One thing I've been putting a lot of thought into is how to teach to mastery in an environment where I'm on a strict schedule and have very limited time. I bet Black and Wiliam weren't thinking of people who have to jam what would be a whole year of algebra in high school into a semester. Still, I have decided, there will be quizzes at least weekly next semester.
This semester I gave twenty quizzes in calculus (the best 10 counted), and I'm thinking of giving quizzes every class next time I teach something from the algebra / precalc / calc sequence. Next time I'm going to make them VERY short, 3-5 minutes, and give them at the exact beginning of class. My bet is that the instructional face-time lost will trade well with increased studying.
Compare using <, >, = 0.635 __ 0.365To me, this is a simple comparison—but do teachers typically ask for work to be shown on this kind of question? If so, does the student write a subtraction problem, or perhaps draw a number line? I'll find out from Christopher's teacher, but I'm wondering about other peoples' experience. I have no problem with the requirement that the kids show their work; I think it's probably good at this stage. But I've got to know from the get-go what 'showing your work' means for each given problem, so we can practice it from the get-go.
The reason the early grades are so critical is because that is where adults have the most influence over a studentís behavior. Thereafter, peers take on a more important role in a studentís behavior. Although the progression is fairly obvious, school personnel may not respond in time to prevent this negative spiral (i.e., behavior gets worse over time). Fortunately, this negative progression can be stopped. However, teachers must be ready and willing to set up their classrooms to stop the cycle. Teachers cannot wait. They must begin to take steps to consider how they are going to promote appropriate behavior and prevent management problems from the 1st day of class.-- KDeRosa - 07 Dec 2005
Third, well-paced instruction keeps students engaged and, in turn, reduces behavior problems. Inappropriate behavior often occurs during down time when students are not occupied with productive tasks. Engelmann and Becker (1978) reported that when teachers maintained a pace of about 12 responses per minute, students answered correctly about 80% of the time and were off-task only 10% of the time. However, when teachers asked only four questions per minute, the studentsí accuracy dropped to 30% and they were off-task about 70% of the time. Clearly, a brisk pace contributes to the effectiveness of instruction.From The Components of Direct Instruction which is probably the best concise summary of DI I've found to date. -- KDeRosa - 08 Dec 2005