Girls' experiences in learning school mathematics.

During the past few decades, gender issues in mathematics education emerged as a controversial topic. Researchers found that female students, at both elementary and secondary levels, perform less well than their male counterparts on standardized tests (Ansell & Doerr, 2000; Beaton et. al., 1996). In other studies, female students, compared to their male counterparts, exhibited lower self-confidence in approaching mathematics and, as a result, were more likely to avoid taking advanced math courses in high school (Eccles et. al, 1983; Meece, Wigfield, & Eccles, 1990). Researchers have argued that female students' lower self-confidence and lack of motivation in school mathematics constitute a complex phenomenon in which various sociocultural forces are dynamically involved. For example, Reyes and Stanic (1988) argued that different sociocultural factors influence female students' experiences with school mathematics, affecting their self-confidence in and motivation for pursuing advanced mathematical knowledge.

Recent national reports and professional studies have underlined that early adolescence is the critical time for female students to develop their motivation and academic identities (Bruner, 1996; Dick & Rallis, 1991; Marlow & Marlow, 1996; National Research Council, 1989; Sadker & Sadker, 1994). However, relatively few studies have explored the first-hand experiences of young adolescent girls with school mathematics. Furthermore, the majority of previous studies on students' motivation have been based on individual psychology that tends to separate students' consciousness from its sociocultural context (Pajares & Graham, 1999; Seegers & Boekaerts, 1996; Wigfield, 1994; Wigfield & Eccles, 1992). As a result, as Atweh and his colleagues (1998) argued, it is hard to find studies that seriously investigate the sociocultural context of students' mathematical learning and their experiences with school mathematics. Similarly, the overall picture of girls' experiences with school mathematics, as well as the dynamic and complex relationship between their motivation and its sociocultural milieu, has not been sufficiently explored.

Therefore, it is important to investigate the everyday experiences of young adolescent girls with school mathematics from a new perspective that does not separate their motivation from its sociocultural context. Such studies will enrich educational researchers' understanding of the nature of students' motivation, including the complexities and dynamics of young adolescent girls' thoughts and attitudes towards school mathematics, in relation to various sociocultural factors surrounding them.

The following cross-case study of four young adolescent girls illuminates their experiences with school mathematics and the impact of sociocultural context on their motivation. In particular, the researcher has examined girls' motivation, based on an innovative concept from Bahktin's circle, "multiple voices and multiple selves." This new theoretical standpoint enables the researcher to explore several significant aspects of girls' experiences with school mathematics and to deconstruct their voices and selves in relation to various sociocultural forces that dynamically constitute aspects of their identity and motivation for learning school mathematics.

Conceptual Framework

This study is based on two different but interrelated theoretical frameworks: Feminist theory and sociocultural approaches to the mind as elaborated by Bakhtin's circle. These two different streams of theory have significantly contributed to our understanding of gender issues in mathematics education during the last few decades.

Feminist Theories

Feminism is "both a theory of women's position in society and a political statement focused on gaining equal rights and opportunities for women and changing existing power relations between men and women" (DeMarrais & LeCompte, 1998, p. 35). In the area of education, feminists concentrate on how school curriculum and practices contribute to maintaining the unequal distribution of power between men and women.

Fundamentally based on a feminist perspective, gender studies in mathematics education emerged from an awareness of the mathematics achievement gap between male and female students, which often prevented women from advancing to more professional occupations and, as a result, from accessing power in a patriarchal society. One of the most important contributions made by feminist scholars concerns women's unique approaches to self-development and academic leaming (Belenky, Clinchy, Goldberger, & Tarule, 1986; Brown & Gilligan, 1992). Belenky and her colleagues (1986) argue that women's method of learning can be qualitatively different from that of men. Women, as the authors explain, tend to develop and value a connected mode of learning, while men are more likely to pursue a separated mode based upon a Cartesian view of the world and individuals. More interestingly, in their book, Belenky and her colleagues present the concept of voice as a critical aspect of one's identity formation. To them, voice is not mere vocal sound through which we communicate with each other. Instead, having or speaking one's own voice holds inexorable existential and epistemological meaning: Voice is conceived as the process of constructing self, personality, and identity, as well as one's way of knowing.

