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[I]n regular classrooms we learned that students need to be able to write answers to between 70 and 90 simple addition problems per minute in order to be able to successfully and smoothly master arithmetic story problems. However, some students seemed to level off at around 20 or 30 problems per minute, and no amount of reward or encouragement seemed to help. Some of our colleagues (Starlin, 1971; Haughton, 1972) decided to check how many digits those students could read and write per minute—critical components of writing answers to problems. As you might guess, they were very slow, which held down their composite performance. With practice of the components on their own to the point of rapid accurate performance (for example, reading and writing digits at 100 per minute or more), students were able to progress smoothly toward competence on solving the written math problems.
source:
Doesn't Everybody Need Fluency?
Carl Binder
Monday, July 9, 2007
how fast to do story problems?
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7 comments:
Use Sopris or Saxon or almost anything, but don't use mad minutes. The sequencing is horrible. SRA and McGraw=Hill have alternatives that are much better, mostly from the DI folks.
thanks - !
but is it possible to order from SRA & McGraw-Hill?
To be able to write somewhere between 70 and 90 simple addition problems implies that you can read the question and write the answer in less than a second.
Is this believable?
"Is this believable?"
Yes, I think it is. The student can't be thinking about the answers, though; they have to be automatic.
(I'm assuming that "simple addition problems" involve adding two 1-digit numbers.)
The idea of breaking down a skill into its basic components as a way to master that skill makes so much sense.
My light bulb moment came when my daughter was struggling with long division because she had not mastered basic math facts. Her school wasn’t overly concerned because they would spiral back. They told me she was on her way to understanding the concepts. (Although, they did suggest we do flash cards at home.) After mastering her math facts using Saxon, long division became easier to learn. DUH!!!
This idea of exposing students to lots of random math topics without building upon critical component skills doesn’t work for my daughter. I don’t imagine it works very well for many kids. SO MUCH WASTED CLASS TIME.
She can now do about 60 addition problems per minute. We just started working on word problems using bar modeling, which seems like an effective graphic method to break down a word problem into its key components. It almost seems like a work-around to her reading comprehension difficulty, or maybe a component skill in improving her reading comprehension? I don’t know, but I can see that if she can get to the point where she can quickly depict a word problem in bar graph form, combined with her math facts fluency, she’ll be in a good position to handle word problems successfully.
This fluency business is riveting. I'm downloading THE WHOLE THING!
Time seems like the "missing link" to me....
Without exception, people who are expert in what they do can do it fast.
They don't do the "hard stuff" fast - writing new software, writing books, etc.
They do the subroutines fast.
The fluency research is also compatible with the finding that experts have some kind of "super-chunking."
Experts, when they look at a chess board, somehow see ZILLIONS of different chess arrangements that have been played before, in other games. All of their knowledge is activated....it's all connected. (I already said this in another comment: it's Carolyn's observation about math being a "seamless whole" for her.)
Somehow practicing component skills to fluency - which is probably the same thing as what cognitive scientists call "overlearning" - makes the components connect.
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