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 Subject: RE: Jeff's Wednesday ToolFest Question Author: Mathman Date: Jun 15 2005
On Jun 15 2005, Jeff L wrote:

All I can suggest is available practice sheet generators [you can make your own
or I can tell you how using a spreadsheet].  As you say, there is "skill"
involved, and as with any other similar endeavour, skill comes only with
practice.  So ...practice, practice, practice.

Look for other related difficulties they may be having, and strengthen those
[also with practice].  I'm referring here particularly to the times-table,
which is not usually memorised by those who have sought other means such as
software, or finger-math for even that.  One skill builds on another.

For long division they need to be able to use the "gzinta rule". That is, they
need to gain some skill at recognising what numbers divide into which [a
consequence of really knowing the times-table].  Again, that is a skill that
takes practice, and so an earlier exercise in problems such as 127/25 will
require the knowledge that division requires multiples of 5 [or 25], and,
further, that the closest one less than 127 is 125, so a result of "5" is a good
start to the first guess.  Other first "guesses" could include "6", since the
"2" of "25" divides the "12" of "125" by that amount, but further work [doing
the multiplication for subtraction] would reveal that to be wrong.  Long
division is not a simple single stage algorithm.  It is complex, and depends
much upon earlier skills.  They must be taught not just "how to" do something,
but what to look for while doing it.  It might be advantageous to have them do
an exercises with several problems and just work each out to determine the first
digit.  Their reward will be marks for doing them only that far, and they will
see some success.  Then move on a stage to the first subtraction then carry down
to the next figure, and so on, ending there for marks to that point before
moving ahead until they can do the entire thought process.  It is in fact a
skill, a method, a device, not a natural phenomenon, so they need to learn the
process ...step by step.  The skill involves even going up blind alleys, as with
guessing "6" rather than "5" in the above, but coming back very quickly ...with
practice.

Software?  I don't think it is an advantage at all in this important early
study, except to generate problems for practice, which involves earlier
knowledge and skill ...i.e. "number sense".  Such problems [and final answers]

I'm going back at least 30 years to when I was teaching myself to program in
BASIC.  Very early in the game [and it was a game] I set myself the task of
developing an algorithm to calculate a long division to any desired number of
decimal places, not those limited by the burnt in instructions given by "PRINT
12/7".  i decided on using string manipulations.  The point is that is was then
that I discovered how dmaned difficult long division really is.  I then stopped
taking it for granted, and thinking it was easy for them because it was easy for
me.  It's not.  It requires much thought, and much practice for the beginner.