What is the point of an assignment? Any assignment...homework, project, essay, test: what is the point of the assignment?
For a teacher, the answer to this question would probably vary depending on the assignment. Homework may be for the sake of practicing a particular skill. An essay may be for the sake of demonstrating a thorough understanding of a historical event. The list goes on. However, from the standpoint of the students, the point of any assignment is essentially the same: to finish the assignment and get as many points as possible. I had a revelation this week: this attitude about the purpose of assignments is one of the reasons students, parents, and other teachers have difficulty understanding discovery-based learning in general and Harkness in particular. For most people, the purpose of the assignment is to complete the assignment, and the presumption made is that the students already have a reasonable if not a complete understanding of the underlying material. However, the point of most assignments in a more discovery-based approach is to learn the material by doing the assignment. The presumption made is that the students have an understanding of the background material necessary to discover the material, and the point of the assignment is not to show what they already know, but rather to use what they already know to learn something new.
The confusion on the part of the students, parents, and other teachers is understandable, especially when it comes to mathematics. The textbooks are written with the idea that the material will be explicitly shown to the student (by the teacher, by reading the textbook, etc.) and that the student will do the exercises to practice what they were shown. Even when it comes to word problems, the textbooks explicity show the students what to do, and the exercises are about practicing. Problem solving, creativity, critical thinking, students making connections for themselves...none of these are the goal of the mathematics textbooks. And since the textbooks have not really changed very much in decades, none of these were the goal of the mathematics education most of us received. Since many teachers teach the way they were taught (for the record: up until two years ago, that statement would have described me), it's easy to see why so little has changed in mathematics education.
Contrast this with what happens in some upper level mathematics books...for instance, an abstract algebra book. The written portion of the book is, in general, not repleat with examples that the students are expected to mimic in the homework. Instead, the section contains the background and foundational material, and the students are expected to creatively use that information to make connections and discover more of the material. In other words, the homework isn't for practice and it isn't for demonstrating a command of the content of the course. Instead, it is geared toward extending the material presented either by the professor or by the textbook. This is why so many students who "have always been good at math" stuggle so mightily when they reach these kinds of math courses. I believe it is also why they struggle in college science classes that require them to do the same thing. To be clear, most college calculus courses don't require this, and therefore neither does the AP Calculus test. That being said, many students then struggle in the subsequent courses that creatively use the calculus skills they supposedly know in ways they have not been shown...so much so that some colleges are beginning to rethink the way calculus is being taught.
Here's the problem for those of us who teach high school: we are now being asked to prepare the students to be creative, make connections, and think critically on standardized assessments to solve problems the likes of which the students have not necessarily seen before. The basic skills being tested are not the issue, since they are (in mathematics, at least) the same skills that we have expected the students to learn for decades. However, instead of asking the kids to regurgitate what they have seen, they are asking them to use the skills in ways that, while reasonable, are ways they have not encountered.
If we don't ask the kids to be creative as part of their daily experience of mathematics, how can we expect them to be successful on the new standardized assessments or in the (college) courses that proceed from ours? If all they are used to doing is following the prescription laid out by the textbook or by the teacher, how can we expect them to be successful when they are presented with an exercise (or, in "real life", with a situation) that does not rely on any previously-seen prescription? It is going to take a fundamental shift in the method of delivery from the textbooks and the teachers to prepare the students. It is going to take a fundamental shift in the attitude of the students, parents, and other teachers about the purpose of assignments, both in and out of class. As I said above, the current attitude is completely understandable, so we need to explain the rationale behind these assignments. We also need to adjust the way we grade these assignments...which should naturally lead to a conversation about formative assessment. We need to help other teachers understand why teaching the way we were taught isn't going to be enough if we want our students successful.
Put simply, we need to help everyone involved see why we are including more discovery-based teaching and why we are expecting the students to gain a deep understanding of the material that goes beyond the surface-level comprehension that was required of us in school. Simply knowing what to do is no longer enough; the students need to understand the "why" of the material, and they need to understand it well enough to be creative with it. We need them to see that, for the most part, completing the assignment is no longer the point; what the student can learn by doing the assignment is. Much as I enjoy teaching through Harkness, I have become convinced that the students need me to teach through Harkness. And I need to help the students, parents, and other teachers understand this as well.
I have no illusions about what this means. This is calling for a revolution.
Let the revolution begin.
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