AVAILABLE from Sex-Role Stereotyping-In Mathematics

DOCUMENT REbUME

ED 259 923 SE 045 894

TITLE Sex-Role Stereotyping-in Mathematics Education. A Course to Reduce Math Anxiety and Sex-Role Stereotyping in Elementary Education. INSTITUTION City Univ. of New York, Flushing, N.Y. Queens Coll. SPONS AGENCY WomL.n's Educational Equity Act Program (ED), Washington, DC. PUB DATE 84 NOTE 58p.; A product of the Teacher Education and Mathematics Project. For related documents, see SE 045 888-896. AVAILABLE FROMWEEA Publishing Center, 1984 Education Development Center, Inc., 55 Chapel St., Newton, MA 02160. PUB TYPE Guides - Classroom Use - Guides (For Teachers) (052)

EDRS PRICE MF01 Plus Postage. PC Not Available from EDRS. DESCRIPTORS Attitude Change; Elementary Education; *Elementary School Mathematics; Females; Higher Education; Instructional Materials; *Mathematics Anxiety; Mathematics Education; *Mathematics Instruction; *Sex Bias; Sex Role; *Sex Stereotypes; Student Attitudes; *Teacher Education; Teaching Methods IDENTIFIERS *Teacher Education and mathematics Project ABSTRACT This Teacher Education and Mathematics (TEAM) module is designed to increase students': (1) awareness of the existence of sex bias in curriculum materials and in classroom practices; (2) skill in identifying sex-role stereotypes in materials and practices; and (3) skill in counteracting sex bias in instructional materials and practices. It consists of an instructor's text and student materials. The instructor's text provides specific directions for guiding the lessons and commentary designed to help teachers build positive mathematics attitudes. The format is one of "facing pages" whereby the right-hand page provides step-by-s.ep teaching directives and the left-hand page provides teaching insights, other options of instruction, and psychological or attitudinal strategies, when appropriate. Space for the instructor to add notes about a particular point in the lesson or about teaching experiences with the class (for future reference and use) is also provided on the left-hand page. When there is no commentary applicable to the points in the lesson, the entire left-hand page has been alloted to "notes." Student materials include various worksheets, assignments, and readings which focus on such area:: as views of females and males in mathematics curriculum materials and the content analysis of mathematics textbooks. (JN)

*********************************************************************** * Reproductions supplied by EDRS are the best that can be made * * from the original document. * ************t********************************************************** ,16 614.t-fe,t

. - . ,

. ., U.S. DEPARTMENT OF EDUCATION NATIONAL INSTITUTE OF EDUCATION . EDUCATIONAL RESOURCES INFORMATION CENTER (ERIC) This document has been reproduced as received from the person or organization originating it. . . L 1 Minor changes have been made to improve , . reproduction quality.

Points of view or opiruons stated in this docu mint do not necessarily represent official NIE position or policy.

, r. . ..

:;2 , . .

1,rt , I.

P'71),. "PERMISSION TO REPRODUCE THIS -, ... (*; T MATERIAL IN MICROFICHE ONLY z r"'; , HAS BEEN GRANTED BY f 1," Libbki LOPie1d_L__ . . . ,..

. . . . :.; 0.

. . . . . - TO THE EDUCATIONAL RESOURCES " . INFORMATION CENTER (ERIC)." `- ". . .; . eta

!:-.:tt.,.-.,....-_..-- -.,--:---1,:::',71,,,,.;;;,5:';, ;.. i.,..',.;.:: -1'... cr ,-, _.,., = - 1 . ',',. r ..' ;.:',,ir.--,,,,:i ,,1-'.14`,.2ftp,,11.4,::::e. ' cr:r.151.,`,..." 11%-',

f.-_.;',, 14-441C,

4,Y

::-:-T,V.:*.:","-.,.;

;

tp 47, TEACHER EDUCATION AND MATHEMATICS

A Course to Reduce Math Anxiety and Sex-Role Stereotyping in Elementary Education

SEX-ROLE STEREOTYPING IN MATHEMATICSEDUCATION

Elaine B. Chapline and Claire M. Newman Project Codirectors

Assisted by: Francine Sicklick and Elenor Rubin Denker

Queens College of the City University of New York

Women's Educational Equ'ty Act Program U.S. Department of Education

T. H. Bell, Secretary Discrimination Prohibited: No person in the United States shall, on the grounds of race, color or national origin, be excluded from participation in, be denied the benefits of, or be subjected to discrimination under any program or activity receiving Federal financial assistance, or be so treated on the basis of sex under most education programs or activities receiving Federal assistance.

The activity which is the subject of this report was produced under a grant from the U.S. Department of Education, under the auspices of the Women's Educational Equity Act. Opinions expressed herein do not necessarily reflect the position or policy of the Department, and no official endorsement should be inferred.

Printed and distributed by WEEA Publishing Center, 1984 Education Development Center, Inc., 55 Chapel Street Newton, Massachusetts 02160

ii PROJECT STAFF

Elaine B. Chapline Claire M. Newman Project Codirector Project Codirector Psychologist Mathematics Educator

Carol Kehr Tittle Elenor Rubin Denker Evaluator Evaluation Associate

Francine Sicklick Annette Berson Mathematics Associate Project Associate

Sarah Knecht Dorothy Watkins Research Assistant Research Assistant

Katherine Flanagan Administrative Assistant

Lucille Joseph Kim Longo Secretarial Assistant Secretarial Assistant ACKNOWLEDGMENTS

The Teacher Education and Mathematics projectwas a comprehensive effort that required the cooperation of many people. It is impossible to identify all the Queens College faculty and staff whose assistance,support and encouragement helped bring the project to fruition.

The consultants listed below were most helpful in their advice,comments and suggestions.

James Bruni Mitchell Lazarus Mathematics Educator Mathematics Educator Lehman College of CUNY Independent Consultant

Hilda Cooper Edna Meyers Mathematician Psychologist Queens College of cuNy City College of CUNY

Sheila Crowell Frederic Paul Editor Mathematics Educator Caribou State Education Department, New York Elizabeth Fennema Mathematics Researcher Anne Peskin University of Wisconsin Mathematics Educator City College of New York Stanley Kogelman Mathematician, Author Lila Swell Mind Over Math Psychologist Queens College of CUNY Ellen Kolba Editor Caribou .1

CONTENTS

I. INSTRUCTOR'S TEXT

Introduction . 1-3

Overview 1-5

Beginning the Program 1-7

Content Analysis of Math Materials 1-9

Classroom Practices J-11

II. STUDENT MATERIALS II

"Teachers and Sex Bias in Mathematics,"by Elizabeth Fennema . . 4 11-3

"Sex Roles in Mathematics: A Study of the Status of Sex Stereotypes in Elementary Mathematics Texts,"by Henry

S. Kepner, Jr. and Lilane R. Koehn . . 11-8

"Update,on Sex-Role Stereotyping inElementary Mathe- matics Textbooks," by Helen F. Kuhnke 11-17

"Sex Stereotypes in Mathematics andScience Textbooks for Elementary and Junior High Schools," by Jcsephine Mlinar . . 11-22

"Sexual Stereotyping in Mathematics: Beyond Textbooks," by Laurie H. Reyes 11-27

Views of Females and'Males in Mathematics Curriculum Materials 11-29

Content Analysis: Mathematics Texts 11-30

Classroom Tasks and Activities 11-31

"Teachers Are Iportant," Script bySheila Crowell, Elenor Rubin Denker, and Ellen Kolba 11-32

vii SEX-ROLE STEREOTYPING IN MATHEMATICS EDUCATION

INSTRUCTOR'S TEXT r

INTRODUCTION

The Sex-Role Stereotyping in MathematicsEducation module was designed for use in a course or workshopseries concerned with mathematics and women's issues. It consists of an Instructor's Text and StudentMaterials. Both parts of ..the moduleare designed°for use in a loose-leaf notebook.

The-Instructor's Text indicatesspecific steps the instructorcan take to build lessons that make studentsaware of the nature and extent of sex bias in curriculum materials. This is accomplished by a "facing pages" format. The right-handpage contains directive text that indicates how the instructor may proceed,step by step, in presenting the lesson. The left-hand page, "Commentary and Notes,"provides teaching insights, other options of instruction, and psychologicalor attitudinal strategies, when appropriate. Space for the instructor to add heror his own n tes about a particular point in the lesson or about teachingexperie ce with the class (for future reference and use)is also provided on th_ left-hand page. When there is, no commentary applicableto the points in the lesson, the entire left-handpage has been allotted to "Notes."

Student Materials includes worksheets,assignments,,and readings.

1-3 NOTES

ss,

1-4 OVERVIEW

The purposes of this moduleare to increase (1) students' awareness of the existence of sex bias in curriculummaterials and in classroomprac- tices, (2) students' skill in identifying sex-rolj-stereotypesin materials and practices, and (3) students'skill in counteractingsex bias in instruc- materials and practices.

A variety of learning activities has beenincluded whiel provides for whole-class, small-group, and individualparticipation.

43.

1-5 COMMENTARY AND NOTES

This slide-tape show is available from: ..". Feminist Press Box 334 Old Westbury, New York 11568

Purchase price: $300.

Alternative ways of introducing the topic can be through the instructor's presentation of materials on sex bias, through readings, through discussion of personal experiences, or through review of textbooks and workbooks.

Expect that many feelings associated with past experiences 017 be touched. Students may express widely differing reactions, some feelingthat they had, and others that they had not, personally experienced sex bias.

These articles are included in Student Materials.

teelings of the need for fairness to males may be expressed. Don't be surprised. if students feel strongly and take strongpositions.

_1 z 1-6 BEGINNING THE PROGRAM

Introduce students to thepresence of sex bias through theuse of a slide- tape show that has demonstrated impacton knowledge and attitudes.

Images of Males and Females in Elementary a School Textbooks in Five SubjectAreas

This preseatation, by Lenore J.Weitzman and Diane Rizzo, provides detailed data based on content analyses ofthe most widely used textbooks in science, mathematics, reading, spelling, and socialstudies. For many people its description of the latentcontent of textbooks is a revelation. Ap- proximately 45 minutes should be scheduledfor viewing the program, which consists of three slide carousels andan audiotape. Time for discussion should be provided, since the materialstend to arouse feelings and to provoke questions and ideas.

Ask: "How did you feel about thisinformation? Have you thought about these sex equity issues before? Were you encouraged to do nonstereotyped things by teachers?How were stereotyped conceptions ofsex roles fos- tered, in your experience?"

Ptovide students with additional {reformationby assigning some or all of the following:

1. Fennema, E. "Teachers and Sex Bias in Mathematics." Mathematics Teacher 73 (March 10;J): 169-73.

2. Kepner, H. S., Jr., d L. R. Koehn. "Sex Roles in Mathematics: A Study of the Stat : :s of Sex Stereotypes in ElementaryMathe- matics Texts."The Arithmetic Teacher 24 (May 1977): 379-85.

3. Kuhnke, H. F. "Update on Sex-Role Stereotyping in Elementary Mathematics Textbooks."The Arithmetic Teacher 24 (May 1977): 373-76.

4. Mlinar, J. "Sex Stereotypes in Mathematics and Science Textbooks for Elementary and Junior High Schools." In Report on Sex Bias in the Public Schools. New York: Education Committee, National Organization for Women, New York City Chapter, 1973.

5. Reyes, L. H. "Sexual Stereotyping in Mathematics:Beyond Text- books."The Arithmetic Teacher 26 (April 1979): 25-26.

Allow sufficient time for students to discuss theirreactions to the ideas they have read.

Ask: "What surprised you most in the article(s)you read? What have you noticed in your readings from other sources?How did these ideas feel to you as you read them?Has it seemed to you that the womenwere wearing aprons, baking cookies, and ironing, whereas the boyswere getting to do all tne things that sounded adventurous?"

