At the end of the last unit, quite a few of the students were struggling with the basics of vectors, as the grades on the last test made evident. Knowing that some of the material to follow depended on understanding this information, the other honors pre-calculus teacher and I came up with an optional replacement assignment for the students to do. The descrpition itself was simple: convince me you know what you're doing when it comes to addition, subtraction, scalar multiplication, finding unit vectors, determining component form from magnitude and direction, and determining magnitude and direction from component form. How this was to be accomplished we didn't specify. They could write a short paper, make a poster, make a video...whatever. The "how" wasn't important. Just convince me you know what you're doing, and the score you earn will replace the score for the vector exercise on the test.
To say that it went well would be an understatement. Granted, overall what the kids turned in wasn't necessarily creative, as most turned in explanations of the above topics with an example of each (though one student did write new lyrics to "The Devil Went Down to Georgia" and performed the song in class), but afterwards the students said that they definitely learned a lot from doing the activity, and the subsequent exercises we have done in class have convinced me that this is, in fact, the case.
So, after the most recent test, we have given the students the opportunity to choose one problem from the test and turn in a similar project to convince us they really do understand the material the particular exercise was assessing. Again, we were specific enough so they know what skill/knowledge we want them to demonstrate, but beyond that the assignment is fairly open-ended. And I have no doubt that when they turn in the assignment next Wednesday, we will have achieved the same result as before: quality work from which the students learn the material well.
Notice by the way that none of this is focused on "extra credit". The focus is on understanding the material and demonstrating that understanding, period. Yes, the assignment helped the kids' grades, and while that may well have been the initial motivation for doing the assignment, I'm hopeful that enough of them got enough out of the first assignment that they will see the true importance of doing the second one.
All of this got me wondering: Why do we have the students complete some sort of in-class assessment wherein the students have to demonstrate their mastery of the material by doing exercises prescribed by the teacher? If the answer is: because that's how they're going to be assessed on state-mandated standardized tests, or because that's how they're going to be assessed on college entrance exams, or that's the way they're going to be assessed in the next course or in college, or because we've always done it this way, then haven't we missed the point of assessing the students? These may well appear to be practical reasons, but are they valid? I understand that there needs to be some sort of assurance that the students did their own work, and for the record we achieved that with the assignment described above since the exercises that have been assigned since then that depended on knowledge of that material have been completed well by the students. And there are plenty of teachers I know who, for various reasons, would never dream of giving an assignment as open-ended as the one described above. But seriously, if the point of assessing the students is to give them an opportunity to demonstrate their mastery of the material, then how is the above assignment any different than a short essay in an English or history class?
My current conclusion: we need to give the students more variety when it comes to the opportunities we give them to demonstrate their understanding of the material. There needs to be accountability, but we need to admit that, in the same way that we differentiate instruction, we need to differentiate assessments.