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=     Problem Solving 101: Linear versus Gestalt Thinking Styles      =
=                                                                     =

Do you have a child who absolutely cannot follow a simple sequence of
directions without changing the order or doing several of them in
parallel? Or, are you one of those individuals who cannot follow
a recipe without making changes? The problem may be rather easy to
identify and solve. A mismatch between organizational and thinking or
processing styles could very well be at the heart of the difficulty.

Linear sequential thinkers process information in a pieces to whole
fashion. This processing style is thought be be associated with
left hemispheric dominance and is present in over 70% of the population
according to estimates I've seen.

Gestalt thinkers, also called holistic, process information in a
whole to pieces fashion. This processing style is thought to be
associated with right hemispheric dominance and its prevalence in the
population is estimated to be less than 30%. Some individuals are 
cross-dominant or have no dominant hemisphere.

Gestalt thinkers do well at games or activities which require pattern
analysis or pattern matching. The oriental board game, Go, is an example
of a game where the strategies are best developed using a whole to parts
method. When I play Go, I picture the board as I want it to be and then
work towards that goal. This type of thinker is more likely to try and
solve problems by using parallel solutions or groups of steps.

Linear thinkers do well at games or activities which can be broken down
into sequential steps. Chess is an example of a game where the strategies
are commonly broken down into linear sequences. It isn't hard to find
activities which are organized in a linear sequential fashion since the
vast majority of people think this way. Recipes and navigating from
a set of written directions are two common examples of linear sequential

Tony Buzan in his book, Using Both Sides of Your Brain, presents ideas 
for incorporating both linear and gestalt thinking strategies in your 
learning and teaching. Knowledge maps (also called webs) are a technique 
which he recommends for gestalt thinkers to use in their note taking. 
Concepts are written in bubbles or on lines which connect the idea to 
related ideas or concepts. A "hub and spokes" hierarchical system of 
relatedness is used starting at the center and flowing outward with less 
important or more detailed information appearing at the outermost edges 
of the diagram. 

Before I read Buzan's work, I was unaware that outlining is a linear 
sequential processing technique. Now, I give my students the option of 
using either method, webs or outlines, according to which works better 
for the individual. It's a mistake to force "webs" upon students who are 
strongly linear in their preferred processing style.

Some of my students have at times experienced a "block" caused by 
a mismatch between their thinking style and the manner in which either 
the textbook or the teacher presents the information. This is especially 
common when I'm tutoring mathematics and science -- two subjects
which tend to be broken down into very small incremental steps or day by
day lessons. 

For younger students, I reorganize the material for them, usually 
creating a summary lesson that is taught first and is followed
by the textbook lessons. With older students I've found it's more 
effective to teach them how to recognize the differences in the two 
processing styles. Together, we then reorganize the material the student 
is having difficulty with according to the preferred processing method. 
For a gestalt thinker, this usually involves presentation of an overview
of the concept, reading the chapter summary, and then working through 
the individual lessons. In mathematics we use sketches, drawings, and 
pictures to reorganize information.

Reorganizing information according to the student's preferred processing
style has been effective in breaking through "mental blocks" and
in helping children learn to process information in the "opposite"
style when necessary. Holistic thinkers are more willing to put the
effort into concentrating on linear sequencing when their own style of
processing is acknowledged and taken into account. Linear thinkers are
less bewildered by a global or holistic presentation when they realize
that it's still possible for them to break the "whole" into small,
easily digested, pieces.

=                                                                     =
=               Problem Solving 102: Memory Skills                    =
=                                                                     =

As children mature two things happen with regards to short-term memory.
First, they learn to "chunk" information. This allows them to combine 
several items into one "chunk," e.g. pick up your socks, shoes, and 
bookbag becomes "grab my stuff." Second, their short term memory 
capacity grows towards the normal adult level of plus or minus 7 items.
Individuals who are able to keep larger numbers of items in
their short term memory usually do so by "chunking" or by using a
relational method (this is related to that).

         Age Range      Item Limit
         ---------      ----------
         3-5  yrs        +/- 2
         6-8  yrs        +/- 4
        9-12  yrs        +/- 5
          13+ yrs        +/- 7

                     --- Kim's Game ---

Kim's Game is a fun way to help children learn to chunk information.
You need a tray, a towel or piece of cloth large enough to cover the
tray, and a collection of odds-and-ends (about 30). Items are usually
small things like a pencil, eraser, crayon, pins, box of tic-tacs,
stick of gum, keys, etc. Everyone playing needs a piece of paper and
something to write with. The leader starts by explaining the rules
while the tray is covered. The tray is then uncovered and the players
are given one minute to "memorize" the contents of the tray. At the
end of one minute, the tray is covered and everyone starts writing.
The player with the most correct items on his list wins the game.

                     --- Math Facts ---

A little subterfuge is needed with some gifted children in order to
encourage them to memorize math facts and to then be able to quickly
recall those facts under time pressure. We use games. At times, I've
even turned the game into "Fizbin" -- a game, from StarTrek, where 
the rules change on the fly  -- to insure that the players must use
memorized facts rather than computing them during a turn. Usually,
it's enough to keep calling out new math facts that depend upon the
previous correct answer.

An easier tack to take is the use of educational games which require
that math problems be answered within a few seconds or the player 
experiences an unwanted consequence (losing points, turns, or treasures).
This approach is much easier on the parents since the adults are
never required to "show-off" their own math skills under duress.

In our household, we also play "war" with cards (you either add, 
subtract, or multiply the cards) with Mom as the referee when
needed. A table of math facts can be substituted for the referee.
The kids will usually encourage each other to "speed it up."

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