I-713 COMMENTARY AND NOTES

Textbooks can often he found in the children's section of the library if a curriculum materials center isn't available. Recently published texts should be included i- the supply, along with some from the late 1960s and early 1970s.

Note the nature and eAtent of students' participation in this activity. Some students are uncomfortable with the idea of sex bias and find it very difficult to detect any instances of bias. It is helpful to the student to feel accepted, even though the instructor points out many instances of bias that individual students didn't see.

1-8 CONTENT ANALYSIS OF MATH MATERIALS

Have students read "Views of Femalesand Males in Mathematics Curriculum Materials" in their StudentMaterials, page 11-29. Ask the students to evaluate these materials forsex bias.

After a brief discussion of theirreactions, show students how observations can be formalized by means of guidelines, suchas those in the Student Ma- terials section under "ContentAnalysis: Mathematics Texts," page 11-30.

Check on students' understandingof what each categorymeans by having them generate examples drawnfrom their reading or experiences (e.g., "This book showswomen in 'female' occupations, suchas secretary or nurse, and men in 'male' occupations, suchas engineer or scientist or police officer").

Organize the students in pairs andhave each pair, using the guidelines, analyze a randomly selected section (10to 12 pages, for example) ofan elementary school mathematicstext. Students can share their findings in a class discussionor in discussion groups of eight to ten students.

Elicit students' responses to the materialsthey are using. Encourage students to express their feelings. Help keep the discussion moving by asking questions suchas "How do others feel about this point?" and "Does this experience seem similar to (ordifferent from) your own?"Summarize ideas to emphasize key gpints.

1-9 CLASSROOM PRACTICES

Introduce this segment of the module by havingstudents read to themselves or perform the script "T :chers Are Important," which is foundin Student Materials, page 11-32. Allow about 20 minutes for reading; if acted, probably half an hour will be required.

Invite students' reactions to the readingor performance. Ask, "How did you feel about Millie's problem in teaching math? Did you have other ideas about how Millie could have handled herproblem? What interested you most (least) about the problem presented? How did you feel about Sue's interaction with Millie?"

Direct students' attention to "Classroom Tasksand Activities" in Student Materials, part II, page 31. Have students examine and analyze the list for the presence of bias. Discuss their judgments about the samplepre- sented. Ask for comments-drawn from theirexperiences.

Ask: "In what wayscan teachers counteract the effects of sex-role stereotyping in curriculum materials and inclassroom practices?" Make a list of those suggestions for studentsto keep as a resource. The list might include items like the following:

1. Point out to students ways in which girls andboys (women and men) are portrayed in textbooks.

2. Rewrite math problems (for children and/or with children)to provide nonstereotyped portrayals of males and females.

3. Have students point out instances of stereotyping they findin books they use.

4. Be conscious of the ways in whichyou, as the teacher, assign tasks in the classroom. Give assignments on a sex-neutral basis.

5. Provide materials to supplement classroomresources that describe girls (women) as successful andcompetent in a wide variety of activities.

6. Volunteer to be on the committee of teachers who willrecommend texts to be bought. Check to be sure that sex-neutral materials are recommended for purchase. SEX-ROLE STEREOTYPING IN MATHEMATICS EDUCATION

STUDENT MATERIALS TEACHERS AND SEX BIAS INMATHEMATICS

A.look at some ways that teachers can improve the mathematics education of girls, as well as that of boys.

By ELIZABETH FENNEMA filter that keeps women, as wellas some University of WisconsinMadison men, from many desirable professions and Madison, WI 53708 vocations. What do teachers do that differentially Teachers are important! They makea major impact on students' feelings about influences males and females in their learn- mathematics as well as on their learning of ing and feelings about mathematics? In mathematics. Although other people such many subtle ways, teachers treat females as counselors and parents also have an ef- differently than they do males, and this dif- fect, it is the day-by-day interaction with ferential treatment is a negative influence teachers that is the most powerful influence on females' studying of mathematics. From on students. Students' feelings about them- the first grade throughout high school, selves as learners of mathematics, theirper- teachers pay more attention to males than ception of the usefulness of mathematics, to females (Schonborn, 1975). Not only do and their willingness to continue the study males receive more disciplineor blame of mathematics beyond minimum require- from teachers, they also receivemore ments are all directly influenced by teach- praise from teachers. In high school mathe- ers. matics classes, high-achieving boys receive Unfortunately, there is much evidenceto significantly more attention from teachers indicate that teachers are differentially in- than do high-achieving girls (Brophy and fluencing females and males in their learn- Good, 1970). And this is true not only for ings and feelings toward mathematics. male mathematics teachers but for female Partly as a result of this differentialtreat- mathematics teachers as well. As teachers ment, females, to a much greater extent are spending more time with males, not than males, are receiving inadequate mathematical education in high schools. This inadequate educationwas demon- Females are receiving strated by the results of the first National inadequate mathematical Assessment of Educational Progress education in high schools. (NAEP), where the superiority of adult males clearly appeared. In additionto data from NAEP, the predominance of males in only are they helping males more, but also all mathematics-related careers for which they are communicating, albeit subtly, that women lack mathematical skills, has been males' concerns in mathematicsare more attested to by many authors. Although the important than females' concerns and that reasons for this domination can be traced mathematics learning is more essential for to many causes, a major reason is that males than for females. many. if not most, women are inadequately Not only do mathematics teachers inter- prepared in mathematics. Without ade- act more with males than they do with fe- quate mathematical training, women will males, they also reinforce or reward males never achieve equity with men in the world and females for different types of behavior. of work. Mathematics is truly the critical Males are rewarded for behavior stereo-

March 1980

16 11-3 typed as male, and females are rewarded males to be more anxious than the females. for behavior stereotyped as female. It ap- Male students thought that mathematics pears that in mathematics, computational was more personally useful than did the fe- behavior is rewarded in females, and male students. Once again, the mathe- higher level cognitive skills, such as prob- matics teachers' perception was different lem solving, are rewarded in males (Fen- than the students'. The teachers thought nema, 1977). What is rewarded is usually that mathematics was potentially more use- what is learnedand there is a'tendency ful to their female students than to male for females to be better at computational students, tasks and males at higher level cognitive One can only speculate why the teachers' skills (Fennema, 1977). As one advances in perceptions differed so much from the stu- the study of mathematics, these higher dents' 'feelings. The teachers might have answeted the questions the way they thought was most socially desirable. On the Mathematics is the other -hand; it is difficult to see why it critical filter to would be believed that it is socially desir- many desirable jobs. able for males to be more anxious about mathematics than females. A more reasonable explanation appears to be that the level cognitive skills become increasingly teachers are inaccurate in their perceptions important, and mathematics becomes in- of girls' feelings toward mathematics. creasingly incongruent with the female ste- These inaccurate perceptions are caused, at reotype. least partly, from the stereotypic belief that Mathematics teachers are less concerned math is a male domain and that it is highly ahout providing remedial help to females essential that males learn it. Teachers than they are to males (Gregory, 1977). might be more anxious about males learn- Males are much more apt to be referred to ing mathematics and, as a result, feel that remedial clinics for assistance than are fe- the boys themselves are more anxious. males, even when the achievement levels of No matter what the explanation of the the girls and boys are similar. teachers' responses is, it is clear that many Teachers have different perceptions of teachers do perceive males and females dif- males and females as learners of mathe- ferently as learners of mathematics and do matics, and these perceptions are often in- hold different expectations for female and accurate. In a recent survey, information male learners of mathematics. These per- about attitudes toward females, males. and ceptions and expectations, in turn, do influ- mathematics was gathered from fifty-two ence teacher treatment of females and male and twenty-four female mathematics males as learners of math. They expect teachers in ten midwestern high schools. boys to be better problem solvers, to persist Two attitudes that appear to be strong in- in their mathematical activities longer, and fluences in females electing to study mathe- to be more interested in math. Female stu- matics were selected for study: perceived dents ire less likely to be referred for usefulness of mathematics and anxiety mathec ics assistance Lnan are male stu- about learning mathematics (Fennema, dents (Gregory, 1977). Underachieving fe- 1977). Information about the same atti- male students are less likely to be behavior tudes toward mathematics was also col- problems than are underachieving males lected from 1200 ninth- and tenth-grade and, as a result, less visible to their teach- mathematics students in the same schools. ers. Although the female students indicated To more clearly recognize teacher be- that they had significantly higher levels of haviors that contribute to sexism in mathe- anxiety toward mathematics than did the matics education, consider the following male students, the teachers perceived the scenarios. (Most scenarios are from E. Fen-

Mathematics Teacher

II-4 t.

nema, A. Becker, P. Wolleat, and J. Pedro Eric: Oh yeah, x to the fifth. I get it inMultiplying Options and Subtracting now. Bias,an intervention program designed to eliminate sexism in mathematics education, This is an example of both loweredex- 1979, and developed under a grant from pectations for females as well as the fact the Women's Educational Equity Act Pro- that problem solving is perceivedas more gram. Office of Education, 400 Maryland important for males. By sticking with the Avenue, S.W., Room 2136, Washington, male, the teacher helped him to,havea suc- DC 20202.) cessful experience. Her behavior alsocom- municated to both students that mathe- Scenarit, I matics was more important for males than (John and Sue, seated side by side ina for females. mathematics class, are workingon a Scenario III mathematics problem.) Teacher:If the Rams have 3 touchdowns John: Sue, have you got this problem? and the Packers have 2 touch- Sue: If you find the square root c.fA, downs. and a safety, how many you'll get the answer. more points will the Packers Teacher:Has anyone figured out how to need to win the game? get the answer? Betty: Mr. Brown, how many points in (John's and Sue's hands both go up.) a safety? Teacher:John, how did you getit? Teacher:(Ignoring Betty's questiun) Carl? John: If you find the square root ofA, you'll get the answer. How can a female (or anyone) participate in problem solving if they don't know Teacher:That's right! Did everyone see how John got the answer? anything about the components of the problem? It is only good teaching to use ex- Many women report that other receive amples understood by all students. credit for .their good ideas, and this scenario demonstrates a teacher rewarding the Scenario IV wrong student. Although it would have Teacher:Today, we are going to havesev- been difficult for the teacher to notice this eral men tell us how theyuse student-to-student interaction, shouldn'ta math in their careers. teacher be alert so that praise for good work goes to the correct recipient? Another Women use (or should be able to use) point can be raised from this scenario. mathematics in their careers also. Both girls and boys should see examples of both Some women feel it is somehow unfemi- nine to appear to be too smart in mathe- women and men using mathematics. Role matics, so they are reluctant to volunteer. models are important! Teachers can help young females to realize Scenario V the importance of class participation. Janetis taking too long to solve a mathe- Scenario II matics problem. She finally exhibits the (Mathematics clas withthe teacher mov- frustration she is experiencing by getting ing around providing individual help) teary-eyed. Teacher:Have you figured out the an- Teacher:That's OK, dear. Don't worry swer,Marcia? about it if it doesn't come out Marcia: Uh, no. Not yet. right. Teacher:Eric, how about you? Casserly (1975) refers to the phenome- Eric: I can't get it! non exhibited here as the "tear trap." Feel- Teacher: Come on, Eric. You can do it. ings of frustration cannot be alleviatedby What's the exponent? permitting a teary-eyed girl to fail in prob-

