Fundamental Differences

Well, today was the last day of school before winter break, which in my classroom means we eat waffles and "celebrate" Undiramahanukwanzrohgurmas (I'll let you try to figure out the combination of holidays and Holy days). It also means it's a good time to reflect on the half year that has passed and the "lessons learned" about the Harkness Method:

(1) Harkness requires the students to be prepared. The daily discussions don't work if the kids aren't prepared. The class doesn't move forward if the kids aren't prepared. And I mean this in a very positive way, because the class shouldn't move forward if the kids aren't actually learning the material. Their preparation or lack of preparation, and their subsequent progress or lack of progress, are more obvious in a Harkness classroom, and that's a very good thing.

(2) Harkness requires the teacher to think of the course as a whole, instead of planning chapter by chapter or topic by topic. Good teachers already know that this should happen, but in a regular classroom, if you fall behind and need to take things day-by-day for a few days, it's ok. Not so in a Harkness classroom. The planning that we had to do over the summer was absolutely crucial, and there is no way that we could be teaching this way without having the overarching vision of the entire course in mind. In a set of e-mails last week, the other honors pre-calculus teacher and I were planning for the bulk of what we need to do in terms of pace and timing when we return in January. This long-term planning is not a luxury...it is essential for Harkness to work.

(3) Harkness requires the students to truly understand the concepts, and not just memorize a few facts and algorithms. The whole point is to have the students learn how to solve problems, and as such the questions on the worksheets and on the tests need to use the skills and concepts in ways which they have not seen before. The basic mechanics must be solid, but just using the mechanics or using them in word problems the likes of which they have seen repeatedly in class and in the homework does not help the kids learn how to problem solve and does not test to see if they are learning how to problem solve. This shift from "the students imitate the teacher and the textbook" to "the students creatively solve problems" is difficult for both the students and the teacher. Students are used to being shown how to do the homework exercises and required to do strictly similar exercises on the tests. Teachers are used to telling the students how to solve the exercises and directly answering any questions. Harkness requires the students to struggle with the material and through the struggle put the pieces together. It requires the teachers to lead the students to the answers through carefully constructed questions on the homework and responding to their questions with questions in the classroom. It is unfamiliar territory in many ways, but the resulting understanding of the material is well worth it.

(4) Harkness takes patience, both from the students and from the teacher. The students need to understand that we are slowly building the material for the entire course during the entire course, so some questions they may have will not be answered for a while (though encouraging them to seek the answers on their own is a great idea). The teachers need to understand that requiring the students to put the material together will take more time than just telling them what they need to know. They also need to fight the instinct to save the kids when they are struggling, and instead lead them through the struggle by solid questioning techniques. Both need to understand that the short track only leads to a surface-level, short-term understanding of the material, whereas the slow but steady patient discovery of the material is both deeper and more permanent.

(5) Harkness is harder than being in a "regular" classroom, both for the teacher and the students. The focus, the creativity, the mental energy, the ability to handle frustration, and the perseverance required in a Harkness classroom are all more difficult. But the rewards are more than worth the extra effort.

A quick story to wrap up the week, and the year: a student whom I had in class first trimester came to me today to tell me that he had retaken the SAT a few weeks ago. Despite the fact that he had forgotten his calculator, he earned a better math score this time. I know it's just one piece of anecdotal evidence, but I see the benefits of Harkness all over his success. The problem-solving skills promoted by a Harkness classroom, along with the fact that we have relegated the calculator to its proper place as a tool to be used as necessary and not a crutch upon which we rely without questioning, deserve at least some of the credit for this success. This student's story was the perfect way to start my break.

Work, Work, Work...

We are now one week away from the beginning of our winter break, and I haven't been this ready for a break in a long time.  Put simply: I'm exhausted.

When I describe the Harkness Method to some people, they mistakenly get the impression that all I do is sit around and listen to the students while they do the work.  And while on the surface that description is true, just sitting around has turned out to be more exhausting than lecturing for several reasons:

