Rethinking Bodies of Learners through STEM education
Miwa Aoki Takeuchi
University of Calgary
Takeuchi, M.A. & Dadkhahfard, S. (2019). Rethinking bodies of learners through STEM education. In
P. Sengupta., M-C. Shanahan., & B. Kim (Eds.). Critical, transdisciplinary and embodied
approaches in STEM education (pp.199-216). New York, NY: Springer.
EDT 840, 2500 University Drive NW
Calgary, AB Canada, T2N1N4
We would like to appreciate all the participants in the studies described in this chapter. A special
thank-you goes out to the participants we called Karim and May. We also thank Dr. Lesley
Dookie, Dr. Ayush Gupta, Dr. Pratim Sengupta, Dr. Marie-Claire Shanahan for their comments
and feedback on an earlier version of this manuscript. One of the studies described here was
funded by the Grant-in-Aid for Scientific Research [12J02927]. Any opinions, findings and
conclusions expressed herein do not necessarily reflect the views of the funding agency.
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In the context of public discourse, STEM education is often coupled with its utilitarian value for
economic growth and productivity. Under such discourse, learners are reduced at best to human
capital, focusing on the production of economic value. Sen (1997) contrasted human capital with
what he termed as human capability, which is “the ability of human beings to lead lives they
have reason to value and to enhance the substantive choices they have” (p.1959). What images of
STEM education can we visualize if we place human capabilities at the center? Rather than
treating learners as human capital or disembodied entities, we attempt to shed light on learner
bodies. Drawing from the integral theoretical perspective of sociocultural theory with queer
theory and critical race theory, we conceptualize learner bodies as the locus of negotiating the
norm, emotions and desires, and view them as fundamentally cultural and historical. Utilizing the
counter-storytelling practices framed by critical race theory, we introduce the stories of two
learners, May and Karim. May’s story tells us how the informal mathematics knowledge she
embodied came to be subjugated through formal school curriculum and pedagogy. Karim’s story
illustrates how his body queered normative mathematical representation and that facilitated a
shift in his positional identity and participation in mathematics learning. The stories of learners
with a fuller account of their cultural and historical bodies can help interrogate the underlying
assumptions surrounding the current mathematics education. Reconceptualizing learner bodies
prompts us to examine how we can mobilize the traditional boundaries of STEM education.
Keywords: learner bodies; human capital and human capabilities; sociocultural theory;
critical epistemologies (queer theory and critical race theory); equity in
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In the context of public discourse, Science, Technology, Engineering and Mathematics
(STEM) education is often coupled with its utilitarian value for economic growth and
productivity (e.g., Committee on Science, Engineering and Public Policy, 2007; Council of
Canadian Academies, 2015; Science Technology and Innovation Council, 2009, 2015).
Historically, in the United States, STEM education was proposed in response to the rising threat
for national security during and after the Sputnik-spurred education reforms (Bybee, 2010).
Such discourses linking scientific innovation with national security were prominent in driving
the development of a curriculum document in the United States known as, A Nation at Risk
(National Commission on Excellence in Education, 1983). This document characterized the
strong link between STEM education and national security, until the discourse surrounding
STEM education changed in the post-Sputnik era. Broadly speaking, one of the leading
narratives surrounding STEM education in the post-Sputnik era is filling workforce demands in
the globalized and dynamically changing market (as represented in Committee on Science,
Engineering and Public Policy, 2007). Standardized STEM education practices prevalent in the
United States have also been critiqued as they prioritize economic competition and neoliberalism
through the medium of education (Hoeg & Bencze, 2017; Strong, Adams, Bellino, Pieroni,
Stoops, & Das, 2016).
Internationally, the leading narratives that shape STEM education in the United States are
not necessarily shared with other countries. Shanahan, Burke, and Francis (2016) maintain that
STEM education in a Canadian context can be best viewed as a boundary object with a definition
that is not fixed or monolithic but partially shared and situationally defined among various
stakeholders. Still, one of the most influential and conspicuous discourses around STEM
education is filling STEM related workforce demands and boosting economy as observed in
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recent policy-related documents in Canada (Council of Canadian Academies, 2015; Science
Technology and Innovation Council, 2009, 2015). In another country such as Japan, which is the
context of one of the stories introduced in the following section, STEM education has begun to
be discussed in relation to promoting students’ employability in the STEM fields (especially in
computer sciences) (Japanese Cabinet, 2016). Under the dominant discourse around STEM
education, learners are reduced at best to human capital, in which the aspect of producing
economic value is overemphasized.