Ed.'s note: MultiplyingOptions and SubtractingBias, cited above, is available fromthe Council of Teachersof Mathe- matic's, 1906 AssociationDrive, Restoro VA 22091 11-5 lem solving. Ways must be sought to keep into consideration when, teaching: rate of the girl on task so she can feel success and learning, background etperiences, and increased confidence in m?thematics. overall ability. However, sex is not an individual difference that should be considered. Scenario VI There is n3 individual difference important John is a gifted student who is excelling in to the learning of mathematics that all fe- mathematics. His teacher has encouraged males exhibit and all males do not, or vice him to join the mathematics club and ar- versa. Each person in class should be ranged for him to take an advanced mathe- treated as an individual whose needs and matics class at the local college. Mary, also abilities must be considered. Boys as a a gifted student, finds mathematics very group should not be treated differently easy and she likes it. Her teacher feels she than girls as a group, any more than all should try to become more outgoing and brown-eyed people should be treated as a involved with other girls and social events group having specific learning needs. Ex- at the school. The teacher urges Mary to pectations of females should be as high as join the debate team and a women's social expectations of males. Work demanded club. and received from females should be the Teacher beliefs about sex-appropriate same high quality that is demanded and re- behavior result in different treatment of ceived from males. Evidence clearly in- boys and girls. Not all females should have dicates that when females, especially high? to succeed in social activities when some achieving females, are expected to learn are much more suited for other types of mathematics, they not only learn, but their roles. at.hievement increases. In successful, bright Unfortunately, these scenarios are not girls' own words, "they were never treated fiction. They have been derived from re- like a girl," (Casserly, 1975). ports by many females reflecting on their Not only must teachers become sex blind learning of mathematics. Teachers do treat in the treatment of their students, they male and female learners differently, and must overtly help their students, especially this differential treatment reinforces in fe- their male students, overcome the se. typ- males, as well as in males, the belief that ing of mathematics. High school males mathematics is a male domain. overtly stereotype mathematics as a male domain (Fennema and Sherman, 1978). It is placing a heavy burden on young girls to ask them tc, disregard what male peers be- Sex is not an individual lieve is appropriate behavior. As long as difference that should males continue to stereotype mathematics be considered. as a male domain, it will be difficult to encourage very many females to study it. There are also some specific things that The identification of teacher behaviors teachers can do to reduce sexism in mathe- that differentially influence males and fe- matics education. All conversations and re- males should be viewed positively. Once marks should be monitored so any negative such influential behaviors are identified, or belittling references about women as change can take place. Teachers can con- learners or doers of mathematics are elimi- sciously observe their own behaviors and nated. Feelings about mathematics should change those that contribute to females' be discussed students. Since more fe- feelings that mathematics is unimportant males than males do report they are ,.nx- for them. Most important, teachers can de- ious about mathematics, providing help for velovsex blindness in their mathematics mathematics anxiety will tend to benefit fe- classes. there are many important individ- males. (This is not in conflict with the idea ual differences that teachers should take o: sex blindness. Although more females

Mathematics Teacher 21 I1-6 than males may be anxious, not all females and Mathematics: Research Perspectives for I. flange are anxious, nor are all males confident. (NIE Papers in Education and Work: No. 8). Wash- ington. D.C.: National Institute of Education, pp. Anxious males deserve help as well as do 79-135, 1977. anxious females. The anxiety is what is im- Fennema, E., and L. Reyes. "Longitudinal Study of portant, not the sex of the anxious person.) Teacher/Peer Influences on Sex-related Differences Although feelings about math anxiety in Mathematics." (In press). Fennema, E., and J. A. Sherman. "Sex-related Differ- should be appreciated, standards should ences in Mathematics Achievement and Re' teed not be lowered in the hopes that this will Factors: A Further Study."Journal for Research in lower anxiety. Such lowering of standards Mathematics Education 9 (1978):189-203. merely suggests or reinforces a belief that Gregory, M. K. "Sex Bias in School Referrals."Jour- nal of School Psychology 5 (19745-8. one is not capable of learning mathematics. Mullis, I. V. S.Educational Achievement and Sex Dis- Students should acknowledge and take re- crimination.Denver, Colo.: National Assessment of sponsibility for their own learning. Persons Educational Progress, 1975. who feel that their success is du 3 to an in- Schonborn, B. G. "An Investigation of the Attitudes of Elementary School Teachers toward Sex-Role ternal, stable factor are much more apt to Behaviors of Elementary School Children." Un- continue working in the area. Females, as published doctoral dissertation, University of kill- well as the males, should participate in nois, 1975. high level cognitive activities. All students should be informed about the usefulness of mathematics. The fact that many career options are closed to those without knowledge of mathematics should be emphasized. Schools should not be making mathematicians of everyone (even if they could). However, p-eparation in studying mathematics beyond the mini- mal requirements keeps many options open, and schools should ensure that all students, females as well as males, have as many options as possible. Teachers are important! Teachers can influence females and they should! As Grace Burton (1979) so aptly said, it is "the gentle persuasion of secondary school teachers of mathematics" that will enforce a change in the mathematics education of women.

BIBLIOGRAPHY Brophy. J. E., and T. L. Good. "Teachers' Communi- cation of Differential Expectations for Children's Classroom Performance: Some Behavorial Data." Journal of Educational Psychology 61 (1970):365- 14. Burton, G. "Regardless of Sex."Math' latics Teacher 72 (1979):261-70. Casserly, P.L. An Assessment of Factors Affecting Fe- male Yartkipants in Advanced Placement Programs in Mathematics. Chemistry, and Physics(Grant No. GY-11325). Washington, D.C.: National Science Foundation, July 1975. Fennema, E. "Influences of Cognitive. Affective, and Educational Variables on Sex-related Differences in Mathematics Learning and Studying." InWomen

T I, 7 SEX ROLES IN MATHEMATICS: A STUDY OF THE STATUS OF SEX STEREOTYPES IN ELEMENTARY MATHEMATICS TEXTS

Henry S. Kepner, Jr.'and Lilane R. Koehn

An associate professor of curriculum and instruction at the University of Wisconsin- Milwaukee, Henry Kepner i3 responsible for the elementary, and secondary mathematics education programs on that campus. Lilane Koehn teaches at the Nicolet High School in Glendale, Wisconsin.

Examples like the following were indicate sex stereotyping is one identified in the early 1970s by of the most important factors in parent groups, educators, admin- the goverhance of behavioral.de- istrators, and legislators as velopment, motivation, and self- representative of elementary , concept (Brody). Recent reports mathematics materials that pre- from the National Assessment of sent a stereot-ped view of wom- Educational Progress (NAEP) show en: that in most other learning areas tested "females tended to do bet- The Ruth is baking cookies. ter than males. However, the re- recipe calls for 3/4 cup of sults for science and consumer sugar. If she wants to dou- mathematics shows females ,,at a ble the recipe, how much definite disadvantage. These sugar should she use? data seem to reinforce the old stereotypes about female inabil- Miss Jones types 30 letters ity to cope with 'technical' or today. If she types 12 by 'logical' subjects" (NAEP 1975 lunchtime, how many trust she [a], p. 35). type after she returns? Extensive sex stereotyping has Based on this awareness, argu- been well documented in earlier ments for the eliminationof textbooks (Mlinar 1973, Rogers sexism in educational materials 1975). But has sexism been elim- have been clearly stated in nu- inated from the more recently pub- merous journals, policy state- lished elementary mathematics ments, and legislative acts series (1971 through 1975)? To (Brody 1973, Texas Education answer this question the authors Agency 1974, California State examinedtuts from eight major Department of Education 1974). publishers, chosen on the basis The key concern is that texts of recent publication dates and may provide norms for howboys wide use of the series in schools. and girls, and men and women The first-, fourth-, and seventh- should behave. Research data grade texts were examined in each

I1-823 series to determine whether sex The authors found that an stereotyping had persisted in efficient way to evaluate a activities and occupations por- telt was to page through the trayed in illustrations and in book twice--one time recording written problems. This sam- data on illustrations (all pling6f grade levelswas se- pictures, charts, and graphs), lected to identify differences and another time recording data that might appear as the format on problems (written exercises changed from pictorial mathe- and examples). matics to symbolic mathemat- For the first category (equal ics.

representation), recording the . number of males and females shown EVALUATION OF THE TEXTS in the illustrations ormentioned in the problems was sufficient. "All those attitudes and ac- For categories 2 and 3 (occupations which demean or stereo- tions and activities), lists of type individuals or groups occupations and activities in- because of their sex" is a volving" males and those involv- common definition of sexism ing females were constructed for (Sexism in Textbooks Commit- each text. The of each tee 1974, p. 1). The authors mathematician identified was used this definition and the listed in category 4. Identifi- California State Department of cation of attempts to use sexu- Education guidelines to de- ally neutral language (such as velop an evaluation form for salesperson, fire fighter, or use with each text. (See fig- chairperson) or of blatantly ure 1.)

Figure 1

Evaluation Form for Sexism in MathematicsTexts

Illustrations Problems Male Female Male Female 0 1. Equal representation (record frequency of males and females)

2. Occupations engaged in (list each occupation engaged in by a male or female)

3. Activities participated in (list each activity participated in by a male or female)

4. Mathematicians represented (name the mathematician identified)

5. Sexually neutral language (note attempts to use sexually , neutral language, and note blatant sexist language)

11-9 24 se)Ast language (such as the Equal representation in prob- weaker sex, authoress, or man- lems occurred in only one text- kind) was planned in category 5. book. Two of the textbooks included more females (52% and 51%) RESULTS AND OBSERVATIONS than males in the problems. The percentages of males and females In examining the illustrations in the problems for the twenty- in the twenty-four books chosen, four textbooks studied are con- the authors found only one book tained in table 2. that equally represented the sex- Equal representation of the es and two books-that showed more sexes in problems or illustra- females (51%) than males. In tions in a book at a particular twelve, or one-half of the books, grade level did not indicate 60 percent or more of the people equal representation at all grade shown in illustrations were males. levels. For example, in Series H In two of the books, over 90 per- an equal representation ofthe cent were males. The percentage sexes in illustrations occurred of males and females shown in in the first-grade book. The each of the eight serles is listedpercentage of males in the il- by grade level in table 1. lustrations rose to 62.5 percent

Table 1 Percentages of males and females in illustrations Grade 1 Grade 4 Grade 7

11 2t F

Series A 59% 41% 67% 33% 66% 34% Series 8 53 47 63 37 64 36 Series C 63 37 52 48 53 47 Series D 49 51 57.5 42.5 58 42 Series E 100 0* 68 32 66 34 Series F 52 48 66 34 56 44 Series G 49 51 59' 41 63 37 Series H 50 50 62.5 37.5** 92 8

*17 illustrations **8 illustrations

Table 2 Percentages of males and females inproblems Grade 1 Grade 4 Grade 7 M F

Series A 0% 0% 62% 38% 66% 34% Series B 48 52* 54 46 57 43 Series C 0 0 49 51 56 44 Series D 0 0 57 43 63 37 Series E 56 44** 50 50 57 43 Series F 58 42 65 35 56 44 Series C 0 57 43 56 44 33*** Series ti 61 10 30 82 18

*23 problems * *l8 problems ***9 problems 2

II-10 V

Table 3 Occupations given to males and to females in the grade 4 book of Series F

Male Female

Illustrations farmer nurse shoemaker

Problems doctor clerk farmer homemaker owner of a shop princess in the fourth-grade bookand to They were shownas bakers, law- 92 percent in theseventh-grade yers, doctors, builders, farmers, book. (See table 1.) football players, Occupations given to males salesmen, astro- and nauts, and so on. females were listed foreach of In one text, malesand females the texts studied. For example, were given the same occupations. table 3 is the list for Book 4 of Book 1 of Series F Series F. In the illustrations, identified both males and females males were cited in as police offi- two occupa- cers, fire fighters, postal tions; females inone. em- Each sex ployees, musicians, and was identified in threeoccupa- educators. The number of activitiespar- tions in written problems. In ticipated in by malesand females this book, males were givena total of four different was approximately thesame at occupa- each grade level, although tions, as were females. males typically participated in In elementary mathematics more. This is shown in the texts, males usually ratios given were shown in table 5. in a greater diversity of The types of activi- occu- ties, however, pations than females. were vastly dif- This is ferent. shown in table 4, which The activities females gives the engaged in were predominantly ratio of male occupationsto fe- passive, particularly inthe il- male occupations forillustra- lustrations.Their most strenu- tions and written problems,as ous activity was runninga race, well as a ratio for bothillus- skipping rope, or ridinga bicy- trations and problems combined. cle. Boys, on the other hand, When several occupationswere spent most of their timeengaged cited for eachsex, the types of in strenuous physicalactivity. occupations were not thesame. This included playing (See table 3.) football, Teacher, clerk, basketball, baseball, homemaker, and nurse soccer, were the oc- tennis, golf, lifting weights, cupations most often given to fe- running hurdles, doing males. Half of the seventh-grade gymnas- tics, or climbing mountains. books mentioned teacher as a fe- Female activity increased male occupation; three mentioned in the textbook problems. Besides clerk. In the twenty-four books doing their householdduties, studied, chemist and doctorwere they played Ping-Pong, the only professional golf, and occupations, basketball; and went diving,hik- outside of nursing and teaching, ing, bowling, and running. given to females in the Males illustra- were still involved in a multi- tions. There seemed to be no tude of sports, but theyalso did prevalent occupation formen. work around the house--tilinga Table 4 Ratios of occupations given to males to occupations given to females (Combined illustrations and problems, illustrations, and problems) Grade 1 Grade 4 Grade 7 Comb. Illus. Prob. Comb. Illus. Prob. Comb. Illus. Prob.

