Preservice teachers examine gender equity in teaching mathematics

388 Teaching Children Mathematics / March 2007

SUPPORTING TEACHER LEARNING Maureen D. Neumann

The National Council of Teachers of Math-ematics recognizes that mathematical knowl-edge is essential for employment and full

participation in our society. The strategic inclusion of the Equity Principle in NCTM’s Principles and Standards for School Mathematics (2000) refl ects the need in the mathematics education community to eliminate long-standing disparities in mathemat-ics performance. However, incorporating equitable pedagogical practices into one’s instruction does not mean that every student should receive identical instruction; rather, it “demands that reasonable and appropriate accommodations be made as needed to promote access and attainment [of mathematics knowledge] for all students” (NCTM 2000, p. 12).

Although NCTM asserts that equity in math-ematics learning is a goal, achieving that goal is much more complex. NAEP average scale scores have risen since 1990 for both male and female stu-dents; however, gender gaps have not narrowed. On the 2003 NAEP test for fourth graders, girls scored three points lower than boys. Some researchers view this difference as a relatively small gap in achievement. However, other scholars believe that this small, persistent gap could explain the gender differences of women entering mathematics-related occupations (McGraw, Lubienski, and Strutchens 2006).

Mathematical profi ciency is critical to the future careers of all students. Most high-paying science and technological positions require strong math-ematical skills. These positions have historically been fi lled by white males; women and minorities have been poorly represented in these fi elds. People who are innumerate in the twenty-fi rst century will

Preservice Teachers Examine Gender Equity in

Teaching Mathematics

Maureen D. Neumann, [email protected], teaches mathematics education courses for preservice and in-service teachers at the University of Vermont, Burlington, VT 05405.

Edited by Fran Arbaugh, [email protected], and John Lannin, [email protected]. Arbaugh and Lannin are members of the mathematics education faculty at the University of Missouri–Columbia, Columbia, MO 65203. “Supporting Teacher Learning” serves as a forum for the exchange of ideas and a source of activities and pedagogical strategies for teacher edu-cators in their day-to-day work with prospective and practicing teachers. Readers are encour-aged to send manuscripts appropriate for this department by accessing tcm.msubmit.net.

increasingly fi nd themselves in the same position as those who were illiterate in the twentieth century. It is essential that mathematics teachers engage all students in developing a deep understanding of mathematics by seeking to eliminate inequitable teaching practices. In this article, I discuss aspects of gender equity that exist in mathematics class-rooms, describe a project that I use with preservice elementary school teachers to help them recognize possible inequitable practices, and share ways of adapting this project to address other aspects of inequitable practice.

Inequity in Mathematics TeachingMathematics teaching is a product of society. It refl ects and serves the interests of particular groups and can be “examined by looking at the social system in which mathematics is created and used” (Martin 1997, p. 155). Claims that females do not have the “gene for math” or are “less biologically capable” of doing mathematics are unsubstanti-ated (Martin 1997; Zaslavsky 1996). Zaslavsky (1996) worked to expose the belief that certain large categories of people—women, minorities, and working-class people—are incapable of learn-ing high-level mathematics. Her research showed that teachers are guilty, perhaps unconsciously, of this type of stereotyping. Teachers often think that “girls succeed because they try hard whereas boys succeed because of their innate ability” (Perez 2000, p. 28). However, Principles and Standards for School Mathematics asserts, “Well-documented examples demonstrate that all children, including those who have been traditionally underserved, can learn mathematics when they have access to high-quality instructional programs that support their learning” (NCTM 2000, p. 14).

Teachers need to uncover any inequitable instructional practices and change their attitudes and beliefs about who can learn mathematics (Zaslavsky 1996). Teachers communicate unwrit-

Copyright © 2007 The National Council of Teachers of Mathematics, Inc. www.nctm.org. All rights reserved.This material may not be copied or distributed electronically or in any other format without written permission from NCTM.

Teaching Children Mathematics / March 2007 389

ten expectations of their students’ academic success through their verbal interactions during classroom instruction, their comments on student papers, their tracking of students into ability groups, and their lack of consistent support for students who need a deeper mathematical understanding (NCTM 2000). Disparities between girls and boys are rooted early in children’s schooling. As early as second or third grade, girls perceive themselves as lower in mathematical ability than boys (Fennema et al. 1998; Hanson 1992). The ways teachers instruct can contribute to the continuation or elimination of these patterns.

