The purpose of this workshop is to explore the promise and practice of culturally relevant teaching of mathematics.
Expanded Success Initiative, NYDOE, Manhattan NY
August 13, 2015
Participants explore, discuss, and interact with central notions of mathematics, reform teaching, and culturally responsive approaches in the mathematics classroom.
2. Agenda and Activities
The purpose of this
workshop is to explore
the promise and
practice of culturally
relevant teaching of
mathematics.
Participants explore,
discuss, and interact
with central notions of
mathematics, reform
teaching, and culturally
responsive approaches
in the mathematics
classroom.
Session I. But That’s
Just Good Teaching
Session II. Culturally
relevant teaching of
mathematics
Session III. Making
Culturally Relevant
Teaching Work for
Students – Designing,
Questioning
2
3. Real Goals
Examine the “real” trajectories and “stories” of
the students in our midst – particularly those
who struggle.
Examine our “real” impact on Black student
success through our teaching.
Examine our “real” mindsets that help or
hinder the success of Black students in
mathematics.
Explore how we move forward in engineering
for excellence for mathematics success for
Black students.
4. Where are We Going? Demands of
21st
Century
New
technologies
New problems
New media
New
connections
Communication
Thinking
Connecting
Inventing
Adapting
“Let’s face it, we really don’t know what
2034 will look like. We only know that it
will not look like 2014 and that what we
need then, we may not be the ones
even creating it.” LM
5. SESSION I: BUT THAT’S
JUST GOOD TEACHING
Participants explore mathematics reform
and its demands - common core. This
reform is not new although entirely
different from what we have experienced,
our parents have experienced and even
what are children's parents have
experienced.
6. The Facebook Problem Solving
Community Example
Solving this problem
in the workshop and
with friends on
facebook highlighted
the nuances of
current math reform!
7. What Was your Math Story?
“I grew up learning that mathematics was only for
some people – the ones that could get IT quickly,
that they were brighter and smarter. Because I
was one of the ‘Bright’ ones, I didn’t question
this…until I started teaching” LM
Reflect: Think about your experiences with
mathematics. What was your math identity? How
was it taught to you? Why did you excel or not?
How do you rate you overall experience through
the years?
8. Big Questions
What is Mathematics
How do you teach mathematics?
How do students learn mathematics?
How do your experiences as a student of
mathematics compare with the way in which you
teach mathematics?
Who can learn mathematics?
What do your responses to the above questions
have in common?
How do our mindsets contribute to any gaps and
issue we see in the learning of mathematics?
9. Challenge Our Story: An Act of
Courage
“Every act of teaching, of counseling, of
intervention, gives away our belief system
about each of those four questions.” LM
"If you believe that mathematics is ONLY
information, you will only present IT by giving
IT; if you only present IT; you will think only
SOME kids can get IT. If you believe that than
our kids will be destined to have decisions
made ON them and not BY them.“ LM
10. 1 Activity: Myth, Fact, or
Debatable?
1) Mathematics is a collection of related facts
involving numbers, symbols, laws and
procedures.
2) Students learn mathematics by carefully
absorbing the material and activities
presented.
3) Good teaching requires understanding the
mathematics curriculum well enough to present
it so that students understand the basics.
4) Students either have a natural talent for
excellence in mathematics—or they don’t!Consider the implications of each answer on your
current experiences with students. E.g. If I believe (1) is
Fact, what will I believe about who can do
mathematics?
11. Mathematics reform messages represent a
very deliberate message about
mathematics that is dynamics, teaching that
is student centered and the notion that all
students can learn
Mathematics Reform
12. New Vision—Mathematics for
Understanding!
Mathematics is dynamic making sense of the
world around us.
All students construct mathematical
knowledge for themselves from their own
experiences and prior knowledge.
Good teaching means teaching for
understanding centered around on what
students know and do.
13. What Does a 21st
Century
Vision for the mathematics classroom Look like
stude nts are co nfide ntly e ng ag e d in DO ING
m athe m atics,
pro ble m so lving
re aso ning
criticalthinking
co llabo ratio n
inq uiry.
