KTM User Pages
19 Oct 2005 - 14:14
from Carol Gambill, on teaching algebra to 8th graders:
I have developed totally scripted lessons for each algebra unit that require absolute focus and attention, constant oral responses, and intense involvement from every student.
Demanding and receiving absolute focus and attention isn't that hard once you've had enough practice. I'm sure if we could watch a video of KIPP instructors at work, we'd see rapt attention. The way to command rapt attention is to call on the students constantly. For mainstream teachers, calling on students means asking a question. KIPP does lots of class chants, which I'd like to incorporate into my own small class if I could find out what the KIPP chants are. I suspect all kids would profit from learning math chants. (I had to do whole-class phonics chants when I was a kid.) But outside KIPP, 'constant oral response' means constant question-and-answer. Everyone has to be ready with an answer at all times. The art of Asking a Good Question is almost never mentioned in math ed writings. The constructivists talk about real-world problems and 'challenges'; domain-knowledge folks talk about 'direct instruction' or 'scripted instruction.' But the problem with the phrases 'direct instruction' and 'scripted instruction' is that they call to mind a teacher delivering a lecture. I don't know how Zig Engelmann teaches his classes, but as far as I can tell, scripted instruction for most of the educational world actually means asking excellent questions you've thought about, written out, and committed to memory before hand. The Saxon Math books in the early grades have tons of questions scripted in. Another problem: many of us think of questions as a query that arises spontaneously in the course of a class. The teacher is lecturing away, and suddenly the spirit moves him or her to stop and ask a question. Scripted instruction means you don't ask questions off the top of your head. You think about the questions you're going to ask. Some questions are better than other questions, and you think about that. You test-run your questions with real students; then you throw out the good ones & revise & modify the good ones to make them even better. The questions are in the 'script.'
[T]eachers should present information to the class, but stop every minute or two to ask questions or pose problems based on this information. This produces far faster learning than asking students to discover answers with little help. It is also much more effective than straight lecturing, as most kids will not pay attention to a long lecture--but they will if forced to respond frequently to the information given. The benefits of balancing questioning and information delivery in learning are underscored by a classic study by psychologist A.I. Gates. In that study people spent different proportions of time reading (absorbing) information versus attempting to recall what they read. People learned the most when they spent about 80 percent of their time trying to answer questions about the material. If they spent less time recalling facts, they learned les. But if they spent more time in recall, their learning also tapered off. A similar ratio should be employed in the classroom. Math teachers can query students in a variety of ways. They can pose general questions about a math concept to test students' understanding of it. They may explain a problem-solving method using an example problem and then ask the students to solve similar problems. Teachers may even given students a chance to figure out the answer to a new type of problem while providing feedback and hints, and ultimately the answer when none is forthcoming.
Using direct instruction, you don't talk for longer than 2 to 3 minutes at a time. Then you ask a question or pose a problem.
Math Coach, page 30-31
direct instruction on direct instruction
The Sweetwater Union High School District has posted videos of what looks to be a professional development workshop on direct instruction. I've watched all of them; they're terrific. The video on guided practice goes over reserach on teacher effectiveness:
The questions a teacher asks in class are the near-equivalent of the problem sets in a textbook. Ourside class you learn math (mostly) by doing problems; inside class you learn math (importantly) by answering the teacher's questions.
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I left this comment in another thread but it belongs here as well. Check this article out: Student-Program Alignment and Teaching to Mastery Zig has the answers to all your direct instruction questions and a few more you probably haven't even thought of yet. There's been a lot of experimentation, research, and field testing incorporated in his teaching techniques. -- KDeRosa - 19 Oct 2005
Does he script questions? -- CatherineJohnson - 19 Oct 2005
Highly scripted. Choral responses. Mastery learning. Zig is the grandfather of Direct Intruction -- he invented this stuff. -- KDeRosa - 19 Oct 2005
He has choral responses!? I LOVE choral responses. I KNOW those are going to work; I know this on sheer gut instinct. -- CatherineJohnson - 19 Oct 2005