Nonlinear Evaluation

Questioning the assumption of the linear relationship between (stuff) and evaluation result.

A nonlinear story about this topic. It started with my family getting a dog. Then, while watching people interact with the dog, I started thinking about dogs as a Human Litmus Test. I mean, except for those that have had some dog-related trauma in his or her life, only a non-human can resist the happiness power of a dog. I didn’t mean that you could judge how good a person was by how they interacted with a dog, but I thought you could see if they at least had some hope for being ‘good’. Then, as things often go for me, I thought about teaching and teacher evaluation, and wondered if there was a Teacher Litmus Test, i.e. a simple question or scenario that would tell you if a teacher was on the track to being good (whatever that means), versus needing lots of intervention. Finally, I turned it around to thinking about how we evaluate students and how, whether is it appropriate or not, we treat our assessments as if they measure some sort of linear growth or difference in a student’s abilities.  And thus we reach the point of thinking about how our assessments do and can relate to the underlying factor we want to measure.

If you graph the scores you give against some sense of what has been truly learned, then you’d probably get a graph like one of these:



Someone who considers him or herself an easy or generous grader, might choose the blue line; someone who consider him or herself a tough grader, might choose the green line, but since we all think we are fair graders, I suspect most would pick the red line.  I’ll consider all of these to represent linear grading.

But, there are many things in our classes that really don’t fit this model. How about attendance? How about prerequisite skills? How about extra-credit or remediation options? These probably look more like these graphs:


The pink graph brings into question if all measures must have positive derivatives. Purple asks if something is earned from just signing up for the class.  Orange and blue let us go from caring to not caring or vice-versa (per change in learning).  Black reminds us that not everything can be measured continuously (or can be pretended to be measured continuously).

So, what’s the point? We should consider thinking about the underlying assumptions that go into our grading practices and make sure they match the reality of what is going on.  We don’t have to stick to linear grading if we think (and know?) that some of the elements of learning are not linear.



Maxims for Teaching

A look at General Neyland’s 7 Maxims (for football) and how they might be translated into Maxims for Teaching.

English: Robert Neyland Statue
English: Robert Neyland Statue (Photo credit: Wikipedia)

It’s time for the first game of the year in the Vol Nation, and for those draped in the orange robes of Vol history, it is time to review Gen. Robert Neyland’s 7 Maxims. Neyland was coach from 1926-1952 (with breaks for wars, etc.) and was a winner. His football strategy was defined by 7 Maxims:

  1. The team that makes the fewest mistakes will win.
  2. Play for and make the breaks and when one comes your way – SCORE.
  3. If at first the game – or the breaks – go against you, don’t let up… put on more steam.
  4. Protect our kickers, our QB, our lead and our ball game.
  5. Ball, oskie, cover, block, cut and slice, pursue and gang tackle… for this is the WINNING EDGE.
  6. Press the kicking game. Here is where the breaks are made.
  7. Carry the fight to our opponent and keep it there for 60 minutes.

And here’s my transformation into maxims for teaching, with discussion:

  1. The teacher that makes the fewest mistakes will have the most impact.  I take this maxim to mean that one should take care of mistakes as they come so that at the end of the day all would say very few mistakes were made. Many mistakes are a natural, and useful, part of the daily classtime. A good teacher turns those mistakes around and makes them a positive part of the class.
  2. Teaching happens in unexpected moments, and we should look for and make such moments happen. And when they do, we should take advantage to make learning happen. This might be an unexpected question or answer, or just some new twist on a topic. Good teachers are flexible and can take advantage of these opportunities, but they also don’t just wait for such things happen.
  3. If you are working at your teaching and things don’t seem to be going well, don’t let up, but keep on doing what you are doing with more effort. This is especially true if you are trying something new. A good teacher knows his or her skills at teaching, and when things can go better, put in the extra effort to make it happen.
  4. Protect the class transitions (e.g. beginnings and ends of sections) and the lead examples and points of the course. And when things go well, protect the atmosphere of success all the way to the end. The transitions are critical moments in a course and if handled poorly, can lead to a irreversibly lost class. Second in importance comes the main points that the course is built on. Finally, success builds on success, so if things go well, keep it up.
  5. Create good habits (and a common vocabulary), but remember the ultimate goal: LEARNING. Having good routines with a matching language in a class is a great way to build student knowledge and to create a learning atmosphere (besides just being fun). But it is important to remember that the goal isn’t the routines (or the fun) but it is learning.
  6. (Seems like just a repeat of #2, with a touch of #4)
  7. Be persistent and consistent and always look for opportunities to push the students to learn, for the entire hour, for the entire semester. This isn’t about covering more material, but of taking advantage of every opportunity, especially those where there is learning happening, to push for more.

So as you move from ‘sage on the stage’ to ‘guide on the side’, consider the Maxim’s in your teaching.