Addressing the Equity Principle in the Mathematics ClassroomAuthor(s): Tonya G. Bartell, Margaret R. Meyer, Libby Knott and Thomas A. EvittsSource: The Mathematics Teacher, Vol. 101, No. 8 (APRIL 2008), pp. 604-608Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/20876221 .

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CONNECTING

Tonya G. Bartell and Margaret R. Meyer

Addressing the Equity Principle in

the Mathematics Classroom

The publication of Curriculum and Evalua tion Standards (NCTM 1989) marked the

beginning of a period of significant change in mathematics education. However, that document

and many contemporaneous calls for reform lacked a clear focus on equity (Meyer 1989). A decade later, Principles and Standards for School Mathematics

(NCTM 2000) began to address that shortcoming. The first of the six Principles is the Equity Principle: "Excellence in mathematics education requires equity?high expectations and strong support for all students" (NCTM 2000, p. 12). The placement of the Equity Principle as first on the list highlights its importance as a cornerstone for the other Prin

ciples. It raises "an essential goal and a significant challenge" (p. 12) that sets the stage for the remain

ing Principles and Standards. But what does equity mean, and how will we recognize it when we see it?

A yearlong professional development seminar for secondary mathematics teachers that focused

This department consists of articles that bring research insights and findings to

an audience of teachers and other mathematics educators. Articles must make

explicit connections between research and teaching practice. Our conception of

research is a broad one; it includes research on student learning, on teacher think

ing, on language in the mathematics classroom, on policy and practice in math

ematics education, on technology in the classroom, on international comparative

work, and more. The articles in this department focus on important ideas and

include vivid writing that makes research findings come to life for teachers. Our

goal is to publish articles that are appropriate for reflection discussions at depart ment meetings or any other gathering of high school mathematics teachers. For

further information, contact the editors.

Libby Knott, knott@mso.umt.edu

University of Montana, Missoula, MT 59812

Thomas A. Evitts, taevit@ship.edu

Shippensburg University, Shippensburg, PA 17257

on the Equity Principle opened with this ques tion: "What is equity in a mathematics classroom?" The question was posed to provide the teachers an

opportunity to make their conceptions of equity explicit. We began with the assumption that teachers would have varying conceptions of equity (Secada 2003) and that these would be largely unexamined

(King 1991). Making these conceptions explicit, we believed, could have implications for classroom

practice (Borko and Putnam 1996; Weissglass 2003). This article summarizes what we learned from these teachers about their conceptions of equity and

highlights a first step teachers can take in working toward equity in their mathematics classrooms.

THE CONTEXT This seminar was offered to high school mathemat ics teachers as a part of the work of the Diversity in Mathematics Education Center for Learning and

Teaching at the University of Wisconsin-Madison.

Twenty-six teachers from the same school district met once a month, for two and a half hours per seminar session, over the course of the school year. All four of the district's high schools (grades 9-12) were represented at the seminar, and these teachers totaled about 25 percent of the district's high school

mathematics teachers.

Each month, the seminar participants were asked to reflect on readings related to equity in mathemat ics education (see, e.g., Gutstein [2003]; Ladson-Bill

ings [1995]; Moschkovich [1999]; Secada [2008]). Participants explored such topics as conceptions of

equity, the effects of pedagogy on student classroom

participation, teacher expectations, tracking, institu tional racism, support for English language learners in mathematics, culturally relevant pedagogy, and the

teaching of mathematics for social justice. Further,

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participants engaged in activities in their own math ematics classes that were related to seminar read

ings and discussions. They observed one another's classrooms to examine student participation patterns, gathered data about which students were multilin

gual (so that they could access this information as a resource), and asked their students about their

thoughts on gender differences in mathematics learn

ing. Finally, during the seminar itself, participants engaged in activities and discussions structured so that their reflections were focused on how these top ics intersected with their classroom practices.

Data collection and analysis In an effort to document teachers' conceptions of equity, seminar participants were given pre and post-seminar surveys. The surveys included

questions on teachers' expectations for low- and

high-performing mathematics classes, their beliefs about the nature of mathematics and their role as a

teacher, and their definitions of equity. One specific question included on both the pre- and post-semi nar surveys was, "How would you define equity in a mathematics classroom?" We also collected teach ers' written reflections and assignments that were informed by seminar readings and activities.

