transformations of dreams and persistence of meanings

8/9/2019 Transformations of Dreams and Persistence of Meanings

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TRANSFORMATIONS OF DREAMS AND PERSISTENCE OF MEANINGS: GIRLS ON

THE FAST MATH TRACK, TEN YEARS LATER

Maria Droujkova, Amanda Lambertus, Sarah Berenson

Natural Math, North Carolina State University, University of North Carolina at [email protected], [email protected], [email protected]

Girls on Track is a longitudinal study in its eleventh year, following over three hundred fast

math track middle-school girls. Each cohort started with a summer math camp data collection

via observations, surveys, content tests, school records, and interviews. Every several years we

interviewed study participants about their current relationships with STEM disciplines, familydynamics, and career plans. This paper focuses on the significance of mathematics in the

development of plans and dreams of four women from the first cohorts. These case studies areviewed against the backdrop of all study data. Over the years, our models became more centered

on girls and their immediate communities and networks, rather than the institutional track.

Roles of mathematics in the persistence of deeper meanings of women's lives are significantly

more complex than sequential milestones in the linear school-to-career "pipeline" model.

Focus

This paper centers on four case studies of women who were on the fast math track in middle

school ten years ago. One of them is now a math major, two are in applied STEM fields, and one

is a journalism major. We compare and contrast the view of STEM as a direct job goal, andeducation as a series of step toward that goal through a narrowing, increasingly more challenging

pipeline (Barker & Aspray, 2006; Blickenstaff, 2005; Stage & Maple, 1996), to the view of

mathematics as a personal strength, an asset in a variety of shifting career roles, and a tool forconstructing meaning (Belenky, McVicker Clinchy, Coldberger, & Tarule, 1986;

Csikszentmihalyi, 2008; Jungwirth, 1993; Wenger, 1999). This paper is a step toward an

integrated model connecting academic track point of view and personal and communitysignificance of mathematics. Such a model can provide a greater diversity of perspectives in

STEM education, and ultimately support better solutions of human problems through

pedagogical developments.

Theoretical BackgroundThe under-representation of women in science, technology, and engineering careers continues to

be a big national concern (Barker & Aspray, 2006; National Research Council, 2001). In thenineties, the differences in elementary and middle school mathematical achievements between

girls and boys, pronounced in earlier studies, ceased to be significant, as, for example, data from

the Third International Science and Mathematics Study show (Beaton et al., 1996). However,girls do not persist at the same rate as boys in continuing their study of mathematics beyond

middle school, taking less rigorous courses and leaving the pipeline leading into science,


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engineering, and technology field careers, with mathematics serving as a filter or a gatekeeper

(Blickenstaff, 2005).

These and other reports cite the importance of rigorous high school mathematics as vital toimproving the quality of the workforce for the twenty-first century, and call for increased

intervention efforts that encourage girls and young women to select rigorous advanced

mathematics courses beginning as early as middle school algebra and continuing throughcalculus in high school. However, fewer studies are done about the meaning and significance of

mathematics in the lives of girls and women (Jungwirth, 1993), and social structures outside of

classes, such as "geek circles" (Varma, 2007) that may support STEM careers. This paper is anexploration of the significance of mathematics in the persistence of meaning threads in the first

ten years since the middle school.

Four Cases And Their Threads Of Meaning

From the pipeline point of view, Cara is the very model of a modern female STEM career

woman, studying for a PhD in mathematics. Lorna is an example of someone who switched from

a math path to an applied and traditionally female-oriented biomedics path, still staying close to

STEM. Hellen selected hydrology, another STEM application, and Kelly dropped out of the fastmath track and STEM career path, initially wanting to be a veterinary doctor, but by high school

going into journalism. In this part of the paper, we explore the roles of STEM in some examplesof personal meaning threads that emerged from these four cases. In the next part, we situate the

threads within a model that comes from the larger study.Cara: The Conceptual Architect

Cara is a poster woman for the math pipeline model. She is currently studying for her PhD inmathematics. In her undergraduate years, she took all available math courses at her institution,

and obtained a math major and two STEM minors. In high school, Cara was taking all math

courses earlier than the average, and at a more advanced level, which defined her as a fast mathtrack student. She partially attributes the rather surprising fact that she never met a math teacher

she did not like to always being in earlier, faster classes that tend to be assigned to better

teachers.However, Cara experienced a switch in future job plans in high school, in a scenario not rare for

girls that age (Blickenstaff, 2005): she did not like the math requirements of her chosen career.