In lieu of human capital, Amartya Sen emphasized the theoretical construct of human
capabilities. According to Sen (1997), human capital focuses on “skill and knowledge as well as
effort — in augmenting production possibilities” (p.1959); in contrast, the concept of human
capabilities underlines the significance of “the ability of human beings to lead lives they have
reason to value and to enhance the substantive choices they have” (p.1959). Sen does not deny
the fact that economic growth can lead to the expansion of human freedom to choose the kind of
lives they want to live. However, as is often the case, the argument around human capital tends
to concentrate on productivity and economic growth and does not extend the discussion to “why
economic growth is sought in the first place” (Sen, 1997, p.1960). Alternatively, Sen claims the
centrality of individual freedom as the force and means of social development as well as end of
Sen (1999) draws on a childhood recollection to demonstrate his motivation to highlight
human capabilities. As a child, Sen observed a man, Kader Mia, a Muslim daily worker, get
knifed and killed in a largely Hindu area. Kader had to travel to the area hostile to Muslims in
search of work to financially support his family. Being impacted by this encounter with Kader,
Sen searched for ways that centralize human capabilities in economic and societal development,
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with his strong belief that “human beings are not merely means of production” (p.296). Including
the layer of human capabilities highlights “the instrumental role of capability expansion in
bringing about social change (going well beyond economic change)” (p. 296). In light of human
capabilities, freedom is conceptualized as the means and end of development. The means and
end of STEM education, therefore, exceed beyond growing human capital, which mainly
concentrates on the production of commodity and economic value, and should include fostering
agency among students for social and political development along with the well-being and
freedom of people.
Theoretical Framework: Integrating Perspectives from Sociocultural Theory, Queer
Theory and Critical Race Theory to Conceptualize Learner Bodies
What images of STEM education can we visualize if we place human capabilities at the
center? Rather than treating learners as human capital or disembodied entities, the lens of human
capabilities allows our focus to be on the cultural and historical nature of learner bodies, which
hold the stories of who they are and who they are becoming. This lens sheds light on the
expansion of freedom of bodies for all the learners through STEM education.
In the domain of mathematics education, learner bodies came to light in relation to the
complex, embodied mathematical thinking (e.g., Abrahamson & Sánchez-García, 2016; de
Freitas & Sinclair, 2013; Hwang & Roth, 2011; Lee, 2015; Ma, 2017; Nemirovsky, Tierney, &
Wright, 1998; Radford, 2009). These studies on learner bodies draw from various epistemologies
and ontologies; ecological dynamics (as seen in Abrahamson & Sánchez-García, 2016), sensuous
cognition (as seen in Radford, 2009); material phenomenology (as seen in Hwang & Roth,
2011), new materialism (as seen in de Freitas & Sinclair, 2013); distributed cognition (as seen in
Ma, 2017). Others (e.g., Lee, 2015; Nemirovsky et al., 1998) designed the interaction among the
RETHINKING BODIES 6
body, mathematics learning, and technology and made the interaction explicit. We seek to further
advance this line of research by shedding light on how certain bodies are forced to be hidden in
the public space of learning, how the mobilities of certain bodides can be restricted or liberated,
and how such negotiation of bodies interact with the stories and histories of the learner. As
detailed in the following sections, we believe that insights from queer theory and critical race
theory will lend a hand in this endeavour.
In conceptualizing learner bodies as cultural, historical and political, we integrate insights
from sociocultural theory, queer theory and critical race theory. Sociocultural theory emphasizes
the cultural and historical nature of our bodies in learning, as the human mind is conceptualized
as extending beyond the skin and is mediated by cultural and symbolic tools (Vygotsky, 1978;
Wertsch, 1998). Philosophically, one of the central mandates of sociocultural theory is to
overcome the Cartesian dualism, which is well-represented by Il’enkov (1977) as “thought
lacking a body and a body lacking thought” (p.19). Instead, sociocultural theory conceptualizes
the “thinking body” (p.18) of living being. From this perspective, seemingly biological functions
such as sleeping patterns are afforded and constrained within the cultural practices that we
engage in. Rogoff (2003) succinctly summarizes this perspective by stating that humans are
“biologically cultural” (p.63). From this perspective, learner bodies are fundamentally cultural
and historical, as they are shaped through the cultural practices, for example, as demonstrated in
Saxe and Esmonde’s (2005) trace of the change in Oksapmin bodily counting system over time.