te ache rs who facilitate a co m m unity o f
stude nts
rig o ro us and re le vant tasks,
building o n stude nt unde rstanding and
strate g ie s to
14. “…the new statewide Common Core
Learning Standards, which demand that
students have solid conceptual
understanding, a high degree of procedural
skill and fluency, and the ability to apply the
math they know to solve problems inside
and outside the math classroom. ” –
NYDOE
Consider this Statement
15. Common Core Differences
Fewer topics; more generalizing and linking of
concepts
Emphasis on both conceptual understanding
and procedural fluency starting in the early
grades
Focus on mastery of complex concepts in
higher math (e.g., algebra and geometry) via
hands-on learning
Emphasis on mathematical modeling in the
upper grades
http://schools.nyc.gov/Academics/CommonCoreLibrar
y/About/Standards/default.htm
16. Shifts in Mathematics Teaching
Less Emphasis More Emphasis
Emphasis on answer-getting Emphasis on Big ideas
Mathematics as definitions
and prerequisites
On connections, applications
Memorizing procedures Conjecturing, Reasoning
Teacher for right answers Students validate arguments
Classrooms of individuals Classrooms as communities
18. Activity: The Characteristics of a
Good Problem
Consider the facebook problem and reflect on
the characteristics of good problems.
Where they similar to this:
Answer is not obvious
Encourages reflection and communication
Can emerge from students/community/culture
Challenging/Risky
Mathematically Rich
19. Problem Solving Standard
Build new mathematical knowledge through
problem solving.
Solve problems that arise in mathematics and
in other contexts.
Apply and adapt a variety of appropriate
strategies to solve problems
Monitor and reflect on the process of
mathematical problem solving
The only way to build new knowledge is through novel situations like
problem solving
20. Fundamental Forces Working
Against Our Work
a) Faulty notions about African American and
Hispanic students and their experiences
b) Resistance to equity notions because of the
protection of privilege
c) Confusion about the nature of mathematics
and mathematics teaching; and
d) Misinformation and miscommunication
between the various stakeholders.
22. Will we have the courage to move from our
“experiences” of the past – how we were
taught and perceived? It is our biggest
challenge. LM
What Holds Us Back? Four
Forces
23. A New View
Mathematics is
dynamic sense
making of the world
around us through
modeling, the study of
patterns, relationships
and function
Mathematics is the
new civil right – Bob
Moses
“Mathematics is THE
21st
century Literacy”
Mathematics is
almost always used to
make decisions about
people, resources,
and things – Bill Tate
“Not believing a child
can do mathematics
is as immoral and not
believing they can
read or write”
24. SESSION II: CULTURALLY
RELEVANT TEACHING OF
MATHEMATICS
A Culturally Relevant Vision of Teaching
Mathematics has in it the power to do
what has not been done enough – to
reposition students and most importantly,
transform teachers.
25. Teachers struggled to see mathematics as
a relevant, cultural discipline from which
cultural and societal inquiry can emanate
and flourish (Matthews, 2003)
Challenging Obstacles in
Responsive Teaching
26. Even when mathematics tasks are around
the context of students’ lives, instruction
may fail to maximize its potential to engage
students (Enyedy & Mukhopadyay, 2007).
Challenging Obstacles in
Responsive Teaching
27. Students of color are often subjected to
instructional strategies that emphasize
authoritative, didactic, and/or whole group
instruction (Gay, 2000).
Challenging Obstacles in
Responsive Teaching
28. Culturally Relevant Pedagogy
To empower students intellectually, socially, emotionally, and
politically drawing from their individual, cultural and community
identities.
The focus will be on academic success, honoring cultural AND
community identities, AND a potential to participate in a just, caring
society.
Culturally Relevant teachers are relationship driven, caring and see
all students and their communities– particularly those who have not
been served well in school mathematics– as possessing untapped
promise for being successful in the mathematics classroom..
29. How? The “Culturally Relevant”
Mathematics Teacher
Will transcend the reality of mathematics reform,
standards, and accountability..
Challenge the ‘cultureless’ promotion of school math.
Build from the cultural experiences of students.
See excellence in mathematics achievement as within
the possibilities of all students.
Challenge inequitable math curriculum and course
structure.
Uses math classroom as a site of liberatory practice.
Reflect: Is this possible? Has your training
and background prepared or exposed you
to this
30. How? Deliberate Shifts into Culturally
Relevant Teachers: Amplifying Reform
Teachers should:
encourage multiple
perspectives and
problem solving
methods;
probe to redirect or
focus student thinking;
draw out student
thinking;
identify misconceptions;
and
encourage students to
revise thinking.
Build from student
cultural thinking
Seeks out societal/community
contradictions. Empowers
students as change agents
Sees ALL children
as problem solvers
Reform Language The shift for CRT teachers
31. Beyond “Surface” Teaching of
Mathematics
Teachers begin to question the “privilege” status
surrounding school mathematics
Teachers consider experiences where
mathematics is see as a means to navigate the
world – not an end.
