RON MCDERMOTT spoke of Math Facts to DAN TRIPLETT on 12-30-96
RM>DT>I know that many kids memorize facts...but can they apply them? 
RM>Two different cognitive levels... Reaching the first doesn't
RM>mean you reach the second...
Yes....and I bring up this point because I see some teachers emphasizing 
the learning of the times tables (in my school).  I don't know if they 
carry out the teaching of the multiplications facts to understanding 
them as well.  
RM>DT>But I see many kids, even 5th graders, still struggling with 
RM>DT>some basic math concepts.  I am left to wonder why?
RM>1. Many kids simply don't CARE why, they just want a nice,
RM>   easy formula to follow that ALWAYS works.  I see it every
RM>   day in physics, and I'm sure Sheila does in math.  It's
RM>   much easier than investing the effort in understanding.
I can understand this at a higher level.  Do we really need to 
"understand" how all algorithms work or is it enough to understand how 
to manipulate the numbers?  Some of that higher math stuff is really 
weird (at least to a math novice it can appear to be weird).  
RM>2. Many kids simply don't work hard enough, or long enough,
RM>   or with enough concentration to "get" more than a 
RM>   rudimentary understanding of the concepts.
This is certainly true....some probably give up when the answer isn't 
immediately apparent.  
RM>3. Some teachers have given up trying for true understanding
RM>   because so few of their kids (in the teachers' mind) are
RM>   going to "get" it anyway.
Yes...and Im not entirely sure if this is true or not.  Sometimes one 
needs only to find the right "switch" and the light (of understanding) 
comes on.  I would think that kids have different "switches."  Maybe we 
just need to find them?
RM>4. There IS the possibility, largely ignored these days, 
RM>   that some kids are not going to "get" the higher order
RM>   understandings because of a lacking in their internal
RM>   wiring.
This goes along with #3.  Perhaps it is safe to say that "most" kids can 
get the stuff.  There are always exceptions...of course there are some 
with "internal wiring problems."  
RM>Yes, but is it possible that despite ALL efforts, some kids
RM>are simply not going to "get" it?  Along the lines of my
RM>discussions with Carl, there seems to be this underlying 
RM>assumption that everything hinges on what WE do, rather than
RM>on what the KIDS do...  Teaching we control; LEARNING is
RM>pretty much out of our hands as long as kids have the choice
RM>to learn or not...
I used to give guitar lessons and I would tell my students that I cannot 
"teach" them anything.  I can show _them_ how to learn something.  If 
they took the lesson home, and worked at the ideas I presented them, 
then and only then would they learn it.  I think this idea is true about 
everything we learn.  Only when we as the learner work with a 
concept/skill will we advance in our knowledge and understanding about 
it.  
RM>SK>The reasons why they aren't learning the facts is because they are
RM>SK>not getting enough help on the material, and that includes help in
RM>SK>the home from the parents.
RM>With deference to Sheila's point, this is ONE reason, and
RM>extending it from "help" to "direction of effort" is
RM>another, but there is still the matter of the kids DOING
RM>the learning....
True...but I think motivation is our (parents and teachers) 
responsibility.  Still, kids with "attitudes" have to accept the 
responsibility for their own lack of learning I suppose.  
RM>DT>This has to do with learning how to study and memorize (which 
RM>DT>actually take time and effort).
RM>DT>And all too often this important item is left out.
RM>Very often in our discussions, for example !
RM>DT>I believe that many kids exit the learning mode once the 
RM>DT>dismissal bell rings. 
RM>Many never ENTER it !
How true....and at the upper grades the responsibility for turning on 
the learning mode can be placed more and more on the student's 
shoulders.  But at the elementary grade level it seems to me that 
educators need to find ways to encourage learning....like instead of 
covering the material we help students "uncover" it.
Dan
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