Series A * * * 5:1 1:0 4:1 6:2 4:0 2:2 Series B * * * 4:3 2:2 3:2 6:4 3:3 3:1 Series C * * * 2:5 1:2 2:5 7:3 0:1 7:2 Series D 1:1 1:1 * 2:1 0:1 2:1 2:0 1:0 1:0 Series E 1:0 1:0 * 2:2 * 2:2 7:1 3:1 4:0 Series F 8:6 8:6 * 4:4 2:1 3:3 10:9 9:6 3:3 Series G 0:1 0:1 * 5:0 4:0 3:0 4:1 1:1 3:0 Series H * * * 3:1 * 3:1 9:0 4:0 5:0

*No male or female occupations were cited in the text.

Table 5 Ratios of male to female activities SCombined illustrations and problems, illustrations, and problems) Grade 1 Grade 4 Grade 7 Comb. Illus. Prob. Comb. Illus. Prob. Comb. Illus. Prob.

Series A 3:1 3:1 * 8:9 6:3 5:7 6:6 4:3 4:3 Series B * * * 7s6 3:0 4:6 17:145:3 15:11 Series C 5:4 5:4 * 9:117:9 2:2 11:7 6:0 7:7 Series D 6:5 6:5 * 10:12 2:0 8:12 5:3 * 5:3 Series E * * * 7:5 4:1 3:4 4:3 2:1 3:2 Series F 2:3 2:3 .* 24:1514:7 11:10 11:119:6 3:6 Series G 5:2 5:2 * 5:6 4:3 2:4 6:2 2:0 4:2 Serlles H 3:3 3:3 * 2:2 * 2:2 7:5 2:0 5:5

*No activities were pitad that involved males or females.

V floor, building a fence, shovel- ematics textbooks. Prose is used ing snow, raking leaves, mowing only in brief explanations or a lawn, and cooking. problem sets. There were few activities in any of the twenty-four books SUMMARY that males and females participated in together. An operational definition of sex- Names of mathematicians did ism in textbooks was given by the not appear until in the seventh- Sexism in Textbooks Committee of grade books. Of the seven se- Scott, Foresman and Company (1974, ries in which they did appear, p. 1): the number mentioned ranged from Textbooks are sexist, if they one (Series B and D) tofourteen omit the actions and achieve- The mathematicians (Series G). ments of women, if they demean were all males. women by using patronizing lan- The authors found neither bla- guage, or if they show women tantly sexist language nor overt or men only in stereotyped efforts to use nonsexist language. roles with less than the full This could have been due, in part, range of human interests, traits, to the format of elementary math- and capabilities. Research has revealed sexism in sessment results showed the ef- earlier mathematics texts. Is fects of sexism on "more diffi- there sexism in the more recent- cult exercises and word problems." ly available mathematics series? Adult and 17-year-old males out- This review of the first-, performed females on these exer- fourth-, and seventh-grade texts cises (NAKP 1975 [b], p. 21). from eight popular series pub- With sexism prevalent in text- lished in the years 1971 through books published as recently as 1975 indicates that sexism is 1975, it will be several years still very much in evidence. before nonsexist mathematics( Males and females were seldom texts appear in most elementary treated equally in the illustra- classrooms. Multi-year adoptions tions and problems in these texts. and revised editions, with only The number of males identified minor changes, will prevent sud- was greater than the number of den changes in the commercial ma- females identified in twenty of terials available to students. the twenty-four texts examined. Teachers must be involved in see-. Males participated in a greater ing that future adoptions pre- variety of activities and occupa- sent an equal view of males and tions than females.Typically, females in mathematics materials. female roles were passive rather In the interim, classroom teach- than physically active, except ers must consciously seek to pre- when they participated in house- sent women in a wider variety of hold activities. Females were activities and occupations involv- not portrayed as having a full ing mathematics. This can be range of interests, traits, or done through .supplementary exer- capabilities. cises and problem settings con- Few situations existed where structed by the teacher or a males and females participated school-wide group. together in an activity, except in family settings.This is a UPDATE subtle form of sexism trans- mitted by textbooks. Since the original data were col- There was little evidence of lected, new texts have appeared. sexist language in the materials The authors carried out an analy- surveyed. In large part, this sis of three widely advertised was a result of the standard new series. Two are revisions of mathematics text format of ex texts used in the original study: amples and computational exer- Series E' (1975-76) and Series G' . cises. (1976). Series G' has no seventh- While specific mathematicians grade revision. One new series were identified only in the sev- was added to the study, Series I enth-grade texts, these individ- (1976-77). uals were exclusively male. An examination of the illus- This is one more way in which trations in these texts indicated mathematics texts presented only minor changes in the percent- mathematics as a male activity. age of males and females shown. Psychologist Jerome Kagan has One exception was the revised found that children display in- Book 1 in Series E'. The 1972 hibitions about learning subjects text had males in 100 percent of they feel are inappropriate for the Seventeen recorded illustra- their sex. Recent National As- tions. In the 1975 revision,

28 11-13 Table 6 Percentages of males and females in illustrations Grade 1 Grade 4 Grade 7 M F

Series E' 68% 32% 612 392 61% 39X Series G' 51 49 54 46 a Series I 55 45 58 42 53 47

*No revisedseventh-grade text.

Table 7 Percentagesof males and females in problems Grade 1 Grade 4 Grade 7 M F M

Series E' 0% 0% 45% 552 43% 57% Series G' 0. 0 47 53 A Series I 0 0 52 48 48 52

A No revised seventh-grade text.

males were identified 68 percent in the past (table 8), males were of the time in almost seventy not pictured in traditionally fe- recordings (table 6). male occupations. A rare excep- A study of sex roles in the tion was a male hairdresser in problems indicated a noticeable Book 7 of Series E'. shift. Although problems were The number of activities par- not human-oriented in the new ticipated in by males and females first -grade texts, the problems remained approximately equal in in the fourth- and seventh-grade the new texts. The advantage, texts showed a larger percentage now, is to tile females (table 9). of females than males, with only In activity settings, females one Look having males identified typically remained in passive more often (table 7). roles. However, there were ex- In the more recent texts, fe- amples of females engaged in more males were cited in an expanded physical activities such as pound- range of occupations. This was ing nails, racing a boat, tiling most notable in the seventh- a floor, delivering newspapers, grade texts. In Book 7 of Se- building a cage, playing base- ries E', females were identified ball, and plowing a field. There in the following occupations: were also isolated examples of welder, draftswoman, zoo keeper, males cooking, planting flowers, film reviewer, political candi- sewing on a button, and cheer- date, disc jockey, luggage car- leading. rier, veterinarian, and truck With respect to the identifi- driver. An overview of all cation of mathematicians, Series texts suggested a stereotyping E' mentioned three, all males, of women in the roles of doctor in the fourth-grade text. In and construction worker. the seventh-grade text, 9 male Although females were cited and 4 female mathematicians were in many more occupations than identified. Table 8 Ratios of occupations given to sales to occupations given to females (Combined illustrations and problems)

Grade 1 Grade 4 Grade 7

Series E' 0:2 11:7 19:19 Series G' 0:1 2:0 Series I 4:1 16:6 10:16

*No revised seventh-grade text.

Table 9 Ratios of male to female activities (Combined illustrations and problems)

Grade 1 Grade 4 Grade 7

Series E' 1:1 9:11 6:3 Series C' 2:1 7:10 Series I 6:6 12:18 6:9

*No revised seventh-gradetext.

There was an increaseduse of CONCLUSION sexually neutral language in the new texts reviewed. This was After thorough examination of primarily accomplished through the texts, the authorsare con- the avoidance of singular pro- cerned about the possibility of nouns. The use of la. was much stereotyped sex-role changes in more common in these texts. the series. Females have been In comparison to the data col- stereotyped into roles as.doc- lected on texts published in the tors and construction workers. 1971-75 period, a review of texts They were typically playing base- in the 1975-77 period showssome ball or basketball. Although changes in sex roles. The most these roles are being P3signed noticeable change is the greater to females, there is little in- variety of occupations given to dication that male rolesare females in illustrations and prob-changing. Neither was there an lems. Although less complete, increase in joint male-female there is an involvement of fe- activities. TeaCner awareness males in physically strenuous and involvement are still needed activities. to present a balanced view of The detailed tallying ofoc- males and females in mathematics. currences shows that the appear- ance of males and females in Authors' Note. The names of illustrations and problems is the textbook series, referred to more balanced. Although not as Series A-H, E', G', and I in equal in number, the percentage this article, can be obtained by differences are less than in ear- writing to the authors. lier texts.

3u 11-15 References

Brody, Celeste M. "Do Instruc- Selected Results from the First tional Materials Reinforce National Assessment of Mathemat- Sex Stereotyping?"Educa- ics. Denver: Education Commis- tional Leadership (December sion of the States, June 1975. 1973) :119 -21. (b). Male-Female Achieve- California State Department of ment in Eight Learning Areas. Education. California's New Denver: Education Commission Textbook and Instructional of the States, 1975. Materials Law. Sacramento: Rogers, Margaret Anne. "A Differ- Calif.: The Department, July ent Look at Word Problems- - 1974. Even Mathematics Texts Are Mlinar, Josephine. "Sex Stereo- Sexist."Mathematics Teacher typing in Mathematics and Sci- 68 (April 1975):305-7. ence Textbooks for Elementary Sexism in Textbooks Committee of and Junior High Schools." In Women: Scott, Foresman and Report on Sex Bias in the Pub- Company. Guidelines for Im- New lic Schools, pp. 56-59. proving the Image of Women in York: Education Committee, New Textbooks. Glenview, Ill.: York Chapter of the National Scott, Foresman and Company, Organization of Women, 1973. 1974. National Assessment of Educational Texas Education Agency. State Consumer Math: Progress (a). Board of Education Textbook Policy 3331. Austin, Tex.: The Agency, 1974.

11-16 UPDATE ON SEX-ROLE STEREOTYPING IN ELEMENTARY MATHEMATICS TEXTBOOKS

Helen Fuesy Kuhnke

An assistant professor of mathematics education at the State University of New York-College at New Peitz, Helen Kuhnke teaches preservice and in-service elementary teachers. She also works on curriculum development and does in- service workshops for surrounding school systems.

