Published on: **Mar 4, 2016**

- 1. SUPPORTING TEACHER LEARNING Maureen D. Neumann Preservice Teachers Examine Gender Equity in Teaching Mathematics T he National Council of Teachers of Math- increasingly find themselves in the same position as ematics recognizes that mathematical knowl- those who were illiterate in the twentieth century. edge is essential for employment and full It is essential that mathematics teachers engage participation in our society. The strategic inclusion all students in developing a deep understanding of of the Equity Principle in NCTM’s Principles and mathematics by seeking to eliminate inequitable Standards for School Mathematics (2000) reflects teaching practices. In this article, I discuss aspects the need in the mathematics education community of gender equity that exist in mathematics class- to eliminate long-standing disparities in mathemat- rooms, describe a project that I use with preservice ics performance. However, incorporating equitable elementary school teachers to help them recognize pedagogical practices into one’s instruction does possible inequitable practices, and share ways of not mean that every student should receive identical adapting this project to address other aspects of instruction; rather, it “demands that reasonable and inequitable practice. appropriate accommodations be made as needed to promote access and attainment [of mathematics knowledge] for all students” (NCTM 2000, p. 12). Inequity in Mathematics Although NCTM asserts that equity in math- Teaching ematics learning is a goal, achieving that goal is Mathematics teaching is a product of society. It much more complex. NAEP average scale scores reflects and serves the interests of particular groups have risen since 1990 for both male and female stu- and can be “examined by looking at the social dents; however, gender gaps have not narrowed. On system in which mathematics is created and used” the 2003 NAEP test for fourth graders, girls scored (Martin 1997, p. 155). Claims that females do not three points lower than boys. Some researchers have the “gene for math” or are “less biologically view this difference as a relatively small gap in capable” of doing mathematics are unsubstanti- achievement. However, other scholars believe that ated (Martin 1997; Zaslavsky 1996). Zaslavsky this small, persistent gap could explain the gender (1996) worked to expose the belief that certain differences of women entering mathematics-related large categories of people—women, minorities, occupations (McGraw, Lubienski, and Strutchens and working-class people—are incapable of learn- 2006). ing high-level mathematics. Her research showed Mathematical proficiency is critical to the future that teachers are guilty, perhaps unconsciously, careers of all students. Most high-paying science of this type of stereotyping. Teachers often think and technological positions require strong math- that “girls succeed because they try hard whereas ematical skills. These positions have historically boys succeed because of their innate ability” (Perez been filled by white males; women and minorities 2000, p. 28). However, Principles and Standards have been poorly represented in these fields. People for School Mathematics asserts, “Well-documented who are innumerate in the twenty-first century will examples demonstrate that all children, including those who have been traditionally underserved, canMaureen D. Neumann, Maureen.Neumann@uvm.edu, teaches mathematics education coursesfor preservice and in-service teachers at the University of Vermont, Burlington, VT 05405. learn mathematics when they have access to high-Edited by Fran Arbaugh, arbaughe@missouri.edu, and John Lannin, LanninJ@missouri.edu. quality instructional programs that support theirArbaugh and Lannin are members of the mathematics education faculty at the University of learning” (NCTM 2000, p. 14).Missouri–Columbia, Columbia, MO 65203. “Supporting Teacher Learning” serves as a forum Teachers need to uncover any inequitablefor the exchange of ideas and a source of activities and pedagogical strategies for teacher edu- instructional practices and change their attitudescators 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. and beliefs about who can learn mathematics (Zaslavsky 1996). Teachers communicate unwrit-388 Teaching Children Mathematics / March 2007 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.
