Settling In

This week, the "new" has finally begun to feel normal for the students.  Despite the fact that this was homecoming week, complete with all of the interruptions (fun and wonderful as they are), the classes have truly begun to care for themselves.  Courtesy of the predictability of the daily routine, if I don't have any announcements to make at the beginning of class, the classes are pretty much self-starting at this point, which is great.  And courtesy of a bit more new material being woven into the exercises, the discussions are going much deeper, with different students interpreting some of the exercises or definitions in very different ways, which leads not so much to a debate as to a thorough discussion of the material...which is really great to watch and to participate in.  I've been struggling with trying to strike a balance between being too helpful and not being helpful enough.  It's tough to quickly discern whether a discussion that has taken a "wrong turn" will lead to a correct interpretation in the long run or will only lead to confusion.  So I need to constantly be aware of my participation in the discussions, making sure I don't lead them to the method I used (which defeats the purpose of having them solve the problems), but likewise making sure they are being guided to a viable method that, for the most part, they are discovering or creating themselves.

In creating the worksheets over the summer, we kept in mind that since most of the students in the class are juniors, the ACT and SAT are looming large in the near future for them.  In the past we have given the students weekly review sheets containing exercises that, at least in part, served the purpose of reviewing some of the material they had in all likelihood forgotten.  However, this year we have put at least one review exercise on each of the worksheets.  And, as in the past, it always seems to be the geometry problems that cause the most difficulty. For instance, this week we spent at least an hour of class time on one problem...yes, one problem...that we still haven't resolved as a class.  It made for great discussion, though, really forcing the kids to justify their assumptions about the picture that was given in the problem and about the relationships that result from those assumptions.  Honestly, it's the kind of discussion I wish we could have about lots of the exercises and concepts.  To get there, though, means writing the correct kinds of questions that will lead to those discussions.  As such, the worksheets are already being revised, and will probably be in a constant state of revision.

One final thought for this week: it occurred to me this week that despite the fact that we haven't done a lot of basic mechanics practice ("drill and kill"), the kids have gained a remarkable fluency with the basic mechanics of the material.  Factoring, solving exponential and logarithmic equations, and the like, have not been specific "stand alone" questions, but rather have been necessary to solve some of the exercises on the worksheets, and in the process the kids have remembered (or in some cases, finally really learned) and practiced the mechanics.  It truly put my mind at ease on Thursday when the kids were using and explaining the laws of logarithms...all without me saying a word.  The worksheets and discussions are not sacrificing the basics for the "advanced", which makes me all the more convinced that this really is the best way for kids to honestly learn and not just memorize the material.

Video #1

Here is the first of what I hope will be several videos showing how things are run in my classroom.  This clip is short (just under two minutes), but it gives you a feel for the level of the kids and the kinds of conversations they have.  This is one of three tables in my classroom, and while they were having this discussion I was at one of the other tables, so pretty much all of this is student-directed, including one student who is noting who goes to the board and who makes a "helpful" contribution, whether it's a comment, a question, or whatever.  Other than review and test days, this is what the classroom looks like (or at least it's what it should look like) every day.

Classroom Photo

Just a quick "update": this is the set-up of my classroom.  My table is just off the right side of the photo.

Taking Notes

One thing I have noticed during the last week is the difficulty students have taking notes.  Don’t get me wrong, the students are taking notes.  They have two notebooks for my class: one in which they keep all of the work they do at home while working through the exercises on the worksheets, and one in which they place a “clean” set of notes after the daily discussions.  It is in the clean set of notes that I have noticed the difficulties.

You see, in a “normal” math class, the lectures provide information not so much about the skills the students need, but rather examples of specific types of exercises the students will be expected to do on the homework and on the tests.  In fact, a few years ago I took the time to type my lecture notes, complete with examples, and have given them to the students in the past as a means of making sure the notes they had were, for lack of better terms, “complete”.  This kind on note-taking leads to and perpetuates the lie we have told the students (or at least led the students to accept): they are supposed to memorize a specific algorithm for each particular type of exercise.  Because they have been trained to take notes in this way in math class for years now, the students are having a difficult time transitioning to taking notes on the skills they will need to master, the definitions they will need to understand, and the relationships they will need to see.  And in this, they are having difficulty taking the skills learned on one worksheet and using them on the subsequent worksheets.  They are looking for similar problems of the same type rather than exercises that require the same skills.  The frustration with this has begun to set in, and several students are now asking that I give them notes rather than having them rely on one another to discern the important information they are to glean from the daily discussions. 