She wanted to be and prepared to be an architect, taking and enjoying AutoCAD classes.However, conversations with people from the field convinced her that architecture required "the

wrong kind of math": a lot of tedious number crunching and memorization for field exams. She

examined her strengths and decided to be a mathematics major, because she deemed she was

stronger at conceptual understanding. Her current major is a very applied area of mathematicalmodeling, with prospective jobs in the private high-tech companies or a combination of private

and academe research. This is the superficial story, however. The threads of meaning that

emerged as interview data categories are the following.Controlled information and communication. Cara is a family-centric, strongly religious

person for whom obeying authority and controlling information and communication sphere is a

matter of explicit attention and utmost importance. She would not take a programming class atschool because of the immaturity of other students in it, for example. Likewise, she rejects much

of social networking: "Everybody uses Facebook, so I would not." For Cara, mathematics is

associated with a pure, controlled, conceptually advanced system she can embrace and follow in

the company of a selective group of people. This thread is the reason Cara does not want to take


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an academe path, because she can't control who she will be teaching, and her past experiences

clearly demonstrated teaching occasionally becomes rather unpleasant because of the

randomness of students.Close groups of geeky, serious friends became an integral part of this thread. Cara talked at

length about following older friends' advice in choosing classes, the academic advisor, and

leisure activities. She is an avid gamer, for example, and a path into web site programming, thenarchitecture, then mathematical modeling has been supported for her by gaming since she can

remember herself. Gaming with friends, as a part of an exclusive, geek culture REF reinforces

STEM orientation for Cara."I am very practical."Cara spends a lot of time carefully researching, planning and

discussing with her network of family and trusted friends all matters of learning and future

career. She selected her graduate advisor based on the fact he hooked every graduate student

with a multitude of internships, providing job connections and opportunities from early on. Caragraduated with multiple minors by applying AP courses to her college work. She carefully

selects professors for her classes, which, again, leads to "never met a math or science professor I

did not like." This thread pulled Cara toward an advisor with a strong business network, and a

career in the private sector.Modeling. Far beyond being a mere future job, or even a career, modeling is a thread of

meaning for Cara. In middle school, she and her friends made art, and she was the personcreating web sites to host their art projects. She explained how building architectural

constructions, using software, grew out of these early pursuits, and then modeling real life

phenomena with mathematics was a continuation of the same thread. While architecture and web

sites seem hands-on and visual, Cara approached web design from the coding rather thanWYSIWYG perspective, and architecture from programming - so her "design" thread has been

growing into the increasingly conceptual and mathematical direction of modeling.Lorna: The Academic Caring

Lorna was going to be a mathematician or a math teacher, but higher-level math courses

proved too abstract for her. She describes one class where she struggled and succeeded

somewhat, but the next one "started with that proof that square root of three is irrational, and Ihad no idea how to even start, so I dropped the course and switched my major." She decided to

switch to biomedics.Parenting as teaching. In her interviews, Lorna talked about her mother in detail, tenderly

remembering the many advanced, very pleasant academic interactions from her early childhood

on. She describes her mother as very smart, despite having to support the family from the age of

fifteen as a first-generation immigrant from India, and not getting a college education. When

Lorna progressed into math courses beyond those her mother had before, their roles reversed,with Lorna teaching math to her mother as a way to understand it better. This may explain

Lorna's success at landing a job at the Sylvan Learning center as a calculus tutor, with

"everybody there at least twenty years older than I was." Lorna also sounded indignant (withapologies, catching herself at it) about parents of struggling school or college students not

helping them better throughout their academic lives. She sees parenting as teaching, and teaching

as so much related to caring as to be, metaphorically, parenting. She tutored relatively advancedmath throughout high school, and chose the math major as a continuation of this "caring" thread.

As college mathematics became more abstract, Lorna could not assume this caring role

anymore. She described her dismay at being able to understand material with some help from

another student, but not having enough mastery over it to help others. While capable of being a


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math student, she was no longer in the position of "math parent" and therefore decided to change

things around. Biomedics supports her image of "parenting" or "caring" through the participation

in an advanced and sophisticated field.There's nothing I can't do. Another defining thread in Lorna's life is her incredible

assertiveness. For example, she described several instances of persevering through multiple

rejections while landing jobs as a young teen, and most recently finding a biomedics internshipthat took waiting by doors and multiple calls to five different professors repeatedly saying, "No."