One way for teachers to address gender ineq-uity is to identify their own inequitable teaching practices and then work to improve these. Lampert (2001) documented her struggle to include all students and adapt to meet their needs. Her sys-tematic investigation into her teaching by reflect-ing on video recordings helped her focus on what “make[s] it possible for students to perform in different ways to different kinds of competencies” (p. 367), thereby enabling her to better meet the needs of all her students. Paley (1986) related that tape-recording herself enabled her to hear what she really said to students, not what she thought she said or how she thought she handled situations. The audio tape served as an objective, nonbiased observer in her classroom.

The Equity Teaching Analysis ProjectThe Equity Teaching Analysis Project (Equity Proj-ect) was designed to introduce elementary preser-vice teachers to equity in instructional practice by analyzing an actual teaching experience within an undergraduate mathematics methods course. This systematic analysis helps the preservice teachers see the need to make their teaching of mathematics more equitable. The term more equitable is defined here as “fostering equity in the quality and quantity of statements made by male and female students while learning mathematics during a period of K–6 classroom instruction.” The concept for the Equity Project was developed from the work of a colleague, Charles Rathbone, who initially taught a version of this project in his mathematics methods course.

The Equity Project is conducted during pre-service teachers’ third year in their undergraduate teacher education program. They enroll in a three-credit mathematics methods course that is part of a larger block of professional coursework in literacy. Field assignments with K–6 students are supervised by university faculty and public school teachers who serve as mentors.

Often elementary preservice teachers do not realize that their actions reflect or contribute to


Verbal interaction categories (adapted from Shepardson and Pizzini 1991) and examples

Categories Examples

PraiseAcademic—Teacher rewards students and rein-forces the intellectual quality of academic work.

Nonacademic—Teacher rewards students and reinforces work or activity not related to the intel-lectual quality of academic work.

“Interesting strategy.” “I like your thinking in solving that problem.”

“You’re being nice and quiet today.” “I like how you put your name at the top of your test.”

Academic CriticismIntellectual quality—Teacher directs critical re-marks at the lack of intellectual quality.

Effort—Teacher attributes academic failure to lack of effort.

“I don’t think you’re good at mathematics.” “This is a simple problem that you got wrong.”

“You’re not trying hard enough.” “You could do the math if you just put your mind to it and worked harder”

Nonacademic CriticismMild—Teacher makes negative comments about violations of conduct, rules, and forms; behaviors; and other nonacademic areas.

Harsh—Teacher makes negative comments that attract attention because they are louder, longer, and stronger than mild criticism.

“Megan, you need to raise your hand.” “Tom, stay in line.”

“Tom, I told you to get in line! I don’t want to talk to you again about this. The next time I say some-thing, no recess!”

QuestionsLow-level—Teacher asks questions that require memorization of facts.

High-level—Teacher asks questions that require higher intellectual processes—i.e., that ask the student to use information, not just memorize it. These are considered open-ended questions or probing/pressing questions.

“What number follows 59?” “What is 6 times 5?”

“How did you figure out that 62 times 51 equals 3162?”“How did you know that 60 follows 59?”

Academic InterventionFacilitates—Teacher facilitates learning by provid-ing students with suggestions, hints, and cues that encourage and enable them to complete the assignment themselves.

Short-circuits—Teacher prevents or short-circuits student’s success by taking over the learning process.

“How does solving 60 times 50 help you solve 62 times 51?”“Looking at the hundreds chart, what do you notice about the numbers that follow numbers that end in 9?”

“Give me your pencil. When multiplying, you first….” “You’ve got this part wrong—60 times 50 is 3000, not 300.”

InformationAcademic—Teacher gives information related to the lesson content.

Nonacademic—Teacher gives information that is procedural or related to classroom management.

“The sum of the interior angles for any triangle is 180º .”

“I need everyone to put their desks in groups of 4 for today’s lesson.”