However, previous research also suggested that for many women and girls, keeping and speaking their own voices is not an easy endeavor. Brown and Gilligan (1992) revealed that young adolescent girls gradually silence their voices as they move through adolescence. Brown and Gilligan explain that young adolescent girls begin to suppress their own individual voices as they learn, through experience, that expressing their real thoughts and feelings can damage their relationships with others. They understand, at least intuitively, the "good little girl" image prevalent in our society. In their efforts to conform and fit in--by pleasing others--they silence themselves.

The phenomenon of "losing one's own voice" among adolescent girls also appears in many other studies, showing their inner conflicts and the distorted development of their academic and personal identities in a male-dominated society (Rogers, 1993). Harter, Waters, and Whitesell (1997) theorize that young adolescent girls' loss of their own voices in a school setting reflects their false self-manifestation. The researchers argue that girls, as they become more aware of social expectations and pressures, gradually develop and manifest false self-identities by silencing themselves.

Sociocultural Approaches to Mind

Sociocultural approaches to the mind are derived from the work of Vygotsky and Bakhtin's circle, focusing on cultural psychology that stresses the primary role of communication and social life in our construction of meaning and cognition itself (Wertsch, 1991). Sociocultural approaches to the mind begin with the assumption that "action is mediated and that it cannot be separated from the milieu in which it is carried out" (Wertsch, 1991, p. 18). These approaches emphasize the importance of the sociocultural, as well as the historical, environment in the formation of an individual's mind. They argue that the origins of human consciousness can be found not in a separated individual entity, but in the external processes of its social life, in the social and historical aspects of human existence.

Bakhtin's entire work, including the conception of self, is based on criticism of the individualism and dualism that were prevalent in Western society during his era. He argues that human consciousness is not a self-sufficient and pre-constituted entity, but is formed through the dialogic struggle between contending voices and discourses. "The entire gamut of social and cultural phenomena, including 'self-ness' is profoundly inter-subjective or dialogic in nature" (Voloshinov, 1973, p. 34), even though it seems to happen only within an individual's mind. Therefore, one's identity and motivation, as part of the "self-ness" phenomenon, are constructed through the operation of dense and conflicting discourses, cultural and social practices, and institutional structures.

One of the most important contributions made by Bakhtin and his colleagues is that their theory enables educational researchers to recognize the multiple sociocultural layers embedded in one's speech: There are more than one voice and one identity in an individual's spoken word. Bakhtin (1981) states:

  As a living, socio-ideological concrete thing, language, for the
  individual consciousness, lies on the borderline between oneself and
  the other. The word in language is half someone else's. It becomes
  'one's own' only when the speaker populates it with his own intention,
  his own accent, when he appropriates the word, adapting it to his own
  semantic and expressive intention. Prior to this moment of
  appropriation, the word does not exist in a neutral and impersonal
  language, but rather it exists in other people's mouths, in other
  people's contexts, serving other people's intentions: it is from
  there that one must take the word, and make it one's own. And not all
  words for just everyone submit equally easily to this appropriation,
  to this seizure and transformation into private property: Many words
  stubbornly resist, others remain alien, sound foreign in the mouth of
  the one who appropriates them and who now speaks them; they cannot be
  assimilated into his context and fall out of it; it is as if they put
  themselves in quotation marks against the will of the speaker.
  Language is not a neutral medium that passes freely and easily into
  the private property of the speaker's intentions; it is populated--
  overpopulated--with the intentions of others. Expropriating it,
  forcing it to submit to one's own intentions and accents, is a
  difficult and complicated process. (p. 114)

Acknowledging the sociocultural nature of language, the incessant tensions and dynamics among different intentions and powers deeply embedded in it, Bakhtin believes that subordinate groups can generate a differentiated incomplete set of knowledge, which is at least partially resistant to dominant discourses and ideologies. Influenced by Bakhtin's idea of language as a discursive practice of social life, some feminist theorists and critical theorists have developed the concept of "language (voice) of possibility" and "language (voice) of resistance" (Bauer & McKinstry, 1991, p.4; Giroux, 1991, p. 53). They view discursive practices through language as the method of dismantling the oppressive social reality in which people are situated.

