The Logic of Learning

WARNING:  Direct, possibly rude, certainly philosophical language ahead!

If learning has not happened, has teaching taken place?

If the learner hasn't learned, the teacher hasn't taught.

These are variations on one of the most illogical notions to come down the pike.  It may well be, in the words of Bertie Wooster, "the rummiest thing I've heard in a lifetime of rummy things."  Let's dispense with pleasantries and get down to logic.

Definition:  necessary condition -- A necessary condition for some state of affairs S is a condition that must be satisfied for S to obtain.  (http://philosophy.wisc.edu/hausman/341/Skill/nec-suf.htm)

Definition:  sufficient condition -- A sufficient condition for some state of affairs S is a condition that, if satisfied, guarantees that S obtains.  (ibid.)

A simple undergraduate logic or philosophy class introduces these basic terms.  Let me illustrate with an example.

Oxygen is a necessary condition for me to live.  I must have oxygen to breathe.  If I do not have oxygen, I cannot breathe and will die.  Another way to say it is "without which not."  Since without oxygen I would not live, oxygen is a necessary condition for my life.

Oxygen is not a sufficient condition for me to live.  There is plenty of oxygen in the morgue, and we do not see dead people jumping up to do the mambo.  Another way to say it is "with which must."  It is not true that with oxygen in the room a person must live.  Oxygen, therefore, is not a sufficient condition for my life.

The absurdity of statements like, "If the learner hasn't learned, the teacher hasn't taught," is that they are based on the idea that teaching is a sufficient condition for learning, and this is not the case.  Here are a few of the approximately 1,873,244,952 infinite number of reasons why.

1.  Teacher teaches, student gives outward indication of attention, student is thinking about the cute so-and-so two rows over.

2.  Teacher teaches, student gives outward indication of attention, biological factors* cause student not to remember (*including lack of sleep, lack of food, medical issues, etc.).

3.  Teacher teaches, student gives outward indication of attention, social factors* cause student not to remember (*including relational issues at school, abusive conditions at home, etc.).

4.  Teacher teaches*, student refuses to learn (*teaching being taken to include all appropriate methods of classroom management, motivation, etc.)

I think we get the point.  It is entirely possible for a good teacher to teach well and for a student or even multiple students in the class not to learn.  In fact, I will go so far as to say that teaching is not even a necessary condition for all learning (remember the definition above).  If it were, then no one could learn without a teacher teaching, and that is obviously not the case.  No one needs to teach me that I will feel better if I put on a coat before going out in sub zero temperatures.  I can learn that just fine on my own by going out once or twice without one.

It is true, of course, that teachers and teaching are important.  In many, perhaps even most, cases, teachers provide the most efficient means of learning something.  There are even instances where teaching is, in a strictly logical sense of the phrase, a necessary condition for learning.  For example, there is no way I am going to learn quantum mechanics without a teacher teaching me.  Even then, it is no sure bet, but you can take it to the bank that it won't happen without a very patient, kind, patient, knowledgeable, patient, loving, and patient physics teacher.

Yet it is simply not the case that teaching is a sufficient condition for learning.  Does bad teaching make the learning more difficult?  It certainly does.  Can bad teaching stop learning entirely?  Of course it can.  What one cannot do, ever, anywhere, under any circumstances...EVER...is make the logical claim that because a student has not learned teaching has not occurred.  It may be true, mind you.  A student may not have learned because teaching, or good teaching, did not occur, but that is not a conclusion you can logically draw solely from the lack of learning itself.