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?
- 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.
- 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".
- 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.
- 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.