Is  A  B  C  D  a.  parallelogram  ?  What  sort  of  a  figure  is  A  B
Is   it    true   that   the   diagonals  C  £>?

of  parallelograms  bisect  each     What  do  you  know  about  the
other?  diagonals  of  such  a  figure?

Is,    therefore,    A  E   equal  to     What   lines  in  the  figure  are
EC}  therefore  equal  ?

How  does  this  knowledge
help  us  in  our  (main)
problem?

While  the  essence  of  the  heuristic  method  lies  in  the  fact
that  the  pupil  is  not  told  things,  but  led  to  see  them  himself,
The  Mode  of  the  mode  in  which  this  is  done  may  vary.  The
s  uction.  problems  may  be  formulated  for  the  pupil  in  a
syllabus  or  in  a  text-book  especially  prepared  for  heuristic
work,  and  the  recitation  mode  of  instruction  used  with  it.  The
individual  mode  might  also  be  used.  An  ordinary  text  may
also  be  used  and  the  matter  developed  with  the  class  geneti-
cally. In  the  genetic  mode,  the  class  as  a  w'/!^'/*?  discovers  the
theorems,  but  no  attempt  is  made  so  to  conduct  the  work  that
each  pupil  independently  does  so.  If,  however,  the  latter  is
the  aim,  and  the  class  exercise  is  devoted  to  discussing  work
done  and  outlining  work  to  be  done,  we  have  the  heuristic
mode  in  its  extreme  form.
The  method  is  not  without  its  dangers  and  disadvantages,
some  of  which  should  be  mentioned  here.
I.  Theoretically  it  would  seem  that  7nore  time  would  be
requisite  for  such  rediscovery  than  for  learning
Disadvan-  and  understanding,  proofs  imparted  by  text  and
^^'  teacher.