Lorna says, "There's nothing I can't do if I put my mind to it!" Her early childhood and teen years

experiences with mathematics, especially tutoring, supported that image of assertiveness andpower.

But what about dropping off the math track in college? Paradoxically, Lorna claims she

wanted to do it to keep her feeling of power, includingmath power. The major switch had her

take quite a few advanced science classes in her last college semesters, and she wanted to feelcapable and confident, especially about mathematics involved. It was a challenge, but in ways

appropriate for her personally. It is Lorna's self-confidence that kept her from continuing with

the math major, which, given her previous track, she was likely quite capable of getting, just not

in that parenting, helping, assertive manner that was so important for her.Hellen: The Art Of The Science

Hellen fondly recalls doing math with her big brother when she was young, but back then,she wanted to be an entertainer. "Saturday Night Life people seemed so happy!" Starting from

high school, though, she turned toward sciences, and is currently applying to enter a graduate

school in hydrology. Hellen's threads of meaning reveal a surprising path toward science for her.Ownership through creativity. Hellen is an outgoing, friendly person who smiles a lot. She

mentioned how she can make others laugh, and how entertaining others was so important that

she considered it as a career. But what really hit a chord with Hellen was designing her own

science experiments. She specifically recalls a biology camp where she did this over severalsummers, and a school project about water quality that got her interested in that endeavor. Later,

she liked classes where she could be creative about her assignments, making beautiful and

meaningful outlines and working hard on presentations. For her, science is about design, it is acreative, almost humanistic endeavor. Theater is still her big hobby. Hellen was thrilled that at

her graduate school interview, her writing skills were highly prized as something that will give

her an edge as an applicant. She is looking forward to graduate school experiences being moreopen for that sort of creativity than undergraduate courses. Designing experiments is the thread

that pulls Hellen toward STEM.Multi-generation networks. Family and friends play a big role in Hellen's professional

orientation. Her dad went to the science camp that somewhat determined her choice of subject.She mentioned keeping in touch with camp counselors, who were undergraduate students at a

time, and following in their steps. Hellen kept connections with many of them, now advising her

on the choice of a graduate school. Since her creativity, including scientific creativity, is alsoaudience-oriented, the network thread playes a key role in pulling Hellen into the direction of a

STEM career.Kelly: Stories With A Face

Kelly studies to be a journalist, works as a journalist for several student organizations, and

volunteers in various journalist capacities for friend and community projects. In the middle and

high school, she wanted to be a veterinarian, but an experience with an internship made her

realize it's not a job for her. However, anything and everything about journalism is tremendously


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satisfying. She wants to present important and interesting stories either through being a news

anchor, or through investigative reporting. Are there any threads in Kelly's life related to

mathematics? Here are two examples."People relate to my stories with a face"- Kelly talks about the importance of information

being personal and human, delivered by someone listeners know, recognize, and trust. She thinks

it is her particular cognitive strength to give stories a twist people appreciate and understand, andto present information in interesting ways. She works for days and weeks improving her videos,

"But when you are done and there is three minutes of it, you can see a strong story." Visual and

information literacy at this level, while not directly mathematical, is related to situated STEMskills.

"It takes a village."Kelly is a highly networked woman, she has many friends and is a

member and a leader of many student organizations. Mathematics was always challenging for

her, took more time, and required more efforts than other subjects. School mathematics was alsoseparate from life mathematics such as finances, and not something ever, ever used. Kelly's

family, however, rallied around her, helped her when they could and hired tutors when they

could not. Kelly noted the very positive feeling that she was constantly supported in challenging

and extrinsic hardships, and able to pass these gatekeepers through collective efforts of herfamily and her own hard work. In a sense, mathematics was something to rally against.Situated complexity. As a possibility not yet set in stone, Kelly considers going into investigativereporting, and she discusses at length the joys of seeing unexpected twists in stories, playing

devil's advocate and otherwise deeply interacting with her daily subject matter. Undoubtedly, this

requires logical abilities and very likely at least some statistics and data analysis, but Kelly does

not see this as mathematics (Lave & Wenger, 1991). She does acknowledge that her work as aclub treasurer involves math, but again, she sees that as very different from "school math"

(Hoyles, Noss, & Pozzi, 2001). The use of technology and software she describes in her award-

winning short video work is sophisticated too, but mathematics in it is very much applied.Kelly's thread of complexity in everything she does suggest high logic abilities, without an

attempt to explicate them or to apply them to any STEM direction.

