Rubber band lesson planning

Oliver Knill
August 18, 2018

Abstract: Building in flexibility is important when planning a lesson. This is summarized here in three principles: the first is a divide and conquer strategy: cut each lecture into smaller pieces, which then are put together to a larger story. This builds structure. The second is a rubber band strategy: built in elements which can be stretched, shortened or expanded. The third advise is to discard teaching ideologies and build on techniques that works for you. Not every technique (including the principles mentioned here!) work for everybody.

Introduction

Teaching both depends on the format and the person. Unfortunately, many educators advocate strict guidelines and try to impose their ideologies on others. Having experimented myself with techniques of others, I know that some work but others don't for me, even so the corresponding teacher has no problem with it. I know also that some techniques I use myself are not for everybody. Not only every teacher is different, I also noticed that classes can be very different. A few active students can change the dynamics of the course.

Extreme cases are "completely scripted and rehearsed lectures" other examples are "lecture free, flipped classroom set-ups", where the teacher only moderates. An other extreme are ``inquiry based approaches", where the students structure the class. Each format can makes sense. A ``worksheet based" lecture allows for more coordination, especially if classes are taught in parallel, the scripting however cuts the creativity of the teacher produces "teachers robots" and destroys presentation skills and class discussion. The inquiry based approaches where students find and present their own proofs needs a teacher with great people-skills, charisma and the ability to extremely fast understand also obscure or unpolished thoughts and bend them right.

Having observed many lessons both as student, graduate student, postdoc, or while organizing large lecture courses, I have seen many different teaching styles. It is amazing how many different approaches really work. Some teachers like to improvise and be spontaneous, reacting well to input from the class. Other teachers have difficulty with ``reading the class" and feel more comfortable with a scripted approach. The same is the case for seminar talks and it is fortunate that video technology has enabled more and more to bring these lectures to a larger public.

The teaching depends also on how comfortable the teacher is with the material and how much experience the teacher has. The formal format and set-up (lecture hall or classroom) can be an important factor. Also imposed boundary conditions. For a Pecha-Kutcha talk, where 20 slides are shown 20 seconds each, a rehearsal is required. The format does not allow for much flexibility. If a class is taught many times already, there is the problem of choice: too many stories could be told. Each lecture allows a variety of bits and pieces which can be combined. Examples of structural challenges are a messy or defective blackboard, noise from construction or close by classrooms, or if previous classes do not clear out the classroom on time, cutting the time of a lecture.

Just because there are so many factors, one has no control about, I made good experience with three principles which also are easily adaptable: a ``divide and conquer" approach" as well as a ``rubber band approach". The third is being open and flexible with the teaching style.

Divide and conquer

First of all, each lecture needs to have a clear topic and goal. This is part of the overall syllabus and should not be negotiable later on. Having to shuffle around the material during the semester is poor preparation. It sometimes is necessary, for example, if the class is taught the first time and a approach does not work as intended or if the enrollment is different than expected. The size of the enrollment also leads to a wider spectrum of students making more ambitious approaches less realistic.

Now, if a specific lecture and material has been decided on, one has to plan the lecture. What worked well for me in general is to spit up the lecture into 5-6 different parts, even make a short table of content so that students have a guide line. Then, in each section, try to start from scratch, build an independent story.

Here is an example of a blackboard from Summer 2018: on the left is an outline which brings some structure into the lecture.

Click on the picture to see it large.

Rubber band approach

The are two possibilities to stretch or shorten a lecture. One is to leave out an entire section or add it in. Good lecture planning allows for a smaller less important section so that this is the one which gets cut if less time than expected is available.

There are various parameters which can cut a lecture shorter than anticipated. There can be more discussion than expected, the previous teacher might clear out the room too late (a really bad habit), or there are some activities which take longer. Then there are things which always can happen: like that a computation takes longer or that a student insists to see more details to some part.

An other possibility is to stretch or shorten individual parts like the choice of example problems. There are small things one can adapt. One can chose the functions in such a way that almost no computations are necessary. With more time, one can add more complexity. After an optimal preparation, there is for any problem, a lighter and heavier version, which allows to build in flexibility.

Flexibility and tolerance

Teaching dogmas are a bit like ideologies or even resemble religious quests. Some become obsessed with a particular method and then in an almost missionary manner try to convince others how to do it. Even the advise given here might not be for everybody. There are some teachers who need to read from prepared notes for example. This includes experts in a field who present material and theories they have created themselves or taught for half a century. One can see on Youtube some very good mathematicians who talk about their own work and read from a piece of paper. It can destroy spontaneity. A talk in which the speaker reads verbatim from some slides for example (talking with the back to the audience to the slides) is almost comic. But it can also make sense. In very rare circumstances it can happen that a person lacks any improvisation skills, is insecure or shy and even is afraid to speak in front of a large audience. In such a case, it is better to have a scripted ``anker man" approach rather than a disaster without structure at all. I have also seen personalities, who can with zero preparation time pull off a lecture and do well. I myself can't do that and need to prepare for a lecture even if I have taught it for 30 years. Also this can be psychological as being prepared calms the nerves.

[Added November 9, 2018]: About tolerance: there are obvious teaching techniques which have not worked on some levels. It is funny for example that the ``flipped classroom techniques" which have a terrible track record in high schools of the US (we are not doing well at all in K-12) are pushed to higher education, a system which has a good track record (higher education is measurably healthier as one can see that the rankings of US universities is internationally quite good, unlike high school!) Still, educators try to impose (almost religiously) some techniques from high school which obviously did not work at all to higher education. Why are there are experiments going on in higher education pushing failed pedagogical approaches? Well, one has to experiment and it can make sense in the light of tolerance, since if something fails on one level (high school), it does not mean that it fails also in an other (higher education). My personal interpretation why flipped techniques failed is that the teachers become unmotivated, can be less prepared and don't need to be any more so qualified (flipped techniques mean often that students look at canned videos of some good looking telegenic but clueless anker-men) then do some pre-written worksheets, where solutions are available. You don't have to know a subject to teach that. It is of course pushed by adminstrations a lot (with lots of propaganda) because it is much cheaper and boosts student evaluations. The collateral damage is that it completely destroys teaching culture. Look at the TIMSS Tapes for example. You see great teaching technique examples and some great teachers. This is all destroyed with students just watching a 2year old uninspiring videos and filling out some worksheets which have been written years ago by somebody else.

Document history: August 18, 2018. Document posted.
August 20, some typos.
November 9: add last paragraph in part 3 and add document history.