey, I researched problem ideas that utilized calculus in the areas from the survey.


I created first Calculus I and later Calculus II courses based on these problems.  Student interest and motivation has increased as students state how these real life applications have helped them connect the concepts they are learning to practical application.  Here are some student comments about the course.


The problems developed for both Calculus I and Calculus II were tied to careers and most often had a connection to Utah.  Students loved these connections with careers and to things familiar to them.  A couple of student comments on problems:  


"This is a project we completed was about a gas pipeline being laid through a desert. It was an interesting project to me, because I'm actually somewhat familiar with the area in this fictional problem."  


"I am going into a medical field and until this course did not see any calculus connection, but now I realized everything in the medical field is about rates of change.  The problems such as the Flu Epidemic and Bio-availability of a Drug were very interesting to me."


Here are links to problem scenario videos.  I researched and came up with the problem ideas and then e-Learning helped script them and storyboard them and made them into these videos.  


Each module begins with a video.  The idea here is if a student was working for a company and needed to solve a problem, the first thing they'd need to do is determine what data they needed to solve the problem so everything is not given to them in story problem form.  After they analyze the problem, they submit that analysis including what type of information they think would be necessary in order to solve the problem.  After learning the applicable calculus concepts, students return and solve the problem at the end of each module.


Video showing each component of a problem module for this course.





Flipped Classroom Active Learning Calculus

After successful building the online calculus, I turned to improvements for my live calculus classes.  I'd attended a conference presentation on Active Calculus and was convinced that was the way to teach students calculus, having them actively involved in learning activities.  Expanding upon the work of Suzanne Mozdy, I created first and Calculus I and then a Calculus II Active Calculus course.  This course have the following features:

  • Calculus videos in Canvas that students watch before attending class 

  • Just-in-time MyOpenMath problems embedded in Canvas to refresh on pre-req skills in algebra and trigonometry

  • Weekly reflections on calculus and learning

  • In class activities that are done in groups or for classroom discussion

Student response to this type of class has been overwhelming positive.


I am loving the opportunity to have the students do things I always wished I could have them do but there was never enough time when I was busy lecturing.  There are discovery activities as well as enrichment and reinforcement.  These activities have been adapted from the OER text Active Calculus as well as some I have developed myself.

Other faculty have taken parts of this course and copied them into their own versions of teaching calculus.

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