Teachers begin to emphasize critical thinking
about the world around them using
mathematics.
Teacher begins to extend the classroom,
building collective relationships, to include
community. The mathematics learning
experience moves beyond the “my” as in “my
students” to the “our” as in “our students”.
33. CRTM: Criticalm athe m atical
thinking
Critical mathematical thinking involves viewing
mathematical knowledge critically, which
includes making conjectures, developing
arguments, investigating ideas, justifying
answers, validating one’s thinking
– Principle s and Standards fo r Scho o lMathe m atics (NCTM, 20 0 0 )
34. CRTM: Building on Student’s
Informal Knowledge
Effective mathematics teaching requires
understanding what students know and that teachers
should build on students’ previous experiences
– Principles and Standards for School Mathematics (NCTM, 2000)
35. Our Limitations
Teachers’ orientations and beliefs about “others”
are limiting and harmful.
Teachers may see culture as only belonging to “other”
people and may automatically default to “bad”
perceptions (rap, hip-hop).
Teachers’ beliefs and knowledge about
mathematics may be too limiting and rigid.
May believe mathematics is only about written numbers.
Teachers may be unwilling to question “privilege” status,
being good in mathematics affords.
36. Additional Reading
36
Ladson-Billings, G. (1994). The Dre am ke e pe rs: Succe ssfulte ache rs o f African
Am e rican childre n. San Francisco, CA: Jossey-Bass, Inc.
Leonard, J. (2008). Culturally Spe cific Pe dag o g y: Strate g ie s fo r Te ache rs and
Stude nts. New York, NY: Routledge.
Martin, D.B. (2009). Liberating the production of knowledge about African
American children and mathematics. In Math Teaching, Learning and Liberation
in the Lives of Black Children. New York, NY: Routledge.
Matthews, L., Jones, S., & Parker, Y.A. (2012). Advancing a framework for
culturally relevant, cognitively demanding mathematics tasks. In J. Leonard & D.
Martin (Eds.),The brilliance o f Black childre n in m athe m atics: Be yo nd the
num be rs and to ward a ne w disco urse .
Nieto, S. (2010). The Lig ht in The ir Eye s: Cre ating MulticulturalLe arning
Co m m unitie s. New York, NY: Teachers College Press.
Stein, M. K., Smith, M. S., Henningsen, M. A., & Silver, E. A. (2000).
Im ple m e nting standards-base d m athe m atics instructio n: Acase bo o k fo r
pro fe ssio nalde ve lo pm e nt. New York, NY: Teachers College Press.
Tate, W.F. (1995). Returning to the root: A culturally relevant approach to
mathematics pedagogy. The o ry Into Practice , 34(3), 166-173.
37. Additional Reading
37
Gutstein, E., Lipman, P., Hernandez, P., and de los Reyes, T. (1997). Culturally
relevant mathematics teaching in a Mexican American context. Jo urnalfo r
Re se arch in Mathe m atics Educatio n, 28 (6), 709-737.
Irvine, J. J. (2010). Culturally relevant pedagogy. The Educatio n Dig e st, 7 5(8),
57-61.
Ladson-Billings, G. (1995). But that’s just good teaching! The case for culturally
relevant pedagogy. The o ry Into Practice , 34(3), 159-165.
Leonard, J., and Guha, S. (2002). Creating cultural relevance in teaching and
learning mathematics. Te aching Childre n Mathe m atics, 9 (2), 114-118.
Moses, R. P. and Cobb, C. E. (2001). Radicale q uatio ns: m ath lite racy and civil
rig hts. Boston: Beacon Press.
Nelson-Barber, S. and Estrin E. T. (1995). Bringing Native American
perspectives to mathematics and science teaching. The o ry into Practice , 34(3),
174-185.
38. The Brilliance o f Black Childre n in
Mathe m atics: Be yo nd the Num be rs and
To ward a Ne w Disco urse
Counters the “deficit” thinking
regarding Black children and
their achievement in
mathematics
15 chapters, five themes
Cultural-historical perspectives
Policy and Black children’s
mathematics education
Learning and learning
environments **
Student identity and student
success
Preparing teachers to embrace
the brilliance of Black children
39. SESSION III: MAKING
CULTURALLY RELEVANT
TEACHING WORK FOR
STUDENTS – DESIGNING,
QUESTIONING
A Culturally Relevant Vision of Teaching
Mathematics has in it the power to do
what has not been done enough – to
reposition students and most importantly,
transform teachers.