The awareness of sexism in the Most pictures show girls pas- curriculum (Frazier 1973) and sive and boys active--girls in- the numerous articles on sex- doors; boys outdoors, being role stereotyping in elementary skillful and adventuresome. textbooks prompted me to take a close look at some elementary Throughout the texts, girls are mathematics series myself. Since shown sewing, baking, mopping, I had immediate access to them, making beds, dusting, and wash- I examined two sets of elementary ing dishes. mathematics texts, kindergarten Girls are affectionate, fright- through grade six, both with 1974 en easily, and cry. copyrights. I am pleased to report that my examination of these Boys are strong and silent, almost never cry. books indicates that apparently an all-out effort has been made Pictures showing boys and girls to eliminate the sexist bias and together frequently have the offensive sex-role stereotyping. boy doing something clever, and the girl thrilled to watch. BACKGROUND The housewife in the textbooks The critics of elementary text- is hard to believe. Everything goes smoothly and she is always books had made a valid case. Sex- happy and calm. She also has role stereotyping was found in spelling, science, mathematics, little to do and often is shown sitting. reading, and social studies books. Weitzman and Rizzo (1975), in one Motherhood is shown as the only of the most comprehensive studies optic. for girls. done on the subject, found ample evidence of sex-role stereotyp- Weitzman's report, however, made ing: the point that the average woman

11-17 32 in the United States spends only into stereotyping when it sep- one-third of her adult years arates people. Sets of boys raising children.''Most women will are usually doing things while want to work, or will be forced sets of girls are sorting such to work, during the other two- things as hair color/eye color. thirds. of their lives. Again, sets of men are doctors, The criticism of children's lawyers, pilots, astronauts, readers has had much general pub- mailmen--you name it.Women licity and was further documented may be waitresses, nurses, in a booklet, Dick and Jane as stewardesses, and funny hat Victims: Sex Stereotyping for wearers, but not much more Children's Readers.Here, too, (Stacey et al. 1974). authors cautioned that children Federbush did mention that sex bias are assimilating the content and in books is almost certainly com- values of their books as they mitted unintentionally, and without learn to read, without giving it malice--at least without conscious any conscious thought. They ad- malice. But because it is fre- monished that "school readers quently so subtle or so ordinary must assume their responsibility looking, we must continue to make in directing the subliminal sure that it is exposed and cor- learning process towards more rected. She suggested that a set psychologically constructive of guidelines be drawn up and pre- ends" (Women, p. 32). sented to companies to use as di- The most surprising accusation, rectives to authors and artists however, has been sex-role ste- preparing new books. The main reotyping in mathematics books. categories would deal with-- In a consciousness-r04.sing paper- back, And Jill Came Tumbling Af- adult stereotyping, in oc- ter: Sexism in American Educa- cupational and family life; tion, Federbush categorized the boy-girl activities, values stereotyping in three phases: and groupings; problems involving male/fe- the standard textbook vari- 1. male competency in mathemat- ety, where pictures of girls ics; and showed them doing girl jobs inclusion of female mathe- like sewing, cooking, and other maticians. female chores, while pictures of boys showed them doing boy Federbush also suggested that a jobs like sailing, mountain good safe rule of thumb would be climbing, woodworking, or go- to divide all roles and activities ing to the moon. The standard evenly wherever possible. It texts even verbalized, "Susan would certainly be more reason-

couldn't do the problem . . . able than the current textbook Jim showed her how," or "I pictures and descriptions. "What guess girls are just no good is desirable is realism (female in math," said Joe; taxi drivers) plus a little ex- aggeration (female astronauts)- - 2. the historical omission and the way life is moving in variety--not one female mathe- America, what is extraordinary matician was ever mentioned; today may be commonplace tomor- 3. the new mathematics vari- row" (Stacey et al. 1974, p. 182). ety, where the use of sets gets Federbush felt that carrying out

II -18 3J the program of action that she New female roles suggested "would be one more step toward helping our young and our "Miss Cabot runs a paint store." very young women feel like un- "Brenda is a potter. . . ." "Allison has a sandal shop. apologetically capable and as- . . ." piring human beings." "Meg wanted to change her bed- room furniture around." (She WHAT I FOUND measured her things and madea scale drawing. In the past boys Obviously, my consciousness of usually were the measurers.) sex stereotyping in mathematics "Bertha could walk .7 kilo- texts was aroused. Reading the meters." copy and viewing the pictures in A girl is pictured jumping the mathematics textbooks that I over a fire hydrant. This clear- had access to revealed that (a) ly shows new action and freedom there definitely was aconcern from Mary Janes and pretty dresses. for adult stereotyping, (b) boys "Mrs. Brown hired Mr. Washing- and girls were frequently in- ton to lay tile in her kitchen." volved in tasks jointly, and (c) "Madeline was drivingone car, problems involving male/female while her husband followed in the competency in mathematics let other." 11 the girls be smarter sometimes. . . . . Miss McConnell will Nothing was done about the in- leave the United States for a busi- clusion of female mathemati- ness conference in Oslo, Norway." cians, but there were no comments Her travel agent prepares a chart, about men of mathematics either. route, and expenses. Men and women, boys and girls, In a picture of a school medi- cal center, the doctor is defi- were featured in unusual stereo- . typed roles. In instances where nitely female. names were used or sexes were On a problem-solving page, designated, new roles emerged both sexes were involved, but for both sexes. In their new the picture shows a girl as a roles females had different jobs, scientist and the copy reads, took the initiative, were active, "Flora uses mice to test differ- displayed responsibility, and ent diets." made decisions. Males were also "Miss Anton is going to paint 24 new houses." shown in nonstandard situations-- In another prob- they were not always the he-man lem Miss Anton also hangs wall- roles. There were pictures that paper. snowed that men could do some do- A girl is pictured on parallel mestic chores without losing bars as a gymnast simply to dem- face--to be sure, these tasks onstrate parallel lines on a ge- were more likely chosen than done ometry page. out of necessity. Another garage scene shows men In the following examples the and boys working, but Mrs. Wash- first lines of the problem often ington buys gas. (Women are out made the point. Sometimes the of the kitchen.) picture carried the message even if the page was all practiceex- ercises:

11-19 New male roles two boys and a girl were doing examples on the blackboard, one boy "George is using his science and the girl had the correct 'an- textbook and measuring foods for grams of protein." swers. There were a few ambiguous sit-. "Jack had trouble making a uations. The artwork would show box. He asks his father. . . ." a drugstore scene and both a male "Jack used 2/3 cup of milk for and female were in uniform. There a batch of pancakes." was no way of telling which was "Gary is making milkshakes for the clerk and which was the some of his friends."He uses a pharmacist. In a large bakery recipe. both sexes were in uniform work- "Alan is making cookies. His ing side by side. If Jay and recipe calls for. . . ." Schminkl' (1975) put the heavy re- "Matt is having trouble choos- sponsibility on the classroom ing one of these buckles." He teacher to counteract the impact decides to put them in a box and of sex stereotyping in textbooks, then reach into the box without then the publishers of these looking to pick one. The prob- textbooks have made it easier lems relate to probability. for the teacher who chooses to "Tom bought 4 1/2 yds. of ma- set the tone for career expecta- terial. . . ." tions. "Mr. Allen made 36 loaves of Nonsexual terminology also bread." avoided stereotyping. "Central A man is pictured as a gar- City has 1600 transportation dener. workers. Twenty percent drive To be sure, all the roles were buses. How many workers drive not turned around. Boys still hadbuses?"On one page the artwork some special tasks such as paper evaded making the differentia- routes, playing ice hockey, ga- tion and one could only infer rage helpers, and Boy Scouts. that it was a picture of a police Girls were still playing jacks, officer. raising flowers, and going shop- ping fcr mother. CONCLUSION

Boys and girls together The review of these two mathematics textbooks series shows a The greatest number of pages positive response from the pub- showed boy-girl activities with lishers to the critics of sex similar values and groupings. role stereotyping, which indi- Boys were not the active members cates that the blase: in text- with girls watching the events books can be eliminated when a from the sidelines. Together concerted effort is made. The they were fishing; sailing boats; conscientious work of many peo- ice skating; preparing for hikes; ple in citing the sex role ste- going to museums; helping in the reotyping has had far-reaching library; going to the airport; effects in many areas. Even if participating in potato sack the change in the curriculum and races, swimming meets, and soft- in society is not immediate, ball games. Sometimes the girls consciousness raising must be even won or came out ahead. When considered an important accom- plishment.

11-20 O

References

Frazier, Nancy, and Myra Sadker. I/r "Sex Bias: The Hidden Currie- ulum in the Elementary School." In Sexism in School and Society. New York: Harper & Row, Publish- ers, 1973. Jay, Winifred T., and Clarence W. Schminke. "Sex Bias in Ele- mentary School Mathematics Texts." Arithmetic Teacher 22 (March 1975): 242-62. Stacey, Judith, Susan Bereaud, and Joan Daniels, eds. And Jill Came Tumbling After: Sexism in American Education. New York: Dell Publishing Co., 1974. Weitzman, Lenore J., and Diane Rizzo. "Sex Bias in Textbooks." Today's Education 64 (1975): 49-52. Women on Words and Images. Dick and Jane as Victims: Sex Ste- reotyping_for Children's Read- ers. Princeton, N.J., 1972.

11-21 36 SEX STEREOTYPESIN MATHEMATICS AND Books: Propaganda and the Sins of Omission SCIENCE TEXTBOOKS FOR ELEMENTARY AND The set of all girls who have short hair and the set of all r:rls who JUNIOR HIGH SCHOOLS have 1.lue eyes. (Gundlach et al., Mathematics 5 [Cr. 5] )