Unfortunately, few researchers have applied this new concept, "girls' voices of possibility and resistance," to the exploration of gender issues in mathematics education. However, it is likely to become an extremely valuable, highly promising perspective from which to study gender issues in mathematics education, since it enables us to examine the complex and dynamic process of female students' consciousness, including their motivation for mathematics learning, within various sociocultural contexts. This perspective also helps researchers in their search for a way to ultimately help female students break the repeating cycle of gender inequity in mathematics education. Most significantly, it emphasizes the voices of female students. In doing so, it promises to open the only avenue--i.e., reclaiming and practicing their own voices--to developing their new, empowered identities in the domain.

Voice, Motivation, and Sociocultural Context

Motivational researchers, influenced by Bakhtin's theory, have redefined the concept of motivation in a holistic way, acknowledging the constant tension and confluence of intrapersonal, interpersonal, and cultural aspects of the individual's learning and motivation. Social constructivists also believe that language is at the heart of all of these socialization and learning processes. As insiders in classroom culture, students' perspectives are crucial in providing keys to understanding these transactive motivational processes (Oldfather & Dahl, 1994; Oldfather & McLaughlin, 1993).

Oldfather (1992) has proposed a redefinition of intrinsic motivation for literacy learning called the Continuing Impulse to Learn (CIL). Explicitly linked to learners' social construction of meaning, CIL, a form of motivation, originates in and is defined by the cognitive, affective, and social processes that learners experience as they engage in the construction of meaning. Oldfather explains three aspects of CIL--classroom culture, interpersonal domain, and intrapersonal domain--and argues that the quality of student-teacher relationships, students' perceptions of cognitive ownership of their own learning process, and generative literacy curriculum in class are all factors that support or fail to support students' CIL (Oldfather & Dahl, 1994). Other educational researchers lend credence to Oldfather's argument. For example, Duckworth (1987) reported the importance of classroom environment to support students' own intellectual pursuits. Wood, Bruner, and Ross's earlier study (1976) also emphasized the importance of social support from peer interaction in students' learning process, reinforcing the arguments of Oldfather and Duckworth.

Focusing on mathematics education, Erchick (1996) argues that in mathematics classrooms many students who feel unheard, who recognize a dis-synchronicity between their voice and the dominant voices, find no "place" for themselves. She contends that many adolescent girls may fail to develop a positive academic identity in mathematics because the culture of these classrooms, which reflect mathematics as a male domain, discourages them from expressing their own voices, thereby depriving them of the means to develop their positive identity in the discipline.

Research Questions

This study centers around two primary research questions. First, what kinds of sociocultural factors or forces exert positive or negative influences on young adolescent girls' motivation for learning school mathematics? Furthermore, how do these sociocultural factors or forces contribute to or undermine young adolescent girls' motivation? Second, how do young adolescent girls react, respond to, or resist these sociocultural influences and develop their own identity in the mathematics domain?

Methods

The following is a cross-case study based on in-depth interviews with four young adolescent girls, attending fifth, sixth, and seventh grades in their elementary or middle schools. As a research design, case study is often used to investigate complex social units consisting of multiple components that are potentially important in understanding a phenomenon. Merriam (1998) argues that, in case study design, the researcher's main "interest is in process rather than outcomes, in context rather than a specific factor, in discovery rather than confirmation" (p. 19).

Participant Selection

Four young adolescent girls, each attending a different elementary or middle school located around a medium-sized university town in the Southeast, participated in this study. In selecting the participants, consideration was given to their status in five sociocultural factors: age, ethnicity, socioeconomic background of the family, school environment, and level of mathematics performance. The four participants included one Asian-American girl in fifth grade, one Caucasian girl and one African-American girl in sixth grade, and one Hispanic girl in seventh grade. Their mathematics achievement levels varied, ranging from enrollment in an advanced mathematics class for gifted students through placement in a Title I mathematics class. Their family backgrounds and school environments varied widely as well. Therefore, the type of participant selection for this study can be categorized as either a purposeful sampling (Patton, 1990) or a criteria-based sampling (LeCompte, Preislee, & Tesch, 1993).

