Time  and  Scope  of  the  Study  of  Mathematics

Harris  *°  has  pointed  out  that  in  the  first  stages  of  the  de-
velopment of  the  mind,  the  mathematical  process     ^.       ,

is  decidedly  more  complex  than  the  other  mental     the  study  of
^  ^  Mathematics

processes  which  are  taking  place  at  that  time.  be  begun?

"  The  reason  why  it  requires  a  higher  activity  of  thought
to  think  quantity  and  understand  mathematics  than  it  does  to
perceive  quality  (or  things  and  environments)  lies  right  in  this
point.  The  thought  of  quantity  is  a  double  thought.  It  first
thinks  quality  and  then  negates  it,  or  thinks  it  away.  In  other
words,  it  abstracts  from  quality.  It  first  thinks  thing  and
environment  (quality),  and  then  thinks  both  as  the  same  in
kind  or  as  repetitions  of  the  same.  A  thing  becomes  a  unit
when  it  is  repeated  so  that  it  is  within  an  environment  of
duplicates  itself."

Several  very  important  consequences  for  the  practical  teach-
ing of  mathematics  can  be  drawn  from  the  fact  formulated.
I.  The  mathematical  process  may  not  be  introduced  before


^°  Psychological  Foundatio7is  of  Education,  p.  343.
