After Exeter

Now that the conference at Exeter has come to an end, a few reflections on the week:

(1) The week-long courses were great, not only in terms of content but in also in terms of modeling the Harkness philosophy.  From a content standpoint, it was nice to be doing math again rather than teaching it.  From a pedagogy standpoint, it was great to see some of the nuances in action, nuances which can be difficult to detect when you're in the heat of the classroom.  And putting both the content and the pedagogy together, it was fun but aggravating to be the one who is frustrated rather than being the one providing the frustration for others.

(2) The camaraderie among the conference participants was equally great.  There was a seriousness of purpose that led to an almost instant bond with the people with whom I had the pleasure of working.

(3) No, the Exeter materials are not appropriate for every class.  The materials were written for the caliber of kid that attends Exeter, and as such they are not right for every classroom in the country.  Likewise, a private school has more independence when it comes to curriculum, and because of that the materials do not necessarily translate to every classroom in the country.  That being said, I am now more convinced than ever that the Harkness method is appropriate for the vast majority of the classrooms in the country.  The only thing standing in the way is the commitment by the teachers to write the worksheets appropriate for their classroom (both in terms of the level of the kids and the curriculum) and the support of the administrators.

(4) New England is delightful.  From the people of the town of Exeter that I met walking around town to the people in Boston who asked if we needed help maneuvering the subway and train, as well as recommending a restaurant during our two-hour layover (including an approximately 25-year-old blind girl...no kidding), the experience with the people was great.

(5) Finally, I need to increase the awareness of Harkness to the rest of my district and to the districts around me.  The method was never mentioned in any of my undergraduate education nor in any of the professional development since then.  And yet, it's the method of choice at one of (if not the) best high schools in the country.  More people need to know about it, and those of us who spent the past week at Exeter are just the ones to do it.

Time Travel

Day two at Exeter, the first day of "real" classes and Harkness discussions, was wonderful and enlightening on many levels.  I signed up for two content-related classes, knowing that this would mean having homework each night since the classes were going to be taught via Harkness.  The homework has been fun, the discussions today were good, and much as I witnessed in my classroom on the few days when there were only 12-14 students present, the depth and for the most part the focus of the conversations were solid.  There was also a panel discussion about how to run things in a classroom of 25+ students, which was not so much a "how-to" manual as a sharing of ideas...all good stuff.

However, as I was sitting in the math class today as a student, I wondered what things would have been like had this been the way I was taught in high school.  Would I have the same appreciation for it then as I do now?  Would I have actually enjoyed some of the math courses (I loved some but loathed others)?  For that matter, what would it have been like if my college courses were run this way?  Would I have been enthusiastically in favor of such a method, or would I have simply been trying to get through the material regardless of how well I understood it?  It's tough to tell from this vantage point, of course, but one thing is for certain: I need to make sure I instill in my students an appreciation for Harkness and for the Socratic Seminars they experience in their English classes and for the POGILs they experience in their science classes.  Looking back, I wish this were the way I had been taught.  I wish I had been taught not to fear mistakes but to acknowledge them and embrace the lessons learned from them.  I hope that my kids last year got at least a small sense of this, and I intend to make sure that the kids in the years to come do.  And I need to have this attitude myself moving forward.  There were a lot of things that we did right last year...that really worked well and that are worth continuing.  But being here I'm gaining some of the insights into Harkness that are difficult to see from the outside, especially from hundreds of miles away.  I need to actively look for other potentially better ways of doing things, discuss these ways with other people, and learn from the experience.  It is becoming clear to me that, viewed properly, life is a Harkness table, and it's high time we told the kids (and ourselves) to pull up a chair.

Welcome to Exeter

After a Saturday filled with planes, trains, and subways, the math conference at Exeter began in earnest today, and so far it has certainly lived up  to its billing.  The people running the conference are amazing (in terms of both friendliness and organization), the food is wonderful (in terms of taste, abundance and diversity), and the introductory sessions to the week-long courses are what I expected, namely, some homework and some discussion.  The discussion should be better tomorrow...it lagged a bit today, and I now understand how the kids felt on the first day of honors pre-calc last school year.