Data Collection Method

In-depth interviews were conducted with each participant, with each interview based on a loosely organized interview protocol that allows the interviewer to modify open-ended questions during the interview process. Each interview took at least one and a half hours and was conducted by the researcher at the participant's home. All interviews were audio-taped and later transcribed. All of the students except one had been involved in a previous research project conducted by the same researcher. For this reason, the researcher had already established a good working relationship with three of the participants and had maintained close attention to their family and school environments for an extended period of time. However, data analysis in the present study focused primarily on their interview data.

Data Analysis Method

The data analysis of this study was based on the constant comparative method frequently used in grounded theory studies (Glaser & Strauss, 1967). This method was used because this study proposed to illuminate the commonality and variation across four young adolescent girls' experiences in learning school mathematics in order to develop small theories pertaining to the participants. First, the researcher read through interview transcripts and identified several repeating themes in the data. Based on these tentative themes, the researcher developed categories with which the entire data set was then coded. Categories and properties were compared and networked with each other, generating small theories and themes pertaining either to a particular participant or all four participants in the study. Throughout this process, the researcher actively sought out different points of views from colleagues to ensure the quality of data analysis. For example, initial codes for data analysis and supporting excerpts were shared with the researcher's colleagues on a regular basis. Also, the researcher shared the first draft of findings with colleagues and made revisions incorporating their feedback.

Portraits of Participants

(Names of participants, school, and town are pseudonym). Seran, a fifth-grade girl at Hartford elementary school, is an Asian American, born and brought up in another university town in the Midwest. Her family moved south to Springfield five years ago because both parents were offered faculty positions at the University of Springfield. In Seran's family environment, education has always been the first priority. Though both parents expressed a strong interest in their children's academic progress in school, Seran frequently referred to her father as the most important figure supporting her educational achievement and her motivation in learning school mathematics.

Nisha, an African-American sixth-grader at Warton Middle School, lives with her grandmother in a public housing project in Springfield. Even though Nisha has lived in Springfield, a university town, for twelve years, she has no close relatives who attend the university or any other institutions of higher learning. Since Nisha does not live with her parents or have regular contact with either of them, the amount of parental support available to her is very limited. At present, Nisha's primary caregiver is her maternal grandmother, who is over 65 years old and has very little formal education.

The third participant, Kristin, is in seventh grade at Springfield Middle School. Her father's family was originally from Peru, and her mother grew up in a traditional, lower middle-class, very religious southern family. Although Kristin looks like a Hispanic girl, most of her friends in school and in church are Caucasian. Her father works for a private company; her mother is a secretary at the university. Kristin has an older sister (a high-achieving student at the local high school) and a younger brother in second grade.

Abby, the final participant, is a sixth-grade Caucasian girl originally from a middle-class background. However, for several years her family has been experiencing financial difficulty. Her father has undergone three back surgeries during the last five years, during which time he has been totally unable to work. Her mother, a nurse in a local hospital, is now working sixteen hours a day to support the family. In elementary school, Abby was a good student. Now, however, she feels really insecure about the possibility of achieving academic success. Though she still believes that she "has the brain," Abby suffers constantly from intense anxiety in her mathematics classroom.

Findings and Discussions

The overall data analysis generated five overarching themes: interrelationship among participation, motivation, and learning; the culture of school mathematics and its impact; gender issues; reproducing others' voices; and resistance and establishing one's own voice.