40. How? Using Culturally Relevant
Mathematics Tasks
Mathematics tasks THROUGH which students
mathematize their world, their communities,
and their collective experiences.
Tasks which require that students inquire
about themselves, others and the world
around them.
41. Four Levels of Cognitive Demand
Me m o rizatio n – recall known facts
Pro ce dure s witho ut Co nne ctio ns to
understanding, meaning, or concepts – apply
known procedures to get a predictable answer
Pro ce dure s with Co nne ctio ns to understanding,
meaning, or concepts – apply known
procedures in a new context to get an answer
from which one learns something new
Do ing m athe m atics – develop new procedures
or concepts
42. The CRCD Framework
We developed a framework for building
and analyzing relevant and responsive
tasks for children
We want educators to think long and
hard about the lives of children as they
operationalize it in the mathematics
classroom
Guidance on how to think about
culturally relevant teaching in their
practical classrooms
45. Activity
Take a look at the list of tasks created by
teachers. Does they accomplish responsive
teaching in any way? Rate them using the
checklist!
What are the strengths?
What are the challenges?
How would you grow the lessons?
How does the lesson reflect the four critical
questions?
47. Discuss with a partner or small group, how
to modify the following problem to become
more culturally relevant (or make up your
own problem)
Culturally Relevant Cognitively
Demanding Mathematics Task
47
48. Assessing the Assessment Rubric
of Culturally Relevant,
Cognitively Demanding Mathematics
Tasks
In your group, review the CRCD rubric
Is the rubric appropriate for determining if
a cognitively demanding task is culturally
relevant? Why or why not? What is
missing? What was helpful?
49. A Culturally Relevant Vision
of Teaching Mathematics has
in it the power to do what has
not been done enough – to
reposition students and most
importantly, transform
teachers.
Session I. That's Just Good Teaching
Participants explore mathematics reform and its demands - common core. This reform is not new although entirely different from what we have experienced, our parents have experienced and even what are children's parents have experienced. There has been in fact a conflict of two competing stream. The reform stream is what is undergirding common core curriculum.
Pyramid Problem
Analysis of the problem and teacher
Characteristics of a good problem and 21st century visions
Activity
- Large and Small Group Discussion - Participants consider the mathematics experiences across the several decades of New Math. Back to Basics. Problem Solving. Calculators. Common Core
- Mixed poster participants consider how each of the four questions are 'secretly' and explicity spoken.
- PowerPoint/math problem solving activity
Materials: 6 sets of post its. A package of four big post it posters
Key questions to consider
What is mathematics?
How does the brain learn mathematics?
How should mathematics be taught
Who Can learn mathematics?
Session II. Culturally relevant teaching of mathematics
CRT takes reform and stretches to include deliberate attention to cultural thinking, content and norms. This counters stereotypical views of black children, where they come from, their communities, and aspiration. Ultimately CRT is oppositional pedagogy and seeks to empower students by utilizing critical content and policy. A jurisdiction focused on incorporating culturally relevant practice across its systems will consider programs, practice, policy, Gutierrez model suggest you focus on three things: building on cultural knowledge and critical societal thinking
Key questions to consider
Can we define mathematics differently enough to DRAW from backgrounds, dreams and aspirations of communities and cultures?
Can we overcome our innate/adopted/ingrained/overheard/institutional ideas about Black and Hispanic children and communities?
What is culturally relevant pedagogy? What is its key elements? for Policy? Practice? Perceptions? Programs?
Session III. The Students in Front of You: Making Cultural Relevance Work!
Participants in this session will learn about cognitively demanding tasks and maintaining the cognitive demand, while ensuring that the tasks are also culturally relevant. Participants will utilize and critique the usefulness of a CRCD (culturally relevant cognitively demanding) task rubric to evaluate a set of teacher-created tasks. In addition, participants will create and discuss a CRCD task in groups in order to be able to use this tool in their future lesson planning. The discussions and interactive nature of this session will also add to each participant's knowledge about what culture means in the classroom with an emphasis on race and ethnicity.
Activities
Participants examine whether proposed problems can help change the dynamics/discourse and engagement in their mathematics classrooms.
Participants examine some tasks that have been created on PowerPoint. Note. They are imperfect, problematic and ever changing. But so is math
What is “conjecturing”?
How do you “build new mathematical knowledge”?
model suggest you focus on three things: building on cultural knowledge and critical societal thinking
model suggest you focus on three things: building on cultural knowledge and critical societal thinking