Figure 1


inequity. Before my preservice teachers begin this project, a majority believe that their instruction to K–6 students is equitable. Through video and audio tape recordings, transcriptions, and self-reflection, the Equity Project illuminates how they as teachers create conditions of unequal participation in their classrooms. The project also requires that the teach-ers prescribe immediate changes to their verbal instructions and address their inequitable behavior as part of their critical reflection assignment.

To demonstrate the type of instruction elemen-tary teachers should use with their students, the Equity Project is conducted during a unit on teaching data investigations to K–6 students. For this project, the preservice teachers need to sort, display, analyze, and describe data just as their K–6 students do in their data investigations.

The taskElementary preservice teachers teach and, using either video or audio tape, tape-record a mathemat-ics lesson for twenty minutes. From this recording, they create transcripts of teacher-student discussion. They then code each sentence from the transcripts according to the verbal interaction categories cre-ated by Shepardson and Pizzini (1991), which help identify potential gender inequities: praise, aca-demic criticism, nonacademic criticism, questions, academic intervention, and information (see figs. 1 and 2). The preservice teachers then create a data summary sheet using a spreadsheet computer pro-gram (see fig. 3, p. 392) and graph the data (see fig. 4, p. 394) to represent the verbal interactions that occur during their lesson. The teachers then analyze their transcripts as to both the quality and the quan-tity of the various interactions. This analysis aids the teachers in identifying and interpreting patterns of potential inequitable practice and in creating an intervention plan for their teaching behavior.

For their written report, the preservice teachers begin by discussing equity in instruction. Next, they describe their results and reflect on their analy-sis. Reflection questions help them focus their data analysis discussion (see fig. 5, p. 395, for sample reflection questions).

Hidden inequities in teaching mathematics The Equity Project opens elementary preser-vice teachers’ eyes to their inequitable teaching practices. Although more than 200 teachers have completed the project during the last five years, the insights of three of them—Melissa, Ellen, and

Megan—are representative of the thinking that emerged from the larger group.

Melissa noticed that her classroom management strategies often enabled boys to receive more sub-stantive mathematics instruction:

As I reflect on [my classroom management strategies], it becomes clear that the boys who were acting out and not being cooperative were rewarded with more opportunities for learning! I look back over my transcript and realize that I tried to manage behavioral issues in the class by inviting the disruptive person to the front of the room and asking [him] a high-level math question.… In all cases, the disruptive students that I engaged in high-level questioning were boys. The boys would stop the negative behav-ior and become engaged in math concepts that were being explored. I did not realize that this was rewarding behavior with opportunities to learn math. I rewarded girls [who demonstrated] more cooperative behavior with nonacademic

Sample of elementary preservice teacher’s transcript and coding

To begin the lesson, the teacher demonstrates a chip trading game using deci-mal numbers. The teacher has drawn a chart on the blackboard and taped the chips on the board. The chips are used to represent a decimal number, and the teacher challenges the students to interpret the representation.Teacher [low-level question, directed to male student]. How would you say that number, Boy 1?Boy 1. Two and forty-two hundredths.Teacher [low-level question, directed to male student]. I’m sorry. What did you say?Boy 1. Two and forty-two hundredths.Teacher [academic praise, directed to male student]. Yes, two and forty-two hundredths. [academic praise, directed to male student] I like the way you used “and” in there, as you were taught. Teacher [high-level question, directed to whole class]. Now what would hap-pen if I took these chips off?[low-level question, directed to whole class] How would I say that? [academic information, directed to the whole class] That’s a little bit different. [low-level question, directed to female student] Girl 1?Girl 1. Two and four tenths. Teacher [academic praise, directed to female student]. Two and four tenths, good. [high-level question, directed to female student] And why is it two and four tenths and not hundredths?Girl 1. Because you don’t have any chips in the hundredths?Teacher [academic praise, directed to female student]. That’s right. Let’s do one more to refresh our memories. [Puts more chips on the board.] [low-level question, directed to male student] Okay, Boy 2?Boy 2. Three and twenty-five hundredths.Teacher [academic praise, directed to male student]. Good, three and twenty-five hundredths. [low-level question, directed to whole class] Does everyone agree with that?Whole class. Yes.