This is also my first trip in New England, and thus far it's great.  The people in Boston and here in Exeter and very warm and helpful, and the weather, while really hot and humid during the day, has been very pleasant in the evenings.  There is also an acute sense of history about almost everything you see, especially the buildings, which something you don't get to experience as much in Ohio, since most of the history at home involves the geography rather than the architecture.

My hope is to give a short update each day this week, though my math homework may make that difficult (it's been a long time since I've used "I have homework" as an honest excuse for anything), so we'll see how it goes.

Grading

Now that the school year is over, this blog will probably become less Harkness-focused (though that will certainly still be the main theme of many of the posts) and include other topics that hopefully will be of interest.

Today is the first such post.  Over the summer, some of the teachers at my high school have been asked to begin to rethink the grading practices both in our classrooms and in the district.  Having read the book provided by the district that will serve as the starting point for our discussion in the fall, the push seems to be toward eliminating any scores that do not directly evaluate how well a student has learned the material for the course.  The goal is to have the grade be an accurate reflection of how well the student has mastered the material, and I agree that if we're honest about it our current grading practices do not do this.  Among other things, this would mean not giving credit for homework, since homework is intended to be practice and not actual evaluation.  It would also mean eliminating extra credit, since it distorts the accuracy of the grade.

In my mind this raises two immediate issues:

(1) Using this sort of a standards-based grading system, the traditional method of assigning letters to certain percentages simply doesn't make sense.  For example, let's say that there are five standards the student is to meet during a certain marking period.  Throughout the term, the student has demonstrated (through in-class discussions, project presentations, tests, etc.) that they have mastered one of the standards, are proficient in three of the standards, and not proficient on the remaining standard.  To what letter grade does this correspond?  If we base the letter on mastery, the student is at 20% mastery - a really low F on a traditional scale.  If we base it on proficiency, the student is at 80% - a B- on a traditional scale, and very different than the F just mentioned.  Or should the letter grade be some combination of the two?  These are good questions to which I don't currently have an answer.  However, this makes me very curious to see how the grading is done at Exeter - definitely a question I'll be asking during the conference in two weeks.

(2)  Any change in the way the letter grades are assigned is going to be met with a lot of questions from the students, the parents, and the community, let alone something as drastic as this.  We will need to educate each of these groups regarding not only the new system itself (if we put such a thing in place), but also the rationale and research behind it.

If anyone reading this has comments, suggestions, or ideas, please send them along.  I would love to have a good discussion here, and to include the discussion here in the conversation we will be having in my district in the fall.

Lessons Learned

With the school year now completed and my classroom cleared, and having thoroughly enjoyed the first morning of not waking up at 4am, it's probably time to reflect on the year while things are still relatively fresh in my mind.

First, exams went well this week, with the median grade being a B+, which is higher than in years past and higher than the median score at the end of second trimester.  As I admitted in an earlier post, I understand that we're talking about a limited amount of data here, but the reduction in the number of questions during the review for the exams and the increase in the scores on the exams themselves certainly point to Harkness being a better method of delivering the material to the students, at least in terms of their retention of the material.

So, what were the key points I feel I need to keep in mind for next year, and what would I tell someone who is thinking of changing their classroom over to a Harkness classroom?

