I can't believe it was two weeks ago that I posted Calculus Food For Thought. Time flies. Anyway, I've had time for some thought and time to talk to some other teachers and my class. Here are some of my thoughts:
I've been working harder than they have; even by their own "calculations".
Their sense of preparedness to write the exam matches their estimated effort. I realize this wasn't a "scientific" data collection, nor is the analysis very scientific but these results provide some small additional evidence to what I have already long believed. Almost anyone, who is willing to try, can do advanced math. Their marks (yes I know, I haven't shared the marks with you -- and I'm not going to .... well .... maybe some averages would be apropos?) are more a reflection of their effort rather than their ability. Why do capable students consistently fail to apply themselves to doing their best work? What's the lack of motivation here? Is it cultural; a failure to appreciate the value of learning? Maybe we don't challenge them enough .... maybe I challenged them too much?
No, they were almost evenly split: Was I too hard or too easy on you? (remember, n = 15, rather small).
I think I have to emphasize more work without the calculator. 40% of the class thought so and while it's not a majority that's too big a percentage for my liking.
The next two questions were interesting (What was the best learning experience you had in this class? What was the worst learning experience you had in this class?) both in the particular answers and in the number of answers. They felt they learned the most from group work and take home assignments. A friend of mine thought the preference for take home assignments was a selfish desire for easy marks but I don't think my assignments are that easy. And, while it is possible they can copy from each other, anecdotally, I got more individual students seeing me for extra help and really learning and understanding the material when they had to do these assignments. Regular take home assignments are also a feature of math courses taught at the university level, so this is a good preparation for post secondary education in mathematics as well.
The variety of answers to the second question I read positively. Some things work best for some folks and not others; everyone learns differently. I had enough variety in the ways I presented and evaluated material so that I managed to aggravate everyone at least once. ;-)
In the class discussion we had of these last few questions, the students were overwhelmingly in favour of more take home assignments.
Right now they are working on their take home exams. (The 6 questions from Form B for you AP Calculus teachers out there.) On the exam they had 90 minutes to do 6 questions like these. I've given them about two weeks.
The standard is: Everyone must get 100% on this exam. Anything less is unacceptable. Here's why: They can get help from me, talk to each other but not show each other any written work (yes, I know, I'm naively optimistic). I'll tell them what they need to fix in order to get that perfect mark. There are no excuses for getting less than 100%. They sure are motivated to get that perfect mark; and I'm very picky about the degree to which they must explain written answers where required.
More than one student has told me this would have been an even better review before the exam. I've decided to test the theory out with my grade 12 precalculus class. I'm giving them their "Go For The Gold" assignment next week. Same conditions. The minimum expectation for everyone is 100%. Anything less is unacceptable. I will send letters home to the parent of any child that gets less than 100% or fails to hand in the assignment. It will explain the assignment (last semester's final exam, it is worth 5% of their class mark), that the child has chosen not to get the 100% mark they could have, and it will have to be signed and returned to me. Whatever mark they get is what will be recorded. And their paper will be returned to them with a single comment; Unacceptable.
I want to try this idea out with the whole department next year. We'll have two of these "Go For The Gold" assignments each semester with the standard set at 100%. I'm hoping that when we do this across the school it will create a bit of a buzz in the community. Every student must get 100% on this assignment which will be handed out on the same day with the same deadline in all our classes. I'm hoping it will change the culture of the school, get the kids focused on learning and help them prepare for and improve their performance on exams. Imagine, every math student in the school gets 100%. What impact will that have on the culture of the school? My grade 12 students are my guinea pigs this semester. Let's see if it works ....