Saturday, September 8, 2012

"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.


  1. Johnothon,
    I am really interested in how your experiment goes. I have thought a lot about how to do this, and this year for the first time have groups of 4 in my classroom instead of a U.

    I think this is my first nod to the idea the learners have to start talking about the math more than me.

    Please continue to post your thoughts, ideas, successes and failures, because there are many people who are interested in how to duplicate these efforts.

  2. My plan is to post at the end of each week, and eventually to put up some videos (need to get permission first, which is currently in progress).

    And one of the things on my list of topics to include this week is that I need to learn to shut up and let them have the conversation, which is a difficult transition to make.

    Thanks for the interest...looking forward to a good conversation here as well.

  3. Wow! I am impressed by your efforts! I only ran into Exeter material about 2 weeks ago and I could not shake the idea to begin a student/learning-centered classroom for my 11th and 12th grade Precalculus and Calculus classes. I am interested in the worksheets that you have been using with your students. I found your blog and Glen's blog this weekend. This is my first official year in teaching, but was fortunate to have had a student teaching experience rich of fantastic tasks to engage the student learning. My 9th graders (an integrated course Common Core class) this year have had that kind of teaching from the beginning of the school year but I just recently got permission to modify my teaching from our local college for which my 11th and 12th grade students are doing their math class as concurrent enrollment. I actually passed out the first 10 pages of Math 4 from Exeter on Friday to begin the students on a deeper journey. Have you seen the commentaries that Glen has eluded to for Math 3? I just emailed Exeter to see if I could have access to Math 4. Some of the "older" teachers here have advised me to just use the "great" curriculum left by my predecessors (and save time because I am finishing my Masters in Math Ed now as well, graduating in February). But I know differently and these past 3 weeks have proven to me that my students have not "learned" the math and can barely regurgitate it. After a few discussions about how we actually learn mathematics, they are all on board for a new experience... so now I need to deliver. Am I jumping in too early?

  4. If you feel you are ready for it, then no, I don't think you're jumping in too early. My honest advice, though, would be:

    (1) Make sure you have the support of your administration. The folks at my school and in our central office have been completely supportive, realizing that the Common Core is going to require a lot more than just slapping a new label on an old textbook. It's going to require a different way of presenting the material to the kids and getting them to understand the material in a different way. I have the good fortune of not needing to convince my administrators of this, as they already see the need, and lucky for me they see Harkness as a solid model for producing the required change.

    (2) Explain what you are doing to the parents and the kids; don't wait for the questions about your "new methods". In other words, be proactive.

    (3) The materials from Exeter, while amazing, did not line up directly with the curriculum at my school. So, we used the way they were constructed as a guide to making our own worksheets. No, it wasn't easy; yes, it has been worth it. If the Exeter materials fit your curriculum, all the better. If they don't, this could be a roadblock, since it's not really about the individual worksheets or exercises, but rather how they build and compliment one another to form to a complete "whole", and trying to create the worksheets as you go may be difficult if not impossible.

    (4) You need to know your math, better than you were taught it. The open-endedness of the questions doesn't just allow for alternate methods of solving the invites it, and you need to be ready to discern whether or not the method the student used is mathematically sound.

    (5) Some of the students, despite the initial enthusiasm, will want to revert back to the "old way", mostly due to a desire to return to a "comfort zone". Listen to them, respond to their concerns, but be firm in your convictions that this truly is the better way.

    (6) The "old teachers" also have a comfort zone, and part of that comfort zone is having everyone else with whom they teach teaching the same way they do. This is one more reason to have the support of the administration. As for the "great curriculum": regardless of how great it is, it is not going to serve the students with the Common Core. And despite the fact that PreCalc and Calc are not part of the Common Core, the basic concept being promoted by it is very different than what the old curriculum emphasized, and it is that concept that needs to be infused into all of the courses, regardless of whether or not there is a test sitting at the other end.

    Hope this helps...and if you have any great revelations along the way, please share.

  5. Thank you for taking the time to lay out your thoughts, they were extremely helpful. After some deep pondering and a look at the commentary for Math 4 this morning in an email from a contact at Exeter, I've decided to prepare better for next year. This preparation includes how to educate the parents. There is so much mathematics to understand and because I didn't learn this way, I know that I would be better prepared after actually having gone through the material myself. It is so hard not to get excited about this type of idea!

    My 7 Calculus students looked at the problems over the weekend and we discussed their goal(s) in taking this course. All of them do see that the way that they have always "learned" math was not the most memorable but want to pass the college exam at the end of the semester. They enjoyed working together on Friday so we decided to keep the same format with all of us seated together (we have set up our tables like yours) and we work on problems (from the book and others that I supplement-some may be in a task to begin our class discussion) together. I am thinking of a recent article I read about a learning cycle: develop understanding, solidify understanding and then practice understanding:

    I hope to try to step back and encourage the students to make their own connections like Exeter does in working through meaningful problems. I look forward to learning more from how you make it work in your classroom! Thanks again!