Our analysis consisted of reviewing teachers'

survey responses several times while looking for

recurring themes across teachers' statements. After

multiple passes through the data, as themes emerged, we compiled a list of codes by aggregating similar

responses. The coding scheme aimed to characterize the nature and content of teachers' comments.

TEACHERS' CONCEPTIONS OF EQUITY Four conceptions of equity emerged from this examination of teachers' responses: (1) equity is about instruction; (2) equity is about creating a

specific classroom environment; (3) equity is about

equal opportunity; and (4) equity is about appropri ate curriculum. These four categories are explained in detail in the sections that follow, and we discuss the implications of these conceptions for mathemat ics teachers who are attempting to take a first step toward equity in their own classrooms.

Equity is about instruction "Some students may need no, or very little, 'extra attention' to succeed, some may need more. Equity is giving all students the necessary tools/attention needed to he successful."

This statement is typical of teachers who concep tualize equity in relation to instruction (36% of

responses). Teachers whose responses fell into this

category saw equity as being determined by the teacher: It is the teacher's responsibility to ensure

that each student receives whatever he or she needs to be successful. This responsibility, according to seminar participants, includes teachers being responsive to various students' learning prefer ences. As one teacher stated, in an equitable math ematics classroom "a variety of learning styles and

problem solving methods are validated."

Equity is about creating a specific classroom environment "All students should he expected to achieve. The class room should he set up in a way to convey the expectation and make students responsible to work and achieve."

In this group of teachers (31% of responses), equity in a mathematics classroom is about creating a particu lar classroom environment. Responses in this cat

egory were focused on having high expectations for all students, as the statement above suggests. Another dimension of this category included responses related to the importance of creating a classroom environ

ment that strives to include all students and that fosters students' beliefs that they can succeed. Repre sentative of this dimension is one teacher's statement that equity is "success in a safe environment where

nobody feels they cannot achieve."

Equity is about equal opportunity "All students should have equal opportunities to reach their full potential. Gender, race, other language learn

ers, etc. should all be viewed with the same potential...."

Some teachers (20% of all responses) related equity in a mathematics classroom with equal opportunity for all students. This conception is slightly differ ent from the previous one, which was focused on teacher expectations and the creation of an inclu sive environment within a single classroom, and also includes the broader schoolwide context. This notion of equal opportunity in mathematics educa tion was often explained as students having the same opportunity to take particular mathematics courses (e.g., college preparation courses) or receive

quality mathematics instruction.

Equity is about appropriate curriculum

Equity in a mathematics classroom requires "[ujsing materials that are relevant to students' lives and using their background knowledge as a starting point for discussions of math concepts."

Twelve percent of teachers' responses fell into this final category. Here, responses centered on the

importance of making mathematics curriculum rel evant to students and building on students' life expe riences to engage more students in the mathematics. As one teacher stated, equity in a mathematics class

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room is "accessible curriculum [which is] relevant to all students, engaging?can 'hook' kids, even if they are not successful they can rebound, ideally, repre sentative of students' reality/ incorporates social jus tice." Appropriate curriculum is viewed as a means to achieving equity in a mathematics classroom.

It is worth noting that responses in each of these four categories point to the primary role of the teacher in achieving equity. Instruction, classroom environment, equal opportunity, and curriculum are all under the control of teachers. These responses reflect a belief that teachers share a responsibility in working toward equity.

This summary of our study could end here, after we note that teachers' conceptions of equity were

consistent with the Equity Principle. Teachers'

responses, like the Equity Principle, stressed the

Instruction, classroom

environment, equal opportunity, and

curriculum are all under the control

of teachers

importance of "high expecta tions and worthwhile opportu nities for all" and that "equity requires accommodating differences to help everyone learn mathematics" (NCTM 2000, pp. 12, 13). However, in the context of the seminar, it became clear that making conceptions of equity explicit did not help teachers identify particular strategies that might promote equity in their math ematics classroom. Identifying teachers' specific responsibili

ties within the larger context of equity in mathemat ics education was a primary concern of the seminar

participants and a key focus of one seminar activity.