- 2. ten expectations of their students’ academic successthrough their verbal interactions during classroom The Equity Teaching Analysisinstruction, their comments on student papers, their Projecttracking of students into ability groups, and their The Equity Teaching Analysis Project (Equity Proj-lack of consistent support for students who need a ect) was designed to introduce elementary preser-deeper mathematical understanding (NCTM 2000). vice teachers to equity in instructional practice byDisparities between girls and boys are rooted analyzing an actual teaching experience within anearly in children’s schooling. As early as second undergraduate mathematics methods course. Thisor third grade, girls perceive themselves as lower systematic analysis helps the preservice teachersin mathematical ability than boys (Fennema et al. see the need to make their teaching of mathematics1998; Hanson 1992). The ways teachers instruct more equitable. The term more equitable is definedcan contribute to the continuation or elimination of here as “fostering equity in the quality and quantitythese patterns. of statements made by male and female students One way for teachers to address gender ineq- while learning mathematics during a period ofuity is to identify their own inequitable teaching K–6 classroom instruction.” The concept for thepractices and then work to improve these. Lampert Equity Project was developed from the work of a(2001) documented her struggle to include all colleague, Charles Rathbone, who initially taught astudents and adapt to meet their needs. Her sys- version of this project in his mathematics methodstematic investigation into her teaching by reflect- course.ing on video recordings helped her focus on what The Equity Project is conducted during pre-“make[s] it possible for students to perform in service teachers’ third year in their undergraduatedifferent ways to different kinds of competencies” teacher education program. They enroll in a three-(p. 367), thereby enabling her to better meet the credit mathematics methods course that is part of aneeds of all her students. Paley (1986) related that larger block of professional coursework in literacy.tape-recording herself enabled her to hear what she Field assignments with K–6 students are supervisedreally said to students, not what she thought she by university faculty and public school teacherssaid or how she thought she handled situations. who serve as mentors.The audio tape served as an objective, nonbiased Often elementary preservice teachers do notobserver in her classroom. realize that their actions reflect or contribute toTeaching Children Mathematics / March 2007 389
- 3. Figure 1 Verbal interaction categories (adapted from Shepardson and Pizzini 1991) and examples Categories Examples Praise Academic—Teacher rewards students and rein- “Interesting strategy.” forces the intellectual quality of academic work. “I like your thinking in solving that problem.” Nonacademic—Teacher rewards students and “You’re being nice and quiet today.” reinforces work or activity not related to the intel- “I like how you put your name at the top of your lectual quality of academic work. test.” Academic Criticism Intellectual quality—Teacher directs critical re- “I don’t think you’re good at mathematics.” marks at the lack of intellectual quality. “This is a simple problem that you got wrong.” Effort—Teacher attributes academic failure to lack “You’re not trying hard enough.” of effort. “You could do the math if you just put your mind to it and worked harder” Nonacademic Criticism Mild—Teacher makes negative comments about “Megan, you need to raise your hand.” violations of conduct, rules, and forms; behaviors; “Tom, stay in line.” and other nonacademic areas. Harsh—Teacher makes negative comments that “Tom, I told you to get in line! I don’t want to talk attract attention because they are louder, longer, to you again about this. The next time I say some- and stronger than mild criticism. thing, no recess!” Questions Low-level—Teacher asks questions that require “What number follows 59?” memorization of facts. “What is 6 times 5?” High-level—Teacher asks questions that require “How did you figure out that 62 times 51 equals higher intellectual processes—i.e., that ask the 3162?” student to use information, not just memorize it. “How did you know that 60 follows 59?” These are considered open-ended questions or probing/pressing questions. Academic Intervention Facilitates—Teacher facilitates learning by provid- “How does solving 60 times 50 help you solve 62 ing students with suggestions, hints, and cues times 51?” that encourage and enable them to complete the “Looking at the hundreds chart, what do you assignment themselves. notice about the numbers that follow numbers that end in 9?” Short-circuits—Teacher prevents or short-circuits “Give me your pencil. When multiplying, you student’s success by taking over the learning first….” process. “You’ve got this part wrong—60 times 50 is 3000, not 300.” Information Academic—Teacher gives information related to “The sum of the interior angles for any triangle is the lesson content. 