Clearly, it is implied that the set of children (boys)who are characterized by their physical activity and theset of children (girls) who are characterized by their physicalappearance are disjoint. Consider the following family activities ina camping scene from a second-grade text (Duncan, Modern SchoolMathematics, 2 [Gr. 2] ): Female: Mother cookson outdoor grill; girl watches baby. Male: Father sets up tent; boy helps father;boy sails boat; boyromps with dogs. I. The Sex Component of Set Theory The female members of the familyare occupied with "homemaking" activities. The male members, by contrast,are involved in physically vigorous. "building" or "play" activities. The Is the following an innocent exercise in permutations andcombinations? two boys at play are obviously engaged in optional activities, which permit themto develop inde There were 4 boys and 5 girls ata party. In how many different pendence and to increase theirrange of experience. No such choice is ways can one girl be matched with one boy for a game? apparent in the female activities. (Deanset al.,Developing Let's examine the first-grader's view of male and female roles. Mathematics, Book 3 [Gr. 3]) Con- sider the pictures found in the first 100pages of a first-grade text (Dun- Problem: To diagram theproper relationship between boys and girls. can, Modern School Mathematics 1 [Cr. 1] ): Answer: Activity shown Activity shown Female: or implied: Male: or implied: (serving food) C Indian girls none sailors sailing queen ruling (with king) band members marching, playing G B dolls none music witches casting spells king ruling (with queen) TABLE B (Note boys at head of table.) Eskimo girls none bakers baking C G B girls buying balloons pirates plundering ships girls skipping rope circus performers performing knights jousting (Abstraction of picture found in Keedy et al., man observing stars Exploring Modern Mathematics, Book 1 [Gr. 7j) downs downing man selling balloons Are the following sets joint or disjoint? boy raising pumpkin boys swimming The set of all boys who play football and the set of all boys who Ittrictertninate: Indian chiefs ruling Indians play baseball. skiers Indian men war dancing variously dressed none Note: B) josphine Mlinar. Reprinted with permission from Reporton Sex men Bias in the Public Schools. Copyright () 1973 by the Education Committee, National Organiration for Women, New York City Chapter (28 East 56th Stree:, New York, There arc curious differences between the male and femaleimages. New York 10022). In the first place, there are manymore male images (15 to 7)In the 3/ Sex Stereotypes in Mathematics and Science Textbooks Books: Propaganda and the Sins of Omission second place, only one male picture is totally passive(no action shown models are presented? Surely there could beno problem here, since or implied), whereas nearly half of the female pictures (three)are mathematics is intrinsically abstract and asexual. passive. The var... i male adult rolesare generally realistic(sailor, band member, baker, circus performer,astronomer, clown, balloon sales- Female mathematicians: None. man) and include severalways of earning a living, The female adult Male mathematicians: Eratosthenes; Coldbach;Euclid; John Napier; roles are not realistic (queen, witch) andno reasonable way of earning Fibonacci; Pascal. a living is shown. The girls, however, may spend money (buying The great algebraist Emmy Noether is noteven mentioned. Even balloons). Stein's book which is very abstract, conformsto the practice of omitting The seventh grade se9s the pattern repeated in problems (Keedy female role models (Stein, Fundamentals ofMathematics [Gr. 8-10] ). et al., Exploring Modern Mathematics, Book 1 [Gr. 7] ): All the mathematicians aboveare cited with corresponding accomplishments. A girl could not help but conclude that there Female activities: Buying chocolatecreams; using flour; buying ging- are no female ham; baby-sitting to mathematicians; and ifthere are, they have never done \anything earn extra money; walking to school; being 4 feet worthwhile. tall; finding mixed numerals inan easier way (than boys); writing a Is there a ray of hope in the darkness? The fractional numeral; using Spitzer et al. series, a skirt pattern; serving candy; using lace on a Elementary Mathematics, appears at firstto be totally unbiased as to sex. blouse; ordering a floor tile; making towels; making dresser scarves. The reason for this is that nearly all of the examplesof boys and girls Male activities: Gardening; buildingscenery; growing 2% feet taller; in the text (on nearly every page) depict classparticipation. Thus, nearly planting grass; cutting a board; paintinga room; hiking 50 miles; running all the examples are nonstereotyped. Nevertheless,nonclassroom activities 100-yard dash; being 5 feet tall; findingan average; copying a house plan; are very much stereotyped: having a 7 foot board; finding mixed numerals; showing a shorter way Female activities: Papering cupboard shelves; using red ribbon;filling an ( than a girl's) to writea fractional numeral; painting a living room; aquarium; reading. driving; trying to correcta fractional numeral; filling boxes with candy; Male activities: Assemblinga fishing rod; playing with planes; making a making baskets (basketball); delivering groceries by bicycle; cutting boardwalk across a puddle; buying paint (Spitzeret al. [Cr. 4] ). Loading bookshelves; cutting a board; dividing fractions; carrying the ball ina a truck with newspapers; loading a truck with melons; markingcans in a football game; selling pine trees. grocery; finding the height of a water tower; finding how far radar signals Girls and women spend a great deal of time sewing and cooking. travel in 1 hour; racing a boat; practicing music; catching fish; helpingin Walking to school is their most strenuous activity. Girls baby-sitto earn a local paper drive (Spitzer et al. [Gr. 6] ). "extra" money. Their accomplishmentsare the private production of Hem we have all the usual stereotypes: female restriction to indoor, clothing and food, which wear out andare eaten respectively. Girls, nonstrenuous, nonremunerative, and nonscientific activities which produce unlike boys, don't spend leisure time playingor relaxing. no permanent result. Boys may also engage in such activities, but Boys and men spend considerable time in carpentry, painting, and generally their activities havesome, if not all, of the opposite character- gardening, which result in relatively permanent accomplishments. They istics, and are much more varied. engage in strenuous sports in which they achieve public recognition. The art of mathematics sex stereotyping is obviously far advanced They earn money (delivering groceries, selling pine trees)or practice and all-pervasive. Some recommendations toremove sex stereotyping are: money-making activities (copying a house plan) and nowhere isit 1. Inform publishers that henceforth texts will be screened for suggested that this money is "extra.' Male examplesare used 28 times; frequency and type of male and female role models and examples. Only female examples only 15 times. Only in schoolmay boys and girls nonstcreotyped books will he acceptable. participate on an equal basis. 2. All current texts should be screened similarly. Publishers should Finally, let us consider the field of mathematics itself. What role be notified of necessary corrections. Books should be dropped from the official textbook list if correctionsare not made immediately. Sex Stereotypes in Mathematics and Science Textbooks Books: Propaganda and the Sins of Omission II. Sex Education in the Science Lab Adult female: Nurse describing a heart, showing pulse to boys, and giving them shots; packers in an assembly line packingcorn. A scientist is a human being like yourself. lie has much the same sort of everyday problems you have. But he also attempts to solve Adult male: Driving a combine; herding cattle; sprayingtrees. problems about what is in the world around him. To do this, he is Girl: No activity. always looking forfacts thatwill help answer his questions. Boy: Exploring woods; watching a butterfly; climbinga log; dismembering (Emphasis added.)(Beauchamp etal., Everyday Problems in a flower; listening is 3 nurse describe a heart; observing a pulse as shown Science [Gr. 8-9]) by nurse; eating a sandwich; holdinga grapefruit; getting a shot from .rode 1: Establishment of adult sex-role models a nurse. Aim: To establish clear differences between adult male and female Grade 3: Establishment of femininenurturance; sex roles. To prepare girls for later invisibility via paucity of pictures of establishment of male technological aptitude adult women. Means: Examples of children imitating adult sex roles and pictures Mm: To prepare girls for their future dutiesas homemakers via illustrating appropriate sex-role differentiation. appropriate adult and child role models. To inculcatea sense of male technological monopoly in all areas except homemaking. Adult female pictures: Walking in the rain; shooing pigs intoa sty; Means: Pictures illustrating homemaking and nurturant behavior checking a thermometer and putting a coaton a buy; taking a coat from in females. Careful exhibition of acceptableuses of technology by each the closet; getting caught in an elephant's tnmk. sex. Adult male pictures: Walking in the rain; holding balloons; settingout Adult female: Sewing; ironing; baking. smudge pots in orange groves; holdinga briefcase; walking against the wind; swimming around a capsized boat; extricatinga truck from the .tdult male: Reading the paper. mud; paintine: a gutter; introducing a circus act; clowning: selling Girl: Feeding goldfish; placinga plant in the sun; looking at a plant; balloons; spilling nails; riding a motorcycle; hosing downa sidewalk; looking at teeth in a mirror; exploring woods; polishinga floor; watching putting cows in a Lan. TV. Adult role model imitations Boy: Holding mirror for a girl; wearing an outgrown suit; fe...dinga Boy raises chair above head, while girl holding chair waist-high looks puppy; exploring woods; demonstrating a magnetic field of electric on admiringly. current; watching TV; drawing with a soldering iron; experimenting with current. Father paints, boy piles fallen twigs inwagon, boy mows lawn, girl sweeps. Grade 4: Inculcation of male leadership role Man rides motorcycle, boy drives horwcart, boys climbtree, girl bounces on pogo stick. Aim: To present leadership as an inherently male function. To drive home the connection between power and maleness. To further vmpliasia.o Grade 2: Establishment of acceptable femalesex roles the invisibility of females outside the classroom. To present scientistsas outside the home exclusively male. Means: "Investigation pages" to encourage student experimentation, Aim: Establish appropriate female occupations. Contrast with male with males shown as leaders in experimental activities. Pictures andtext occupations which tend to exert control over th *mediate environment. which depict males almost exclusively, Description of the work of male Emphasize female service to males. Accustom h.rls to invisibilityvia a !:cientists only. lack of pictures of girls, combined withmany pictures of boys encom- passing a wide range of experiences. A. Investigation Pages: Means: Pictures indicating acceptable behavioz and subjects. "Chemical and Physical Changes" 1. A male short-order cook frying pancakes. 41 42 Sex Stereotypes in Mathematics and Science Textbooks Books: Propaganda and the Stns of Omission Melting iceA boy checks a thermometer and records tempera- John H. Glenn (rocket pilot) ture while a boy and a girl watch. Vilhelm Bjerknes (meteorologist) 3. Physical state of butterTwo girls check a thermometer and record temperature. B. Pictures 4. Physical changes: a man saws wood, a boy breaks twig, a girl Adult female: Watching male TV image; singer ("girl"). tears paper. Adult male: Using a solar cell; repairing a telephone line; shaving 5. A boy in a baseball uniform eats lunch. with an electric shaver; TV cameraman; male announcer; male TV 'Energy to Do Work" image; satellite ground controller; disk jockey; doctor; TV engineer; Two girls make a pendulum, thena boymeasures the pendulum, driving a car; riding a rocket chair. swings pendulum, adds weight to pendulum, and shortenspen- Girl: Talking on the telephone; schoolgirls "transmitting a pict'ire." dulum. Boy: Talking on the telephone; jumping off a wagon. B. Pictures: C. Text Adult female pictures: Removing cake fromoven. 1. "You have heard your father talk about the battery in his car. You Adult male pictures: Putting anti-freezein a car; extinguishing a know he cannot get the car started without it." (Emphasis added.) candle with a jar; extinguishinga candle with a tweezer; adjusting 2. Discussion of Isaac Newton and Newton's Laws of Motion. chemical equipment; James Prescott Joule; packing boxes;driving a 3. Discussion of action and reaction when boy jumps out of wagon. tractor; driving a locomotive; adjusting equipment ina plant. . Action and reaction with reference to man riding a rocket chair. 5. ":ransportation necessary to visit one's grandmother in California. C. Text: 6. "The girl here is singing into a microphone." (Picture of a mature Adult female: No activity. woman) Adult male: Joule's work; Einstein's work. 7. Thomas Edison's inventions. 8. Policemen's use of radar. Girl: No activity. Boy: Pushing a box; playing baseball. Grade 7: The male scientist D. Scientists Described: Aim. Depiction of male participation in various scientific activities. James Joule, Percival Lowell, Clyde Tombaugh, othermen indexed. Admission of Marie Curie to the male scientist elite. Means: Pictures of male scientists at work. Text describing male Grade 5: The male as paid worker scientific accomplishments. Multiple male scientist role models. Emphasis on male use of technology. Aim: To firmly inculcate the image of the male as paid worker. To emphasize the concept of womanas child; to denigrate the value of A. Pictures her work. To further stress women's invisibility. To present male scientist Female: Madame Curie in lab; radioactive testing of piston wear. role models. Male: Pierre Curie inlab; researching of radioactive substances; Means: Pictures of males in various remunerative occupations. Text radioactive testing of piston wear; inspecting an atomic reactor; references to males in various activities, especially science. Omission of assembling a satellite; Ernest 0. Lawrence by his cyclotron; observing femalesinpictures. A "Scientists in Action" section acclaiming the a fusion demonstration; adjusting a stellerator; Newton; Ruatford; accomplishments of male scientists. Joule: lighting a piece of wood in a solar furnace; with fuel cell; generating electricity with a teakettle; with sunlight collector; with A. Scientists in Action: cesium cell; with biochemical cell. Luther Burbank ( botanist ) Indeterminate: Using Geiger counter. Robert I hitching% Goddard ( rocket developer) 44 43 Sex Stereotypes in Mathematics and Silence Tcl`books Books: Propaganda and the Sins of Oniissibri B. Text of extricating a model plane froma tree; using an electron microscope; 1. Scientists whose accomplishmentsare described using high-speed photographic equipment; using analytical balance; Female: Marie Curie. working in a lab. Ma/e: Antoine Henri Bequerel; Pierre Curie; Ernest Rutherford; Mathematics Textbooks Ernest 0. Lawrence; Milton S. Livingston; Enrico Fermi; Otto Hahn; Glenn Seaborg; Edwin McMillan; Abe lsun; Aristotle;Sir Isaac New- GradeText Section(pp.)Reviewed ton; Benjamin Thomson Rumford; James Joule; ThomasEdison. 1 Duncan, Modern School Mathematics 1 1-100 2. "Primitive man used only his musclesto produce energy, but he Duncan,Modern School Mathematics 2 100-200 soon found out that he could not do very much work by himself. 3 Deans et al.,Developing Mathematics, 50-150 Book3 Animals were probably man's first outsidesource of energy, but 4 Spitzer et al.,Elementary Mathematics, 1-25 they could not provide all theenergy man wanted. Man then built Book 4 machines to use the energy of wind andwater and eventually 3 Gundlach et al., NewLaidlaw 1-50 began to use fuels such Mathematics Program, Mathematics5 as wood, coal, and later oil to supply the 6 Spitzeret al., Elementary Mathematics, 25-50 energy needed to run his machines." Book 8 7 Needy et al..Exploring Modern 100-200 (pictures) "Man needs a great deal of energy to operate the large machines Mathematics,Book 1 150-200 (problems) that do his work. Before the invention of engines that burned fuel 8-10Stein,Fundamentals of Mathematics, 1-100 to release energy, the only available sources of energy, in addition Second Course to man's own muscles, were animals, water, and wind. Water wheels are one of the earliest known machines used by man to obtain Science Textbooks

