1.
Dr.
Dorothy
Y.
White,
University
of
Georgia
Yopp
Distinguished
Speaker
Series
in
Mathematics
Education
March
4,
2014
Characterizing
Preservice
Teachers’
Mul5cultural
Mathema5cs
Disposi5ons
2. Warm-‐Up
Think
about
your
first
teaching/academic
job
and
the
students
you
encountered.
How
would
you
describe
your
students?
department?
school?
What
did
people
value?
What
did
you
have
to
learn
and
do
to
work
in
that
space?
Think
about
your
second
teaching/academic
job
and
the
students
you
encountered.
How
would
you
describe
your
students?
department?
What
did
you
use
from
your
first
job
to
help
you
in
your
second
job?
What
did
you
have
to
learn
and
do
to
work
in
that
space?
3. Warm
Up
Culture
has
been
characterized
as
the
consistent
ways
in
which
people
experience,
interpret,
and
respond
to
the
world
around
them;
It
represents
the
“ways
of
being”
of
a
collec5ve
popula5on
(Marshall,
2002,
p.8)
As
an
African
American
female
and
Na5ve
New
Yorker,
I
experienced
culture
shock
when
I
moved
to
Maryland
and
then
to
Georgia.
Research
is
oWen
biographical.
4. Overview
Background
Overview
of
MCMD
Descrip5on
of
the
Unit
Tool
list
Ac5vity
and
Preliminary
Findings
Analysis
Ac5vity
Conclusions
and
Implica5ons
Audience
Feedback
and
Sugges5ons
5. Background
The
rela5onship
between
culture
and
learning
is
well
documented
in
the
literature
(Boaler,
2006;
Engle,
2006;
Gu5errez
&
Rogoff,
2003)
Mathema5cs
classrooms
are
cultural
spaces
where
various
forms
of
knowledge
and
self
are
validated
(Nasir,
Hand,
and
Taylor,
2008)
6. Background
Teacher
educa5on
ins5tu5ons
are
responsible
for
challenging
Preservice
teachers
to:
Cri5cally
reflect
and
discuss
issues
of
diversity
(de
Freitas,
2008;
Kidd
et
al,
2008;
Leonard
&
Evans,
2008;
Rousseau
&
Tate,
2003)
Understand
and
learn
how
to
recognize
students’
cultural
backgrounds
while
engaging
them
in
challenging
mathema5cs
(Kitchen,
2005;
Leonard,
2008)
Develop
mul5cultural
disposi5ons
(Dunn,
2005;
Garmon,
2004;
Mills
and
Ballantyne,
2010
)
7. Background
Mathema5cs
teacher
educa5on
researchers
are
designing
and
studying
experiences
for
preservice
teachers
to:
Classroom
observa5ons
and
lesson
planning
(Aguirre
et
al.,
2013;
de
Freitas,
2008;
Drake
&
Norton-‐Meier,
2007;
Koestler,
2012;
Leonard
&
Evans,
2012);
Field
placements
and
student
interviews
in
diverse
sekngs
(Dunn,
2005;
Fernandes,
2012;
Guiterrez,
2009;
Leland
&
Murtadha,
2011),
Family
and
community
funds
of
knowledge
projects
(Civil,
2007;
Drake
&
Norton-‐Meier,
2007;
Turner
et
al.,
2012)
8. Background
These
experiences
are
designed
to
help
PSTs
become
"culturally
conscious"
(Bennen,
1995;
Gay,
2002;
Villegas
&
Lucas,
2002)
of
their
own
cultural
socializa5on
in
mathema5cs
educa5on
and
to
understand
how
this
socializa5on
affects
their
aktudes
and
behaviors
toward
cultures
of
other
ethnic
groups.
9. Background
Teachers’
disposi5ons
toward
students’
cultural
background
play
an
important
role
in
their
teaching
prac5ces
and
effec5veness
(Thornton,
2006)
Garmon
(2004)
iden5fied
three
disposi&onal
factors
as
“cri5cal
in
facilita5ng
the
changes
that
occurred
in
[a
preservice
teacher’s]
beliefs
about
and
aktudes
toward
diversity”
(p.
204).
However,
we
need
to
further
iden5fy
the
essen5al
factors
that
comprise
cri5cal
reflec5on
and
responsive
disposi5ons
in
mathema5cs
educa5on.
Preservice
teachers
need
to
develop
disposi5ons
in
mathema5cs
that
I
call
mul$cultural
mathema$cs
disposi$ons
(MCMD)
10. Background
“habits
of
mind
including
both
cogni5ve
and
affec5ve
anributes
that
filter
one’s
knowledge,
skills,
and
beliefs
and
impact
the
ac5on
one
takes
in
classroom
or
professional
sekng.”