180º .” Nonacademic—Teacher gives information that is “I need everyone to put their desks in groups of 4 procedural or related to classroom management. for today’s lesson.”390 Teaching Children Mathematics / March 2007
- 4. inequity. Before my preservice teachers begin this Figure 2project, a majority believe that their instruction toK–6 students is equitable. Through video and audio Sample of elementary preservice teacher’s transcript and codingtape recordings, transcriptions, and self-reflection, To begin the lesson, the teacher demonstrates a chip trading game using deci-the Equity Project illuminates how they as teachers mal numbers. The teacher has drawn a chart on the blackboard and taped thecreate conditions of unequal participation in their chips on the board. The chips are used to represent a decimal number, and theclassrooms. The project also requires that the teach- teacher challenges the students to interpret the representation.ers prescribe immediate changes to their verbal Teacher [low-level question, directed to male student]. How would you sayinstructions and address their inequitable behavior that number, Boy 1? Boy 1. Two and forty-two hundredths.as part of their critical reflection assignment. Teacher [low-level question, directed to male student]. I’m sorry. What did you To demonstrate the type of instruction elemen- say?tary teachers should use with their students, the Boy 1. Two and forty-two hundredths.Equity Project is conducted during a unit on Teacher [academic praise, directed to male student]. Yes, two and forty-twoteaching data investigations to K–6 students. For hundredths. [academic praise, directed to male student] I like the way you used “and” in there, as you were taught.this project, the preservice teachers need to sort, Teacher [high-level question, directed to whole class]. Now what would hap-display, analyze, and describe data just as their K–6 pen if I took these chips off?students do in their data investigations. [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-levelThe task question, directed to female student] Girl 1? Girl 1. Two and four tenths.Elementary preservice teachers teach and, using Teacher [academic praise, directed to female student]. Two and four tenths,either video or audio tape, tape-record a mathemat- good. [high-level question, directed to female student] And why is it two andics lesson for twenty minutes. From this recording, four tenths and not hundredths?they create transcripts of teacher-student discussion. Girl 1. Because you don’t have any chips in the hundredths?They then code each sentence from the transcripts 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-levelaccording to the verbal interaction categories cre- question, directed to male student] Okay, Boy 2?ated by Shepardson and Pizzini (1991), which help Boy 2. Three and twenty-five hundredths.identify potential gender inequities: praise, aca- Teacher [academic praise, directed to male student]. Good, three and twenty-demic criticism, nonacademic criticism, questions, five hundredths. [low-level question, directed to whole class] Does everyoneacademic intervention, and information (see figs. 1 agree with that? Whole class. Yes.and 2). The preservice teachers then create a datasummary sheet using a spreadsheet computer pro-gram (see fig. 3, p. 392) and graph the data (see fig. Megan—are representative of the thinking that4, p. 394) to represent the verbal interactions that emerged from the larger group.occur during their lesson. The teachers then analyze Melissa noticed that her classroom managementtheir transcripts as to both the quality and the quan- strategies often enabled boys to receive more sub-tity of the various interactions. This analysis aids stantive mathematics instruction:the teachers in identifying and interpreting patternsof potential inequitable practice and in creating an As I reflect on [my classroom managementintervention plan for their teaching behavior. strategies], it becomes clear that the boys who For their written report, the preservice teachers were acting out and not being cooperative werebegin by discussing equity in instruction. Next, rewarded with more opportunities for learning!they describe their results and reflect on their analy- I look back over my transcript and realize thatsis. Reflection questions help them focus their data I tried to manage behavioral issues in the classanalysis discussion (see fig. 5, p. 395, for sample by inviting the disruptive person to the front ofreflection questions). the room and asking [him] a high-level math question.