This is the last week of the trimester, so in part I have spent the week looking at the worksheets as a whole and reworking them for next trimester. In our school, the year is broken into three terms, and a standard course is two terms in length. That means a student could have the two halves of the course during 1st and 2nd term, 2nd and 3rd term, or 1st and 3rd term. There are advantages and disadvantages to this, but from a teaching standpoint, it means that one period each day I will be teaching the first half of the course again next term, and as such one of the advantages is the immediacy with which we get to reflect on the first half of the course as a whole and make the changes we feel are needed instead of having to wait until next year.
So, things that need to change:
(1) We need to cut the number of worksheets. The allotted time in the trimester along with the unforeseen interruptions (students being pulled out of class, field trips that take enough students out of my class to have an impact, etc.) made 37 worksheets simply too many to cover. Put honestly, there were times, especially toward the end of the trimester, where things just felt rushed, and not being able to take the time to thoroughly discuss the exercises is antithetical to Harkness. Taking into account Thanksgiving and Winter Break, and that 2nd trimester always has the potential for a random snow day, reducing the number of worksheets is imperative. In particular, we included a few worksheets at the beginning as a means of introducing Harkness, worksheets that were mainly review. These are being cut from the course next trimester, along with other changes.
(2) We had an expectation going into the trimester that the students should be able to complete one worksheet every day. Because of this, we felt that 37 worksheets was a reasonable number. Knowing now that this led, at times, to a "rushed" atmosphere in the classroom, we need to be clear from the beginning of the trimester that the expectation is for the students to thoroughly discuss each of the exercises and to take notes on the material and methods used to solve them. Obviously we have a certain amount of material that we need to cover, but based on this trimester, setting the focus on the depth of the discussion is important, and with fewer worksheets, the pace should not be a problem.
(3) In addition, there are a few topics in our curriculum that are labeled with the phrase "if time permits". In the past we have always had time to get to these topics, so in writing the worksheets over the summer, we felt comfortable spreading the topics throughout the worksheets. However, because of the discovery involved with and the depth of the discussions resulting from using Harkness, the time that in the past was more than available ran short. As such, we are re-arranging some of the questions on the worksheets (about 10-15 questions total) to place all of the "if time permits" topics on the last few worksheets. The last few worksheets will also include some "trimester review" exercises (just as they did this trimester), so hopefully there will not be a break in the flow of the material.
(4) Since the entire process is so new to the students, they need to be reminded often of the "ground rules" for the discussions. This didn't happen nearly enough this trimester, so my plan is to have the students read through the handout outlining the ground rules every Monday at the beginning of class. Hopefully it will set the tone for the week and keep the groups focused not only on the math but on the group dynamics.
In preparing for the second half of the course, the lessons we have learned from the last few months have influenced the worksheets we have been making. In particular, we have set the goal at 30 worksheets, meaning we want to cover the entire course in 30 worksheets. Hopefully, this will allow for a more relaxed atmosphere and allow the students to thoroughly discuss the exercises, as mentioned above with regard to the changes we are making on the worksheets for the first half of the course.
Finally, as the students are preparing for exams this week, I hope that they will take Harkness home with them as they review for their other classes. The lessons learned in my classroom from Harkness should be about more than just the mathematics. It should also be about a way of discussing anything, whether the "anything" is material in other courses, planning a school-wide event, or preparing for a speech and debate tournament. There are many residual benefits from using Harkness, and even if they don't realize it, I hope the students can take the method with them into the other parts of their lives. It's funny, but for as much as we as educators have talked for years about preparing our students not just for future classes but for life, my experience is that we've never really done it. This year, for the first time, I feel like I actually have an opportunity to do so, and it's an opportunity I'm not about to let slip past me.