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Rapid-response (non-linear) teaching: report January 25, 2018

Posted by apetrov in Blogroll, Education, Near Physics, Physics, Science.
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Some of you might remember my previous post about non-linear teaching, where I described a new teaching strategy that I came up with and was about to implement in teaching my undergraduate Classical Mechanics I class. Here I want to report on the outcomes of this experiment and share some of my impressions on teaching.

Course description

Our Classical Mechanics class is a gateway class for our physics majors. It is the first class they take after they are done with general physics lectures. So the students are already familiar with the (simpler version of the) material they are going to be taught. The goal of this class is to start molding physicists out of physics students. It is a rather small class (max allowed enrollment is 20 students; I had 22 in my class), which makes professor-student interaction rather easy.

Rapid-response (non-linear) teaching: generalities

To motivate the method that I proposed, I looked at some studies in experimental psychology, in particular in memory and learning studies. What I was curious about is how much is currently known about the process of learning and what suggestions I can take from the psychologists who know something about the way our brain works in retaining the knowledge we receive.

As it turns out, there are some studies on this subject (I have references, if you are interested). The earliest ones go back to 1880’s when German psychologist Hermann Ebbinghaus hypothesized the way our brain retains information over time. The “forgetting curve” that he introduced gives approximate representation of information retention as a function of time. His studies have been replicated with similar conclusions in recent experiments.

EbbinghausCurveThe upshot of these studies is that loss of learned information is pretty much exponential; as can be seen from the figure on the left, in about a day we only retain about 40% of what we learned.

Psychologists also learned that one of the ways to overcome the loss of information is to (meaningfully) retrieve it: this is how learning  happens. Retrieval is critical for robust, durable, and long-term learning. It appears that every time we retrieve learned information, it becomes more accessible in the future. It is, however, important how we retrieve that stored information: simple re-reading of notes or looking through the examples will not be as effective as re-working the lecture material. It is also important how often we retrieve the stored info.

So, here is what I decided to change in the way I teach my class in light of the above-mentioned information (no pun intended).

Rapid-response (non-linear) teaching: details

To counter the single-day information loss, I changed the way homework is assigned: instead of assigning homework sets with 3-4-5 problems per week, I introduced two types of homework assignments: short homeworks and projects.

Short homework assignments are single-problem assignments given after each class that must be done by the next class. They are designed such that a student needs to re-derive material that was discussed previously in class (with small new twist added). For example, if the block-down-to-incline problem was discussed in class, the short assignment asks to redo the problem with a different choice of coordinate axes. This way, instead of doing an assignment in the last minute at the end of the week, the students are forced to work out what they just learned in class every day (meaningful retrieval)!

The second type of assignments, project homework assignments are designed to develop understanding of how topics in a given chapter relate to each other. There are as many project assignments as there are chapters. Students get two weeks to complete them.

At the end, the students get to solve approximately the same number of problems over the course of the semester.

For a professor, the introduction of short homework assignments changes the way class material is presented. Depending on how students performed on the previous short homework, I adjusted the material (both speed and volume) that we discussed in class. I also designed examples for the future sections in such a way that I could repeat parts of the topic that posed some difficulties in comprehension. Overall, instead of a usual “linear” propagation of the course, we moved along something akin to helical motion, returning and spending more time on topics that students found more difficult (hence “rapid-response or non-linear” teaching).

Other things were easy to introduce: for instance, using Socrates’ method in doing examples. The lecture itself was an open discussion between the prof and students.

Outcomes

So, I have implemented this method in teaching Classical Mechanics I class in Fall 2017 semester. It was not an easy exercise, mostly because it was the first time I was teaching GraphNonlinearTeachingthis class and had no grader help. I would say the results confirmed my expectations: introduction of short homework assignments helps students to perform better on the exams. Now, my statistics is still limited: I only had 20 students in my class. Yet, among students there were several who decided to either largely ignore short homework assignments or did them irregularly. They were given zero points for each missed short assignment. All students generally did well on their project assignments, yet there appears some correlation (see graph above) between the total number of points acquired on short homework assignments and exam performance (measured by a total score on the Final and two midterms). This makes me thing that short assignments were beneficial for students. I plan to teach this course again next year, which will increase my statistics.

I was quite surprised that my students generally liked this way of teaching. In fact, they were disappointed that I decided not to apply this method for the Mechanics II class that I am teaching this semester. They also found that problems assigned in projects were considerably harder than the problems from the short assignments (this is how it was supposed to be).

For me, this was not an easy semester. I had to develop my set of lectures — so big thanks go to my colleagues Joern Putschke and Rob Harr who made their notes available. I spent a lot of time preparing this course, which, I think, affected my research outcome last semester. Yet, most difficulties are mainly Wayne State-specifics: Wayne State does not provide TAs for small classes, so I had to not only design all homework assignments, but also grade them (on top of developing the lectures from the ground up). During the semester, it was important to grade short assignments in the same day I received them to re-tune lectures, this did take a lot of my time. I would say TAs would certainly help to run this course — so I’ll be applying for some internal WSU educational grants to continue development of this method. I plan to employ it again next year to teach Classical Mechanics.

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