Exams... Huh! What are they good for?

Absolutely Nothing.

NO NO NO!  The trimester/semester exam is the most important teaching tool in my kit.  One of the great advantages to my school's physics program over the years has been our trimester calendar, in which we have a set of major exams before Thanksgiving, and another in early March.  We're about to lose that advantage, as it's pretty clear that our upcoming redesigned schedule will put us on semesters.  I'm okay with that, because the new schedule is likely to have so, so many important improvements: longer class periods, more down time during the day and during the week, more creative use of time outside the standard class day... if the price of all these benefits is one rather than two mid-year exams, so be it.

Yet, I become ever more frustrated with those who see the elimination of an exam week as a one-week gain in "teaching time."  No, folks, exam time is teaching time.  An exam period is the one portion of the school year in which I’m guaranteed to be able to expect diligent and focused attention from my entire class.  I use the exam – not just the exam itself, but the process of preparing for and debriefing from the exam, too – as my most important teaching tool. 

Would the soccer team countenance skipping the state playoffs in order to spend the season's last week on skill development?  I mean, the only reason we even have playoffs is because our egomaniac coaches are trying to imitate professional leagues.  Would the fine arts department cancel performances of the winter musical?  Production week is extremely stressful and time consuming; without the deadline and pressure of the performance, we'd have more time to rehearse and develop our roles.

Right?  Or nonsense?  Yet these are exactly the arguments I hear against exams in general: they're too stressful, they take away time to teach skills, we only even give exams because colleges do.   I would love to change the conversation about exams, not just at my school, but the world over.

Consider the following student phenotypes, and how they've benefited from both November and March exams over the years:

* The overwhelmed freshmen who were always behind were graced with hours upon hours of relaxed time to sit and study one subject for a while without six teachers screaming for assignments.  These folks built significant confidence with strong exam showings because they had the chance to actually prepare stress-free for a day.

* The borderline honors-regular students who didn't think they could handle the higher level class.  Strong performance on the exam often clinched the point:  YOU BELONG HERE.

* Contrariwise, the students who worked hard in honors but might not have belonged, got a fair evaluation of where they stood.  We could then make the decision for them to stay or to go based on an exam for which they had every chance to prepare – no fooling themselves that “oh, I’ll be able to study better for the AP exam in the spring.” I note that my physics teaching peers have been quite jealous of my Thanksgiving exam period, in which I can drop a junior or senior into regular physics without that showing up anywhere on his transcript.  The fact that I can reasonably say “stick it out through the trimester exam” allows me to reclass students if necessary when we’re only through 1/3 of the year and they’ll still be successful in the lower course.

* The smart freshmen who don’t see the connection between careful, diligent everyday work and true understanding.  These students’ poor exams allow me to say in so many words, “See, here’s why you have to pay attention every day; you can’t just expect to ace the exam, like you did in middle school.”  These folks generally turn in much better work in the weeks after Thanksgiving.

* The students who argue with their teachers about whether they’re doing enough or the right kind of studying outside of class.  The Thanksgiving exam allows us to say, “Hey, we just tested your contentions – you had all the time in the world to prepare, and you didn’t do well.  Now maybe you ought to listen to your teacher’s suggestions.”  (Or, "Yup, you're right, you aced the exam, maybe we should back off and let you study your way.")

* The students who utterly bomb their first set of freshmen exams… but yet have ten more exam periods on which to learn from their mistakes and improve.

* Every Senior I Have Ever Taught who, without a March exam that colleges might see, would have stopped working seriously months before.

An exam is not an evil, onerous implement used by teachers to torture their students.  An exam period is a pedagogical tool, a way of showing students unambiguously how they’re doing, a way of showing teachers what the students have really learned.  The process of preparing for a trimester exam is one of learning, of reminding everyone how the course fits together.  Students take my review sheet and its corrections very seriously, because of the upcoming exam; I hope no one believes that a cumulative review would be as effective without an imminent formal “exam.” 

Furthermore, even after the exam is given, the exam is still useful – I invariably use the exam throughout the following trimester as a way to remind the class of previous topics.  “Tomorrow we will take a quiz on which you will explain the answers to exam problems 35, 44, and 16.”  Not only do students go back over their exam , but they take the exercise ever more seriously because they know that another exam will be on the way.

So the next time a student, parent, or college asks incredulously, "why do you make your students suffer through cumulative exams?" please respond with some of the above arguments.  Let's try to stop the fear mongering. We don't tell a football player "You'd better not screw up this championship game;" we don't let players tell each other "Oh, I just know you're going to screw up and lose this championship game for us."  So let's not say the exam equivalent, "You'd better study extra hard so that you don't fail," or from a student, "I just know I'm going to fail these exams."  Let's help the wider world understand why we give exams, why we enjoy giving exams, why the entire process of an exam week is as critical to the learning process as is any week of lecture and homework.

And then let's let the quality of our exam preparation, the exam itself, and the debriefing process be worthy of the time we dedicate.  But that's a topic for a whole other set of posts.

Mail Time: Should I teach the elastic collision equation with velocities?

A correspondent writes in, in reference to an AP Physics 1 class:
[Edited for space]:

I have been teaching elastic collisions problems using an elastic equation : Vf + Vi = Vf + Vi to solve problems that are missing two of the velocities. We discuss that as long KE and momentum are conserved then we can take KE and momentum equations and divide them to get the elastic collision equation with just velocities.  

I recently was tutoring a former student who is now in a local college about solving these types of problems and she told me that her professor said that the equation does not work and that its not physics! She was told that I was completely wrong!!! I immediately went to a Giancoli textbook. Giancoli does derive this equation following same reasoning that I derive for my students.

BUT... I hate to think that I have been teaching this wrong!  I was hoping you might be able to offer some clarity.    I went through [the professor's] problems and compared my solutions to the professor's solutions and I do get the answers he gets, just in a lot fewer steps.  Any suggestions? Should I not teach elastic collisions this way?

Fascinating question.  My answer is twofold -- one answer on philosophy, one answer on content:

1. You are teaching absolutely correctly.  I don't know what her professor is on about.  Remember, "professor" means neither "good teacher" nor "better than you at introductory physics."  It's so easy for a high school physics teacher to be intimidated by folks with PhDs, or by education "experts."  As long as you are carefully self-evaluating -- and you obviously are, based on paragraph 3 above -- then do things your way.  I can't emphasize enough that even my well-tested methods and ideas are not for everyone.  The best physics teachers, like the best chefs, are creators, not imitators.

2. On this specific issue of elastic collisions: You might consider why it's necessary to teach quantitative solutions to elastic collision problems at all.  Yes, you need to be able to check whether a collision is elastic by comparing KE before and after the collision.  But even with the simplified relative speed equation that you reference, solving for speed in elastic collisions is more calculation that we need for AP 1, or even for my taste in any intro course.  That's not to say you're wrong to teach it, as I did for years... I just don't think it does enough to be worth the time it takes to teach and solve the problems.