WHOSE RESPONSIBILITY IS IT? Working toward equity may seem an overwhelm

ing task for a classroom teacher, but teachers must remember that it takes many groups of people to

work toward equity. To illustrate this point, we divided the seminar participants into groups of four or five and assigned each group one of the fol

lowing perspectives: (a) teacher, (b) student, (c) families and community, (d) school and district

administrators, (e) policymakers, and (f) university teacher educators. (This activity is adapted from a

presentation given by Fran Arbaugh of the Univer

sity of Missouri, Columbia, Mo.) These perspectives were drawn from the roles and responsibilities outlined in chapter 8 of Principles and Standards for School Mathematics (NCTM 2000). Each group was

then given multiple sheets of flip-chart paper, mark

ers, and this prompt: "We can close the achieve ment gap by Using their assigned perspective, the teachers in each group brainstormed for specific actions that could be taken to close the achievement

gap. These lists were displayed on the wall. Partici

pants moved around the room, read the lists, and added responsibilities they felt were missing before

discussing the lists as a whole group. Every group, no matter its perspective, easily identified numer ous actions that could be taken.

The majority of the discussion centered on the actions teachers could take to address the achieve ment gap. Not too surprisingly, some of these actions

closely reflected the participants' conceptions of

equity: having high expectations for all students, using appropriate pedagogy, and having an inter

esting, meaningful, and connected curriculum.

However, additional responses highlighted the role of the teacher in the larger school community (e.g., communicating with administrators as well as with

parents and community members) and the impor tance of connecting with students (e.g., caring about students and encouraging them to value education).

The teachers' reflections on this activity clearly indicated that they recognized the nature of any attempts to address the achievement gap. When they saw all the responsibilities enumerated for the differ ent groups, their own extensive list did not seem as

overwhelming. However, because few of the actions went beyond what teachers felt they were already trying to accomplish in their own classrooms, they expressed a need to get more specific and to examine these "good teaching" practices through an equity lens.

FOCUSING ON THE INDIVIDUAL STUDENT To help the teachers identify more specific actions

they might take, we asked each to identify one current student who was performing below proficiency level or with whom there was little personal connection. Over the course of one month, each teacher was to get to know his or her identified student better and use this information to guide subsequent teaching. We sug gested that teachers start with the following questions:

What is the student's racial or ethnic identity? What does the student's appearance indicate about him or her?

What is the student's family like? With whom does the student live? Does he or she have siblings?

Gather information about the student's family. What are the student's hobbies or personal inter ests outside school?

What are the student's plans beyond high school?

In addition, teachers were asked to write a one

page reflection about what they learned about this student and how it informed their teaching. Without

exception, the teachers felt that they had benefited

personally from getting to know the targeted stu dent better, and some also reported benefits for the student.

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One teacher modified her instruction (pseud onyms have been used for all students):

I have already modified my interactions with Richard

regarding tests, as I believe he needs confidence as

much as anything.

Another teacher experienced more empathy for his student:

Getting to know Cheng has helped me understand where

he's coming from when he has a question on homework

or a test. Quite often it's just a language thing and I just

have to define a word for him or rephrase something for

him. I also understand what's going on, for instance, if

he doesn't get his homework done on a particular day

because he really had to work since he's a bread winner

for his family and he is dealing with all the stress that

goes along with having to take on those responsibilities.

One teacher saw increases in student achievement:

There have been two positive results from my interven

tion with Wilfredo. The first is that he has been notice

ably more friendly when he sees me out of class. He has

smiled and said "hi" several times. The second is that

Wilfredo earned an A on the third test of the quarter. I

can't prove this was a result of the connection I made

with him, but it's a reasonable assumption.

One teacher detected a change in her student's level of engagement:

I am not quite sure how it was that Sara and I bonded.

One day she made a comment to me and I worked it

from there. When I found out she knitted, I related

that to my roommate who knits and told her that she

was actually teaching me to knit too. It is a great thing

to talk about and create some trust. Now Sara talks

to me about all kinds of things, what she does on the

weekends, what she's reading, what is going on in her

other classes, and that sort of thing. I am not too sure

how this new relationship has informed my teaching,

but I know I have created a better environment for

Sara and the rest of the class benefits from that. Sara

now answers more questions in class and it is good for

the other students to hear her answers and explana

tions. Sara is a great math student.

These responses suggest that a teacher's per sonal connection with mathematically struggling students can affect students' participation and achievement in mathematics.