… In all cases, the disruptive studentsHidden inequities in teaching that I engaged in high-level questioning weremathematics boys. The boys would stop the negative behav-The Equity Project opens elementary preser- ior and become engaged in math concepts thatvice teachers’ eyes to their inequitable teaching were being explored. I did not realize that thispractices. Although more than 200 teachers have was rewarding behavior with opportunities tocompleted the project during the last five years, learn math. I rewarded girls [who demonstrated]the insights of three of them—Melissa, Ellen, and more cooperative behavior with nonacademicTeaching Children Mathematics / March 2007 391
- 5. Figure 3 Elementary preservice teacher’s data summary sheet: Comments directed at children by teacher Verbal Interaction Boys Girls Whole Class Totals Categories No. Percentage No. Percentage No. Percentage No. Percentage Praise Academic 7 47% 8 53% 0 0% 15 13% Nonacademic 3 38% 0 0% 5 62% 8 7% Academic criticism Intellectual quality 0 0% 0 0% 0 0% 0 0% Effort 0 0% 0 0% 0 0% 0 0% Nonacademic criticism Mild 6 75% 0 0% 2 25% 8 7% Harsh 0 0% 0 0% 0 0% 0 0% Questions Low-level 14 30% 15 32% 18 38% 47 42% High-level 0 0% 0 0% 2 10% 2 2% Academic intervention Facilitates 1 100% 0 0% 0 0% 1 1% Short-circuits 1 100% 0 0% 0 0% 1 1% Information Academic 1 11% 1 11% 7 78% 9 8% Nonacademic 4 20% 0 0% 16 80% 20 18% Total Tallies/Percentages 37 33% 24 21% 51 46% 112 100% praise/encouragement. (Equity Teaching Analy- really surprised to see this. I didn’t even notice sis Project 2002) that I was doing this. (Equity Teaching Analysis Project 2004) Melissa realized that she rewarded negative behav- ior by having the boys answer questions that helped The transcript analysis made Ellen realize that, by push their mathematical thinking. The students who asking boys probing, open-ended questions about sat quietly were not given the same opportunity. mathematics, she was subconsciously limiting the With this awareness, she planned to change her opportunities for other students to learn. Asking practice by asking high-level questions to all stu- higher-level questions can assist students in learn- dents, including those who were not disruptive. ing mathematics at a deeper level. Ellen’s analysis Ellen, too, realized that she asked more higher- helped her realize that the quantity and the quality level questions of boys than girls, enabling the boys of the interactions that elementary teachers have to think about the mathematics at a deeper level: with their students were necessary for promoting equitable practice. I noticed something really interesting about my Megan, another third-year student, noticed her interactions with students when I asked higher- use of language to shape students’ behavior: level questions. I don’t think I probed the girls as intensely as I probed the boys. When I asked All of my nonacademic criticism was towards a girl a question about place value and she gave boys.… I think that I am going to have to be me the right answer, I just told her that she was more aware of my academic praise as well. right. However, whenever I asked a boy … Fifty-four percent of my academic praise was whether he gave a correct or incorrect answer, again to boys, compared with about 31 percent I would always follow up with, “How do you given to girls.… I have noticed many things that know?” or “Why did you do it like that?” I was I would not have been able to pick up on with-392 Teaching Children Mathematics / March 2007
- 6. out (analyzing) a transcript. (Equity Teaching looked over it” (Equity Teaching Analysis Project Analysis Project 2001) 2006). Even though the gender gap in the NAEP mathematics scores has not changed in the lastLike her peers, Megan found that the transcribing ten years, research has established that boys areand coding of her teaching helped her become more becoming increasingly disaffiliated from schoolsconscious about the amount of praise and criticism because of the classroom management strategiesshe gave students. being used (Sullivan and Bishop 2005). Tarlie now tries to address the behavior problems of both girlsFollowing preservice teachers and boys in her class.into in-service