Responding to a message by Dan, to Charles on ...
DT>If you were more specific I could comment more here.  It would be 
DT>artificial where a more concrete experience would accomplish the same 
DT>things.  If I want to teach fractions I can do it abstractly on work 
DT>sheets that "show" using diagrams certain examples about whole, half, 
DT>fourths, and so on.  I also could provide manipulative that children 
DT>could "touch" and "see" and manipulate in various way to create 
DT>fractions that one can see.  Pattern blocks can accomplish this very 
DT>well.  It might be well to use food such as a real pie (as opposed to a 
DT>picture of a pie.)  
You re-propose the new NCTM standards - lots of manipulatives (certainly 
important for Kindergarten, perhaps less so as one advances through the 
grades).  It certainly seems logical that studying things that are 
physical processes would be easier if we studied them using a hands-on 
approach (working on an automobile engine is an example that comes to 
mind).  But I wonder about trying to study concepts that are more 
abstract (e.g., fractions) in such a manner.  We can certainly give 
examples (share a couple of pies, if you will), but before long the 
process must be moved to paper.  If we spend *too* much time on the 
practical applications while trying to make the process meaningful to 
everyone, we'll cover no more than one topic per year.
DT>I don't mean to teach only skills that children consider meaningful, I 
DT>mean to teach those skills that we as older and wiser adults know they 
DT>will need later in life in more meaningful ways.  Engage the learner!
I guess we're actually arguing about the word "meaningful" here.  You 
probably are actually referring to providing "meaning" for the math 
concept, and you are *NOT* actually implying that cutting a pie in half 
is "meaningful" for the child, right?
When we use a pie to illustrate the fraction 1/2, is that meaningful to 
a child?  I see it as something less important than that - perhaps 
something of interest, but not meaningful.  In order to make something 
meaningful to a child, we would have to be teaching them things that 
were significant in their lives - for example, how to eat.  How to 
remove and replace a brake lining would be meaningful to an 
auto-mechanic, but it would NOT be meaningful to me.
Is there actually a way to engage every learner by using the same 
examples?  That pie might bore a few of the kids quite quickly - and how 
many pies are you going to cut up as you show halves, thirds, quarters, 
fifths, sixths, etc.?  A ruler is a practical example of using 
fractions, but is it meaningful to kids?  I've seen very few that like 
measurement.
What I'm getting at is expediency.  I'm given 12 units to teach each 
year - seldom complete more than 9.  I can't teach the hundreds of 
concepts and skills I'm responsible for if I spend hours on just the 
simplest of concepts - the meaning of a single fraction.
DT>.DT>If I want to teach spelling I can provide a list of spelling
DT>.DT>words,  test, study, and then retest.  I was taught in college
DT>.DT>that this is the  best way to teach spelling.  But children who
DT>.DT>score well on spelling  tests don't always spell correctly on
DT>.DT>written work. 
DT>
DT>CB>Are you sure that they don't at least spell *better* than those who
DT>CB>do poorly?  
DT>
DT>They may, but the point is that this approach, which seems to teach 
DT>spelling, falls short.  What is the goal of these spelling tests if not 
DT>to teach children how to spell correctly for their written work.
Yes, the point is to teach children to spell correctly for their written 
work, but that doesn't mean you're going to get perfection.  I don't 
know if the research exists, but I would still like to know if those 
children who study spelling in a formal manner don't spell more words 
correctly in their written work than do children who *don't* get formal 
spelling lessons.  And another question - is there a difference in the 
reading skills between the two groups?
DT>Here is where we part company.  If a child can do the work sheet, then 
DT>they know the skill.  Doing the work sheet is a waste of time.  This 
DT>child needs enrichment and not from a work sheet.
You're right - we do part company here.  There is nothing wrong with 
practice and reinforcement.  A skill learned today might well be 
forgotten three days hence without additional practice (short and long 
term memories function differently).  In your class, when a child 
recognizes the letter A, are you suggesting that you never ask him to do 
it again because he knows it?
DT>The child who cannot do the task shouldn't do the work sheet either 
DT>because it is beyond their level of comprehension.
Let me get this straight.  Just above you say that a child doing some 
work they already know how to do is a waste of time.  Now you're saying 
that asking a child to do some work they don't know how to do is a waste 
of time.  The only thing I can figure here is that you have a 
single-minded idea of what a work-sheet is and you are holding on to 
that notion with a bulldog's determination.
In my mind, work-sheets (sheets of paper with work on them) are not 
inherently bad.  Some are badly written, but others provide drill and 
practice that reinforces skills for long-term memory development, others 
provide the path to learning development (guiding a child through a 
library project, for example), and still others may challenge a child to 
seek out information (getting help from a parent or adult).  At the 
middle school level, I give homework most every night (quite often in 
the form of a worksheet) and it serves lots of purposes - it tests the 
child on his recall of the work done that day in class, it may push the 
child into looking in his notes or his textbook to review a process he 
learned and has forgotten, or it might just help the child remember the 
information/process for a little bit longer as we build on that same 
skill the next day.
The process I use was tried and tested long before I became a teacher 
and my best guess is that it will last long after I'm retired.
DT>But I am speaking of this specific kind of work sheet and am not 
DT>saying ALL work sheets.  Just ALL work worksheets of this type.  
All work sheets of *which* type?  You do not distinguish, but I'm not 
sure I'm going to agree with you anyway.  I know many teachers today try 
to avoid the overkill, once popular, of giving the kids a steady diet of 
"seat work" work-sheets, but I see no difference between that and 
assigning a dozen pages out of a book to attack or three "pages" of 
computer work.
Chuck Beams
Fidonet - 1:2608/70
cbeams@future.dreamscape.com
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* UniQWK #5290* Accept me for what I am - completely unacceptable.
--- Maximus 2.01wb
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