CONCLUSION This study and the seminar activities suggest that, as a first step to providing support for all students

in learning mathematics, teachers should explore their conceptions of equity, their role and respon sibilities in closing the achievement gap, and their

knowledge about individual students. Explicitly identifying conceptions of equity can help teachers

recognize their role in working toward equity and

help them focus on aspects under their control?

instruction, the classroom environment, and curric

ulum. Getting to know a mathematically struggling student better can remind teachers that they are

teaching not just mathematics; they are teaching students. Developing a relationship with a student

with whom you are not connecting can serve as a

first step toward the goal of equity. As the seminar participants began to explore

their conceptions of equity and take this first step toward equity within the context of the seminar,

implications for classroom practice arose, leaving these teachers with ongoing questions about math ematics education to consider:

What are some ways teachers can create these

proposed classroom environments, and what are the results of these actions for teachers and students?

What are some ways teachers can take a tra

ditional curriculum and make it relevant to students? How does a teacher balance meeting the needs of each student, perhaps through assigning differ ent tasks for different students, with providing equal opportunity and maintaining high expecta tions for all students?

Further consideration of these questions in rela

tionship to teachers' conceptions of equity is neces

sary as teachers and teacher educators collaborate to develop additional strategies to address the

Equity Principle in mathematics classrooms.

REFERENCES Borko, H., and R. Putnam. "Learning to Teach." In

Handbook of Educational Psychology, edited by R. Calfee and D. Berliner, pp. 673-725. New York:

Macmillan, 1996.

Gutstein, E. "Teaching and Learning Mathematics for Social Justice in an Urban, Latino School." Journal

for Research in Mathematics Education 34, no. 1

(2003): 37-73.

King, J. E. "Dysconscious Racism: Ideology, Identity, and the Miseducation of Teachers." Journal of

Negro Education 60, no. 2(1991): 133-46.

Ladson-Billings, G. "Making Mathematics Meaningful in Multicultural Contexts." In New Directions for Equity in Mathematics Education, edited by W. G.

Secada, E. Fennema, and L. B. Adajian. New York:

Cambridge University Press, 1995.

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Meyer, M. R. "Equity: The Missing Element in Recent

Agendas for Mathematics Education. Peabody Jour

nal of Education 66 (Winter 1989): 6-21.

Moschkovich, J. "Supporting the Participation of Eng lish Language Learners in Mathematical Discus

sions." For the Learning of Mathematics 19, no. 1

(March 1999): 11-19. National Council of Teachers of Mathematics

(NCTM). Curriculum and Evaluation Standards for School Mathematics. Reston, VA: NCTM, 1989.

-. Principles and Standards for School Mathemat

ics. Reston, VA: NCTM, 2000.

Secada, W. G. "Conceptions of Equity in the Teaching of Science." Paper presented at the annual meeting

of the Diversity in Mathematics Education Center for Learning and Teaching, Madison, Wise, 2003.

-. "Teaching Science to English Language Learners:

Building on Students' Strengths." In Language, Culture

and Science Education: Teaching Science to Students

from Diverse Linguistic and Cultural Backgrounds, edited by A. S. Rosebery and B. Warren Arlington, VA: National Science Teachers Association, 2008.

Weissglass, J. "Reasons for Hope: You Can Challenge

Educational Inequities." Principal Leadership 3, no. 8 (2003): 24-29.

ACKNOWLEDGMENTS The preparation of this article was supported in part by a grant from the National Science Foundation

(ESI-0119732) to the Wisconsin Center for Educa tion Research. The opinions expressed in this article do not necessarily reflect the position, policy, or endorsement of the National Science Foundation. <*>

TONYA G. BARTELL, tbartell -udel.edu, ^^^^

Jjl is an assistant professor of mathematics ^^^^H 8 '

^* education at the University of Delaware, ^^^^H W Newark, DE19716. She is interested in ^^^^H

, ^ < teacher professional development, par- ^^^^H ticularly integrating equity with mathe-

^^^^H matics teaching and learning to promote ̂^^^H the success of traditionally underserved

^^^^H students. MARGARET R. MEYER, mrmeyer2@wisc. edu, is an assistant scientist with the Diversity in

^^^^H Mathematics Education Center for Learning and

^^^^H Teaching at the University of Wisconsin-Madison, ^^^^H Madison, Wl 53706. She is also involved in curricu-

^^^^H lum development and implementation, photograph of

^^^^H meyer by paul baker; all rights reserved

^^^^^H

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