placementsI recently observed some former preservice teach-ers from my mathematics methods class who are Concluding Thoughtscurrently teaching in nearby schools. Afterward, The methods used in the Equity Project are not lim-when I interviewed them to learn how the Equity ited to elementary preservice teachers’ mathematicsProject has shaped their mathematics teaching, two instruction. The project could be used to uncoverthemes emerged: (1) they ask questions of all the inequity in science (see Nelsonstudents to learn their thinking; and (2) they address 2006), literacy, and social stud-behavioral problems equitably and consistently. ies teaching or used to reveal People who areWilma, an undergraduate student from spring 2003, in-service teachers’ inequitablecommented on what she had learned from theEquity Project: practices. Further, although this project focused on gender ineq- innumerate in the It was really the first time that it [gender equity] uity, it also has the potential for teachers to examine inequitable twenty-first century had ever even been brought to [my] attention— the idea that you may not realize that you are practices with minority students and students from different will increasingly calling on the same kids all the time and that you socioeconomic status. could be basing a whole lot of assumptions that The Equity Project provides find themselves in may not be true for your class because you feel teachers only an early indica- like they totally get it when you really are only tion of equitable instructional the same position calling on five kids. (Equity Teaching Analysis practices and only from one per- Project 2006) spective—verbal interactions. as those who were To further investigate genderWilma’s teaching reflected this idea of asking allher students questions about their thinking. She equity, teachers need to examine more than the verbal interac- illiterate in thedirected 53 low-level and 20 high-level questionsto different students in the class. Many high-level tions of one lesson because lessons can vary considerably. twentieth century.questions were follow-ups to low-level questions. As they work with students,When queried about why she asked these questions, teachers should consider long-term trends that mayWilma responded, “Because I want to see where exist in their own teaching. One way to addresstheir thinking is and what misconceptions they these trends is for teachers to repeatedly investigatehave, if any. I’m trying to get a quick check in with their teaching over time to see if these inequitableeveryone and then follow up with certain students practices persist and if the self-prescribed interven-depending on what they initially said or where they tion plans had positive effects on students who wereare in their understanding” (Equity Teaching Anal- initially marginalized. Other areas of equity thatysis Project 2006). For this lesson, questioning stu- teachers should examine include the curriculumdents was an integral part of Wilma’s instruction. (Boaler 2002) and student assessment (Morgan and For Tarlie, an undergraduate during fall 2004, Watson 2002). Teachers can work toward equity inthe Equity Project made her realize that she was these areas by determining whether the activitiesmuch harder on boys than on girls regarding behav- are engaging for all students, whether the problemsioral problems. “I [was] more likely to call a boy, or tasks allow struggling students to be successfulto tell him to stop doing something and recognize and gifted students to be challenged, and whetherthat he’s doing something wrong when there’s a the interpretative judgments on student assessmentsgirl right there doing the exact same thing and I are consistent and rubric based.Teaching Children Mathematics / March 2007 393
- 7. Figure 4 Elementary preservice teacher’s graph based on the data summary sheet Teacher Analysis Data Graph 120% Boys % Girls % 100% Whole Class % Total % 80% Percentage 60% 40% 20% 0% Pr-Ac Pr-Non AcCr- AcCr- Non Non Q-LL Q-HL AcInt- AcIn- Inf- Inf- Tallies Ac Int Eff AcCr- AcCr- Fac ShCt Aca Non M H Ac 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 The means of combating inequitable teaching course. This approach also highlights who receives practices are awareness and action. Systematic more substantive feedback during mathematics analysis of a transcript of teacher-student dialogue instruction and who is singled out for behavioral and graphing coded data illuminate the type of ver- problems. These are issues that affect all students, bal interactions teachers used in their instruction. not just one gender. Several research and practitio- This approach highlights whether a teacher limits ner articles examine and address equity in instruc- opportunities for groups of students to learn, limits tion (see scholargoogle.com). Particularly helpful opportunities for building conceptual understand- readings to use with preservice teachers should ing, or limits participation in mathematical dis- begin with the definition of the Equity Principle394 Teaching Children Mathematics / March 2007
