If there is one thing with which I am still struggling when it comes to implementing Harkness in my classroom, it's reviewing for tests. In a traditional classroom, preparing students for a test means making sure they have a specific set of algorithms memorized so there's nothing on the upcoming test that comes as a surprise. Over the years, the students have taken great comfort in the fact that they are able to completely prepare for a test, and that the night before the test they can feel feel completely prepared for the test. This does not fit well in a problem-solving centered classroom, where the focus of the tests is not on how well the students have memorized how to solve a specific set of problems, but on how well they can use a set of concepts and skills on a new set of problems.
With this shift in focus, the review that happens in the classroom the day or two before a test is, by necessity, also very different. In a traditional classroom, working through a few more exercises on the board for the students to see, performing a few more examples for them to memorize, or giving them one more set of questions to see how well they have the required material memorized is pretty typical. This doesn't work in a problem-solving centered classroom, because no matter how many examples the students see, the problems on the test are going to be different. Yes, the test questions cover the same material, and yes, the students have all of the skills required to successfully complete the exercises, but the specific applications and problems on the test are not going to be the same as the ones the students have seen. This makes the night before a test unsettling for the students, since their working definition of "completely prepared" is "there will be no surprises" - essentially an impossibility if the goal is, in a way, to see how well they can handle reasonable surprises.
So the question becomes - and it's the thing with which I find myself having difficulty - how do you help the students review for a test? Based on their previous experience, students have come to expect that any extra practice problems are, in fact, of the "type" that will be on the test. While I certainly give the students extra practice problems, the students have needed to adjust to the fact that these extra problems are, instead, at the same level of difficulty as the test questions, but are not necessarily of the exact same type. And in that, the in-class review is of a different character as well, since it's no longer a matter of showing the kids "just one more example" for the sake of helping the memorization. In short, the focus of the review, both at home and in class, is on the concepts. I have come to realize that determining whether or not the students have a solid understanding of the concepts before the test is far more difficult that determining whether or not they have the required algorithms memorized, and the students are experiencing the same thing. I need to work on this.
On the positive side, the majority of the students have the necessary mechanics on board long before the test review arrives, which means that what used to be the focus of the review is now what the students already understand and are, in some ways, taking for granted. In terms of accomplishing the goal of improving the students' problem-solving skills, this is a huge step forward.