Why meteorologists shouldn’t “teach to the middle”

Once every decade, we take the temperatures of the last 30 years, average them together, and refer to this as the “normal” temperatures for a location.  For example, when you see on the nightly weather report that the “normal high for today is 84 degrees,” that’s simply the average of all the highs for that day from 1981 to 2010.

The number 84 is an average.  Very few, if any, days in the record will actually have had a high temperature of exactly 84!

The same goes for our students.  In any given class, the number of “average” students, perfectly in the middle of the distribution, will be quite small.[Footnote 1]  My argument is this: if we teach to the middle, we alienate and bore our upper tier of students (who are our future colleagues) and at the same time work over the heads of weaker ones who may need the most help.  We likely reach those few students who are truly in the middle of the distribution, but overall to me this is a lose-win-lose situation.  Losing two battles every day is not how I want to spend my career.  Furthermore, the standard we “set by teaching to the middle is a standard of mediocrity.”  It’s okay to be average, kids.  Everyone gets a ribbon.

What, then, is the answer?  Is there one?  How can we possibly differentiate learning when faced with 100 students, or even 40 or 50?  Facilitating a classroom that promotes learning already requires lots of work, and most academics I know don’t believe they have any additional time to devote to it.  Here are some rough ideas, certainly a non-exhaustive list but maybe a starting point at least.

1. Variety in course assignments.  Some of our students will be math stars, while others are incredible artists who struggle mightily with college algebra.  Offering different types of work — calculations, concept mapping, figure interpretation, opinion essays, etc. — allows all students to take part.  I like to believe everyone is good at something.

2. Variety in in-class activities.  I pray that the days of lecturing for an hour a day three days a week are dying (an albeit gruesomely slow death, but still dying).  And reading text on slides as they appear on the screen doesn’t teach to anyone, let alone the middle.  In-class activities and discussions can be like #1 above and also varied in level: a mixture of easy concepts, medium concepts, and the occasional mind-bender sets up a class that everyone can get something out of.  Structured group and team-based activities, discussions, or even quizzes (yes, group quizzes!) help also.

3. Structure in assignments and activities.  “You need structure. And discipline!”  In a room of professionals, we could get away with the activity ‘hey let’s pull up today’s 500-mb map and just talk about it for awhile.’  However, this will likely fall flat in a room of mixed majors or gen-ed students.  At least when I’ve tried it, it has.  Even off-the-cuff activities need structure and scaffolding (take small steps: first let’s find the ridges and troughs, and the vorticity, and the temperature advection, and then ask where are the likely surface features, etc.).

The bottom line here is that we have to find ways to involve everyone (or, realistically, as many people as possible) in the room in the learning process.  If “teach to the ____” is just code for “at what level do I pitch my lectures?” the problem goes much deeper.  To me, the room is more about what learning will be taking place, rather than what teaching will be taking place.

We’d be hard-pressed to find a string of perfectly “average” weather days, instead finding runs of hot and cold which both have their own fun and own beauty.  And each of our classes is made up of much more than a blob of “average” students who are the only ones to deserve our attention.  A classroom includes a spectrum of abilities, and everyone learn something when courses are thoughtfully organized for more than just what we believe the “average” student is capable of doing.

Footnote 1:  Some readers will want to start talking about normal distributions at this point.  I ask, are the students that are at +1σ and -1σ at the same skill level?  What’s really the “average” group, then?  +0.5σ to -0.5σ?  That’s now less than 50% of your class.  The bounds get smaller and smaller…

“The Points Don’t Matter”

[TL;DR:  Tthere is not much difference in the average grade for a course if you redistribute the weights for exams, homework, and the like after the fact.]

When students see a new course syllabus for the first time, the first thing many look for is the breakdown of grading for the course.  “What do I have to do to get the grade I want?”  At least I always did.  Every semester, every class.  Not ashamed to admit it, either.  That university curricula are so grade-centric instead of outcome-centric (and have been for decades) is a rant for another page, and has been addressed thoroughly, here, here, and here among probably a dozen other places.

But does the course grade breakdown really matter that much?  That is, do the weights we assign to each category of work truly have a large impact on final course grades?  To find out, I pulled up the grades for an introductory course I taught a couple years ago and recomputed their final grades using five different weight combinations.  There were about 30 students in the course, and in terms of structure it was rather mundane: lecture, homework, quiz, exam.  It was earlier in my teaching career; forgive me!

Here are the breakdowns I tested, using all the assignments we did that semester:

Homework Quiz Exam 1 Exam 2 Final
Option 1 25% 15% 20% 20% 20%
Option 2 40% 10% 10% 10% 30%
Option 3 20% 10% 20% 20% 30%
Option 4 20% 10% 15% 15% 40%
Option 5 30% 20% 15% 15% 20%

Depending on the instructor, I think any one of these breakdowns would be pretty standard for a lower-division science course that doesn’t have much of a team-based or lab component.  But standard as they might be, each of these five would potentially have huge impacts on student perception of the course and the instructor (especially option 4. Brutal!).  And I’d say it’s highly likely that study and work habits would be different too, depending on what the actual scale was.  I know of no way to test how different those habits would be if students had been presented a different distribution up front — we can only look at how grades would be different after the fact.  If you know a better way, please hit the comment box below.

So yes, I’m making a key assumption here:  to make this comparison I have to assume that perceptions and study habits and such would not be different as students complete any given activity, regardless of which of the five breakdowns would be used.  Again, I know this is a stretch.  For each option, here is the distribution of the students’ final grades:

Highest 75th %-ile Median 25th %-ile Lowest
Option 1 99 87 80 70 53
Option 2 99 87 81 67 54
Option 3 98 88 81 70 52
Option 4 99 88 81 68 51
Option 5 99 86 80 70 53

From a class-average point of view, every option gives a nearly identical distribution!  The greatest variability occurs, expectedly, at the bottom of the distributions which includes students who were badly deficient in one of the categories (rarely attended class so had quiz grades < 50%; missed or didn’t turn in key homework or team assignments; poor test takers; etc.).  I also checked the number of students who achieved 90%, 80%, etc., as those would be my rough cutoffs for letter grades.  No surprise: for this course the number in each category changed by no more than one student (out of ~30) regardless of which category distribution was used.

Because it’s much more recent, I won’t show the results from another course, although they are very similar.  To me, it’s clear that as long as the distribution chosen is a reasonable one, the actual percentages simply don’t matter that much to final grades.  We’ll almost always curve a point or two, here or there, to accommodate bad exam questions and grading mistakes and uncertainty and whatnot, and so even the variability in the lower half of these distributions is just in the noise to me.

Have I tried to use this information to the advantage of my students?  Yes.  Given that test anxiety is real and observable, I’ve lowered the stakes on my in-class exams (toward something like option 5 above) so that those assessments count a little less, and the untimed and out-of-class work counts a little more.  Because of the tendency to think of out-of-class work as “grades I earn” and exams as “grades you give me,” students hopefully will take more ownership of their learning when the percentages shift in their favor.

Even though, ultimately, the points don’t matter.  Much.  🙂