1. What Is Your Math Identity: Reconsidering Equity Based Practices
Lisa Ashe & Denise Schulz
NC Department of Public Instruction

2. Disclaimer
Presentation materials are for registered participants of the 66th Conference on Exceptional Children. The information in this presentation is intended to provide general information and the content and information presented may not reflect the opinions and/or beliefs of the NC Department of Public Instruction, Exceptional Children Division. Copyright permissions do not extend beyond the scope of this conference. 

3. Welcome “Who’s in the Room?”

4. Which describes your belief?
Mathematics for all
Mathematics for all.
Mathematics for “all”
Mathematics for all?
Mathematics for all!

5. Perceptions of Access and Equity
Access & Equity
Parents
Teachers
Students
Administrators
Community
Perceptions of Access and Equity

6. What teachers believe is important influences the decision that they make about what content to teach, how to teach it, and, in many cases, who should receive the content.
Aguirre, Mayfield-Ingram &Martin, 2013

7. Identity

8. What is identity?
The ways that people come to conceptualize themselves and others and how they act as a result of those understandings.
Cornell and Hartmann, 1998

9. Who Am I?
To me
To my students
To my colleagues
To my school/district

10. What’s Your Identity?
Take a moment to think about how you identified yourself.
What descriptors did you use?
What is your identity as a math learner?

11. Think about you as student in your classroom.
Mathematics Identity
beliefs about one’s self as a mathematics learner,
one’s perceptions of how others perceive them as a mathematics learner,
beliefs about the nature of mathematics,
engagement in mathematics, and
perception of self as a potential participant in mathematics.
Solomon, 2009
Think about you as student in your classroom.

12. Mathematics Identity
The dispositions and deeply held beliefs that students develop about their ability to participate and perform effectively in mathematical contexts and to use mathematics in powerful ways across the contexts of their lives.
Aguirre, Mayfield-Ingram &Martin, 2013

13. The nature of mathematics learning experiences that a teacher had in his or her own schooling has a powerful influence on the mathematics teacher identity that he or she develops.
Aguirre, Mayfield-Ingram &Martin, 2013

14. It is important for teachers to understand the impact of the instructional decisions that they make, and the social and academic norms that they create, on a child’s mathematics identity.
Aguirre, Mayfield-Ingram, Martin, 2013

15. Reflect Who are our students? Are they equally smart?
What keeps us (and them) from seeing how smart they are?
Should we teach them all the same way?

16. What is your identifier?
What does it mean to be a learner and doer of mathematics in the context of being ….?
Male
Black
Asian
Hispanic
White
Female
Affluent
English Language Learner
Specific Learning Disabled
Poor
What is your identifier?

17. Reflect Where do these words, phrases, images, stereotypes comes from?
How might they be consequential in the lives of students?
How might they be consequential in the context of teaching and professional practice?

18. Calvin’s Story

19. Interwoven Identities
Am I not being recommended for placement in pre-algebra course because I am no longer a good student who is good at mathematics?
Am I not being recommended because I am perceived as a behavioral problem?
Am I not being recommended because middle school is different from elementary?
Am I not being recommended for placement in pre-algebra course because I am a Black boy?

20. Labeling frames how we think about kids in very subtle ways.
Even labels we think of as
positive can hurt students.
Labeling frames how we think about kids in very subtle ways.

21. Identity Affirming or Identity Challenging
Identity-affirming behaviors influence the ways in which students participate in mathematics and how they see themselves as doers of mathematics.
We see identity-affirming criteria emerging as learners are labeled as “smart,” “gifted,” “proficient,” “at-risk,” or “on grade-level”.

22. Identity Affirming
We affirm mathematics identities by providing opportunities for students to make sense of and persevere in challenging mathematics.
Facilitate meaningful mathematical discourse
Support productive struggle in learning mathematics
Elicit and use evidence of student thinking
This kind of teaching cultivates and affirms mathematical participation and behaviors.
NCTM, 2014
A student who identifies themselves as being at good mathematics might exhibit behaviors and participate to maintain their status as person who is “smart” or good at mathematics.
Teachers affirm mathematics identities by providing opportunities for students make sense of and preserve in challenging mathematics.
Students should be engage with mathematics that requires active participation, asking questions, problem posing, and reasoning.
This kind of teaching values all students’ thinking and uses pedagogical practices, such as differentiated tasks, mixed ability groupings, and publicly praising contributions and perseverance, to cultivate and affirm mathematical participation and behaviors (NCTM 2014).

