I'm hereby pushing any questions about assessment into the foreground. I don't have any insight into maintaining a clean classroom and my kids are still acclimating to Web 1.0, much less all these wikis y'all gush over. But if I've got anything to merit this bandwidth-suck, it's an interest in meaningful assessment.
Kay asked some great questions in the comments. I'll try to keep things concise, but I'm easily excited sometimes.
1. What type of rubric do you use for assigning a final grade?
70% Four-Point Assessment
10% Final Exam.
I look at this rubric. Then I look at my next-door neighbor's and I feel like I have a lot of explaining to do.
Quickly then. Homework is one of the least essential components of my teaching. Especially for freshmen and especially for low-income students, homework has a lame effect.
Speaking in brute generalizations, the motivated students don't need the homework, but do it anyway. The unmotivated students need it but don't do it. Occasionally one of the mid-range students, for whom outside practice is time well-spent, will do an assignment without cheating. That's great, but it doesn't justify hours lost to homework review, the negative vibe it stirs up in class, or, particularly, anything more than a 10% parcel of the final grade.
Assessment obviously dominates my rubric. At one point, back when homework still had the edge, as it does in most math classes, I started playing with a backup copy of my gradebook. I increased the value of my four-point assessments to this absurd-by-conventional-wisdom 70% figure. The result was unexpectedly satisfying: students who clearly understood the material were passing; those who were coasting by on homework completion were unmasked. I haven't adjusted / fudged / or felt guilty over a grade ever since.
2. Do you still administer traditional final exams?
I decided, as of this year, having assessed my students' competence in, e.g., Solving Proportions at least eight times before the end of the year, that I have little use for a comprehensive final exam. I toss 'em a final exam for show but if a student has passed all the concepts, I let her read a magazine.
I'm just trying to trim the fat, y'know? To make class time mean something. To make assessment mean something. I'm positive there are many ways to do this.
3. Do you find students don’t have sufficient practice with longer tests? Could be a possible disadvantage that you might have to counterract, especially for AP classes…
I think your instincts are right on. The highest math I've taught is Pre-Calculus / Trig / Math Analysis. Whatever you call it, it's the class immediately preceding big deal AP calculus. Since it's mainly a grab-bag review of skills students will need for calculus, a checklist of concepts was really the way to go.
California has declared 25 standards for Algebra. It's really easy to build a concept list from that.
AP classes only have one standard, however, and that would require a different assessment structure altogether. Given the patronage system of most high schools, I'm probably a decade away from teaching the big league math. My first step will be to grab up every sample AP exam I can find.
4. How many questions per skill do you use on average for each assessment?
Ideally, I give a student five chances to demonstrate mastery of a concept. (Keeping in mind that "mastery" means they successfully worked a problem twice.) Sometimes, like at the end of the year if our class average is low on a particular concept, they'll see it more than five times. In other instances, if I haven't spent enough time remediating a concept on the openers or during review games, I'll skip it. It'd be the same scores, different test.
I'm wondering now if the tallest hurdle for the entry-level teacher to clear is the difficulty of making her own tests. I have a decent hand with page layout programs so it's never been anything more than an annoyance. If I were a programmer, I'd cook up an Ajax-y utility that'd let the teacher pick the class, the core concepts she wanted, the rigor, and would output a formatted test. Man, that'd be great.
Unfortunately, I struggle enough wearing this one hat.
Thanks for the questions, Kay.
Related: How Math Must Assess