Method or Philosophy?

Next Wednesday, I will be making a presentation to the faculty of our high school on the Harkness Method, how I've been using it in my classroom, and what it has taken to implement it, with the hope being that it piques the interest of some of the other teachers to the point that they will pursue including more discussion-based methods of instruction in their classrooms.  However, the more work I've done for the presentation, the more I've begun to ask the following question: is Harkness really a method, or is it a philosophy?

The reason for the question is this: it seems to me that the real push behind Harkness is the discussions, allowing the students to dig deep into the material during the discussions and coming to a thorough understanding of the material through the discussions.  And even though the students need to prepare for the discussions, the actual shape of the preparation is not really defined.  The preparation my students need to do looks essentially the same as it does in the math classes at Exeter, with the homework exercises scaffolded so the students discover the material through them.  But is this the same way the preparation looks, or even should look, in the other disciplines?  For that matter, is this the way the preparation should look in other mathematics classrooms?

For example, there is the "flipped classroom" model of instruction, where the students watch a video lecture to prepare for class and then do the exercises based on the lecture during class.  Done correctly, meaning that the in-class work is dominated by discussion and problem solving, I can see this as fitting well with the Harkness philosophy.  I can also see the team-based method of instruction, a project-based method with a strong emphasis on in-class discussions, as really being just another form of Harkness.

It should be clear that I'm leaning toward Harkness as being a philosophy with the following components:

• the in-class work is dominated by student-led discussions
• student preparation for the discussions is vital
• the teacher acts as a guide, both in terms of designing the course so that student discovery of the material is possible and in terms of  helping the students learn from their mistakes

Exeter says that Harkness is flexible to the individual style of the teacher.  Until I began to view Harkness as a philosophy, I didn't really understand what that means.  With this view, I'm hoping to be better able to help other teachers help their students by implementing the philosophy in their classroom.  Updates to follow...

Spreading the Word

With the classes running relatively smoothly this year, and with the course exercises in need of far less revision than they were last year, I have had a bit more time to try to “spread the word” about running a discussion-based classroom to the other teachers in my building.  As you can imagine, there has been a great deal of variation in the reactions and responses. 

Some teachers are very interested, seeing the discussion-based classroom as a method that fits well with an emphasis on problem solving.  While interested in trying it out, there is a hesitation that seems to be based on one recurring difficulty: “We were never shown how to teach this way.”  And I completely agree with them.  For all of the talk about problem-based learning, project-based learning, and other such ideas that are really just repackaged and expanded versions of ideas that have been floating around for a couple decades, there have not been substantive changes made in the way teachers are being prepared for the classroom.  Admittedly, I have not been in a “college of education” classroom in a while, but there are currently several student teachers in our building and the first round of observations has begun.  Based on the way they are being evaluated, it’s easy to conclude that things haven’t changed.  The things for which the observers are looking make it evident that there is an assumption the teacher is at the front of the room leading the class the vast majority of the time, and if that’s what the evaluation form is looking for, then it only makes sense that the training the student teachers are receiving puts them at the front of the classroom the vast majority of the time as well.  While I would hope that an ambitious student teacher would be rewarded for doing the kinds of cooperative learning and discussion-based activities researchers are telling us are best, someone going strictly by the forms could easily count any and all of that against the student teacher.  

That being said, “we were never shown how to teach this way” shouldn’t stop us from doing what is best for the kids.  Changing my classroom over to a Harkness classroom has taken a lot of time, effort, and energy, most of it very much behind the scenes.  The classroom management portion of running a discussion-based classroom for 30 students was not something I found in a book or article, but instead relied on me figuring it out.  This isn’t a matter of bragging...it’s simply a matter of fact.  My point is that if we truly believe that running a discussion-based classroom the best way to teach the kids, then we who are currently in the field should be willing to do whatever it takes to make it happen.  To their credit, those who are interested in doing so in my school are actively seeking out the information, and the administrators in my district have been and continue to be incredibly supportive.  It is truly a blessing to be able to call these wonderful people my colleagues.  In addition to this, we should expect the schools of education to be showing those who are about to enter the field how to actually implement the best practices touted by the research.  

Put simply, the time for the chasm that has existed for decades in education between theory and practice to disappear is long overdue.  But those of us who are willing to do the hard work and make the necessary changes in the classroom, both in the schools and in the colleges of education, are few and far between.  And the same is true of administrators at both levels as well.

This, in my opinion, is one of the fundamental problems with our education system as it currently exists. 

In Their Own Words...