23. Status
Defined as the perception of students’ academic capability and social desirability
Indicators of status issues in the classroom:
Participation
Listening
Body Language/Engagement
Organization of materials and resources
Inflated Talk about Self or Others

24. Status vs. Ability
“As long as we have a simplistic view of some students as smart and others as struggling, we will have status problems in our classrooms.”
Horn, 2012

25. Status Interventions
Establishing and maintaining norms that support equal-status interactions
Multiple ability treatment through random group assignment.
Reconsidering mathematical competence as something other than quick and accurate calculation.
Recognize multiple mathematical abilities.
….students begin to reimagine themselves and their peers in the context of their competence and not their deficits.

26. Assigning Competence Posing interesting questions Extending ideas
Making astute connections
Working systematically
Representing ideas clearly
Developing logical explanations

27. Identity & Motivation
Understanding the strengths and motivations that serve to develop students’ identities should be embedded in the daily work of teachers.
Mathematics teaching involves not only helping students develop mathematical skills but also empowering students to seeing themselves as being doers of mathematics.
This understanding of students’ identities gives teachers insights to how and why some students might make positive connections with mathematics and others do not.
Teachers can use this understanding to provide opportunities for students to use mathematics to examine personal, communal, and social contexts.
In providing these opportunities, students may find the motivation and connections with mathematics to see the relevance for their future thus developing a mathematics identity.

28. A focus on learning rather than on labeling is critical
A focus on learning rather than on labeling is critical. Finding ways to build on resilience, rather than focus solely on conditions that make resilience necessary should be primary goals for teachers.
Aguirre, Mayfield-Ingram &Martin, 2013

29. What are your beliefs?

30. How does your identity influence your beliefs?

31. Sort the Beliefs
Unproductive Beliefs
handout

32. Table Talk
What does it mean for students if teachers and/or administrators ascribe to the unproductive beliefs? How do we move from unproductive to productive beliefs?

33. Arguments for Inequity Arguments for Equity
If we spend money in one place, we don’t have it to spend elsewhere.
If my child is forced to collaborate with poor students, he or she will be pulled down academically.
Changing paradigms is difficult, especially when it involves changing attitudes about race and resources!
Arguments for Equity
It’s the right thing to do.
The most advantage and successful students do even better in an equitable school setting.
Financial support for schools may actually increase.
Parental, staff, and community support grows.
The alternative to equity is catastrophic.

34. Unfounded Predictions Are Inequitable
Equity means…
“being unable to predict students’ mathematics achievement and participation based solely upon characteristics such as race, class, ethnicity, sex, beliefs, and proficiency in the dominant language”
Gutiérrez, 2007, p. 41

35. Superficial Reasoning
When teachers inherit a class of students who struggle with mathematics or have been identified as low achievers, too often they assume that procedural, low-level remediation is most appropriate
Aguirre, Mayfield-Ingram & Martin, 2013

36. Deficit Views of Mathematical Learning
Undermines Growth Mindset
“You’re a natural! I love that.”
“Well, at least you tried!”
“Great Job! You’re so
talented!”
“This is hard, Don’t feel bad if you can’t do it.”
“Maybe this just isn’t your strength. Don’t worry—you have other things to contribute.”
Promotes Growth Mindset
“You’re a learner! I love that.”
“That didn’t work. Let’s talk about how you approached it and what might work better.”
“Great job! What’s one thing that could have been even better?”
“This is hard. Don’t feel bad if you can’t do it yet.”
“I have high standards. I’m holding you to them because I know we can reach them together.”

37. Overcoming Obstacles
Educators need to identify, acknowledge, and discuss the mindsets and beliefs that they have about students’ abilities.
Fixed Mindset: Believe that you are either smart or you are not
Growth Mindset: Intelligence and “smartness” can be learned and that the brain can grow from exercise
Dweck, 2006
a ‘growth mindset’ then they believe that intelligence and ‘smartness’ can be learned and that the brain can grow from exercise. The implications of this mindset are profound -- students with a growth mindset work and learn more effectively, displaying a desire for challenge and resilience in the face of failure
‘fixed mindset’ believe that you are either smart or you are not. When students with a fixed mindset fail or make a mistake they believe that they are just not smart and give up. Such students frequently avoid challenge, preferring instead to complete easier work on which they know they will succeed.
Identity affirming