Insights from Queer Theory
Sociocultural theories, however, have not explicitly addressed power, access and
privilege associated with learning (except for recent works advancing this area Esmonde &
Booker, 2016; Gutiérrez & Jurow, 2016; Nasir & Bang, 2012). In order to fully conceptualize
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cultural and historical bodies of learners, we incorporate perspectives from Critical Race Theory
and Queer Theory building further on our earlier work (Esmonde, Brodie, Dookie, & Takeuchi,
2009). Queer theory considers the norms, emotions and desires associated with performing
certain bodies and also the costs of not-performing the normalized body (Butler, 1993; Foucault,
1980; Moraga & Anzaldúa, 1981). “Queer” in queer theory functions as “a marker representing
interpretive work that refuses what Halley has called ‘the heterosexual bribe’ — that is, the
cultural rewards afforded those whose public performances of self are constrained within that
narrow band of behaviours considered proper to a heterosexual identity” (Sumara & Davis, 1999,
p. 192). Queer theory thus meets pedagogy and curriculum by broadening what counts as
knowledge: “not just knowledge about sexuality, but knowledge about how forms of desire are
inextricable from processes of perception, cognition, and interpretation” (Sumara & Davis, 1999,
p. 192). Taking the epistemology of queer theory thus amounts to questioning what counts as
knowledge in STEM or mathematics education.
Queer theory also helps us see how power penetrates into our body. Foucault (1980)
maintains that power “reaches into the very grain of individuals, touches their bodies and inserts
itself into their actions and attitudes, their discourses, learning processes and everyday lives”
(p.39). Power is thus exercised “within the social body, rather than from above it” (p.39). As
such, power reaches into the way learners use or do not use their bodies and how their bodies are
positioned, mobilized or constrained through the configuration of classrooms and schools.
Power is exercised over non-normative bodies through materialization and abjection of
bodies. Butler (1993) elucidates tacit exclusion of unintelligible bodies with the concept of
abject. Butler explains how the boundary created to generate certain subjects simultaneously
excludes other bodies or unintelligible bodies. According to Butler, abject beings are “those who
RETHINKING BODIES 8
are not yet ‘subjects,’ but who form the constitutive outside to the domain of the subject. The
abject designates here precisely those ‘unlivable’ and ‘uninhabitable’ zones of social life which
are nevertheless densely populated by those who do not enjoy the status of the subject, but whose
living under the sign of the ‘unlivable’ is required to circumscribe the domain of the subject”
(p.xiii). This tacit way of exclusion works to oppress the outside of materialized norm and
Such exclusion can manifest in our daily encounters and how we move our bodies and
how we feel about our bodies in social spaces. Adding the lens of racialized bodies into queer
theory, Ahmed (2006) discusses how certain bodies are extended or not extended, and become
more or less mobile in social spaces:
For the bodies that are not extended by the skin of the social, bodily movement is not so
easy. Such bodies are stopped, where the stopping is an action that creates its own
impression. Who are you? Why are you here? What are you doing? (p.139)
In these moments, racialized bodies can feel the loss of place and become estranged. While
acknowledging the emotional stress and social and physical pressure experienced by the
estranged bodies, Ahmed also describes the possibility of such bodily encounters for queering
space by disturbing the order of things and the normative ways of living.
Insights from Critical Race Theory
Critical race theory has its roots in critical legal studies which examine the way law
encodes cultural and racialized norms and it assumes that racism is not a series of isolated acts
but is rather endemic and systemic (Ladson-Billings & Tate, 1995). Critical race theory
legitimatizes racialized individuals’ bodies and voices by using stories as a vehicle (Dixson &
Rousseau, 2006; Ladson-Billings & Tate, 1995). Counter-storytelling informed by critical race
RETHINKING BODIES 9
theory offers space to challenge dominant, deficit narratives (Solórzano & Yosso, 2002).
Counter-storytelling theorized through critical race theory challenges the deficit master narrative
that overemphasizes and individualizes the deficits of non-dominant students and eventually
forces non-dominant students to assimilate into the mainstream (Fernández, 2002; Ladson-
Billings & Tate, 1995; Solórzano & Yosso, 2002). We will elaborate on how we integrated
insights from critical race theory into our methodology in the following section. Integration of
queer theory and critical race theory allows intersectional storytelling with STEM education (as
seen in Leyva, 2016). We hope to bring forth the richness of mathematical knowledge those
learners bodies embodied and the agency that they exercise to queer the norm.
