A few semesters ago I began to teach differential equations to sophomore undergraduates through extended projects, using  professional grade tools – MATLAB, Maple and Mathematica – that scientists and engineers use in their practice.

An older student in the class was a technician at a nationally known engineering company. He was re-training to be an engineer. I asked him if he had set homework to do in his job. He replied “No”. I asked if he had tests, quizzes or exams to do as part of his job. Again he replied “No”.  I then asked if he ever had to do projects. “All the time”, was the answer. So I asked if he was assessed on those projects. He replied that he had to give a verbal and written report to his line manger at the conclusion of a project. I asked what would happen if the project was unsatisfactory, or if he did not complete it on time, or at all. He replied that if that happened a few times he could be fired.

I focus more now on numerical solutions of differential equations because, in scientific and engineering practice, that is what professionals will most likely do. I want students to work on realistic problems, using realistic methods and realistic tools. I want all mathematics written in LaTeX on WordPress blogs. I want them to write coherent accounts of their projects, and be able to present their work to the class.

I’ve had a few semesters doing this now and Spring 2010 I want to change tack a little, maybe ramp it up a notch. This semester I want to find genuine applied  problems that  students can work on, in class, in groups in a studio environment.

The reaction to projects has been overall fairly good. I estimate about 10% of students will complain that this is not how they are used to learning.  The other 90% seem very satisfied with the project approach.

Where I am heading can be seen best in the following video of John Seely Brown. I did not get the project idea from him, but I did get the idea for studio work from him. I like this idea a lot, and I’m hoping my students do too in Spring 2010:

A number of questions are uppermost in my mind as I prepare for Spring 2010:

1. Will the students remember  anything of what they learn in the semester?

2. Will students develop flexible knowledge, that they can apply in novel settings, similar to what they worked on in semester, but sufficiently different to really test their understanding and recall?

3. Will the experience transform them? Will they gain new ways of looking at modeling situations and be capable of drawing analytical conclusions from exact or numerical solutions of differential equations?

Perhaps to the annoyance of the students I will focus each class on the transformative nature of the class experience. I want the students to understand deeply John Seely Brown’s words:

“We participate, therefore we come into being.”

I want them to do this by forming their own study groups, by using all the technological aids available to them. I want them to get excited about their projects, and to communicate what they find to other students and faculty.

I intend to have a mid-semester poster session where one and all will be invited into the class as students explain their poster presentations, and I intend to do this again at the end of semester.

I cannot, any longer, follow a text book – probably written by a self-appointed expert – set exercises for students to do, and set tests and become bitterly disappointed at the results. I’ve done that sort of crap too long. It’s not teaching, no matter how well done.

Vote on whether you think homeworks,  quizzes, tests, exams or projects are helpful in mathematics teaching.

John Seely Brown is right – a teacher is a mentor, not an instructor.