During the summer, the teachers of the math classes at Exeter get together and review the problem sets and compile a series of documents they call the Commentaries. These Commentaries are then used by the Writing Committee to review, edit, and modify the problem sets to make them better for the next year.
First of let me just say, Wow. Exeter’s commitment to the constant improvement of their curriculum is amazing. Contrast that to the situation we have in the public schools. The district spends millions of dollars on a textbook from Pearson, McDougal, or Holt and then we are stuck with those textbooks until the next textbook adoption (every 7 years in NV, unless the budget delays it.)
In the meantime, we complain about the books because we know there are better ways to teach and better ways to work with the material, but we are bound by textbooks that are bound to disappoint. Today I told my department that it would not bother me if we threw all the Algebra 1 textbooks away. It shook them up and made them think a bit about why we teach the way we do. But I digress.
Let’s take a look at a couple of problems and see how the process develops new questions, or if not new questions, new understandings of the questions.
I chose this problem because it is a pretty standard type question, used in Algebra 1 to work with systems of equations. It has multiple questions underneath, and has the zinger question in part e that challenges the learner to figure out some answers without algebra.
The Commentary for the question suggests some methods of solving, and points out the fact that the Algebra is the best way of solving the question. The Commentary does not mention part e, which has a lot of mathematical exploration involved. But the Writing Committee clearly felt something was going on in part e that was not successful, because the 2012-13 question is now:
Identical question, but the committee dropped the exploration question to focus on the mathematics and the generalization found in part d.
Here is another example where the question is really straightforward and does not change from one year to the next, but the commentary is terrific in guiding a discussion.
Very basic question, but the commentary opens up a very different scenario with the material.
Wow, look at that. High school teachers I have known sometimes fall into the “why should we teach something so basic, that is a middle school standard and they should just show up knowing it, but I guess we can review it” trap. It is a trap, and it sucks you in and destroys you if you let it.
Here the Commentary shows that the trap opening, “It is surprising that some students have so much trouble…” but they don’t fall in. They point out to their teachers to look for the shy, the quiet learners and ask questions the quiet learners may not ask but desperately need. Very nice.
What the Commentary is clearly for is to show the TEACHER what traps are possible with the material and to develop better questions in the treatment of the material. Imagine a brand new teacher at Exeter with the problem sets getting the Commentary. They can work the materials easily, otherwise they would not be teaching math, but the Commentary is what allows the new teacher to develop the questions that need to be asked in class.
It is definitely a tough proposition to write the commentaries and get the information from 20+ teachers and simplify those comments down to a short paragraph. But very worth the time and effort to do so. If you are interested in the Exeter problem sets, I recommend you read the commentaries as well.
Below you will find the commentary folder for the 2011 – 12 Problem Sets and the 2011 – 12 sets. The Exeter website has only the updated 2012 – 13 sets with change log.