Today was the second day with groups of 6-7 students, rather than the Harkness standard of 12-14 students. Today went very smoothly. Groups got together independently; they started up where they left off; and although I would like for them to get to the discussions more quickly, they are volunteering/assigning problems and working on them.
One example of the (re-)learning that's occurring: Although the students solved problems like this...
\[\frac{2x}{3}+\frac{3x+5}{2}\leq5\]
...in Chapter 3 (Solving One-Variable Linear Equations), Chapter 4 (Solving One-Variable Linear Inequalities), and Chapter 11 (Rational Expressions and Equations), on Monday the students acted like they had never seen such a problem. You know, fractions are scary!
Today, two days later, and students in every group is showing solutions to this problem, and discussions about errors were occurring. Marvelous!
Using the Harkness method (I need to figure out a name for my evolving method) and selected, appropriate problems from the Exeter Math 1 book has shown me that the student forgot more than I realize--more than they realize. The student-led discussions are bringing back forgotten knowledge--or maybe that the students are actually owning and gaining understanding of work that they have done.
I have also realized that I will have to work hard this summer to rework the problems for my Algebra 1 students for next year. I stole used the Exeter math questions for my students, but I see that my students need to be led more directly in finding connections between problems. They aren't naturally looking for how problems relate. At Exeter and other private schools with small class sizes (Catlin Gabel!), one teacher with 12 students means that the teacher can watch and comment on every problem. With my 25-27 students per class, I cannot hear everything nor participate with each group every moment. I'm sure that connections are being missed, which means reduced conceptual learning. I've got some ideas for next year...
Tomorrow I am gone from school for my District's next CCSS Workgroup. I hope that the students handle themselves while I'm gone. I left a couple of questions for my substitute to answer about his perceptions of the discussions; I can't wait to find out what he thinks.
Today's other Algebra 1 class responded to the smaller groups as positively as did the earlier class. They engaged as smaller groups (6 or 7 students), and made positive progress in their Harkness discussions. Well, almost...
I did have one group that featured a couple of girls almost came to blows. You see, student A was presenting a problem. Student B asked a question of Student C, which C began to answer, which caused Student D to say something like, "Hey, shut up! I'm trying to listen." Student C took umbrage to D's comment, and Students C and D started after each other.
I found out what occurred, ultimately deciding that Student B was the instigator of the side-conversation (although it was math-related, it was rude to talk when someone else was discussing), and apologies came without prompting.
I see this situation as a positive. Student D tends to be quiet and reserved; today, she stood up for herself and the process. Student C was trying to help another student. Excellent!
I also started having the groups track their own discussions. I slightly modified a sheet from Johnothon Sauer, which had each group track the problem number, the presenter of the problem, and which students made a useful contribution to the discussion of the problem. This group tracking seemed to help the groups, since they knew that they were responsible to each other more overtly.
I continue to find evidence of the value of the Harkness method -- the student-centered discussion; the natural ability of the students to find connections when they discuss; the growing comfort in discussing problems, even when the students are uncomfortable with the material.
The one big challenge continues to be that the students won't attempt the problems and record their attempts if they perceive the problems as hard. I'm realizing that my usual method of operation -- teaching by lecture, homework of my own worksheets, answers shown the next day and questions answered, worksheets collected once a week or so -- hid the fact the many students weren't doing homework. I knew that many weren't doing the homework daily; that many weren't turning in the homework packets regularly, or turning in partially done homework packets, but I didn't have to face that problem each day so obviously. With the Harkness method, it's clear when students haven't worked on the problems. My struggle: how to motivate the nightly work?
As I am in the middle of my experiment, I am experiencing the full range of emotions and issues expected of any change.
I started my Harkness experiment on Monday, May 6. The prior Friday I had given my 52 Algebra 1 students the first eight problems (mostly pilfered from Exeter's Book 1), along with some explanation to the intent of the method. I expected that the students would try the problems and come to class ready to discuss.
Yeah. 12 of the 52 students admitted to attempting the assignment. I called an audible and gave the students 15 minutes to independently work, and then the students began.
Fast forward to yesterday (Monday, May 13)... The students had a few problems to work over the weekend, and 14 of the 50 present students had tried the problems. Also, the groups of about 13 students each were just a mess. Lack of preparation and lack of interest came together in a bad way.
After (barely) surviving the day and blaming the students, I thought, "What can I do to improve this?" I took Johnothon Sauer's advice and created groups of about six today.
I had to write this now...my first Algebra class went great! I handed out a sheet detailing what a good group discussion should look like, and the smaller groups did it. I could sit down, engage the students, and the groups worked and were quiet about it. They discussed how to solve a challenging equation, and worked together.
Yesterday, I wanted to quit this experiment; today, I love Harkness!
More later...
I'm late in creating this blog, but here I go...
It was April 3, 2013, when I discovered the Harkness method. I am a member of my school district's Common Core Workgroup, and the group was having its second meeting. I was researching teaching approaches related to the new Mathematical Practices, and I found the math department website for Phillips Exeter Academy. Something just clicked, and I was smitten!
In just over a month, I have spent many an evening scouring the Internet, searching for information, materials and experiences related to the Harkness method. I have gone on an out-of-state classroom visitation to Catlin Gabel and spent the day with Jim Wysocki and his math department, learning about how they implement Harkness. I have had communication with Johnothon Sauer, author of Harkness for Thirty, his blog detailing his experience implementing Harkness in his Precalculus classes. And I have had my two Algebra 1 classes working in the Harkness style for a week.
During this next week, I will discuss my Harkness experiment: how I feel about it, how my students feel, what I've tried and what I need to do. Ultimately I have to decide whether I will commit to Harkness for the next school year. Right now, I believe so.
This whole experiment is exciting, but scary. The new Common Core Standards brings change; the new emphasis on the Mathematical Practices is a big change. My Harkness experiment is my personal attempt to find how and where I am able to change.
