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Saturday, September 29, 2007
Steve's blog
from another comment thread:
"Top-down means that students begin with complex problems to solve and then work out or discover (with the teacher's guidance) the basic skills required."
Steve H:
It never happens, unless you redefine what basic skills are required.
instructivist:
["Top-down means that students begin with complex problems to solve and then work out or discover (with the teacher's guidance) the basic skills required."]
Steve H has been talking a lot about "top-down".
I am wondering if he is using the term in the same sense described above?
Steve said...
"I am wondering if he is using the term in the same sense described above?"
I think I am, but one never knows. Ed school definitions are so fluid. It means that mastery of content and skills are never attacked directly, only as a by-product of other learning.
The is the biggest problem with Everyday Math. There is no initial mastery of the material (except for a few kids). They move right along to new material. This is perhaps better described as distributed mastery. Like top-down learning, mastery of basic skills never gets done properly for many kids.
I have the "new improved" edition of sixth grade Everyday Math and I am amazed at how this jumps out at me. They might have a lesson on some subject that takes up 3 or 4 pages. Often, one or two of the pages are "math boxes" that have little or nothing to do with the subject of that lesson. They are simply review problems of material that should have been mastered in previous years. This is not in-context review of skills. This is just practice that should have been finished long ago. I've been meaning to give some examples and show how different it is from Singapore Math. It appears that 40 percent of the material in Everyday Math is review work. This is NOT distributed practice after mastery. This is distributed mastery, spiraling mastery, or perhaps even top-down mastery. The problem with EM is that there are so many review pages that it's almost impossible to get through all of the units.
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5 comments:
I really like your explanation of EM's distributed master. This has been bugging for awhile and I never could quite articulate what is going on, but I think you've done that.
EM is constant review of material previously covered, but not mastered. The secure goals of each "unit" tend to test stuff covered the previous year. Secure goals do not seem to test mastery of recently taught material.
The only exception is the tremendous volume of material devoted to probability and graphs. These two subjects I believe are taught to mastery and then reviewed.
Unfortunately, these are probably the least important skills an elementary student needs to get out of math in k-6.
I'm not quite following -
hmm...
You're saying that the kids have lots of "review" problems of material that isn't ready to be reviewed, because it hasn't been mastered....
AND that this isn't a Saxon situation, where you do one or two problems a day of material you're still learning
In other words, in Saxon you "memorize" material not by memorizing it, but by doing 1 or 2 problems every day for weeks and months until gradually you've assimilated the material; it's been stored in long-term memory
This is distributed practice (not review, per se).
You're saying that EM doesn't have distributed practice and also doesn't have review, but, rather, has sporadic reappearances of problems the kids have seen but not mastered.
Is that it?
I have GOT to post the cumulative practice article.
It is life-altering.
Here's a sampling of EM Grade 2:
Unit 2 Addition & Subtraction Facts
2.1 Addition Number Stories*
2.2 Addition Facts
2.3 Doubles Facts
2.4 Turn-Around, Doubles and +9
2.5 Addition Facts maze
2.6 Domino Facts
2.7 Weighing Things
2.8 Fact Triangles
2.9 Name-Collection Boxes
2.10 Frames-and-Arrows Problems
2.11 What's My Rule
2.12 Subtraction Maze
2.13 Addition/Subtraction Facts
2.14 Family Letter
*NOT word problems. NOT even close to being word problems.
They blow through these at about a section a day. Monday they begin 2.1 and Tuesday on to 2.2.
After 14 days +/- these second graders are on to unit 3: Place Value, Money and Time). There are 12 Units total that are covered in a frenzy.
"You're saying that EM doesn't have distributed practice and also doesn't have review, but, rather, has sporadic reappearances of problems the kids have seen but not mastered."
Yes. Sporadic and random, with no process (or time) for the teacher to identify and fix the problems. A page of Math Boxes might have problems about mixed numbers, percents, and statistics. There would be a great improvement if the Math Boxes talked only about one type of problem at at time. It would be easier for the teacher to identify and correct problems.
Continuously distributed mastery is quite diffferent than randomly (or spiral-based) distributed practice. Also, there has to be some reasonable time limit for mastery of individual skills. The longer the time frame, the less effective it is, even if it is continuous.
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