(Thorton,
2006,
p.
62)
11. Extending
Garmon’s
work
Garmon
(2004)
White,
Murray
&
Brunaud-‐Vega
(2013)
Openness
is
“Recep5veness
(i.e.,
open-‐mindedness)
to
others’
ideas
or
arguments,
as
well
as
recep5veness
to
diversity”
(p.
202).
Openness
is
recep5veness
to
the
role
of
culture
in
teaching
and
learning
mathema5cs,
Self-‐awareness/self-‐reflec$veness
is
“Having
an
awareness
of
one’s
own
beliefs
and
aktudes,
as
well
as
being
willing
and/or
able
to
think
cri5cally
about
them”
(p.
202).
Self-‐awareness/self-‐reflec$veness
is
perceiving
the
differences
between
one’s
own
culture
and
other
cultures,
awareness
of
personal
beliefs
about
teaching
and
learning
mathema5cs
or
mathema5cs
classroom
culture;
and
(3)
the
ability
to
think
cri5cally
about
those
issues.
Commitment
to
social
jus$ce
is
“A
sense
of
social
jus5ce
as
a
commitment
to
equity
and
equality
for
all
people
in
society”
(p.
202).
Commitment
to
culturally
responsive
pedagogy
12. MCMD
MulAcultural
mathemaAcs
disposiAons
are
intended
to
encourage
mathema5cs
teachers
to
see
mathema5cs
as
a
cultural
ac5vity
and
their
role
as
a
mediator
between
students’
culture
and
mathema5cal
learning.
Mul5cultural
mathema5cs
disposi5ons
are
characterized
by
three
disposi5onal
factors:
1. Openness
2. Self-‐awareness/Self-‐reflec5veness
3. Commitment
to
culturally
responsive
mathema5cs
teaching
13. MCMD:
Openness
Openness
is
recep5veness
to
the
role
of
culture
in
teaching
and
learning
mathema5cs.
It
includes
being
open
to:
1. others’
cultures
and
arguments
about
teaching
and/or
learning
mathema5cs
2. the
idea
that
different
cultures
may
think
about
and
do
mathema5cs
differently
than
oneself
3. the
inclusion
of
culture
in
mathema5cs
classrooms
4. the
value
of
using
culturally
responsive
strategies
to
teach
mathema5cs
14. MCMD:
Self
Awareness/Self
Reflectiveness
Self-‐awareness/self-‐reflec&veness
is
understood
as
perceiving
the
differences
between
one’s
own
culture
and
other
cultures.
Thus,
we
iden5fy
mathema5cs
teachers’
self-‐awareness/self-‐
reflec5on
as:
1. awareness
of
their
personal
culture
beyond
recognizing
that
they
are
different
than
others
2. awareness
of
their
own
beliefs
about
the
influence
of
culture
on
teaching
and
learning
mathema5cs
or
mathema5cs
classroom
culture
they
have
experienced
3. the
ability
to
think
cri5cally
about
those
issues
15. MCMD:
Commitment
Commitment
to
culturally
responsive
mathema&cs
teaching
as
the
explicit
inten5on
of
teachers
to
use
culturally
responsive
strategies
in
the
classroom.
Commitment
includes:
1. using
“the
cultural
knowledge,
prior
experiences,
frames
of
reference,
and
performance
styles
of
ethnically
diverse
students
to
make
learning
encounters
more
relevant
to
and
effec5ve
for
them”
(Gay,
2000;
p.
29)
2. holding
high
expecta5ons
for
all
children
3. exposing
children
to
rigorous
mathema5cs
16. Research
Questions
What
are
preservice
teachers’
mul5cultural
mathema5cs
disposi5ons
(MCMD)
during
a
cultural-‐awareness
mathema5cs
unit?
How
can
we
characterize
preservice
teachers’
MCMD?
17. Context
Large
College
of
Educa5on
Three
Cohorts
of
Preservice
Teachers
Elementary
(PreK-‐5),
Elementary
Mathema&cs
Methods
II
Middle
Grades
(4-‐8),
Middle
Grades
Mathema&cs
Methods
I
Secondary
(7-‐12),
Mathema&cs
Pedagogy
II
19. Context
Cultural
Awareness
Unit
The
unit
enabled
us
to
discover
preservice
teachers’
awareness
of:
1. the
role
of
culture
in
the
teaching
and
learning
of
mathema5cs
2. stereotypes
about
who
can
do
mathema5cs
3. strategies
to
teach
mathema5cs
The
unit
consisted
of
three
parts:
1. ar5cle
search
and
cri5que
2. class
discussions
3. post-‐discussion
reflec5on
20. Component Tasks Development
of
MCMD
ArAcle
search
and
criAque
Search
for
and
write
reflec5on
about
teaching
or
learning
mathema5cs
to
students
who
are
culturally
different
than
themselves
Self-‐awareness
by
iden5fying
their
own
culture
and
comparing
to
others.