Figure 2


praise/encouragement. (Equity Teaching Analy-sis Project 2002)

Melissa realized that she rewarded negative behav-ior by having the boys answer questions that helped push their mathematical thinking. The students who sat quietly were not given the same opportunity. With this awareness, she planned to change her practice by asking high-level questions to all stu-dents, including those who were not disruptive.

Ellen, too, realized that she asked more higher-level questions of boys than girls, enabling the boys to think about the mathematics at a deeper level:

I noticed something really interesting about my interactions with students when I asked higher-level questions. I don’t think I probed the girls as intensely as I probed the boys. When I asked a girl a question about place value and she gave me the right answer, I just told her that she was right. However, whenever I asked a boy … whether he gave a correct or incorrect answer, I would always follow up with, “How do you know?” or “Why did you do it like that?” I was

really surprised to see this. I didn’t even notice that I was doing this. (Equity Teaching Analysis Project 2004)

The transcript analysis made Ellen realize that, by asking boys probing, open-ended questions about mathematics, she was subconsciously limiting the opportunities for other students to learn. Asking higher-level questions can assist students in learn-ing mathematics at a deeper level. Ellen’s analysis helped her realize that the quantity and the quality of the interactions that elementary teachers have with their students were necessary for promoting equitable practice.

Megan, another third-year student, noticed her use of language to shape students’ behavior:

All of my nonacademic criticism was towards boys.… I think that I am going to have to be more aware of my academic praise as well. Fifty-four percent of my academic praise was again to boys, compared with about 31 percent given to girls.… I have noticed many things that I would not have been able to pick up on with-

Elementary preservice teacher’s data summary sheet: Comments directed at children by teacher

Verbal Interaction Categories

Boys Girls Whole Class Totals

No. Percentage No. Percentage No. Percentage No. Percentage

PraiseAcademicNonacademic

7 3

47% 38%

8 0

53% 0%

0 5

0%62%

15 8

13% 7%

Academic criticismIntellectual qualityEffort

0 0

0% 0%

0 0

0% 0%

0 0

0% 0%

0 0

0% 0%

Nonacademic criticismMildHarsh

6 0

75% 0%

0 0

0% 0%

2 0

25% 0%

8 0

7% 0%

QuestionsLow-levelHigh-level

14 0

30% 0%

15 0

32% 0%

18 2

38%10%

47 2

42% 2%

Academic interventionFacilitatesShort-circuits

1 1

100%100%

0 0

0% 0%

0 0

0% 0%

1 1

1% 1%

InformationAcademicNonacademic

1 4

11% 20%

1 0

11% 0%

716

78%80%

9 20

8% 18%

Total Tallies/Percentages 37 33% 24 21% 51 46% 112 100%

Figure 3


out (analyzing) a transcript. (Equity Teaching Analysis Project 2001)

Like her peers, Megan found that the transcribing and coding of her teaching helped her become more conscious about the amount of praise and criticism she gave students.

Following preservice teachers into in-service placementsI recently observed some former preservice teach-ers from my mathematics methods class who are currently teaching in nearby schools. Afterward, when I interviewed them to learn how the Equity Project has shaped their mathematics teaching, two themes emerged: (1) they ask questions of all the students to learn their thinking; and (2) they address behavioral problems equitably and consistently. Wilma, an undergraduate student from spring 2003, commented on what she had learned from the Equity Project:

It was really the first time that it [gender equity] had ever even been brought to [my] attention—the idea that you may not realize that you are calling on the same kids all the time and that you could be basing a whole lot of assumptions that may not be true for your class because you feel like they totally get it when you really are only calling on five kids. (Equity Teaching Analysis Project 2006)

Wilma’s teaching reflected this idea of asking all her students questions about their thinking. She directed 53 low-level and 20 high-level questions to different students in the class. Many high-level questions were follow-ups to low-level questions. When queried about why she asked these questions, Wilma responded, “Because I want to see where their thinking is and what misconceptions they have, if any. I’m trying to get a quick check in with everyone and then follow up with certain students depending on what they initially said or where they are in their understanding” (Equity Teaching Anal-ysis Project 2006). For this lesson, questioning stu-dents was an integral part of Wilma’s instruction.

