It was probably one of the most influential educational experiences I ever had.  While it was happening, however, it might have been among the most stressful!

I was in the first year of my Master’s program, taking two math courses from one of my favorite professors.  That particular semester he chose to try a new experiment:  He decided that – in both these classes – he would give unannounced hour exams!

Not just ‘pop quizzes’, which we may all have encountered, but hour exams, the collection of which comprised a sizeable percentage of our class grade.  He said he had randomly picked the dates of the 3 exams in each class ahead of time, and it didn’t matter when they fell.  If they ended up weeks apart – or on two successive class periods- so be it!

It was a radical move.  Take a minute to imagine the effect on the entire class environment for the semester! As a humorous side-effect, I don’t think there were any attendance problems in those classes that semester!

Can you also imagine the ramifications on a student’s study habits in the class?  You couldn’t really ‘cram’ for every class meeting.  You had to ‘keep up’ and you had to learn the material.

I don’t recall too much about that semester (hey – it was awhile ago!), but I remember this:  I learned as much or more in those two classes as I did in almost any other math class in my long sojourn of seeking degrees. Further, I also learned a lot about what it means to learn a topic in general, and how one does (and doesn’t do) it!

Indeed, I think that experience, as much as anything else, may have started my career-long pondering on the nature of real learning in our educational system.

Now compare this experience with another one 2 or 3 years earlier – in my undergraduate days.  One fall semester, we had a brand new professor, fresh out of grad school, teaching one of our upper-level classes.   He was absolutely brilliant.

As is stereotypical, however, he had developed no ability to share his knowledge with those of us not yet on his level.  I remember all of us frantically trying to keep up as his thoughts spilled from his head to the blackboard, and then rebounding to our notes.

I remember memorizing the proof of one theorem, and later congratulating myself for reproducing it flawlessly on a test!  But, of course, I had no idea what I had written, nor what the theorem really meant.

That may have been the semester in which I learned the least of any math class in my career.  I didn’t really learn to appreciate that material until I began to teach it years later, when, with some experience, the subject’s power – and beauty – really hit me!

There are a dozen implications I’d like to pursue here, and I suspect you’ve thought of many of them. For this column, however, let’s start with one obvious one:  Memorizing something is not necessarily the same as learning it.  Given that, there is a surprising result that has to follow, and it is absolutely crucial:  ‘testing’ is not necessarily the same as ‘evaluating learning’.

Perhaps we take it for granted that student learning is at the heart of everything educational, but learning is simply not a forgone conclusion!   Authentic learning is not always easy to achieve, and almost never easy to evaluate.  Pondering this fact and creating environments in which learning can be achieved and then evaluated is one of the ongoing challenges of any teacher or institution.