Interrelated Phenomena: Participation, Motivation, and Learning

Overall data analysis revealed an interesting confluence among participation, motivation, and learning in the participants' experiences with school mathematics. As the girls explicated their experiences with school mathematics, it became clear that their active participation in learning activities could not be separated from their actual mathematical learning. Students who have actively participated in a learning activity in their mathematics classroom strongly believe that they learned the course content and, at the same time, improved their self-confidence and motivation. Their positive experience with previous learning activities supports their motivation and leads to full participation in the ensuing mathematical learning situation. This kind of intertwined relationship among students' participation, learning, and motivation is quite conspicuous in the data (Lave & Wenger, 1991). Equally significant, at the outset, motivation for mastering mathematics appears to be a product of learning or enjoyable/fruitful participation in a mathematical activity rather than a cause for learning or participation. Later, this developed motivation leads the student to still more active participation that ultimately generates a deeper level of learning. For example, Kristin recollects the time when she was a "really good math student," eagerly participating in math activities and "learning everything." She recalls, "Then, I liked math because my teacher gave us activities or games. I like it (activity-based mathematics lessons) because I learn math in that way (by active participation).... We learned everything while we were actually playing with the stuff he gave us." Seran also describes how social recognition plays a major role in the development of her motivation. "I get excited because I know I already knew it (math content) ... and everybody else asks me, 'how do you know that all?' "Then, I have a big mouth ... That's why I like mathematics." Social construction of a competent self-image, supported by her family and friends, has emerged as an important process in Seran's strong motivation to learn school mathematics.

The Culture of School Mathematics and Its Impact

Data analysis has revealed that the traditional views of mathematics knowledge and how it is taught are still prevalent in the participants' mathematics classes. To these four young adolescent girls, school mathematics is perceived as a set of very abstract and static knowledge that has little meaning in "real life." Not only is school mathematics as a whole decontextualized from their everyday lives, but also each part of the subject is partitioned off from the other parts, hardly creating a holistic, consistent picture of mathematics as a discipline. Kristin describes her confusion when she was forced to "just warm up" her brain working on meaningless operations:

     Sometimes, his morning warm-up activity doesn't even have to do
   with what we learn that day. Like we maybe have something to do with
   integers or learning about regular fractions or graphs. I think how
   these match up.

As a result, the most important value or motivation for learning mathematics, to these girls, is more related to its instrumental or exchange values in their school lives such as "feeling good about myself," "being in a smart class," or "getting into college" (Lave & Wenger, 1991). Yet, to them, mathematical learning often means involvement in boring and repetitive work, such as "adding, multiplying, and subtraction," with more concern for the speed at which such operations are performed than for the students' genuine understanding of the content (Boaler, 1997).

The authoritative and competitive culture of the mathematics classroom was found to be the primary source of the pervasive anxiety or self-alienation among the participants. These girls confess their endless anxiety and even anger toward the mathematics class that seems to undervalue or threaten their self-worth. The majority of participants believe that their mathematics classroom is not a safe place to try out their voices. They are well aware of the labeling practice that is prevalent in the class, and they voluntarily decide to silence themselves.

    Researcher: OK. You may have some reasons for not asking the teacher
    questions, right? Why?
    Abby: Because ... sometimes I get nervous because to me it seems
    like if you ask a teacher the question, it seems like you aren't
    paying attention or something. But then again I know that's not true
    because, I mean, I pay attention during math class.
    Researcher: Could you give me a kind of example? ....
    Abby: Like I said, she (her math teacher) keeps her anger in. But
    she does tend to get a little mad if you ask something when she just
    went over it. And she can tell that you weren't paying attention.
    Then she sort of gets a little bit mad at you, but, um, because you
    should have been paying attention the first time. But then usually
    the people that ask questions are the people that were listening.

It is not surprising that these young adolescent girls' motivation for learning school mathematics is significantly damaged when they intuitively grasp the inexorable tension between their desire to be respected as active learners and the repressive characteristics of instructional culture in their mathematics classrooms. Kristin, who describes her mathematics class as "just another class you have to go in, sit, learn, and work," expanded on how she could motivate students if she were the mathematics teacher. Above all, she called for respect--respect for students' own ways of learning--from teachers:

    Kristin: Uhm ... First, I have to go to them because, you know, or
    I look back at their stuff to see if there are more hands on people
    or if they (students) are more likely to listen? And if my class is
    more hands-on, I will try games and activities and the stuff that
    they enjoy. Or, I might have a survey or something, saying, you
    know, what would you like? You like more hands-on stuff? Or, do you
    like me standing in the front of the room and preaching? So, and
    then if they like me standing up in the room and preaching then I
    will tell my lessons standing up in the room, but if they want me to
    do games and have fun in the class I will try to be using the stuff
    to do.
    Researcher: Then, you seem to believe that the teacher's way of
    teaching does matter to students' motivation.
    Kristin: Yeah. Actually I do. I think that if you have more what
    they like, it will be more fun for them and they will enjoy it more.
    While you were in front of the room and they want to have more
    hands-on stuff and do all that and they are hardly learning
    anything. But, saying, when you have hands on stuff they are
    learning a lot more than (when you) bring them test very driven
    stuff. When you are standing in the front of the room and that's not
    what they're, you know, that's not how they learn, then they will
    make low test grades, you know. You think you need to change
    something.

However, these girls scarcely see the possibility of having their own thoughts and voices respected and heard in their mathematics classes. Instead, they perceive mathematics as just "another class you just have to sit through." Their helplessness and deep-seated anger prevent them from achieving a genuine understanding of mathematical knowledge.

Power issues are another important factor that shape these young adolescent girls' experiences with school mathematics. These girls sense the disparity in power between their teachers and themselves. They understand that they are constantly evaluated and "monitored" in their schools (Foucault, 1975/1995) while being classified with different labels that "keep some people up and others down." Abby projects a sense of helplessness in her response to the researcher's question about her mathematics class next year. Clearly, she believes it is the "teacher's decision," not "ours."

   Researcher: Do you think you are going to be with the same students
   in the seventh grade mathematics class next year?
   Abby: It depends, because some of them might not make really good
   grades and might get placed in a lower class than me. Or I might be
   placed in a lower class than some of my friends. And there's really
   nothing we can do about it because that's the teacher's decision, not
   ours.

Nisha and Kristin strive to preserve their self-worth through their own interpretation of ability grouping, saying "It's OK. Anyway, we're leaming everything that sixth-graders have to learn," or "There's not much difference between my class and others." They are trying to close their eyes to what is going on around them, even though they're already well aware of what is happening to them.

Gender in Play

In these young adolescent girls' mathematics classrooms, male characters are dominant while girls are almost invisible. The majority of participants' previous and current math teachers are males, and the majority of excellent students in and out of their mathematics classes appear to be males as well. Even though girls do not believe that boys are better than girls in mathematics, they admit that male students are active people who are able to occupy the center of their mathematics classroom, regardless of their level of understanding mathematical knowledge. For example, Kristin talks about her mathematics class in which male students enjoy the privilege of teaching other students, even though their way of teaching is not always effective for others. In contrast, male students seem to exert a negative influence on girls' self-confidence in learning school mathematics (Issacson, 1990). Boys' voices are so aggressive and loud that they often, whether intentionally or inadvertently, damage girls' fragile identity in mathematics, especially girls who are vulnerable to outside influences. Boys toss off negative remarks that reflect their arbitrary judgment and belittling of girls' ability to learn mathematics. They say: "You're not good at this," and "You're not smart," or "You'll never do that." Seran, a high-achieving girl in this study, confronted rejection by peers who said, "You'll never be my friend." Less confident girls often respond helplessly: "Everybody sees me not being good at math" or "put six (a wrong answer) on purpose" on a math test.