- 8. (NCTM 2000) and include Cohen (1994), Gilbert Figure 5(2001), Levi (2000), Perez (2000), and Rubel andMeyer (2005). Sample reflection questions for Equity Project written report Questions to think about as you write your paper Did you notice that you were asking higher-order questions to one genderReferences more often than to the other? Why did this occur?Boaler, Jo. “Learning from Teaching: Exploring the Re- Did you notice that you were providing mild criticism to one gender more lationship between Reform Curriculum and Equity.” often than to the other? Why might this be? Journal for Research in Mathematics Education 33 Were you deliberately trying to change the natural outcome of the data by (July 2002): 239–58 being deliberate in whom you were calling on? Why did a certain group of stu-Cohen, Elizabeth G. Designing Groupwork: Strategies dents participate less? Is the quality of your interaction with certain students for the Heterogeneous Classroom. New York: Teach- favoring or disfavoring their learning experience? ers College Press, 1994. Did a group of students dominate the dialogue? Why would this be?Equity Teaching Analysis Project. Interviews conducted 2001–6. Discuss your data analysis and its implicationsFennema, Elizabeth, Thomas Carpenter, Victoria Ja- Were disruptive students getting more “air time”? What does this mean for cobs, Megan Franke, and Linda Levi. “A Longitudi- the learning of students who were well behaved? nal Study of Gender Difference in Young Children’s Were you asking more low-level questions than high-level questions? What Mathematical Thinking.” Educational Researcher 27 does this mean for the type of instruction you are providing? (June–July 1998): 6–11. Do your interactions consist mainly of providing academic information andGilbert, Melissa C. “Applying the Equity Principle.” asking low-level questions? What does this mean for all students’ ability to Mathematics Teaching in the Middle School 7 (Sep- learn mathematics? tember 2001): 18–19, 36. How can gender differences in the classroom unintentionally lead to differenc-Hanson, Katherine. Teaching Mathematics Effectively es in your students’ performance, achievement, and motivation? Discuss what and Equitably to Females. New York: ERIC Clear- this means for your instruction and your students’ ability to learn from you. inghouse on Urban Education, Institute for Urban and Minority Education, 1992. Examine your transcript for the interactions that occurred after you askedLampert, Magdalene. Teaching Problems and the Prob- questions or provided instruction to the whole class lems of Teaching. New Haven, CT: Yale University Who responded to you? Whom did you call on? Were the same students Press, 2001. responding to you when you asked questions to the whole class? How did youLevi, Linda. “Gender Equity in Mathematics Education.” respond to them? What was the gender ratio for students you called on after Teaching Children Mathematics 7 (October 2000): asking a question to the whole group? 101–5.Martin, Brian. “Mathematics and Social Interest.” In Ethnomathematics: Changing Eurocentrism in Math- Mathematics for All!” Mathematics Teaching in the ematics Education, edited by A. B. Powell and M. Middle School 10 (May 2005): 479–83. Frankenstein, pp. 155–72. Albany, NY: State Univer- Shepardson, Daniel, and Edward Pizzini. “Gender Bias sity of New York Press, 1997. in the Classroom—A Self-evaluation.” Science andMcGraw, Rebecca, Sarah Theule Lubienski, and Mari- Children (November–December 1991): 38–41. lyn E. Strutchens. “A Closer Look at Gender in NAEP Sullivan, Mary, and Penny Bishop. “Disaffiliated Boys: Mathematics Achievement and Affect Data: Intersec- Perspectives on Friendship and School Success.” tions with Achievement, Race/Ethnicity, and Socio- Middle School Journal 37 (November 2005): 22–30. economic Status.” Journal for Research in Mathemat- Zaslavsky, Claudia. The Multicultural Math Classroom: ics Education 37 (March 2006): 129–50. Bringing in the World. Portsmouth, NH: Heinemann,Morgan, Candia, and Anne Watson. “The Interpretative 1996. s 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 ofTeaching Children Mathematics / March 2007 395