Issues of coverage raised all the time

We recently re-examined the 3" by 5" feedback cards we collected from attendees at our JMM 2016 SIMIODE Open House and we share them with our thoughts with you.

Under the theme "Issues to Overcome" we found the following:

  • How do you fit it in? What do you drop?
  • Do your colleague resent you rocking the boat?
  • I would like to try but I don’t know what to do.

One concern which arises is the issue of “coverage” and what will happen to the technique coverage in differential equations when modeling is used. We find this concern comes up all the time, at talks we give, in casual conversation, in other talks we attend.  Karen Bliss and Jessica Libertini in their article, Using Applications to Motivate the Learning of Differential Equations. In Advances in the Mathematical Sciences:  Research from the 2015 Association for Women in Mathematics Symposium. Weisbaden GERMANY:  Springer International Publishers.,  have demonstrated in their applied mathematics differential equation course for engineering students at Virginia Military Institute that the introduction of modeling enhances the learning of the mathematics and facilitates more in depth coverage as well as maintaining coverage. Keith Stroyan of the University of Iowa has said that he has never had a student comment on a technique of solution method years after a course, but students ALWAYS remember projects. He quotes a student, “You know, these course projects are difficult, but I understand. They are the answer to the question, `What good is it?’ ” Indeed, COMAP for years has produced modeling materials which enable curriculum advance without loss of content.

As far as colleague resentment, the goal, we have found over years of experience is to inform and engage them, and to send on students who demonstrate a higher order of thinking. Colleagues will see the “product” of your efforts and respect you for this.

With regard to not knowing what to do we have three pieces by colleagues address that issue and offer their experience and advice.

In addition Rosemary Farley offered a blog on her Spring 2016 differential equations course in which she shares her experiences, ups and downs, as well as her materials used.

Under the theme “Realizing Opportunities” we found these remarks interesting:

  • Students could get experiential knowledge of differential equations.
  • Students will expand their horizons.
  • Their brains will explode.

Now we are not quite sure of the last remark, but we are inclined to think it means students would say to themselves something like, “Wow!  I did not know differential equations played such an important role.”


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