Of course, the notes I would be giving them are not the notes they actually want.  Any notes I would give them at this point would focus on the skills, definitions, and relationships, whereas they are requesting notes that cover specific examples for them to memorize.  Since part of the point is that there is more than one way to arrive at an answer (not just “my way”), since the focus is supposed to be on understanding the content and applying it in a variety of situations and not on memorizing an algorithm for each “type” of problem, and since they are supposed to be relying more on one another and less on me, I have no intention of giving them notes.

That being said, the students are supposed to “use their resources”, such as the internet, their textbook, etc., and as such I have placed my typed notes online for them to use.  No, the notes do not contain examples and algorithms for the exercises on the worksheets, but they do contain examples of the skills and explanations of the definitions.  The relationships, however, remain theirs to discover.

Finally, as a follow-up, the permission slips are in and the taping will begin this week.  Hopefully I will have something to upload next weekend.

Shutting Up

Seriously, I need to learn to stop talking. I'm finding it amazingly difficult to help the students by giving them leading questions rather than answering their questions directly. So, this week I took a few steps that should encourage me to shut up.

(1) Each day, I had the students in each of the three groups choose a leader for their table. The student leader was responsible for keeping their group focused, for making sure that everyone is participating, and for organizing who goes to the board to do each exercise. The student leader was also responsible for noting who went to the board and who made a meaningful contribution to the conversation about each problem. They didn't need to detail the type of contribution (asking a question, answering a questions, clarifying a remark, etc.)...just note that a substantial contribution was made on the little, easy-to-follow form I created for them.  This has allowed me to slow down and spend longer at each table listening to each of the conversations, which means I can be more patient while the students struggle with a concept. I'm still noting down what I observe at each table, but the "pressure" to get to the other tables more quickly, just in case I miss something, has been relieved.

(2) I outright told the students that I would not be getting involved in the conversations unless (a) they asked me for help directly; or (b) as a group, all ten students came to a conclusion that was incorrect. I was still going around to the three tables, still sitting with the students listening to their conversations, but the expectation that every time I at down at a table the attention was to refocus on me was removed. Honestly, I still find this very difficult. Twnenty-two years of responding to a question, or even a confused glance, with a direct, "here's-how-to-do-it" answer has ingrained a habit that will not go away easily. At least I'm responding to questions with questions rather than with direct answers more often than I used to, and the kids are asking one another first and having a discussion about the difficulties they're experiencing before asking me to participate..so there is something positive to report.

(3) I began to take videos of the class "in action" (yes, I sent out the permission slips to place parts of the videos on the web; no, I don't have them all back yet). Now, I can see and hear how often I interrupt instead of letting the conversation happen, as well as take a more objective view of how well the class is going.

I heard this week from several unsolicited sources (other teachers, parents, friends in the district) that the kids are really enjoying how the class is being run and that they feel they are getting more out of the class because of it. On the other side, one of the students mentioned in his journal this week that he really wants to go back to the "lecture-take notes-regurgitate" way of doing things. Having run the class using Harkness last May, and now for the first few weeks of this year, I have some unfortunate news for him: I'm not going back. Yes, I understand the struggle and frustration involved from his end, and yes, I get that figuring things out rather than being told takes more time and therefore more patience, both on his part and on mine. However, I also get that the end result is better, deeper, more permanent learning. And because of that, I'm not going back.

So, I need to be more patient and I need to shut up. That should be easy enough. (If you can't hear the sarcasm in that statement, you're not paying attention.)

"Are We Learning Anything?"

Each week for many years now, I have had my students write a one-page journal that serves two purposes.  First, it allows them to summarize the week in terms of the mathematics, and to reflect on what has gone well and on what they need to focus.  Second, it allows them to tell me how things are going.  The response in the journals last week was unanimously positive, and this week pretty much continued the theme.  However, there was one comment that appeared in several journals that I honestly loved seeing: "I don't feel like we're learning anything."

Now, I could list off a number of skills that, while they were certainly introduced to the students in previous courses, the students have brought to a level of mastery during these first couple weeks of the year.  I could also list off several brand new skills and concepts of which the students have achieved a level mastery during these first two weeks.  But, in good Harkness fashion, I'm going to let them figure out that they are, in fact, learning a good amount of new material.  Happily, one of the students has already figured that out, stating in his journal that he "really likes the fact that we are learning without it feeling like we're learning".