1. Lecturing involves preparing a set of notes and, after careful editing and polishing, delivering the information to the students.  Every once in a while, you evaluate the students' work, whether this is homework or a quiz or a test.  It is stressful on your voice for about two weeks at the beginning of the school year, and it can be stressful if you have not taught a particular course in a while, but once things settle in it's really not that bad.  Harkness, on the other hand, involves constantly evaluating students' work in class, and in my classroom, that actually means evaluating the work of at least three students at a time.  Yes, it is easier on my voice (this is the first year in a long time that I have not needed cough drops at the beginning of the year), but mentally, it is constantly taxing. 
2. Lecturing involves being prepared for an essentially predictable set of events.  And after teaching a course a few times, even the questions that the students have becomes essentially predictable, to the point that a good teacher will change the lecture to address the anticipated questions before they are asked.  It also involves doing the homework exercises.  Since you have shown the kids how to do the exercises, the way you do the problem on your sheet will almost always match the correct answers on the kids' sheets, and the kids who don't get the correct answers will either have something that strongly resembles what you have on your sheet, or they will have a blank spot on their sheet.  Quite honestly, if you have to teach the same class more than a couple times a day, this can often get a bit boring.  Harkness, on the other hand, involves preparing the worksheets for the students, designing the questions so they are led to discover the material.  Initially, you think it involves preparing for the questions the students will have or for the mistakes they will make.  However, you quickly realize that you can't predict the many different ways the kids will devise to solve a problem.  So instead, being prepared involves knowing the material you are teaching so well that you can quickly analyze the vast majority of what the kids put together and respond accordingly.  It involves doing the homework exercises so you have the correct answer along with a way to get the answer, but a lot of the time the method the kids use to answer the problem won't match yours.  Even if you teach the same class several times a day (as I do), this doesn't get boring, ever.  The kids in one class normally don't use the same methods as those in another class, so the evaluation of whether or not they are doing an exercise correctly, or are at least going down a path that will lead them to discover  correct method, never ends.  Again, this is way more mentally taxing that lecturing.
3. For many people, lecturing involves following a textbook and assigning problems from a textbook.  Little to no thought goes into the order in which to teach the material because the book provides the order for you.  Little to no thought goes in to choosing which exercises to assign because the teacher's edition of the textbook suggests which exercises are appropriate.  (To be fair, I do know a number of teachers who, despite the fact that they lecture, do not necessarily take the textbook "in order", who make their own worksheets, etc.  However, I also know a lot of teachers and administrators who believe that "the textbook knows best" and would never even entertain the thought of doing something that was not prescribed by the textbook.)  Harkness, on the other hand, involves knowing your material well enough to be able to teach it without a textbook.  It involves thinking through the entire course and planning the delivery of the material in the order and at the appropriate depth for your students.  It involves writing your own worksheets because the exercises in the textbook are inadequate in that they do not lead the students to discovered the material, nor do they encourage the students to do anything other than repeat the processes you have shown them.  

In short, Harkness involves more work, both in terms of preparation and in terms of the day-to-day work in the classroom, which is only fair.  After all, if we're going to ask the kids to start thinking for themselves and not relying on being spoon fed by us, then it only makes sense that we, the teachers, should start thinking for ourselves and stop relying on being spoon fed by the textbook companies.

They Get It

I have been waiting for this week to arrive.  I wasn't sure when it would arrive, but I was confident that it would, and at long last it is here.

I have mentioned before that I have the kids turn in a journal each week.  So far the journals have been pretty straight-forward, telling me about the material we covered, the successes and struggles they are having with the material, and how the groups they are in are working...the usual stuff that I have requested from the students for years.  However, this week the kids in my "part A" class (the first half of the two-trimester honors pre-calculus class) took their first test.  And while there is plenty of room for improvement as far as the grades are concerned, there were two very positive occurrences.  First, the vast majority of the mistakes were either simple arithmetic or not answering the question (i.e., not reading the directions), so from a content standpoint the class is in great shape.  Second, and this is the "event" I have been waiting for, the journals contained passages such as the following:

"This week, the advantages of using the Harkness method became evident for me, especially for our first test. Instead of having to go back and study things that we learned two weeks ago and never talked about again, we built on those things to the point where we were still incorporating some of our preliminary topics into tougher problems. It really benefited me during the test because I didn’t have to go back in my mind to a few weeks ago and think of things that we discussed. Also, instead of having all teachers show us one method to solving a test problem, I was able to use some “shortcuts” that some of my classmates showed me throughout the week(s)." 

"Lo and behold, you somehow pull out [...] an A! A miracle! And I truly believe that it is all because of the Harkness method. In the nights leading up to the test, unlike in past math courses, I was not looking at review problems and having no idea where to start.  Yes, I had a few topics that I needed to reexamine, but I wasn't going into the test stressing that I didn't know that information.  I understood the information with a much higher retention rate."

"I feel much more confident in my ability to succeed in the class.  More specifically with the discussions, I feel that I am contributing my ideas well, and taking a lot out of the processes of my peers.  For example, when we discuss the features of a particular graph, it is always reassuring to have multiple people explain the different aspects of a function - quite frankly, some people are inevitably going to be better at simplifying and furthermore, explaining their process."

What else is there to say?  They get it.  They get the whole point.  They get that it's about understanding the material.  They get that having a discussion makes for a deeper understanding of the material.  They get that it's OK to admit when you're having difficulty with the material and to ask for help.  They get it.  Amen.

Now admittedly, not all of the journals contained such passages.  But the only negative comments in the bunch were about ways to make the discussions even better.  None of them...literally none...were negative to the point of wanting to return to lectures.  Despite the admissions that this does take more work than "the old way", there was the immediate follow-up that it was worth it.

Hopefully this attitude will not only last the rest of the term, but will make it's way into the other sections of the class and have a positive impact beyond this trimester and possibly even beyond this year.  I'm well aware that once a class or a teacher gets a reputation, be it good or bad, it's hard to shake.  And at this point I'm optimistic that Harkness is starting to get a positive reputation.