Reproducing Others' Voices

Not surprisingly, when these young adolescent girls address power issues in school, instead of using their own voices, they frequently repeat the voices of authority, voices they have heard, learned, and internalized. Speaking in others' voices often undermines their feeling of self-worth and causes deep self-alienation, as the thoughts of Kristin and Abby demonstrate. Abby believes that "mean teachers are better teachers" because "they really push you" to learn, even though she suffers greatly in the classroom of "a mean but good mathematics teacher." Her ideal of having "a nice and good teacher" exists only in her imagination; in her real world of school mathematics, she considers that situation an impossible dream. Although they do not like the criteria their teachers use, the girls often apply the same criteria to themselves causing a deeper level of self-alienation. In such event, they feel hurt and uncomfortable acknowledging who they are, and tend not to see the potentials they possess. Kristin, who criticizes her teacher's unfair treatment of students based on their scores, laments, "You know, sometimes I look at my score (on a math test) I got, and think, gosh! How could I get this? (a deep sigh)." Often, these young adolescent girls appropriate the devices used by the teacher and apply them to their peers, producing a delicate and unequal power relationship among themselves. For example, to Seran, helping her friend with math means pushing the friend to complete the same type of simple operations as quickly as possible by limiting the time allowed for those questions. She says, "I'll help my friend learn math ... so I'll ask my teacher if I can borrow her timer. I'll see if my friend can finish all the questions in time." This acceptance of the need to "push" us so that we "get [y]our stuff done" emerged clearly from the data, reflecting these girls' previous experiences and current understanding of school mathematics, which they see not as a joyous learning opportunity but rather as a bitter experience they simply have to accept.

Resistance and Creating One's Own Voice

On a more positive note, however, these young adolescent girls are not merely passive victims of the culture of their mathematics classes and their peers influences. Rather, they actively resist such outside influences, constructing and expressing their own ideas regarding an ideal mathematics class. Their resistance assumes various forms. For example, sometimes they develop their voices to assert their own ideas about what constitutes an ideal relationship between students and teachers, as well as how mathematics should be taught. Kristin elaborates her idea about "a good way of teaching math." "First, I will go to them (students) to see if they like to learn with hands on stuff or games, or want me to preach in front of them." Some of the girls may insist that the teaching authority hear their voices. Kristin rejects one of the commonly accepted school ideologies that define her as lacking the ability to learn mathematics, and she expresses her own counter ideology: "If you teach math and your students don't understand, you have to go back and think about the ways you teach because there must be something wrong with your way of teaching math."

Abby defines an effective mathematics teacher as one who "understands a lot about people" and "helps kids a lot too." A good mathematics teacher, as Abby remarks, is one who observes the ethic of caring, who is eager to offer her help to the most vulnerable people in the class, and who refrains from judging students for "not paying attention."

These young girls also strive to become agents, not pawns, in their own mathematical learning. To that end, they strive to create a classroom situation in which they can feel themselves as active participants capable of controlling the outcome of their own learning. Seran has successfully persuaded herself that her participation in learning school mathematics is fundamentally her personal choice. "I can do it because I did believe that I can do it." It is interesting that Seran, a high-achieving girl who acknowledges the importance of the student's agency in learning school mathematics, tries to help other girls listen to their inner voices as a way of recovering their own agency in their mathematics learning. Encouraging a friend who had lost her confidence in mathematics and was constantly harassed by boys, Seran said, "Don't listen to what others say to you ... They never know what you like or what you actually can.... it's your feeling."

Clearly, cooperative learning, along with consistent mutual support for one another, emerged as a central element in the girls' experiences with school mathematics (Boaler, 1997; Fennema & Peterson, 1987; Leder, (1992). All four girls described the joy they felt when helping their friends with a math problem, and also recollected the moments when their peers offered them kind, life-saving assistance. It is not surprising that the participants, including Seran, the most confident participant, tended to sit close to their friends in their mathematics classrooms. Some did so because they knew that their friends needed their help, while others depended on their friends to be helpers. To these girls, cooperation appears to be a natural responsibility to be accepted and acted upon rather than an option they can choose or refuse. Working together, they elaborate user-friendly strategies that help them learn, understand, or sometimes simply pass their mathematics exams and classes. The girls' cooperation in their mathematics classes is not limited to academic help; it also includes emotional and social support for one another. For example, Abby explains how she and her friends helped each other cope with stress when any of them received a bad grade: "When they make a bad grade they sort of show it to one of their friends and say, man, this is bad, but I can make it up. Just so they're not building up all this anger in their body and then take it out on somebody else.... I know one time I made a really bad grade, and it was only like a 40 something on a test. It was a 49 on a test, and I felt really bad. I felt like, OK, maybe if I show it to one of my best friends that I think will not tell anybody what I made. Maybe it'll just take off all the stress from my body and just sort of make it leave." Three out of four participants perceived the mathematics classroom as an insecure place that implements various labeling practices and threatens their self-worth and confidence as learners. For this reason, they tend to act, through their intimate social network, as mutual caretakers of both their academic needs and their emotional well-being.

