S.P.I.D.E.R.

It is the first weekend of spring break, and having administered the first test of the new trimester last Thursday, I'm honestly feeling really good about the way things are going this trimester.  No, not everyone is the class earned an "A" on the test, but from the standpoint of the daily discussions, the students seem to have a solid feel for what is expected and how to get the most out of the them.  The mistakes on the test were more along the lines of not reading directions or making other sorts of careless mistakes, as opposed to not having any idea what is going on.  And in general, the students who did not participate as much in the discussions were the ones with the lower scores (although I seem to have a couple kids with test anxiety - those who are great during the discussions and just can't seem to put it together on the test).

Beyond the fact that the students are more experienced with Harkness at this point in the year, I did something subtle late last week in my classroom that I think the kids have noticed.  On the side wall of the room, I put the following "guidelines" for the Harkness discussions - one each on six separate pieces of paper, with the font size large enough to be read from most parts of the room:

Synergetic - the discussion is team-oriented and one in which each member participates equally

Practiced - the concepts and skills learned during the discussion are practiced by the students as they review the material and as they prepare for future discussions

Independent - students run the discussion, questions and analyze possible solutions, and summarize results

Developed - the discussion gets deep and builds on itself and on previous discussions; individual questions, worksheets, and discussions do not stand in isolation, but are inter-related

Explored - more than simply a discussion, it is a discussion-based exploration of a topic through the exercises on the worksheets

Reflective - students evaluate their participation in the discussions and look for ways to improve their contribution to the class in order to improve their understanding of the material

The "S.P.I.D.E.R." acronym is stolen from Alexis Wiggins (http://modelsbydesign.wordpress.com/2012/09/16/goodbye-harkness-hello-spider-web/), though I tweaked it slightly for the purposes of teaching math and of being in a classroom with 30 students instead of 15.  

I plan on giving the students a handout with the expectations on it when we return from the break, not so much to inform them of what is expected - as I said above, they really seem to have a good feel for this - but more to quickly refocus them and get them back into "school mode".

Beyond that, there's not really much to report this week.  Things are good, and hopefully they will remain that way.

Other Benefits

This week was testing week in the state of Ohio, as the Ohio Graduation Tests were given to the sophomores. This makes for an interesting schedule at our high school, where we only see our students three of the five days for class, and one of those days it's only for thirty minutes. The general consensus among the faculty is that while they don't necessarily have a better idea, the week is essentially lost due to not seeing the kids every day, and that thirty minutes isn't really enough time to accomplish anything meaningful.

Then, there is my classroom, where life continued as normal. On the days I saw them, the kids came in, started going through the exercises on their own, had solid discussions about the material, got through about six or seven problems...a normal day. The only difference with the thirty minute bell was the number of exercises, but the rest of the day looked the same. Honestly, you would never have known that the schedule for the week was as abnormal as it was, that's how normal things were in my classroom.

Do I understand the frustration of the other teachers who see thirty minutes as not enough time to check homework and deliver a lecture? Yes. Do I understand that having class every other day can make it difficult for the kids to remember what they were doing, or what they did for homework, or if they even had homework? In a memorize and mimic classroom, yes...yes I do. But this week I saw one of the in expected benefits of Harkness: the inconsistency of the week and the shortened bell didn't throw the kids off at all. They knew exactly where they had left the discussion the last time they were in class, came to class prepared, and left for the day having actually accomplished something. Once the kids buy into the system, there is no such thing as a wasted day in a Harkness classroom. There is always time to get a little further, do a little work, at least begin the discussion of a problem...there is far less wasted time.

Because of the testing schedule, it became clear to me this week that my kids have bought into Harkness, and have truly taken control of their own learning. So how was OGT week? It was great for me...nice and normal.

Long Term

The third trimester has begun, so I now have four sections of the "B" part of the honors pre-calculus course.  What this means in practical terms is that I have already taught this material through Harkness before, and as such the worksheets are in "version 1.1" of their existence.  It also means that all of the students in the class know how the class is taught and what to expect.  As happens every year, a few kids have dropped back to regular pre-calculus for the second half of the course. Having made it quite safely through part "A", they heard that part "B" is "so much harder" and have abandoned ship without giving themselves a chance.  It's a strange phenomenon in our pre-calculus course that about 50% of the students come away from the course saying that the first half - the part that contains polynomial, rational, exponential and logarithmic functions, as well as sequences and series - is the more difficult part of the course, while the other 50% of the students are firm in their conviction that the second half of the course - the part that contains trigonometry and the conics - is most certainly the more difficult part.  From my perspective, it seems to come down to the answer to the question, "Is the student more comfortable with mechanics or with pictures?", because the first half of the course tends to be mechanics supported by pictures, while the second half of the course is pictures supported by mechanics.  So, the visual kids are more at home with part B, while the symbolic manipulation kids are more at home with part A.