38. Access and Equity
An excellent mathematics program requires that all students have access to a high quality mathematics curriculum, effective teaching and learning, high expectations, and the support and resources needed to maximize their learning potential.
Principles to Actions, p. 59

39. Equity Is Fairness
Equity does not mean that every student should receive identical instruction; instead, it demands that reasonable and appropriate accommodations be made as needed to promote access and attainment for all students.
Principles and Standards for School Mathematics, NCTM 2000, p. 12

40. Access Supports Equity
The concept of equity includes “the equitable distribution of material and human resources, intellectually challenging curricula, educational experiences that build on students’ cultures, languages, home experiences, and identities; and pedagogies that prepare students to engage in critical thought and democratic participation in society”
Lipman, 2004, p. 3

41. Equity Based Teaching Practices
Going deep with mathematics
Leveraging multiple mathematical competencies
Affirming mathematics learners’ identities
Challenging spaces of marginality
Drawing on multiple resources of knowledge

42. Reflect
In what ways do we withhold from some students the opportunity to engage in, think about and discuss mathematics?

43. Agency

44. Sense of Agency
A high sense of agency is having a high degree of self-exploration that is associated with a high degree of self-direction in determining one’s life course.
Côté & Schwartz, 2002

45. High Sense of Agency
Students with a high sense of agency make decisions about their participation in mathematics.
“I gotta excel in everything I do. Be the best that I can be…being the best means doing your work, asking questions, and being involved in class.” (Bilal)
“Good math students are focused, do their work, and want to make A’s all the time…I am a good math student.” (Andre)
A high sense of agency is having a high degree of self-exploration that is associated with a high degree of self-direction in determining one’s life course (Côté & Schwartz, 2002).
Students with a high sense of agency make decisions about their participation in mathematics.
Bilal show a high sense of agency by stating, “I gotta excel in everything I do. Be the best that I can be…being the best means doing your work, asking questions, and being involved in class.”
Andre’s sums up his sense of agency by stating, “Good math students are focused, do their work, and want to make A’s all the time…I am a good math student.”
In these statements we see a high sense of agency that is resistant to the negative identities imposed on them because these boys perceive themselves as having a sense of control over their academic success because they knew that, in order to maintain their good standing in mathematics, they needed to be participatory in the mathematics classroom.

46. With Math I Can

47. Overcoming Obstacles
Access to rigorous, high-quality mathematics, taught by teachers who not only understand mathematics but also understand and appreciate learners’ social and cultural contexts in meaningful ways.
Classroom environments that foster a sense of community that allows students to express their mathematical ideas.
Context

48. Bus Pass Problem
It costs $1.50 each way to ride the bus between home and work. A weekly bus pass is $16. Which is the better deal, paying the daily fare or buying the weekly pass?

49. Many students reasoned about and solved the problem in a way test designers did not anticipate.
The assessment item was based on a particular set of assumptions.
Many students solved the problem under a different set of assumptions based on their daily lives and social realities.

50. Mathematical understanding is not disconnected from students’ social realities. Students with different backgrounds and experiences draw on these to make sense of ideas and problem-solving situations.
Aguirre, Mayfield-Ingram & Martin, 2013

51. Equity Based Teaching Practices
Going deep with mathematics
Leveraging multiple mathematical competencies
Affirming mathematics learners’ identities
Challenging spaces of marginality
Drawing on multiple resources of knowledge

52. Reflect
“We can never fully understand what (or how) inequitable beliefs and practices affect another person.”
Cathy Seeley

53. Which describes your belief?
Mathematics for all
Mathematics for all.
Mathematics for “all”
Mathematics for all?
Mathematics for all!

54. “Isn’t it time we started acting how we say we believe?”
Roberto Zamora

55. What questions do you have?

56. Follow Us! NC Mathematics www.facebook.com/NorthCarolinaMathematics

57. maccss.ncdpi.wikispaces.net

58. Dr. Robert Berry at UNCG

59. DPI Mathematics Section
Kitty Rutherford
Elementary Mathematics Consultant
Denise Schulz
Lisa Ashe
Secondary Mathematics Consultant
Joseph Reaper
Dr. Jennifer Curtis
K – 12 Mathematics Section Chief
Susan Hart
Mathematics Program Assistant 59

60. For all you do for our students!