1. The size of the group is important.  If I get additional white boards, I plan to reduce the number of students in each group from ten down to seven or eight.  Twelve to fourteen is great if the teacher can sit at the table with the group the entire time, but with 28-30 kids in the class that's simply not possible.  I was able to experience 12-14 in a class during the weeks of the AP tests, groups of 7-8 during third trimester since a few of my classes had 22-23 students, and groups of 10-11 the rest of the time.  The additional board space will allow me to go with four groups next year and break the classes of 30 into what I believe to be the ideal size of 7-8 students.  The larger groups tended to either split into two smaller groups, or to have one or two students not participating in the discussion as much or as well as they should.  The teacher at the table with the students the entire time prevents this from happening with a group of 12-14, but without that option the groups of 7-8 students seemed to work the best.
2. The questions on the worksheets are important.  The exercises in the textbooks are not geared for discovery and discussion, so relying on them is not a good idea.  Even the discovery activities provided by the textbook companies are not sufficient to get the job done, though they might be a good place for someone to start using Harkness in their classroom.  The questions need to be written for the level of the students in the class, stretching them to make the connections and discoveries, but not so far that they break and give up.  Were I to teach a "regular" pre- calculus class, I would need to rework the sheets I have, because they were written for an honors level "audience".
3. Harkness is not a one-day event, nor is it a once-in-a-while method.  It is a philosophy that needs to be infused into every aspect of the instruction and learning.  From the daily work to the review, and next year probably even to the quizzes, Harkness must be at the heart of it all.  Reverting back to feeding the students the information and mechanics even for a day or part of a day will undo a lot of what has been accomplished.  I learned this early in the year and never forgot it the rest of the way out.
4. Harkness is better, but it's not easier.  From making (and revising, and revising) the worksheets to constantly evaluating the students' work during class to grading lots of correct solutions that have been obtained by very different but mathematically sound methods, Harkness is more mentally taxing than traditional lecturing.  I saw that last spring during the ""test run" so I knew what I was getting in to, but having seen the results, I can enthusiastically say that it has absolutely been worth it.

And finally, what reasons would I give for making the switch?  Ultimately, it comes down to a decision: do we want to teach the kids to solve problems, or do we want to teach them to problem solve? What I mean by that is this: do we want to equip them to successfully complete specific types of exercises, or do we want them to be able to use a set of skills and successfully complete whatever is thrown at them that uses these skills?  Do we want them to be completely confident in their abilities when it comes to a limited set of exercises, or do we want them to have enough confidence to be willing to tackle new exercises, the likes of which they may or may not have seen before?  Lecturing prepares the students to solve problems; Harkness prepares them to problem solve.  For nearly 22 years I thought I was teaching the kids to problem solve. Now, I know that I was actually only teaching them to solve problems.  Lesson learned.

Final Week

From my standpoint, class this week went about as well as it could have, and was a great way to end the course.  The two days of school next week are exam days, so at this point the discussion portion of the course is finished, and the positive results of running the course with a Harkness philosophy were on full display.

On Tuesday, the students took the test for the final unit of the course.  For various reasons, the other honors pre-calculus teacher and I decided to make this a group test.  The "rules" for the test were:

• the groups were slightly smaller, with 6 or 7 students in each group
• this was not an open book nor an open note test
• the students were to discuss the exercises as close to usual as possible
• the test was worth 12 points, as usual, but 2 of the points came from participation in the discussion (I went from group to group noting the participation like I do every day)
• each group turned in one test; however, each student was required to contribute to the writing of the solutions

I love stumbling upon a great idea, and boy was this one of them.  I have never seen a group test go as well as this.  There is always the concern with any group work, especially when the grade is significant, that one person will do all of the work and the others will just latch on to that one person.  That didn't happen.  All of the students participated and contributed, pretty much equally, to each of the five questions on the test, and I had no reservations assigning the grades earned by each of the groups.  In fact, the whole thing went so well that we are considering incorporating group quizzes into the course next year.  There still is, and always will be, a need for individual assessments, but considering the group-discussion  nature of the course, it really only makes sense that some of the formal assessments be group assignments.  Probably should have realized this earlier in the year.

As the students left class, I gave them a set of twelve exercises to prepare as a means of studying for the final exam, and on Wednesday and Thursday they discussed the exercises.  On Friday, I was gone at graduation rehearsal, so I prepared an additional twelve exercises for them to work on without the usual preparation at home.  These three days of discussion were the review for the exam...a far cry from the usual review for the exam which tended to consist of me going through the review exercises in detail.  The fact that they were able to get through most of the exercises on Friday without me even being in the classroom is a huge testament to the progress the students have made this year in terms of taking charge of their own education.  And as I sit here writing this on Sunday night, I have received two emails, both of which were requests for answers so they could check the work they had done.  Again, quite the change.

All in all, a great way to end the course.  Hopefully, the grading of the exams over the next couple days will be just as enjoyable.