The overarching methodology for this chapter is framed as critical race methodology
centralizing counter-storytelling (Solórzano & Yosso, 2002). Solórzano and Yosso define the
counter-story as “a method of telling the stories of those people whose experiences are not often
told (i.e., those on the margins of society). The counter-story is also a tool for exposing,
analyzing, and challenging the majoritarian stories of racial privilege” (p.32). There are several
types of counter-stories: personal and autobiographical narratives, a third person voice of other
people’s stories or narratives, and composited stories and narratives drawing on various forms of
data (Solórzano & Yosso, 2002). Counter-storytelling locates a learner within broader
sociocultural contexts and therefore should include political and societal contexts surrounding a
learner when describing a story (Fernández, 2002).
In our counter-storytelling, we decided to use a third person voice to introduce the stories
of two learners. A third person voice narrative allowed us to weave our reflexivity — our
reflection on the relationship with participants — into these stories, while vividly depicting
RETHINKING BODIES 10
portraits of these learners (Langer, 2016). By utilizing the medium of counter-stories, our hope
is to provide fuller and concrete pictures of who those learners are and who they are becoming in
the space and within the norms of school mathematics learning.
Our storytelling focuses on the negotiation of learner bodies as informed by sociocultural
theory and queer theory and also motivated by the counter-storytelling practices framed by
critical race theory. The creation of counter-stories was guided by our theoretical sensitivity that
surfaced the subtleties of meaning and significance to the particular segments of data (Solórzano
& Yosso, 2002). In our analysis, we selected the stories that are illustrative to depict particular
slices of students’ experiences of learning mathematics — negotiating normative practices
around their bodies in learning mathematics.
Both of stories emerged from the ethnographic studies that I (Takeuchi) conducted in
urban cities in Canada and Japan. These studies were framed to capture a thick description of
cultural practices and to reveal a “stratified hierarchy of meaningful structures” (Geertz, 1973, p.
7), which is produced, perceived, and interpreted in a particular social practice. Video and audio
recording was employed, along with ethnographic fieldnotes, to conduct analyses of particular
segments of interaction as well as interviews with participants. By retelling the stories of two
learners, using the data obtained from these two studies, we will reconceptualize learner bodies
in STEM education.
Through my previous ethnographic studies in urban cities in Canada and in Japan, I
(Takeuchi) encountered May and Karim (pseudonyms). I met May when I conducted a study in
an urban city of Japan that mainly focused on the continuity and discontinuity between schooling
and out-of-school experiences for linguistically diverse students and families (for additional
details and a fuller picture of this study, please see Takeuchi, 2018). The study focused on
RETHINKING BODIES 11
Filipina women who immigrated or migrated to Japan to work, and their school-aged children. I
was involved in a local after-school program that was offered to academically support school
learning, especially for those who used a first language or a home language other than the school
instructional language. The study consisted of three phases: ethnographic observation,
ethnographic interviews and design of mathematics learning workshops with the participants.
I met Karim when I conducted a longitudinal ethnographic study of mathematics
classrooms in a multilingual school within an urban city of Canada (for additional details and a
fuller picture of this study, please see Takeuchi, 2015, 2016). The school had approximately 450
students, with representation from more than 30 different language groups; 23% of the students
were born outside Canada, and for approximately 53% of the students, English was not the
language spoken in their homes. The study focused on four newly-arrived students who were
labelled as “English language learners (ELLs)” and their trajectory of participation in classroom
mathematics discourse and their development of identities. The study was conducted in two
Grade 4 mathematics classes taught by Ms. Sally Wilson. The data collected through this study
involved video data of classroom interactions focusing on the four students and interviews with
Ms. Wilson as well as an English as a Second Language (ESL) class teacher.