Openness
by
learning
culturally
relevant
strategies.
Openness
by
learning
how
others
do
mathema5cs.
Class
discussion Share
cultures
and
strategies
discussed
in
ar5cle.
Define
culture
and
create
cultural
tool
list.
Discuss
how
culture
relates
to
mathema5cs
classrooms.
Discuss
stereotypes.
Openness
by
learning
from
peers.
Self-‐awareness/self-‐reflec5veness
by
reflec5ng
on
personal
experiences
in
the
mathema5cs
classrooms.
Post-‐discussion
reflecAon
Write
reflec5on
on
unit Openness
and
self-‐awareness
as
defined
above.
Commitment
by
encouraging
them
to
adopt
culturally
relevant
strategies.
21. Article
Critique
Preservice
teachers
are
interested
in
the
following
cultures:
Black/African
American,
Hispanic/La5no,
English
language
learner,
Low
SES,
Japanese,
Indian,
Rural
White,
Eskimo,
and
Aboriginal.
Some
of
their
ar5cles
discussed
mul5ple
cultures.
Journals
they
explored
included:
Black
Issues
in
Higher
Educa5on
Educa5onal
Leadership
Interven5on
in
School
&
Clinic,
Journal
of
American
Indian
Educa5on,
Journal
of
Learning
Disabili5es,
Mathema5cs
Teacher,
Mul5cultural
Educa5on,
NCTM
1997
Yearbook
on
Equity,
PME-‐NA
Proceedings,
Teaching
Children
Mathema5cs
Urban
Review.
22. Kola
Nut
Activity
The
kola
nut
offering
is
an
aged
cultural
tradi5on
that
is
prac5ced
in
some
West
African
socie5es.
The
offering
is
a
symbol
of
welcome,
peace,
and
hospitality
to
guests.
We
welcome
you
to
this
conversa5on
to
be
conducted
in
a
peaceful
and
posi5ve
manner.
(Ukpokodu,
2002)
23. Culture
is
the
consistent
ways
in
which
people
experience,
interpret,
and
respond
to
the
world
around
them;
It
represents
the
ways
of
being
of
a
collec5ve
popula5on…
[E]lements
of
culture
include:
food,
language,
music,
and
beliefs
about
good
and
evil…
Culture
is
a
feature
of
all
human
groups
and
is
shaped
by
historical,
social,
poli5cal,
economic,
and
even
geographical
factors.
Addi5onally,
culture
is
oWen
reinforced
(posi5vely)
through
our
contacts
with
societal
ins5tu5ons.
Whether
we
experience
such
reinforcement,
however,
largely
depends
on
the
status
posi5on
of
the
cultural
group
to
which
we
belong.
Marshall
(2002)
What
is
culture?
24. Culture
is
learned,
therefore
it
is
adaptable
and
vulnerable
to
changes.
Substan5ve
cultural
changes
rarely
occur
quickly
or
easily.
Through
conscious
(and
sub-‐conscious)
resistance,
people
tend
to
defend
and
protect
their
culture.
Our
own
cultural
ways
of
being
tend
to
strike
us
as
ordinary,
usual,
and
normal.
Consequently,
we
are
oWen
oblivious
to
the
peculiari5es
of
our
own
culture.
It
is
not
uncommon
for
other
people s
cultural
ways
of
being
to
strike
us
as
quaint,
strange,
or
even
pathological.
Marshall (2002)
A
few
common
features
of
culture…
25. Cultural
Tool
list:
What
is
your
culture?
On
the
handout,
create
a
cultural
tool
list
by
lis5ng
ten
elements
of
your
culture.
These
are
the
things
that
define
who
you
are
and
how
you
see
the
world.
Let’s
share
our
cultures.
28. Sharing
our
culture
What
cultural
elements
do
we
share?
What
cultural
elements
do
we
not
share?
Have
you
ever
been
in
a
situa5on
when
you
were
part
of
the
other
culture?
What
did
you
do?
What
cultures
exist
in
mathema5cs
classrooms?
29. Analysis:
3
Voices
The
unit
allows
us
to
examine
the
different
ways
preservice
teachers
talk
about
issues
of
culture
in
mathema5cs
educa5on.
Academic
Voice
–
Ar5cle
Cri5que
Informal/Conversa5ons
Voice
-‐
Class
Discussions
Reflec5ve
Voice
–
Post
Reflec5on
Paper
Each
voice
is
heard
because
we
are
situa5ng
them
differently.
