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%BLACKBOARD LAYOUT PATTERN INFORMATION ORGANIZATION+790711
       %CONNECT RELATION LOGIC SEQUENCE INSTRUCTION 790711

     Students  perceive  relationships  between   abstract
ideas most easily if they are presented in ways which take
advantage of their minds'  developed abilities to perceive
inter-relationships.     Visual   perception   of   inter-
relationships   is  one  of  the  most  highly   developed
abilities,   and should be taken advantage of.   Rarely do
text   books  and  lecture  presentations  take  as   much
advantage of visual abilities to perceive  connections and
inter-relationships  as might be taken.    Visual  lay-out
techniques  can  be  used  to  graphically  portray  which
equations are intimately related to which other equations;
e.g.,  by lines showing that two equations can be combined
to yield another  equation,   or vice versa.   A   logical
organization    of   equations  over  the  surface  of   a
blackboard  can  help  students  internalize  the  logical
organization of the ideas portrayed on the blackboard.  In
a similar  way a logical organization of the locations  of
equations  over  the  page  of  a text book can  help  the
students perceive the  organization of inter-relationships
between relationships.  Usually text books organization is
purely linear---with  little  thought to the possibilities
to  two  dimensional organization of locations of ideas on
the page, much less the possibilities of three dimensional
organization of ideas on adjacent pages.

     Part  of the improvement of instruction will  be  the
development and the sharing of insights into how to better
share insights into  complex  inter-relationships  between
relationships.     In  the  mathematical   sciences   some
imagination   and  use  of  three-dimensional  lay-out  of
symbols  may  be  helpful.    In  more  verbally  oriented
disciplines   it  may  he  helpful  to  develop  ways   of
presenting words in other than just linear strings.   This
may   be  facilitated  by  computer  data  processing   in
information  retrieval  systems.   It may be done by novel
uses of pages of books.  It may be done by creative use of
cross indexing and short-hand notation for cross-indexing.
New ways need  to  be  developed  to  portray  and  convey
perceptions of inter-relationships.  Teachers and students
need to work together to discover which new ways which are
most  effective.   This  will  require  effective dialogue
between  students  and  teachers,   more  effective   than
traditionally occurs.
                                                                                                                               
                         (c) 2005 by Paul A. Smith in      
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