Overall this was a great week. Courtesy of a minor surgery, I was not at school on Tuesday or Wednesday, and the plans I left for the sub were essentially "the kids know what to do". One of my sons is a sophomore at the high school, and when he went into my room before school on Tuesday to get his books from a table in the corner, he said "hi" to the sub and mentioned who he was and that he would be in between each bell to get his books, since using my room as his locker is far more convenient than using his actual locker. The sub called him over and asked, "Is this really the entire lesson plan?" My son quickly read it over, and responded with, "Yep, that's what happens in here every day." The report from the sub was that things went really well...no difficulties, and particular mention that the lesson plans were very complete, with enough for the kids to do the entire bell. Specifically, Tuesday the kids discussed the assigned exercises from the long weekend, and Wednesday they did ten review exercises for the first test, which was given on Friday. Thursday I took questions, just in case there was any lingering confusion from the two previous days (and, happily, there were very few questions), and gave them a few more review questions to work on, so I could make sure they were ready for the test. Having graded the tests, and with the mean being a B+ and the median being an A-, I'm happy with the results. For the most part, the mistakes were careless ones rather than fundamental misunderstandings, and the only kids down close to the D range were those who have not been participating fully in the discussion...in other words, there were very few surprises.
However, one thing that I noticed as we went through the review on Thursday was that while the students were feeling fairly comfortable with the material that was going to be on the test, they were not comfortable with the idea that not everything we had been covering was going to be on the test. And I admit, there are a few "loose ends" from the exercises that were not on the test, the reason being that the topics being taught through those exercises have not been fully covered yet. We haven't completed all of the exercises that cover those topics, so the test questions on those topics will have to wait. This is something the kids aren't used to. What they expect is that the test covers all of the material since the previous test, and after the test we "reset" and begin preparing for the next test over the new material, which will include little to no reference to the old material. They are not used to being patient when it comes to learning the new material, mainly because we tend to shove a bunch of stuff at them all at once, neatly compartmentalized into chapters on exponents and logarithms, or on basic trigonometry, or on the conic sections, rather than allowing them to build their knowledge gradually over all of these topics at once, which is what I'm asking them to do. The reasoning is simple: in future courses and in future applications, the expectation will be that they have relatively rapid recall of any and all of the topics covered in my course. Calculus does not work exclusively with only one type of function as derivatives are taught, and neither do the applications of physics. And yet, we often teach the different types of functions separately.
In talking with other teachers, and in particular with those who cling to the idea that lecture-memorize-mimic is the best way for the kids to learn, I've come to realize that this lack of patience is also one of the reasons why they cling to lecturing. In order to get the kids to receive a large amount of material on a particular topic in a short amount of time (for example, learning everything there is to know about graphing trigonometric functions in under two weeks), lecturing makes sense since there simply isn't time to allow the students to patiently and gradually understand the material. So, in addition to helping the kids gain some patience in learning the new material, I've come to realize that if we are going to get other teachers on-board with changing their classrooms over to a student-centered, discussion-based, discovery method of delivery, we first need to get them to understand that it's not about covering one topic in-depth for two weeks and then moving on, but rather it's about slowly and patiently building all of the topics throughout the term (be it quarter, trimester, or semester). I'm not expecting this to be an easy sell, but I firmly believe it to be worth the effort. After 22 years of teaching through lecture-memorize-mimic, I've come to see the enormous benefits of patiently presenting the material through discovery and discussion. I only hope others will come to see the benefits as well.