The reason I mention this is that the other day one of the students who earned an "A" in the first part of the course but chose to drop back to regular pre-calculus for the second half of the course came to me to return her textbook and said the main reason she chose to drop back was that she struggled with geometry two years ago and with basic trigonometry in algebra 2, so she felt she really just needs someone to tell her what to do.  And with that statement, a small part of my soul died.

One of the best and brightest that our school has to offer chooses to be told what to do rather than to think for herself, and what's worse she sees this as being a good choice.  By implication, others such as her parents and her counselor do as well, because otherwise the change to her schedule could not have been made.  Much as we might think we are teaching the kids to be independent, to think for themselves, to be life-long learners, and so on, apparently what we are really doing is teaching the kids to be completely comfortable with their dependence on us for the information they need to pass our tests and with the lack of drive to even want to actually learn the material beyond this surface-level knowledge.

This is why Common Core and the new end-of-course testing are coming in.  These tests will require the students to have a knowledge of the material that goes beyond the "I memorized this just long enough to pass the test"  stage.  The current graduation test in Ohio tests at this basic level as well, and as such it is not even close to being a good measure of whether or not the kids are ready for college.  We need to stop fooling ourselves into thinking that we are doing anything other than teaching the kids to  perfect their short-term memory.  We need to admit that we have been lying to ourselves for years, and that the changes that are coming are long overdue.

Harkness, of course, forces the kids to put the information together for themselves, to struggle and come to terms with the material, and  to understand it to the point of being able to be at least a little creative with it.  In short, Harkness promotes and effectively does everything that we have claimed to be doing for years.  Having taught "both ways", I guarantee you that traditional teaching doesn't come anywhere close to actually teaching the material to the kids.  Harkness does.

The students and parents are in for a shock when the new standards are fully implemented.  Sadly, there are a lot of teachers who, instead of taking on the challenge presented by the new standards (and admitting the gross shortcomings of the current ones) are either placing their heads firmly in the sand in the hopes that the new standards are just a passing fad, or are abandoning ship faster than the student I mentioned above.  They are unwilling to see the need for the coming changes, or are admitting defeat before they even get started.  And seeing that attitude, another part of my soul dies.

On the positive, optimistic side, the overwhelming majority of the kids in my classes are back for the second half.  And other teachers are taking up the challenge, making changes to their classroom that will better meet the needs of the students as they prepare for the new testing and for college.  I am fortunate enough to teach with several of them, and like them, I'm in this for the long haul.  Hopefully, by promoting Harkness, I can influence others to get on board with the necessary changes and start actually teaching the kids.

Challenges

Well, we have reached the end of the second trimester, which at our school means that I have now taught the entire pre-calculus course through the Harkness method.  It is still amazing to me just how much my philosophy of education and teaching methods have changed in the last year and a half.  The only regret I have is not realizing sooner just how much the students were memorizing (and forgetting) and how little they were actually learning.  As teachers I have come to the conclusion that far too often we sell the students short in terms of their ability.  Experience has taught us that the students can't figure out this material on their own, and that they need us to tell them what to do and how to do it...or so we thought.  The students have learned to expect us to tell them what to do...and getting them to change has been difficult.  

When I directed theatre, I refused to ask the kids  to do shows that were beneath their ability level.  We did tough shows and the kids rose to the challenge every time.  In transferring that to my math classroom, I thought that meant asking the kids to do more difficult exercises.  What I failed to realize before this year is that as long as I showed them how to do the problems and gave them the time necessary to memorize the process, they could and would be successful with the more difficult exercises...but that didn’t mean they actually learned the “more difficult math”.  It just meant they were really good at memorizing.  I now understand that the real challenge is to ask the students to put the pieces together themselves, and that my job is to guide them to the discovery.  The kids can figure out the material themselves if we ask the correct questions.  More importantly: if they aren’t making the connections for themselves, I now understand that what I need to do is not give in and give them the process and the solutions, but rather to ask better questions.  

Going forward, in trying to get other teachers to see the benefits of Harkness, I think this idea of asking better questions will be a difficult sell.  After all, we “learned” the material by imitating our teachers...or did we?  I wonder how many teachers, if pressed to do so, would be able to actually explain the mathematics they have been teaching for years...not just give the process they have memorized, not just show how to push the symbols around, but really explain the mathematics.  And I’m not sure I really want the answer.

As teachers, we need to ask better questions. And to do that, we need to really understand the mathematics.  As such, we need professional development in both teaching methods and in our content areas.  Convincing experienced teachers of this will be a daunting task.  The students will adjust to our requests and rise to the challenge.  Hopefully the teachers will do the same.