unlocking reform and culturally relevant teaching of mathematics

"UNLOCKING CULTURALLY RESPONSIVE

TEACHING FOR MATHEMATICS"

Lou Edward Matthews, Ph. D

August 13, [email protected]

Agenda and ActivitiesThe 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

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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.

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

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.

The Facebook Problem Solving Community Example

Solving this problem in the workshop and with friends on facebook highlighted the nuances of current math reform!

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?

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?

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

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?

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

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.

What Does a 21st Century Vision for the mathematics classroom Look like

students are confidently engaged in DOING mathematics,

problem solvingreasoningcritical thinkingcollaborationinquiry.

teachers who facilitate a community of students rigorous and relevant tasks, building on student understanding and

strategies to develop procedural and conceptual knowledge

“…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

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/CommonCoreLibrary/About/Standards/default.htm

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

…Common Reality

Review

Teacher Presents

New Concept

Guided Practice

"Watch Me"

Independent Practice

"Go for It"

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

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

Fundamental Forces Working Against Our Worka) Faulty notions about African American and

Hispanic students and their experiencesb) 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.

Reframing of African American Mathematics Achievement

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

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” – LM

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”

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.

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

Even when mathematics tasks are around the context of students’ lives, instruction may fail to maximize its potential to engage students (Enyedy & Mukhopadyay, 2007).


Students of color are often subjected to instructional strategies that emphasize authoritative, didactic, and/or whole group instruction (Gay, 2000).


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..

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

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

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”.

Engineering Culturally Relevant Teaching for all students

CRTM: Critical mathematical thinking

Critical mathematical thinking involves viewing mathematical knowledge critically, which includes making conjectures, developing arguments, investigating ideas, justifying answers, validating one’s thinking

– Principles and Standards for School Mathematics (NCTM, 2000)

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)

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.

Additional Reading36

Ladson-Billings, G. (1994). The Dreamkeepers: Successful teachers of African American children. San Francisco, CA: Jossey-Bass, Inc.

Leonard, J. (2008). Culturally Specific Pedagogy: Strategies for Teachers and Students. 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 of Black children in mathematics: Beyond the numbers and toward a new discourse.

Nieto, S. (2010). The Light in Their Eyes: Creating Multicultural Learning Communities. New York, NY: Teachers College Press.

Stein, M. K., Smith, M. S., Henningsen, M. A., & Silver, E. A. (2000). Implementing standards-based mathematics instruction: A casebook for professional development. New York, NY: Teachers College Press.

Tate, W.F. (1995). Returning to the root: A culturally relevant approach to mathematics pedagogy. Theory Into Practice, 34(3), 166-173.

Additional Reading37

Gutstein, E., Lipman, P., Hernandez, P., and de los Reyes, T. (1997). Culturally relevant mathematics teaching in a Mexican American context. Journal for Research in Mathematics Education, 28(6), 709-737.

Irvine, J. J. (2010). Culturally relevant pedagogy. The Education Digest, 75(8), 57-61.

Ladson-Billings, G. (1995). But that’s just good teaching! The case for culturally relevant pedagogy. Theory Into Practice, 34(3), 159-165.

Leonard, J., and Guha, S. (2002). Creating cultural relevance in teaching and learning mathematics. Teaching Children Mathematics, 9(2), 114-118.

Moses, R. P. and Cobb, C. E. (2001). Radical equations: math literacy and civil rights. Boston: Beacon Press.

Nelson-Barber, S. and Estrin E. T. (1995). Bringing Native American perspectives to mathematics and science teaching. Theory into Practice, 34(3), 174-185.

The Brilliance of Black Children in Mathematics: Beyond the Numbers and Toward a New Discourse

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

SESSION III: MAKING CULTURALLY RELEVANT TEACHING WORK FOR STUDENTS – DESIGNING, QUESTIONING


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.

Four Levels of Cognitive Demand Memorization – recall known facts Procedures without Connections to

understanding, meaning, or concepts – apply known procedures to get a predictable answer

Procedures with Connections to understanding, meaning, or concepts – apply known procedures in a new context to get an answer from which one learns something new

Doing mathematics – develop new procedures or concepts

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

Framework for Culturally Relevant,

Cognitively Demanding

Mathematics Tasks

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Assessment Rubric of Culturally Relevant,Cognitively Demanding Mathematics Tasks

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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?

So You Think You Can Draw

Your sister loves street art. You would like to recreate one of her favorite pieces for her birthday. You decide to create a poster board replica of this piece even though you’re not an artist. Suddenly a deeper side of the image strikes you.

This is going to be easy! You notice the tip of his nose at (0,0), the bottom lip at (0,-2)……Where is his right eye, …the bottom of his chin, …..the large patch of grass? What is the domain and range? Explain your reasoning. Try creating a replica on poster board.

photograph © copyright 1994 Ted Mikalsen

Artwork ©1994 Dave Kinsey (aka Büst) in Atlanta, GA. Photographer © 1994 Ted Mikalsen. Used with permission from www.graffiti.org

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http://www.graffiti.org/

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

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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?