For Tarlie, an undergraduate during fall 2004, the Equity Project made her realize that she was much harder on boys than on girls regarding behav-ioral problems. “I [was] more likely to call a boy, to tell him to stop doing something and recognize that he’s doing something wrong when there’s a girl right there doing the exact same thing and I

looked over it” (Equity Teaching Analysis Project 2006). Even though the gender gap in the NAEP mathematics scores has not changed in the last ten years, research has established that boys are becoming increasingly disaffiliated from schools because of the classroom management strategies being used (Sullivan and Bishop 2005). Tarlie now tries to address the behavior problems of both girls and boys in her class.

Concluding ThoughtsThe methods used in the Equity Project are not lim-ited to elementary preservice teachers’ mathematics instruction. The project could be used to uncover inequity in science (see Nelson 2006), literacy, and social stud-ies teaching or used to reveal in-service teachers’ inequitable practices. Further, although this project focused on gender ineq-uity, it also has the potential for teachers to examine inequitable practices with minority students and students from different socioeconomic status.

The Equity Project provides teachers only an early indica-tion of equitable instructional practices and only from one per-spective—verbal interactions. To further investigate gender equity, teachers need to examine more than the verbal interac-tions of one lesson because lessons can vary considerably. As they work with students, teachers should consider long-term trends that may exist in their own teaching. One way to address these trends is for teachers to repeatedly investigate their teaching over time to see if these inequitable practices persist and if the self-prescribed interven-tion plans had positive effects on students who were initially marginalized. Other areas of equity that teachers should examine include the curriculum (Boaler 2002) and student assessment (Morgan and Watson 2002). Teachers can work toward equity in these areas by determining whether the activities are engaging for all students, whether the problems or tasks allow struggling students to be successful and gifted students to be challenged, and whether the interpretative judgments on student assessments are consistent and rubric based.

People who are innumerate in the twenty-first century will increasingly find themselves in the same position as those who were illiterate in the twentieth century.


The means of combating inequitable teaching practices are awareness and action. Systematic analysis of a transcript of teacher-student dialogue and graphing coded data illuminate the type of ver-bal interactions teachers used in their instruction. This approach highlights whether a teacher limits opportunities for groups of students to learn, limits opportunities for building conceptual understand-ing, or limits participation in mathematical dis-

course. This approach also highlights who receives more substantive feedback during mathematics instruction and who is singled out for behavioral problems. These are issues that affect all students, not just one gender. Several research and practitio-ner articles examine and address equity in instruc-tion (see scholargoogle.com). Particularly helpful readings to use with preservice teachers should begin with the definition of the Equity Principle

Elementary preservice teacher’s graph based on the data summary sheet

0%

20%

40%

60%

80%

100%

120%

Pr-Ac Pr-NonAc

AcCr-Int

AcCr-Eff

NonAcCr-

M

NonAcCr-

H

Q-LL Q-HL AcInt-Fac

AcIn-ShCt

Inf-Aca

Inf-NonAc

Tallies

Boys %

Girls %

Whole Class %

Total %

Teacher Analysis Data Graph

Per

cen

tag

e

Verbal Interaction Categories

Key: Pr-Ac—Praise, academic; Pr-Non Ac—Praise, nonacademic; AcCr-Int—Academic criticism, intel-lectual quality; AcCr-Eff—Academic criticism, effort; Non AcCr-M—Nonacademic criticism, mild; Non AcCr-H—Nonacademic criticism, harsh; Q-LL—Questions, low-level; Q-HL—Questions, high-level; AcInt-Fac—Academic intervention, facilitates; AcIn-ShCt—Academic intervention, short-circuits; Inf-Aca—Infor-mation, academic; Inf-Non Ac—Information, nonacademic

Figure 4


(NCTM 2000) and include Cohen (1994), Gilbert (2001), Levi (2000), Perez (2000), and Rubel and Meyer (2005).

References Boaler, Jo. “Learning from Teaching: Exploring the Re-

lationship between Reform Curriculum and Equity.” Journal for Research in Mathematics Education 33 (July 2002): 239–58

Cohen, Elizabeth G. Designing Groupwork: Strategies for the Heterogeneous Classroom. New York: Teach-ers College Press, 1994.

Equity Teaching Analysis Project. Interviews conducted 2001–6.