From The Leaky Pipeline To Persistent Threads of Meaning

Leaky Pipeline

Many studies considering women in STEM careers adopt the "leaky pipeline" perspective,starting somewhere around the first Algebra classes and ending in PhD degrees, with many

women not making it all the way through (Barker & Aspray, 2006; Blickenstaff, 2005; Stage &

Maple, 1996). We summarized the characteristics of several pipeline models from the literature:

The pipeline is linear, with no turns, pauses or detours.

People who drop out of the pipeline are gone forever

Milestones within the pipeline, such as classes or internships, are motivated by being

prerequisites to further milestonesThreads of meaning

Yet this picture does not seem to match women's own views on meaning and significance of

STEM in their lives, or our analysis of the same when we adopt a perspective centered onwomen rather than classes and institutions. From case studies, as well as quantitative analysis of

larger samples of our longitudinal data, emerge individual threads and thread categories of

personal meaning that form each woman's path, and in which STEM has varied significance.Cara's controlled information and communication and "I am very practical," Lorna'sparenting


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as teaching, Hellen's multi-generation network, and Kelly's "it takes a village"threads belong to

the category ofPLNs, personal learning networks (Siemens, 2005) that start with families, and

develop to include friends and eventually colleagues. These threads also belong to theParent

Powercategory. We found that threads from these intersecting categories had a strong impact on

STEM tracks of all study participants.

Cara's modeling, Lorna's ownership through creativity, and Kelly'ssituated complexity areexamples from the thread category ofcontent-specific ways of knowing(Belenky et al., 1986;

Lave & Wenger, 1991) These content threads may not tie with particular academic or curricular

subjects, but are overarching themes or topics important in each person's life and developingfrom naive to sophisticated forms as the person matures. The pedagogical practice of cross-

disciplinary unit studies (McColskey, Parke, Furtak, & Butler, 2003) is connected to this

category.

Cara's "I am very practical,"Lorna's "There is nothing I can't do,"Hellen's ownership

through creativity and Kelly's "People relate to my stories with a face"are example of women's

awareness and focus of theirpersonalities in career paths. STEM skills have particular, complex

relationships with personality traits, a topic women discuss at length in their interviews.

Lorna'sparenting as teachingand "There's nothing I can't do,"and Kelly's "People relate to mystories with a face" are examples from the caring and helpingthread category. While studies

show that women in the academe are not any more likely than men to find job satisfaction incaring or helping roles rather than research roles within the field (Stage & Maple, 1996), girls in

our study integrated caring into career selection and explained how they view their work as

helping people and the world.

Cara's modelingand Kelly'ssituated complexity belong to the category defined by the

abstract-applied gradient. The need for grand causes and abstract concepts, or the need to

immediately see results of pursuit are expressed in, and supported by, different approaches to

STEM.

Conclusions

We would like to finish with a quote about life dreams from Janush Korczak, a Polish pedagogueand a champion of children's rights (Korczak, 1990):

When we don't have enough material to reason, there appears a poetic meaning of what little

we have. Into a dream we transform the feelings that don't get realized in reality. The dreambecomes our life's program. If we only knew how to decipher it, we would see that dreams do

come true.

If a poor boy dreams of being a doctor and becomes a nurse, he fulfilled his life's program. If

he dreams about being rich, but dies on the bare mattress, his dream did not come true onlysuperficially: after all, he did not dream about hard work toward a goal, but about

squandering money away; he dreamed about champagne, but drank moonshine; dreamed

about salons, but had bar brawls; wanted to throw gold to the wind, but wasted coppers.The other wanted to be a priest, but became a teacher or simply a groundskeeper, but, being a

teacher, he's a priest, being a groundskeeper, he's a priest.

She wanted to be a terrible queen, and is she not a tyrant to her husband and children, havingmarried a low-level clerk? Another wanted to be a beloved queen, and is she not ruling a folk

school? The third one wanted to become a great queen, and is her name not covered in glory,

the name of a wonderful, extraordinary seamstress or matron? (p.112)

While the dreams and plans change and transform, the personal meaning threads, and the


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correspondingsignificance of STEMin threads and thread categories are continuous and persist

through time. Examining these meanings and significances at the level of individuals and their

networks can prove fruitful in understanding how to support women in STEM careers.

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