energy from flowing water for his needs.. . .The wind has long Beauchamp etal., Science isFun Weather been a source o" energy used by man." (Emphasis added.) ( Blanc We MoveThings et al., Man, Matter, and Energy [Cr.. 7-9] ) 2 Mallinson etal., Science2 Manamong the Animals of the World 3 Beauchamp et al.,Science is Exploring How Do Living Things Get Grade 8: A career in science (women neednot app/y) Food? Electric Current Aim: To establish masculinity of scientificc'-eers and behavior. 4 Jacobson et al.,Probing into Science Materials of the Earth Means: Coordination of generally nonsexisttext with pictures por- Energy to Do Work 5 traying males in various scientific fields. Use of male scientist role models. Munch-SyrockiBook V Energy and Matter Scientists in Action Depiction of males as scientific thinkers. 7-9 Blanc et al.,Man, Matter, and Energy Matter and Energy Forms and Sources of Energy A. Text: ;tow Do Scientists Think and Work? 8-9 Beauchamp et al., Everyday Problems How Do Scientists Think and Female: None. in Science Work (includes quote used to introduce science section) Male: Aristotle; Galileo; Louis Pasteur; Thomas Edison;Jan Lipper- shey; Zacharias Janssen; Antonvon Leeuwenhoek. H. Pictures Female: Observing through microscope. Male: Repairing a generator; observing electronicequipment; checking gauges; chemist testing material; physicist usingequipment; geologist studying rock samples; geologist charting rock layers; biol- ogist simulating Martian conditions; man ("you") solving problem

45 46 . Sexual Stereotypingin Mathematics: Beyond Textbooks Bt. Laurie Hart Reyes

The May 1977 issue of the Arithmetic Teacher included three articles that discussed some of the issues involved in the problem of sex-role stereotyping and mathematics learning. Fennema and Sherman reviewed and analyzed the sex-related differences inmathematics learning and studying that have been found in research. They hypothe- sized that many females electnot to take mathematics in high school and college because mathematics isper- ceived as a male area of study and therefore inappropriate for females. The other two articlesbne by Kepner and Koehn, the other by Kuhnkeex- amined the extent of sex-rolestereo- typing in elementary mathematicstext- books. In the latter two articles there was a sense that (a) things are changing on their own so we have nothing more to do and (b) once sex-role stereotyping is removed from elementary mathematics texts we will have provided equity for females in the study of mathematics. There is value in recognizing when mathematics texts stereotype girls and boys into inflexible roles. Certainly both girls and boys are capable ofa tremendous variety of interests, feelings, and activities. The view that mathematics is for males and not for females may he seen in textbooks, but changing society's attitudes toward women and mathematics is a very com- plex task. There are many factors that influence girls in choosing whetheror not to take more mathematics courses than those required for graduation. It is not clear'wh at effect removingste- reotyping from elementary mathematics texts would haveon the decisions of girls concerning the study of mathematics. It does not seem likely that

Preentit a doctoral %trident in mathematic% education at shenwer%Ill I mow Reve% ha% taught junior and%woo. hie, %%horn' mathematic and ha% %urerti%ed student teacher% in se,ondary cc hind mathematic% 11-27 4 1 changes in textbooks. will he a major mere important influence on theex key to a remedy. One danger in focus- stereotyping of mathematics than are ing attention on textbooks alone is that textbooks. we might transfer our sense of respon- In conclusion, let us not stop at text- sibility to the publishing companies. books free of rigid sex stereotypes. This could lead to the feeling that once More work needs to be done by teach- sexism has her.i. removed from mathe- ers and researchers who understand the matics books our. job is done. subtle influencesonfemales both at Let us examine some of the other home and at school. Schools can pro- factors involved in the sexual stereo- vide encouragement for females to typing of mathematics. Parents, class- study mathematics. This encourage- mates, and teachers are important ment may be provided through work- molders of attitudes in females (Sells ing with both girls and boys. The atti- 1973). In their AT article (p. 371), Fen- tudes of all people are important in the nema and Sherman say, "Parents development of sex-role standards. perceive mathematics to be more ap- Looking at textbooks is but an early propriate for boys than for girls, and step toward providing equity for fe- by their actions parents offer more en- males in mathematics. couragement to boys than to girls to References learn mathematics. Parents report buy- Brophy. Jere E.. and Thomas L. Good. Teacher- ing more mathematical games for boys Student Relationships; Causes and Con- and offering more explicit reward sequences. New York: Holt, Rinehart and Winston, 1974. and reinforcement to their sons to learn Fennema. Elizabeth. Influences of Selected Cog- mathematics than to their daughters." nitive. Affective and Educational Variables on The attitudes of peers are another Sex-Related Differences in Mathematics Learn- ing and Studying. Washington. D.C.: National factor in females' perceptions of them- Institute of Education. 1977. selves as students of mathematics. In Fennema, Elizabeth, and Julia A. Sherman (a). research in grades 6-12, Fennema and "Sex-Related Differences in Mathematics Sherman (1977a) report that males, Achievement. Spatial Visualization and Affec- tive Factors." American Educational Research more than females, consistently stereo- Journal 14(1977):51-71. typed mathematics as a male domain. -(13). "Sexual Stereotyping and Mathemat- The boys did not stereotype mathematics Learning." Arithmetic Teacher 24 (May ics strongly but in each case did so 1977):369 -72. Kepner. Henry S.. Jr.. and Lilane R. Koehn. significantly more than did girls. It "Sex Roles in Mathematics: A Study of the seems plausible that especially during Status of Sex Stereotypes in Elementary Mathe- adolescence the feelings of classmates matics TextsArithmetic Teacher 24 (May are influential in decisions and atti- 1977):379-85. Kuhnke, Helen Fuesy. "Update on Sex-Role Ste- tudes concerning mathematics. reotyping in Elementary Mathematics Text- Perhaps more influential than either books." Arithmetic Teacher 24 (May parents or peers are teachers' attitudes t 1977):373-76. 11to Sells. Lucy W. Pilot Study of Attitudes toward about the study of mathematics by Mathematics. Unpublished manuscript, Uni- girls. "Teachers are the most important versity of California. Berkeley. 1973.L.1 educational influences on students' important than the textbook is the learning of mathematics ...While mariner in which the teacher presents other educational agents may have in- the textbook. Teachers can easily make "Sexual Stereotypes in Mathe- fluence on educational decisions, it is their students aware of stereotyping matics: Beyond Textbooks," the day by day contact with teachers when it appears. by Laurie Hart Reyes, is re- which is the main influence of the for- Teachers may also examine their in- printed from the Arithmetic mai educational institution. Partofthe teractions with boys and girls. In a re- Teacher 26 (April 1979): 25- teachers' influence is in the learners' view of research. Brophy and Good 26. Copyright@ 1979 by the deselopment of sex role standards. (1974) report that teachers generally National Council of Teachers The..: sex role standards include defini- have more interactions with boys than of Mathematics. Used by per- tions ,,iacceptable achievement in the A th girls. Teachers frequently have mission, including accompany- %arum. suhiect areas.- (Fennema, more positive contacts with boys. ing drawings. 111'7. pp 114-15) Teachers may or may hrliso boys more often, and criticise not use a textbook with sexist problems boys more often than girls. Perhaps anti trations. Regardless ahoy. teachers need to he more aware of the the hook presents lemalcA as mat'.e- quantity and quality of their contacts matiis sitIt it:ills, 1....cher can point with female and male students. It may tuft 'ctetal sexti. ,,ereotypes. More he that teacher-student contacts are a II -28 4 VIEWS OF FEMALES AND MALES INMATHEMATICS CURRICULUM MATERIALS

Directions: Read the.following mathematics problems. These were selected from typical children's mathematicstexts and workbooks and e modified for use here.

How are females and males portrayed inthese problems?

1. Peggy ironed 4 skirts in 15 minutes. Then she ironed 3 blouses in 10 minutes. Which can she iron more quickly, skirtsor blouses?

2. Leon walks 11 blocks to school in15 minutes. Fred walks 13 blocks to school in 20 minutes.Who walks at the faster rate?

3. Betty is making cookies.The recipe she is using calls for 3/4 cup of sugar. How many cups of sugar should sheuse if she doubles the recipe? .

4. Barbara bought a 5-poUnd bag ofsugar. She used 3-1/4 pounds to make jelly. How many pounds of sugar were left?

5. Mary wants to buy some ribbon fora dress she is making. The ribbon costs 30C per yard. How much will 4-1/3 yards cost?

6. Don is picking apples. Each basket he fills holds 1-1/4 bushels. He has filled 2-1/2 baskets. How many bushels is that?

7. Angelo and Mike went fishing together. Angelo caught a fish weighing 4 pounds, 9 ounces. Mile caught a fish weighing 3 pounds, 11 ounces. How much heavier was Angelo's fish than Mike's fish?

8. David feeds his chickens 2-1/2 pounds ofgrain each day. At this rate, how many days will a 10-pound bag of grain last?

9. Carole has a piece of ribbon that is 17 incheslong. She cuts it into 3 pieces of equal length. She wants to know how long each piece is. Which answer below would she use?

5-2/3 inches 5 inches (2 left over)

10. Harry is pounding a nail througha board that is 3/4 inch thick. The nail is 1-3/8 inches long. How much of the nail will stick out the other side of the board when Harry is finished pounding?

11-29 NAME DATE

CONTENT ANALYSIS: MATHEMATICS TEXTS*

ILLUSTRATIONS PROBLEMS . FEMALE MALE FEMALE MALE 1. Representation (record frequency of male and female adults and of . girls and boys)

2. Occupation engaged in (list each occupation engaged in by a female or male) ,

. ,

3. Activities participated in (list each activity participated in by an adult male or female and by a girl or boy)

4. Sex-neutral/sex-biased language (note attempts to use sex-neutral language, and note sexist language)

* Adapted from H. S. Kepner and L. R. Koehn, "Sex Roles in Mathematics: A Study of the Status of Sex Stereotypes in Elementary Mathematics Texts," The ArithmeticTeacher 24 (May 1977): 379-85. Used by permission.

50 CLASSROOM TASKS AND ACTIVITIES

The following classroom teacher quoteswere developed by Annette Berson,

a member of the TEAM staff. .

