2. The Issues
• Students
need
the
opportunity
to
work
and
wrestle
with
mathema;cs
(Hiebert
&
Grouws,
2007)
• expending
effort
to
make
sense
of
mathema;cs
and
figure
out
something
that
is
not
immediately
apparent
• Common
Core
Standards
for
Mathema;cal
Prac;ce
call
for
students
to
“construct
viable
arguments
and
cri;que
the
reasoning
of
others”
including
jus;fying
their
conclusions,
communica;ng
them
to
others,
listening
to
the
arguments
of
others,
responding
to
the
arguments
of
others,
deciding
whether
they
make
sense,
and
asking
useful
ques;ons
to
clarify
or
improve
the
arguments
• How
can
teachers
produc;vely
engage
students
in
wrestling
with
mathema;cs?
3. Maggie
had
3
packages
of
cupcakes.
There
were4
cupcakes
in
each
package.
She
ate
5
cupcakes.
How
many
cupcakes
are
leW?
4. Adam
has
21
cents.
Gumdrops
cost
3
cents.
How
many
gumdrops
can
Adam
buy?
5. Student
explanations
in
mathematics
classrooms
• Related
to
student
achievement
• Our
research
• Others:
Gillies,
Webb
&
Mastergeorge,
Safard
&
Kieran,
Nathan
&
Knuth
• Not
just
any
explaining
–
details
ma_er
• Teachers
can
support
students
to
explain
• O’Connor
&
Michaels,
Gillies,
Mercer
• Ini;al
ques;on:
how
did
you
get
that?
not
sufficient
• 98%
of
the
;me
teachers
asked
• Probing
ques;ons
(sequences),
leading
ques;ons,
bundled
ques;ons
6. Multiple
Dimensions
of
Student
Communication
• Explaining
their
own
thinking
• Engaging
with
others’
thinking
• You
engage
with
others’
ideas
• Others
engage
with
your
ideas
6
7. Engaging with each others’ ideas
Referencing/acknowledging
somebody’s
ideas
in
general
without
details
• I
used
Nomi’s
strategy
• “Does
everyone
agree
with
Sam?”
S
says
no.
• Students
point
to
strategy
like
their
own
Addressing
the
student’s
idea
with
detail
• repea;ng
what
was
already
said
or
wri_en
on
the
board
• sharing
someone
else’s
strategy
for
them
• disagreeing
while
referencing
detail
of
what
they
disagree
with
Addressing
the
detail
of
someone’s
idea
and
contributes
to
someone
else’s
ideas
• S
disagreeing
with
what
was
shared
and
shares
an
alterna;ve
• responds
to
a
S’s
shared
idea
and
adds
to
it
•
construct
strategy
together
8. • Explain
your
thinking
• Engage
with
others’
ideas
to
a
high
degree
• Have
others
engage
with
your
idea
to
a
high
degree
8
9. Relationship
between
Student
Participation
and
Achievement
Par%al
correla%on
with
achievement
Provided
fully-‐detailed
explana;ons
of
how
to
solve
the
problem
.30*
Highest
level
at
which
you
engaged
with
other
students’
ideas
.44*
Highest
level
at
which
other
students
engaged
with
your
ideas
.41*
9
10. If
Seily
has
Iive-‐thirds
liters
of
soda,
what
would
that
look
like?
Draw
and
label
all
parts
11. Some Observations about the Teacher Practices
• Teachers
made
a
variety
of
ini;al
moves
to
help
students
a_end
to
each
other’s
ideas
•
These
moves
all
concerning
having
students
compare
their
ideas
to
other
students’
ideas
• Do
you
understand
what
Adrian
did?
• Do
you
agree?
• Is
your
approach
the
same
or
different?
• Point
to
the
solu;on
that
is
like
your
own
• Can
you
explain
what
he
did?
• More
important
than
the
ini;al
move
for
how
students
engaged
with
others’
ideas
was
how
the
teacher
followed
up
to
press
students
to
make
their
thinking
explicit
11
12. Supporting engagement
T
directed
students
to
discuss
answers
and
strategies
with
each
other
(norm
moves)
• You
are
not
talking
to
me,
points
to
the
class,
you
have
to
convince
them
• Emmy
is
not
convinced
yet
so
lets
see
if
we
can
get
some
more
ideas
• Carlos
are
you
paying
a_en;on,
you
want
to
see
if
you
agree
with
her
13. Supporting engagement
T
asks
students
to
elaborate
on
answers
and
strategies
(to
make
it
possible
for
others
to
a_end
to
its
detail)
• asks
specfic
ques;ons
that
require
students
to
a_end
to
the
detail
• asking
students
to
discuss
specific,
centrally
important
steps
embedded
in
their
strategies
14. Supporting engagement
T
posi;ons
students
to
par;cipate
in
another’s
thinking
• Selects
strategies
that
are
different
to
be
shared
with
the
whole
class
• Have
more
than
one
set
of
work
shared
and
explained
on
the
board
for
each
problem
• Asks
students
to
offer
sugges;ons
to
each
others
strategies
• Did
you
do
it
the
same
way
–
how
is
it
the
same?
• I
love
what
you
did…..
Look
at
this
Lily,
because
Cole
is
at
the
same
place
where
you
are.”
• Cris
maybe
it
will
help
if
you
listen
to
someone
else
and
then
try
again
15. Disrupting existing cultural practice
• Exis;ng
prac;ce,
expected,
experienced
• Dinner
;me
conversa;on
• Teachers,
students
and
families
all
have
ways
they
are
used
to
doing
school
math
• Classrooms,
schools,
districts
• Requires
renego;a;on
rather
than
telling
16. Create
a
space
to
begin…
Count by 1, start 180, count to 230
Count by 7/8
Count by .004 start at 53.280
Count by 10 start 66, count to 266
Count by .99, start at 1
Count by 2, start at 0
Count by 11, start at -77
17. One
of
these
things
is
not
like
the
others…
Listen…
replace
your
talk
with
another
move
23. Productive struggle for each student
• Challenge
our
assump;ons
about
student
par;cipa;on
• Find
the
produc;ve
–
what
students
have
communicated
• Make
explicit
what
it
means
to
par;cipate
(norms)
• Support
it
(follow
up)
• Watch
for
how
the
status
quo
limits
opportuni;es…find
ways
to
challenge
it