This is part of the beauty of the Harkness Method.  Like learning to walk, you don't realize just how much progress you've made.  It seems as though you've always been able to do this, and even though you can now walk more confidently and walk on slightly more difficult terrain, it's still just walking so you've not really learned anything new, right?  It's not until  you take a good, long look at it that you realize just how well you're doing and just how far you've come.  In writing our worksheets, we tried our best to imitate what we saw as one of the essential aspects of the worksheets at Exeter: it's not about gaining complete mastery of something new every day.  It's about making a little progress on several things every day.  Over time, little by little, the progress becomes substantial.  But since it's little by little, the students don't realize that they are making progress, let alone making progress on so many different things at once.

The test on Thursday went well for most of the students...about right for the first test of the year.  The  first test sort of marks the end of the "introductory" phase of any class, with the students now seeing how they will be formally assessed.  Many of the students mentioned that now that they have seen a test, they have a better idea how to study and prepare through the next couple weeks as well as how to study the last day or two before the next test.  Specifically, several students said that they wish there were formal notes for the class (i.e., lecture notes, which are not coming...I'll be talking a bit about this at the beginning of class on Monday), while others said they now have a clearer picture of the kinds of notes they need to take during the discussions (i.e., they "get it").

Finally, open house was this week.  A few parents were curious how the students were going to be able to learn the new material "on their own".  Of course, they're not on their own...the careful writing of the worksheets and my participation in the discussions are more subtle than me standing in front of the room, but it doesn't mean they're on their own.  However, it was during these discussions with the parents that I realized one of the necessary shifts is that the students need to get comfortable with the homework not being the practice of new skills they have seen (and through the practice, the skills are solidified) but rather the homework is where the skills they need to discover are cultivated, and that the in-class discussions are where the new material is solidified.  Also, a few parents were very supportive of the "new method".  I heard more than one story of college graduates who are very knowledgeable when it comes to skills and "book information", but who don't know how to creatively use the information they have to solve the problems they face in their job.  Harkness certainly addresses this weakness, and give the students the problem-solving practice they need while delivering the required new material.

So, overall a successful week...nothing to deter me from continuing having a Harkness classroom.  In fact, plenty to convince me that this really is the right thing to do.

The Adventure Begins

I just began my 23rd year of teaching, and in many ways, I'm starting over.

Last fall I was directed to the website of Exeter Academy (www.exeter.edu) by a friend, who told me that I really needed to look at their curriculum, the worksheets that they use (all created in-house) and, most importantly, their method of delivery.  What I found has had a profound impact on my philosophy of education.

Exeter uses what it refers to as the Harkness Method, named for a visionary benefactor who made a substantial donation to the academy with stipulations as to how the money was to be used:

"What I have in mind is [a classroom] where [students] could sit around a table with a teacher who would talk with them and instruct them by a sort of tutorial or conference method, where [each student] would feel encouraged to speak up.  This would be a real revolution in methods." ---Edward Harkness

This method, which I can best describe as a student-directed Socratic Method, is described in greater detail on the Exeter website and relies on several things:

(1) the questions the students are asked must be worded in a way that allows them to discover the material rather than relying on the teacher presenting the material to t he students; this requires a lot of prep time, and in particular, the textbooks do not have questions appropriate for this purpose;

(2)  the teacher must observe and redirect the conversation the students have about the material, rather than leading the conversation; this requires a major adjustment for the teacher, especially one who is used to lecturing;

(3) the students must take responsibility for their learning; in particular, they must do their homework and take an active role in the in-class discussions; this can be a major adjustment for the students, especially those accustomed to passive participation...or no participation.

I wrote the worksheets and  piloted the method in my Honors Pre-Calculus class last spring as we did the unit on conic sections.  The feedback was overwhelmingly positive (a few students still wanted to be spoon-fed, but played along since this was the only way they were going to learn the material), so the other Honors Pre-Calculus teacher and I spent the summer writing worksheets for the first half of the course, and this year we are using the Harkness Method pretty much exclusively in our classrooms.

This is where the folks at Exeter will think we're crazy: we have around 30 students in each of our classes.  The method, as it exists at Exeter, relies on a maximum of 15 students in a class, so that the teacher can hear, note, and respond (if necessary) to everything that is said.  So, we have needed to tweak the method for 30 in a class.  To do this, the students are separated into groups of 10 and seated around three "tables".  I rotate   around to each of the groups...not ideal, but at least there are only three groups, so I can spend a decent amount of time with each of them, especially if one group gets into a particularly engaging discussion.  So far this year, the feedback from the students has been essentially unanimous and positive. We'll see what happens after tomorrow's test...the first test of the trimester.

Anyway, my plan is to update this blog on a weekly basis, both for personal reflection and in the hopes that some others who have more experience with Harkness will be able to give advice, share wisdom, and commiserate.  So, please feel free to ask questions, give feedback, etc. ...that's part of the point.

'Til next time...