1. "I need a strong boyto hold the flag for assembly."

2. "In your free time, the boysmay complete their woodworking projects, and the girls may do their weaving."

3. "I hear whistling. It must be Steven."

4. "Mary, you look lovely today."

5. Heard in the gym: "Boys, carry the balls. Girls, take the jump ropes and hoops."

6. "Boys, there isan interesting story about the invention of a space phone on page 87. Girls, the story about Helen Keller will interest you."

7. "Which girls would liketo join the sewing club?"

8. "I need a girl volunteerto water the flowers and plants in our room."

9. "We're going to form a committee to planfor our Spring Dance. The boys will be responsible for reservinga room, finding a band, and sending out publicity notices. Girls will take care of the food and decorations."

10. "Jane, please take the attendance."

11. "Robert, you are tall and strong; pleaseopen the windows."

12. Heard in nursery school: "Ann and Judy, clean up the dollcor- ner. Adam, you may put away the blocks."

5i TEACHERS ARE IMPORTANT*

Characters

Millie Gorton, a young teacher Sue Emery, an experienced teacher Children in classes: Roberta, Theresa, Timothy, Maria, Boy, Girl

Scene 1: Teachers' room during lunch hour

Millie: Hi, Sue, how was your weekend?

Sue: It was really good. We went picknicking and hiking in the State Forest. What's new with you?

Millie: Not too much, really. I spent most of the weekend working. You know, I'm going to be observed in a few weeks, and I've been trying to get my class into the shape I'd like it to be in.

Sue: What's been happening in your clash since that problem with Diane?

Millie: You know, I'm really pleased with the way things have been going in general. Most of the kids are quite involved in their projects. They seem to be progressing well in reading and writing. In faLt, the only recent comments I've got from parents have been very positive. I've still got problems with math, though, and I've tried everything I can think of.

Sue: What do you mean, Millie?

Millie: Well, Sue, you know that I've never been good in math. The last math I studied was elementary algebra, which I hated. It was one of the few courses I ever got a C in, and the teacher was a real ogre. Well, ever since then I've stayed away from math. 1 hate balancing my checkbook, or even figuring out how much tip to leave for the waitress after lunch. With all those negative feelings, for me to try to teach math is a real problem. I know that my math feelings have kept. me away from some things, and I'd rea'.1y like my students to develop better attitudes, and really learn some math. (pause) So, I've tried some things and I've been looking around for some good lessons, but I'm not at all satisfied. Do you have any good tricks or advice?

*Script by Sheila Crowell, Elenor Rubin Denker, and Ellen Kolba.

52 11-32 Sue: Well, there are a few things that I do inmy class which might work well for you. I've been teaching math to fourth graders for almost ten years now, and I think it's thesubject I enjoy teaching most.

Millie: Really? I can't imagine anyone ever saying that!

Sue: Yes, really. It's the kind of subject whereyou can actually teach kids to think and play at thesame time.

Millie: I know you're awfully busy these days, Sue, butif you have some time, I'd love to find out whatyou do with math, and maybe you could help me straighten upmy act a little.

Sue: I'd love to, Millie. Then when it comes to music, perhaps you'd help me out - -maybe we couldeven do some things with both classes. We could still, out with our "Teaching Millie Math"campaign, then?

Millie: Oh, Sue, thank you so much. I'm ready to start wheneveryou are. What's the first step?

Sue: I think I'd like to start by watching whatyou are doing now. It will be easier for me to make suggestions then.

Millie: Well, I'll probably be embarrassed, but I thinkyou are probably right; that's a good place to start. When do you want to come in?

Sue: I have a free period right now. Will you be teaching math at all this afternoon?

Millie: Yes, I wasn't planning on it for another houror so, but it would be easy enough to change around. And you will then be seeing the "typical" lesson, because I'm doing allthe things that haven't been going well.

Scene 2: Millie's class

(Bell rings)

Millie: (to class) Okay, boys and girls, lunch is over. Time to get to work. Today we're going to do our math now, and current events second. Please take out your books and check the board tosee what your group is supposed to do. (rustle of books and papers; murmur of childrect's voices) Do you all see your assignments? Group 1, you are to do the problems on page 54. Group 2, the problems on page 67. Group 3, you have pages 81 and 82. Okay, everyone ready to begin? Remember, if you have any questions, please just raise your hand. (sound of pages turning, pencils scratching) Yes, Charlotte--all the probiLms. (more sounds of children writing, pages turning, some whispering) Roberta, do you have a question?

11-33 53 Roberta:.I don't know what you do when you have two long numbers like these to add together.

There's an example at the top of the page. See, you just add the top and bottom number in each column together. Follow the example, Roberta. That's what it's there for. (again, sounds of classroom activity) Theresa, can I help you?

Theresa: Yes. looked-at the example, but I don't understand it. See, it shows these numbers written over in a different way. Like 576 is five hundreds, and seven tens, and six ones. And then you have to take away 239, and 239 is two hundreds, and three

tens, and nine ones . . .

Millie: Yes, but you know how to do that. Remember, you rewrote all those numbers on the page just before this one.

Theresa: Yes, but that's not the problem. I mean, why do I hay.. to do it that: way? Why can't I just take away 239 from.576?

Millie: (sounding unsure of herself) Well . . . Theresa, that's the way they want you to do it on this page.

Theresa: Yeah, but . . .

Millie: Let's not waste any more time, Theresa. Just write each one out Aft the way it is in the example. That's what the assignment is. (classroom sounds fade out)

Scene 3: Sue's class

Sue: Okay, class. You have your assignments for tomorrow. Now, don't forget to wear your white blouses and shirts for the assembly program in the morning. Have a good afternoon. So long now. (pause) Oh, hi, Millie, I'm glad you stopped by. Do you have a chance to talk now?

Millie: Oh, sure! What did you think?

Sue: Well, Millie, I have a few suggestions. First of all, I noticed you have a lot of exciting reading materials and language games in your room.

Millie: Yes, I told you that I was very pleased with the language arts program this year.

Sue: You know there are math games that the students could be using as well?

Millie: Really? I didn't know about those.

54 II-34 Sue: Oh, sure, you can buy them, oryoucan make some and the students could use them after a math lessonor during their free time. That can really help to change thetone of the math in your class.

Millie: What else could I do?

Sue: Wel;L, when you work withyour reading groups, you probably talk with them and ask questions before theystart to read a story. But with math, you just told the class what problemsto do. You didn't review or teach anything. And when the children don't get any particular direction and haveto do everything on their own, including work up their own motivation, they'remore apt to lose interest.

Millie: I guess you are right. I kind of hoped they would ask questions when they didn't understand, and I could workwith them individ- ually at that point.

Sue: Well, that sometimes works, but oftenthe shy students get ne- glected that way. And, too, students don't always know what they don't know.

Millie: (thinking) I guess that's so.

Sue: Millie, do you remember that moment when Theresa askedyou a question?

Millie: Yes.

Sue: You told her to follow the example. It almost seemed that you didn't really understand what the book wanted.

Millie: (embarrassed) You're right again, Sue. I thought I understood it when I looked over the problems to assign, but I didn'treally read them carefully enough, and I couldn'tremember why that problem should have been done in just thatway.

Sue: Okay, so how about if we try these ideas fora few days, and let's see how itgoes, and suppose I come back next week and we'll see i: there areany other ideas or suggestions that I could offer you.

Millie: Sue, what a terrific idea! You know, I think I really can do some of those things. I'll ry a group lesson on measuring. And I'll also try to getsome math games into the class. Why don't you comea week from today after lunch and we'll see how far I've got.

Sue: I'd love to, Millie. See you then!

"wt.. toy t)

II-35 Scene 3: One week later, Millie's class

Millie: . . . and we can set up our aquarium today. The fish have arrived! (cheers from class) Julian and Lintoln, please get the aquarium from the closet. (pause) Be careful. Remember, it's heavy. Sara and Charlene, please make sure the aquarium is clean. Arlene, would you please put a mat on the table so the aquarium won't scratch it. (sounds of busyness) Now we'rn ready to add the water. How much water do you think a tank this size can hold?And how can we find that out? (boy and girl voices, eager to answer, saying, "Miss Gorton, I know") Timothy?

Timothy: You have to measure it.

Millie: All right, Timothy, would you please measure the aquarium.

Timothy: (pause) It's 30 centimeters high, 25 centimeters deep, and 50 centimeters long.

Millie: Maria, how many cubic centimeters is that?

Maria: (pause) That's 37 500 cubic centimeters.

Millie: That's right! Okay, we need 37 500 cubic centimeters of water.

Sue: (whispering) Millie, Ihave to leave now. This really looks, terrific. Can you comeup to my class in about half an hour? I think I'd like you tosee my math lesson today.

Millie: Well, I think I can getsomeone to take the students to gym. I'll see you in half anhour.

Scene 4: Sue's class

Sue: That's a good way of finding the solution, Penny. Now let's take a look at the next problem on page 57. I'll read it out loud while you read it to yourselves. Remember to look and listen for the facts you need to find the solution. (sound of pages being turned) Okay, now. (reading) The boys and girls in Room 4 wanted to raise money for a class pitnic. The boys washed cars at 75 cents a car and made six dollars. How many cars did they wash? The girls baked cupcakes and sold them for 50 cents a half dozen. They made six and a half dollars. How many cupcakes did they sell altogether? (speaking to class) You know, I'm so tired of reading problems where the boys always wash cars and build clubhouses and the girls just get to bake cupcakes and make dolls' clothing.Why don't we change this problem a bit'

11-36 T

411 Boy: Yeah, yeah, the girls did the easierjob and make moremoney.

Girl: They always show the boys doing the thingsthat are more fun. I'd rather washa car. (sounds of a general but mild clamor starting)

Sue: All right, everyone. Suppose we just say that the studentsin Room 4 wanted to raisemoney. They divided into two teams. Team A washed cars, and Team B soldcupcakes. Everything else in the problem coulii stay thesame. O.K.? (general sounds of assent) O.K. Now suppose we go on with the problem. Who can tell me what operationyou will use to find the answer to this question? (classroom sounds fade out)

Scene 5: At the end of the day

Sue: Are you ready to leave, Millie? I'll give youa lift.

Millie: Oh, thank you, Sue.

Sue: How did things go after I leftyou with your aquarium?

Millie: Well, I was very pleased. The students seemed to enjoy learning about metrics that way. And I learned quite a bit myself.

Sue: I was really sorry I couldn't stayany longer. I'm not very familiar with the metric system myself.

Millie: You spent a lot of time talking about thelanguage of the problems in your class. Do you really think it's that important?

Sue: Yes, Millie, I believe it'svery important. So many math problems describe boys doing the running and thebuilding and the girls doing things like cooking and sewing--orwatching. The girls are often made toseem less competent than the boys.

Millie: You know, I guess I do that, too. I have to get over the feeling that math is "masculine."

Sue: Yes. In fact, the only suggestion I had aboutyour aquarium lesson was that you had the boys doing the measuring,and that the girls were doing the cleaning.

Millie: Well, Sue, you know I always though thatI was "liberate'." but you are right. I do tend to keep the boys away from the housekeeping chores. I'll have to bemore aware. But I must say that today's math lesson was one of the best lessons I've ever taught in any subject.

Sue: (laughing) I thought you couldo't imagine anyoneever saying anything like that.

11-37 '5? Millie: Can you believe that I've changed this much? And I know that it will affect the attitudes of my students. I'm delighted, and I thank you for all your help. When that observation team comes next week, I bet I'll get all A's.

Sue: I bet you will, Millie. Let me know how it goes.

Millie: Bye, Sue, and thanks again.

Sue: Bye, Millie. And lots of good luck.

-- END --