Undergraduate
mathematics
students
see
a
lot
of
written
proofs.
But
how
much
do
they
learn
from
them?
Perhaps
not
as
much
as
we
would
like
–
every
professor
knows
that
students
struggle
to
make
sense
of
the
proofs
presented
in
lectures
and
textbooks.
Of
course,
written
proofs
are
only
one
resource
for
learning;
students
also
attend
lectures
and
work,
independently
or
with
support,
on
problems.
But,
because
mathematics
majors
are
expected
to
learn
much
of
their
mathematics
by
studying
proofs,
it
is
important
that
we
understand
how
to
support
them
in
reading
and
understanding
mathematical
arguments.
This
observation
was
the
starting
point
for
the
research
reported
in
this article.
Our
work
uses
psychological
research
methods
to
generate
and
analyse
empirical
evidence
on
mathematical
thinking,
in
this
case
via
experimental
studies
of
teaching
interventions
and
quantitative
analyses
of
eye-‐movement
data.
What
follows
is
a
chronological
account
of
three
stages
in
our
attempts
to
better
understand
students’
mathematical
reading
processes
and
to
support
students
in
learning
to
read
effectively