Fennema, Elizabeth, Thomas Carpenter, Victoria Ja-cobs, Megan Franke, and Linda Levi. “A Longitudi-nal Study of Gender Difference in Young Children’s Mathematical Thinking.” Educational Researcher 27 (June–July 1998): 6–11.

Gilbert, Melissa C. “Applying the Equity Principle.” Mathematics Teaching in the Middle School 7 (Sep-tember 2001): 18–19, 36.

Hanson, Katherine. Teaching Mathematics Effectively and Equitably to Females. New York: ERIC Clear-inghouse on Urban Education, Institute for Urban and Minority Education, 1992.

Lampert, Magdalene. Teaching Problems and the Prob-lems of Teaching. New Haven, CT: Yale University Press, 2001.

Levi, Linda. “Gender Equity in Mathematics Education.” Teaching Children Mathematics 7 (October 2000): 101–5.

Martin, Brian. “Mathematics and Social Interest.” In Ethnomathematics: Changing Eurocentrism in Math-ematics Education, edited by A. B. Powell and M. Frankenstein, pp. 155–72. Albany, NY: State Univer-sity of New York Press, 1997.

McGraw, Rebecca, Sarah Theule Lubienski, and Mari-lyn E. Strutchens. “A Closer Look at Gender in NAEP Mathematics Achievement and Affect Data: Intersec-tions with Achievement, Race/Ethnicity, and Socio-economic Status.” Journal for Research in Mathemat-ics Education 37 (March 2006): 129–50.

Morgan, Candia, and Anne Watson. “The Interpretative Nature of Teachers’ Assessment of Students’ Math-ematics: Issues for Equity.” Journal for Research in Mathematics Education 33 (March 2002): 78–110.

National Council of Teachers of Mathematics (NCTM). Principles and Standards for School Mathematics. Reston, VA: NCTM, 2000.

Nelson, Tamara. “Using Guided Video Reflection to Learn about Equity in Elementary Science Educa-tion.” Paper presented at the annual meeting of the American Educational Research Association, San Francisco, April 2006.

Paley, Vivian. “On Listening to What Children Say.” Har-vard Educational Review 56 (May 1986): 122–31.

Perez, Christina. “Equity in the Standards-Based El-ementary Mathematics Classroom.” Focus 7 (April 2000): 28–31.

Rubel, Laurie, and Margaret R. Meyer. “The Pursuit of

Mathematics for All!” Mathematics Teaching in the Middle School 10 (May 2005): 479–83.

Shepardson, Daniel, and Edward Pizzini. “Gender Bias in the Classroom—A Self-evaluation.” Science and Children (November–December 1991): 38–41.

Sullivan, Mary, and Penny Bishop. “Disaffiliated Boys: Perspectives on Friendship and School Success.” Middle School Journal 37 (November 2005): 22–30.

Zaslavsky, Claudia. The Multicultural Math Classroom: Bringing in the World. Portsmouth, NH: Heinemann, 1996. s

Sample reflection questions for Equity Project written report

Questions to think about as you write your paperDid you notice that you were asking higher-order questions to one gender more often than to the other? Why did this occur? Did you notice that you were providing mild criticism to one gender more often than to the other? Why might this be? Were you deliberately trying to change the natural outcome of the data by being deliberate in whom you were calling on? Why did a certain group of stu-dents participate less? Is the quality of your interaction with certain students favoring or disfavoring their learning experience? Did a group of students dominate the dialogue? Why would this be?

Discuss your data analysis and its implications Were disruptive students getting more “air time”? What does this mean for the learning of students who were well behaved? Were you asking more low-level questions than high-level questions? What does this mean for the type of instruction you are providing? Do your interactions consist mainly of providing academic information and asking low-level questions? What does this mean for all students’ ability to learn mathematics? How can gender differences in the classroom unintentionally lead to differenc-es in your students’ performance, achievement, and motivation? Discuss what this means for your instruction and your students’ ability to learn from you.

Examine your transcript for the interactions that occurred after you asked questions or provided instruction to the whole class Who responded to you? Whom did you call on? Were the same students responding to you when you asked questions to the whole class? How did you respond to them? What was the gender ratio for students you called on after asking a question to the whole group?

Figure 5

Documents

Preservice teachers examine gender equity in teaching mathematics