30. Openness
Everywhere
you
go,
you
will
see
a
child
who
has
a
different
ethnicity.
I
feel
that
it
is
incredibly
important
that
I
know
and
understand
different
techniques
to
help
children
of
another
culture
relate
to
the
mathema5cs
that
I
will
be
teaching.
As
a
teacher,
my
goal
is
to
take
children
from
where
they
are,
and
help
them
to
move
a
linle
farther
in
their
educa5on.
I
also
think
that
this
ar5cle
will
help
me
to
think
outside
the
box
a
linle.
June
31. Self
Awareness/
Self
Reflectiveness
I
have
not
felt
the
oppression
that
all
of
these
minority
groups
have
endured
in
the
United
States.
Although
I
am
a
female,
I
feel
as
though
minority
groups
oWen
encounter
many
more
roadblocks
and
nega5ve
stereotypes
than
women
do.
)
I
feel
that
because
classmates
and
I
were
Caucasian,
many
of
our
teachers
assumed
we
could
handle
the
work
load
that
we
were
given,
even
if
some
of
us
were
not
academically
adept
in
that
regard.
32. Commitment
As
a
future
teacher,
I
will
try
to
be
pa5ent
with
my
students
and
try
to
communicate
mathema5cal
concepts
to
them
in
terms
that
are
culturally
appropriate
for
the
group
of
students.
Karen
As
I
read
the
ar5cle,
I
thought
back
to
myself
about
learning
math
in
elementary
school
and
I
feel
that
these
ac5vi5es
would
have
really
benefited
me
as
a
learner.
I
plan
to
use
one
or
some
of
these
ac5vi5es
in
my
future
classroom.
Judy
33. An
Exercise
in
Coding
Construct
Indicators
Openness
TL-‐
Open
to
learn
strategies
to
teach
math
to
culturally
diverse
students.
D-‐
Open
to
the
idea
that
different
cultures
may
think
about
and
do
mathema5cs
differently
from
you.
I-‐
Open
to
include
culture
in
math
classrooms.
V-‐
See
the
value
of
using
culturally
relevant
strategies
to
teach
math.
Self-‐Awareness/
Self-‐
Reflec5veness
AC-‐
Awareness
of
ones
membership
in
a
collec5ve
or
community
AP-‐
Awareness
of
their
personal
culture
beyond
recognizing
that
they
are
different
than
others
AM
Awareness
of
their
own
beliefs
about:
• Culture
in
teaching
and
learning
mathema5cs
• Mathema5cs
classroom
culture
they
have
experienced,
(ME)
CS
Thinks
cri5cally
about
the
intersec5on
of
various
culture
such
as
teacher’s
culture,
students’
culture,
classroom’s
culture,
and
school’s
culture.
Commitment
Commined
to
using
CR
teaching
and/or
using
CR
strategies
34. Conclusions
and
Implications
Preservice
teachers
need
direc5on
to
understand
“no
culture
is
monolithic;”
and
that
they,
along
with
their
students,
will
create
a
classroom
culture
that
either
supports
or
hinders
student
learning
of
mathema5cs.
For
the
most
part,
however,
the
discussion
reinforces
my
no&ons
that
we
teach
to
diversity
everyday,
no
maDer
who
is
in
our
classes.
Even
if
our
students
are
all
Caucasian,
all
from
middle-‐class
homes,
and
all
labeled
average
learners,
they
are
not
the
same.
They
learn
differently,
they
enjoy
different
ac&vi&es,
and
they
each
have
different
strengths
that
they
can
contribute
to
the
classroom.
35. Conclusions
and
Implications
Cri5cal
reflec5on
and
discussion
influenced
preservice
teachers
understanding
of
the
role
of
culture.
Mathema5cs
teacher
educators
must
explicitly
tackle
issues
of
culture,
diversity,
and
stereotypes
in
methods
courses
to
develop
PSTs’
MCMD.
The
cultural-‐awareness
unit
provides
a
reasonable
star5ng
point
for
the
iden5fica5on
and
development
of
produc5ve
prac5ces
and
habits
of
mind
in
cohorts
of
preservice
teachers.
36. Let’s
Talk:
Questions
we
are
exploring
In
what
ways
can
we
use
the
data
to
characterize
the
PSTs’
MCMD?
What
are
PSTs’
MCMD
in
various
contexts?
In
what
ways
do
MCMD
influence
classroom
instruc5on
and
learning?
How
can
we
measure
MCMD?
How
do
you
balance
teaching
mathema5cs
content
and
pedagogy
while
also
teaching
about
culture?
