Introduction.
3
same direction
in
the
mathematical
field and which will
therefore be
important
for these lectures.
Three
years
ago
I
gave,
for
the
first
time,
a
course
of lectures
with
a similar
purpose. My
assistant
at that
time,
R.
Schimmack,
worked the
material
up
and
the
first
part
has
recently
appeared
in
print
1
.
In
it are
considered
the
different
kinds
of
schools,
including
the
university,
the conduct of
mathematical instruction
in
them,
the
interests
that link
them
together,
and
other
similar
matters.
In
what
follows
I
shall from time to
time refer to
things
which
appear
there
without
repeating
them. This makes it
possible
for
me
to
extend
somewhat
those
considerations. That volume
concerns itself
with
the
organization
of school instruction.
I
shall now
consider
the
mathematical
content of the material which enters
into
that
instruction.
If I
frequently
advert
to the actual conduct of
instruction in
the
schools,
my
remarks
will be
based
not
merely upon
indefinite
pictures
of how the
thing
might
be done or even
upon
dim recollections of
my
own
school
days;
for
I am
constantly
in touch
with
Schimmack,
who
is
now
teaching
in
the
Gottingen
gymnasium
and
who
keeps
me
informed
as
to the
present
state
of
instruction,
which
has,
in
fact,
advanced
substantially beyond
what
it
was in
earlier
years. During
this
winter semester
I
shall
discuss
"the three
great
AV,
that
is
arithmetic,
algebra,
and
analysis,
with-
holding
geometry
for
a continuation of the course
during
the
coming
summer.
Let me remind
you
that,
in the
language
of the
secondary
schools,
these
three
subjects
are classed
together
as
arithmetic,
and
that we
shall
often note
deviations
in the
terminology
of the schools as
compared
with that
at the universities. You
see,
from this small
illustra-
tion,
that
only living
contact can
bring
about
understanding.
As a second
reference
I
shall mention the
three
volume
Enzyklopadie
der
Elementarmathematik
by
H. Weber and
J.
Wellstein,
the work
which,
among
recent
publications,
most
nearly
accords
with
my
own tendencies.
For
this
semester,
the
first
volume,
Enzyklopadie
der elementaren
Algebra
und
Analysis,
prepared
by
H. Weber
2
,
will
be the most
important.
I
shall indicate
at once certain
striking
differences
between
this
work
and
the
plan
of
my
lectures. In
Weber-
Wellstein,
the
entire
structure
of
elementary
mathematics
is built
up
systematically
and
logically
in
the
mature
language
of
the
advanced student.
No account
is taken of how
these
things
actually may
come
up
in school
instruction.
The
present-
ation in the
schools,
however,
should
be
psychological
and
not
syste-
matic. The
teacher
so to
speak,
must
be
a
diplomat.
He
must
take
account
of
the
psychic
processes
in
the
boy
in order
to
grip
his interest
;
1
Klein,
F.,
Vortrage
uber
den mathematischen
Unterricht
an hoheren
Schulen.
Prepared
by
von
R.
Schimmack.
Part
1.
Von
der
Organisation
des mathematischen
Unterrichts.
Leipzig
1907.
This
book
is
referred
to
later as "Klein-Schimmack".
2
Second edition.
Leipzig
1906.
[Fourth
edition,
1922,
revised
by
P.
Epstein.
Referred
to
as
"Weber-Wellstein I".