What do we want our students to know, and how do we know when they’ve learned it?  The first question deals roughly with matters pertaining to curriculum.  The second question deals with the always-tricky question of assessment.
We’ve discussed both these questions before, but let’s look at yet another aspect of assessment that is both subtle and tricky.  Sometimes we can look around and discover that we’re unintentionally assessing something other than what we claim we want.
During graduate school, I took a History of Mathematics course that I’ll always remember.  I liked the course more than I thought I would, and I think I learned a lot as well.  But the overriding memory that remains from that class is that my classmates and I didn’t really get to show what we had learned.
The professor had a habit of giving overly long exams. Rarely did anyone finish an entire exam, and many of us left each test frustrated that we didn’t get to answer questions we knew.  I recall scrawling “I know this!!” on the still-blank last page of the exam as I was forced to turn it in.  I’m sure my protestations did little good (other than therapeutically), because the professor acknowledged that long exams were his goal.   I believe it was his way to separate the wheat from the chaff, so to speak.
I’m not sure I could have verbalized it back then, but I now realize that our frustrations were probably at least somewhat appropriate.  The professor was not necessarily assessing our knowledge of the material as much as he was also measuring our ability to work quickly – an entirely different thing.
This vivid memory helped me in the years following, as I began to give, rather than take, exams. I’m not sure I always succeeded (assessment is tough!), and doubt if my students always agreed, but in the back of my mind, I tried to make what I was assessing match what I had wanted them to know.
In today’s world of rapid and convenient technological access, we are often guilty of falling into the same trap.   Raw information (dates, places, names, etc.) and various skills (times tables, square roots, etc.) are no longer as important as they once were.  Google can find information, if we need it, and calculators can take a square root, if we need it, and both can be done almost instantly.  It’s no longer as important to assess/evaluate those things, as they are now readily available in our everyday lives.
At the same time, this situation provides a golden opportunity to re-ask the first question above.  Yes, we’ve played this tune before, but instead of emphasizing when/where D-Day took place, e.g., we can discuss things like how D-Day affected the outcome of WWII, and therefore changed our lives.  Instead of overly emphasizing times tables, we can better help students learn to use arithmetic (yes, with calculators) to tackle and solve important problems.
The catch is, of course – it’s NOT easy to evaluate those things!  It’s much easier to test for information and skills (especially on standardized tests).  Unfortunately, simple paper/pencil testing isn’t always enough for the things we want students to learn.
So, we must not fall into this assessment trap.  We must take the time to ask what we want students to know, and then struggle together to find ways to authentically evaluate when they are making progress.