"...Perhaps the most telling data set, one that I and others have shared hundreds of times since we gathered them in (Bea) Barrett’s lab (Barrett, 1979; Binder, 2003), shows ranges of correct responses per minute on simple pre-academic component tasks that we were teaching adolescents then labeled “mentally retarded.” We were also working with young elementary school students and a group of professional adults. In 11 of the 16 skills, all of the professional adults completed more correct per minute than all of the regular children and all of our handicapped students. These data reflect what you’d notice if you spent a few minutes with these people. But if we only use percentage correct, as in most classrooms and training programs, we’d think these three groups performed exactly the same, because they were all 100% correct!
We have to let this sink in. In my view, our educational and training programs fail to produce competence in large part because the measurement systems they use cannot discriminate between competence and incompetence. All of us have been trapped in the percentage correct box since childhood, unconsciously thinking that 100% is the best we can do. Rate of response shows us an entirely different picture that allows us to make better decisions..."
source:
Learning, Teaching, and an Evolutionary Imperative
by Carl Binder
Precision Teaching: Why Fluency Matters
I'm sure this is right.
Which leads me to the realization that my preteaching triumph may not have been a preteaching triumph at all.
It may have been a fluency triumph. At the same time I began preteaching math lessons to C., I also began making him practice for speed.
I didn't have a theoretical reason for doing this. It was pure pragmatics. Ms. K's tests are huge, so I figured we could "buy" C. extra points through sheer speed, which would give him more time to sweat over the problems he didn't (immediately) know how to do. So every night I would insist that C. do a set of problems as quickly as possible; then I'd make him do the same or a similar set the next night & do them faster. I've kept this up ever since, pretty much.
His grades on math tests shot up, and I thought it was the preteaching.
But now I'm thinking that while the preteaching helped in class, it was probably the timed practices that helped on tests.
claims for fluency
- knowledge and skills mastered to fluency are remembered better than knowledge and skills mastered only to 80 to 100% accuracy
- knowledge and skills mastered to fluency are easier to combine into "composite" or complex knoweldge and skills under guidance of a teacher
- knowledge and skills mastered to fluency are more likely to combine into composite skills spontaneously, without further instruction, through the process called contingency adduction
source:
"The Shame of American Education" Redux
I'm thinking fluency may be the missing link in a lot of thinking about when and how students finally start making those all-prized connections amongst fragmented concepts & skills.
More later.
preteaching, not reteaching
success
success, part 2
more preteaching results in the offing
preteaching saves the world
preteaching wonders of the world
Shhhhhhh....
ReplyDeleteIf the fuzzy math mafia hear you talking to much about fluency they might kidnap you and force you to perform endless multiplication problems using the matrix method.
well that's the funny thing, of course; you could just as easily become fluent in matrix multiplication as in the standard algorithm
ReplyDeletethe kids who DO become fluent in it will do better!