Each week, I have the students complete a self-assessment, in which I ask them to be honest with me regarding their effort for the week with the homework and in the discussions, the group dynamic, and anything else they feel the need to share.  Here is a representative sample of the comments I received in the "anything else" section this week:

"I feel like from this class, I've understood so many more math concepts on a deeper level than I did previously. I think the past couple of years it was mainly focused on just applying equations or certain steps, but with this method, I can actually think through the problem logically without having to rely on just the equations."

"Throughout the class I have improved my math skills by observing other students' work and comparing it to mine. This helped me to solve problems overall, which before this class seemed to be a weakness for me rather than a developing strength. I am having a great experience in learning math in a new way that brings together problem solving, communication, and collaboration."

"I find that each person tackles a problem differently, or is able to complete different questions in a homework assignment. I think it's cool that each person can contribute in a different way at school because of how they interpreted the homework assignments."

"I think the class structure is VERY well thought out, and it's working very well for me. I retain the concepts much better this way, and the class is actually fun."

"Everyone is positive and supportive of each other, it's always a good atmosphere."

We're in good shape so far.

Patience is a Virtue

Overall this was a great week.  Courtesy of a minor surgery, I was not at school on Tuesday or Wednesday, and the plans I left for the sub were essentially "the kids know what to do".    One of my sons is a sophomore at the high school, and when he went into my room before school on Tuesday to get his books from a table in the corner, he said "hi" to the sub and mentioned who he was and that he would be in between each bell  to get his books, since using my room as his locker is far more convenient than using his actual locker.  The sub called him over and asked, "Is this really the entire lesson plan?"  My son quickly read it over, and responded with, "Yep, that's what happens in here every day."  The report from the sub was that things went really well...no difficulties, and particular mention that the lesson plans were very complete, with enough for the kids to do the entire bell.  Specifically, Tuesday the kids discussed the assigned exercises from the long weekend, and Wednesday they did ten review exercises for the first test, which was given on Friday.  Thursday I took questions, just in case there was any lingering confusion from the two previous days (and, happily, there were very few questions), and gave them a few more review questions to work on, so I could make sure they were ready for the test.  Having graded the tests, and with the mean being a B+ and the median being an A-, I'm happy with the results.  For the most part, the mistakes were careless ones rather than fundamental misunderstandings, and the only kids down close to the D range were those who have not been participating fully in the discussion...in other words, there were very few surprises.

However, one thing that I noticed as we went through the review on Thursday was that while the students were feeling fairly comfortable with the material that was going to be on the test, they were not comfortable with the idea that not everything we had been covering was going to be on the test.  And I admit, there are a few "loose ends" from the exercises that were not on the test, the reason being that the topics being taught through those exercises have not been fully covered yet.  We haven't completed all of the exercises that cover those topics, so the test questions on those topics will have to wait.  This is something the kids aren't used to.  What they expect is that the test covers all of the material since the previous test, and after the test we "reset" and begin preparing for the next test over the new material, which will include little to no reference to the old material.  They are not used to being patient when it comes to learning the new material, mainly because we tend to shove a bunch of stuff at them all at once, neatly compartmentalized into chapters on exponents and logarithms, or on basic trigonometry, or on the conic sections, rather than allowing them to build their knowledge gradually over all of these topics at once, which is what I'm asking them to do.  The reasoning is simple: in future courses and in future applications, the expectation will be that they have relatively rapid recall of any and all of the topics covered in my course.  Calculus does not work exclusively with only one type of function as derivatives are taught, and neither do the applications of physics.  And yet, we often teach the different types of functions separately.

In talking with other teachers, and in particular with those who cling to the idea that lecture-memorize-mimic is the best way for the kids to learn, I've come to realize that this lack of patience is also one of the reasons why they cling to lecturing.  In order to get the kids to receive a large amount of material on a particular topic in a short amount of time (for example, learning everything there is to know about graphing trigonometric functions in under two weeks), lecturing makes sense since there simply isn't time to allow the students to patiently and gradually understand the material.  So, in addition to helping the kids gain some patience in learning the new material, I've come to realize that if we are going to get other teachers on-board with changing their classrooms over to a student-centered, discussion-based, discovery method of delivery, we first need to get them to understand that it's not about covering one topic in-depth for two weeks and then moving on, but rather it's about slowly and patiently building all of the topics throughout the term (be it quarter, trimester, or semester).  I'm not expecting this to be an easy sell, but I firmly believe it to be worth the effort.  After 22 years of teaching through lecture-memorize-mimic, I've come to see the enormous benefits of patiently presenting the material through discovery and discussion.  I only hope others will come to see the benefits as well.