Despite the repeated disheartening experiences with the labels attached to their classes and themselves, young adolescent girls show great resilience in dealing with the unfavorable social circumstances that surround them. Sometimes, these girls accept the competitive and authoritative culture of their mathematics classes; at other times, however, they raise serious questions about themselves and the roles of their teachers. They want their voices heard and their existences acknowledged in their mathematics classrooms. Ultimately, they challenge one of the most commonly accepted ideologies and practices embedded in teaching mathematics in our schools--ability-based streaming. The girls protest, "(T)hey (highly achieving students in math) are maybe older or smarter or whatever. But if they can (succeed), I think we can do it too."

Conclusion

In general, to the participating young adolescent girls, the world of school mathematics is neither a comfortable nor a desirable place in which to reside. Various types of apparatus threaten these girls' feelings of self-worth, undermining their rights as individuals and their freedom to learn. One of these is a teaching authority whose purported responsibility is to help students learn, but which rarely listens to or respects the voices of the learners themselves. Equally important, male figures dominate the center of the mathematics classroom, while young adolescent girls are marginalized, scattered around the edges, saying nothing and feeling almost invisible. Although these girls recognize their vulnerability in such classes, they search constantly, intuitively, for more effective and exciting ways to learn mathematics. They share the insight and wisdom that they have acquired from their personal experiences with school mathematics to reinforce one another's learning and self-confidence. To counteract the many negative voices they hear from outside, they strive to awaken one another's inner voices. Unfortunately, at times their ways of helping each other prove to be ineffective, even resulting in misguided practices that generate further self-alienation and increase the "othering process" among themselves (Popkewitz, 1999).

Unfortunately, giving up and just "sifting through" the minimum number of required classes seems to be the easiest option for girls who are losing their voices and confidence in their ability to learn school mathematics. They do not want to fail, of course, but the unfavorable culture of their mathematics classes, including a deep-seated disrespect for each student's different ways of learning and denial of their agency in their own learning process, fails them. Situated in this kind of sociocultural context, these young adolescent girls speak in multiple voices. Some essentially echo the ideologies they have learned from their schools, parents, peers, and many other sources. Others, however, clearly reflect their hopes and critical consciousnesses that spring from their existential conditions in school and in society at large. Their own words and voices resist the impact of various school practices and ideologies that repudiate their agency and aptitude for learning mathematics. Both individually and in support groups composed of friends, they struggle to reclaim their own agency and self initiative in their learning processes and school lives.

What they confront everyday, however, is a patriarchal schooling system that functions with its own rules and processes and processes and rarely listens to the voices of some of the most vulnerable learners who are deeply disturbed by the system's rules and processes. There seems to be little hope for these unheard voices--unless we, as educators, reconceptualize various school practices and become advocates for these ignored and undervalued students. If we can reinforce these vulnerable young adolescent girls' motivation for learning school mathematics by critically examining many unquestioned practices in our schools, as well as our roles within the system, these girls will be eager to say much more about their ways of learning mathematics. Inevitably, they will be much louder, much more assertive, as they reclaim their voices, rebuild their self-confidence, and reestablish agency in their own learning process. This attempt may lead to a "politicized mathematics class (Noddings, 1993, p. 156)," in which the learning and teaching of mathematics are deeply interwoven with the teacher's and students' political awareness of their choices and actions in their everyday classroom (Noddings, 1993). If this does not occur, however, these girls will have little more to say on the subject. As one of my participants, Nisha, observed, students "don't have much to talk ... about my mathematics class." They will be "just sitting through" mathematics classes until they end.

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Jae Hoon Lim

The George Washington University