End of Experiment Thoughts

The end of the year has come, and I slacked on updating this blog. I will write a couple of concluding posts, and follow with thoughts and ideas as I prepare for the start of the school year with Harkness in Algebra 1.

The Test Brought...

The experiment ended with an exam in the Harkness style. For review I told the students to focus on 15 specific problems from the problem set that they had worked through. The students didn't seem to be interested in reviewing. I allowed them to use their homework/notes on the exam. The problems came partly from the Exeter exam materials (thank you, Richard Hardej of Exeter!), and partly from mimicking the focus problems. I included one problem that they didn't cover in the problem set...

A restaurant has 23 tables. Some tables seat 4 persons and the rest seat 2 persons. In all, 74 persons can be seated at once. How many tables of each kind are there? Show your work or justify your answer.

I hoped to see that the students would attempt draw out the tables, or guess and check, or actually write an equation or two (they had learned systems of equations last semester).

Disappointment...

Well, the exam was a mess, to put it nicely! Top score: 29.5 out of 39 (76%), with the expected distribution -- previous top-performing students scored at the top, and my usual weak students scoring weakly. I decided that the scores would unduly lower grades, so I didn't count the exam results in the overall grades. I did keep a number of the exams for analysis purposes.

Also, I was surprised how many students couldn't get the answer to the restaurant problem. More so, there were many students who didn't even attempt the problem. Frustrating...

But Hope

Interestingly, despite my (not unexpected) disappointment over the results, I still hold hope.

• I learned that the problem set was not at the correct level for my situation. If I had 12 students in one group with my attention, I believe my students could have handled the difficulty level. With four groups of seven, I could not be everywhere, so the students did not delve deeply enough to thoroughly learn the material. My fault!
• The two week experiment was too short a time period for the students to learn how to learn in the Harkness method. I believe that starting from day 1, instilling an investigative and discuss-based bent, will definitely provide better results.
• More so than usual, the students made errors on the exam. However, there seems to be more consistency in the errors. Perhaps it's wishful thinking, but just maybe, the students were learning, but the limited time limited their learning. The same error occurs on test after test. With more time and better problem sets, I believe that the students will learn better, and these errors won't occur.
• Students who did attempt the restaurant problem, did use varying methods to solve the problem. I found diagrams, guessing-and-checking, working backwards (starting from 74, decreasing by 4's and 2's), an attempt to write a system of equations... I'm happy to see the varying attempts. I need to coax students to use varying attempts in homework, and lead them to attempt on the assessments.

Throughout the two weeks of my Harkness experiment, I ran into frustrations. Each time, I tried to reflect and decide what I could do about the troubles, rather than blame the students. I'm happy about that!

With all of this, I have my work to do this summer. I'm energized to devote time and energy into Harkness-izing my Algebra 1 curriculum. But I'm scared that I'll mess up a group of students in the next year... I'm staying positive!