Story of May
Let us introduce May. May was a student I (Takeuchi) met during my ethnographic study
conducted in an urban city of Japan, where I worked with the communities of recent immigrants
from the Philippines. May was born in Manila, the Philippines. She came to Japan when she was
a Grade 4 student in the Philippines. When she started schooling in Japan, she repeated Grade 3
because of academic and linguistic gaps identified by her teacher, and thus she was older than
RETHINKING BODIES 12
other peers in her grade. When I met her, she was a Grade 6 student in a public elementary
school. As for the most fluent language for her, she said, “I can speak Filipino (Tagalog),
Japanese and English… but none is perfect.” She emphasized that Japanese vocabulary
associated with history and geography was particularly challenging. May’s language practices
could be positively seen as translanguaging — the fluid language practices unique to
multilinguals (García & Wei, 2014); however, for her it was instead perceived as a deficit.
The following brief description of Japan’s immigration policy would help contextualize
May’s story. In Japan, which is often perceived as “linguistically and racially homogeneous,”
some industrial areas are becoming much more ethnically and linguistically diverse, as
represented in the percentages of registered foreign nationals in the following cities: Oizumicho,
Gunnma (14.5%); Minokamo, Gifu (7.7%); and Kikukawa, Shizuoka (5.4%) (Committee of
Localities with a Concentrated Foreigner Population, 2012). In addition to these cities, large
cities such as Tokyo, Nagoya, and Osaka have relatively high percentages of “registered foreign
nationals.” Since the late 1970s, a significant number of Filipino women have come to work in
Japan. Filipino migration in Japan is gender-biased: 77.6 % of the Filipino population living and
immigrated to Japan are women (Ministry of Justice, 2013). From my ethnographic interviews, I
came to learn that some of these women came for an arranged marriage and worked in farm
village areas, some of them worked as entertainers in urban cities, and, more recently, some of
them worked as nurses, caregivers and English language teachers and tutors. The immigration
policy of Japan grants citizenship by parentage: children who are born into a family of a
Japanese father or a Japanese mother are granted citizenship. However, a child like May or a
child who was born in Japan from parents who are not Japanese citizens, cannot be granted
permanent residency or citizenship in Japan. This political context placed many children in
RETHINKING BODIES 13
stressful and uncertain circumstances. May, for instance, could not picture where she would be
living in the next year.
High drop-out rates from schools among children of migrant workers in Japan have
started to be documented in recent years, in municipal and national government-issued reports.
In one report (Shinjyuku-ku, 2012), the reasons why these children stopped going to school were
listed as “I don’t understand Japanese,” “I don’t understand the concepts discussed in class,” or
“I can’t make friends.” In the case of May, despite her uncertainty towards her future, she was
viewed as putting much of her efforts to succeed towards her local community. Outside the
school, she consistently attended the community after-school learning support program. There,
she spent at least two hours in the evening, twice a week. She was resourceful — when she
needed support for her studies, she had several friends and adult tutors to reach out to. She was
also active in her school band wherein she played the role of band leader.
Mathematics knowledge May’s body embodied.
One day, when I was at the community after-school program, I noticed that May was
doing something with her fingers, under her desk, to solve a mathematics problem. I was curious
but did not want to disturb her. I then heard from other tutors in the after-school program, some
of whom were retired school teachers, that they were concerned about the use of fingers
observed among students including May. They claimed that the use of fingers was often a sign of
“immaturity” in knowing mathematics and that students should not be allowed to use fingers at
school. After this conversation, I became more curious about what May was doing with her
fingers and so I asked her about it.
It turned out that May was using her fingers as a tool for multiplication. Her explanation
revealed an algorithm for multiplication using fingers, employed for the multiplication of
RETHINKING BODIES 14
numbers between six and nine (the algorithm can be slightly modified and extended to the
multiplication of numbers between 11 and 15). For example, May used this algorithm when
calculating 8×7. Each hand represented one factor. Five was represented by the closed hand, and
any number above five was represented by the number of open fingers. In the case of 8×7, one
hand showed three open fingers (and two closed fingers) and another hand showed two fingers
(and three closed fingers). May added the number of open fingers and multiplied this number by
ten [Product A; e.g., (3+2)×10 for the calculation of 8×7]. Then, she counted the number of
closed fingers in each hand and multiplied these two numbers (Product B; e.g., 2×3 for the
calculation of 8×7). Adding the Product A and Product B (e.g., 50 + 6) provided the
multiplication product (which in this example, was 56).
Historically, this finger multiplication method was invented and employed in Florence,
Italy, to deduct the multiplication table up to 10×10 to the multiplication table of 5×5, from a
statement of the algebraic identity (5+a)(5+b)=(5-a)(5-b)+10(a+b) (Ball 1888). By using the
distributive property of multiplication, the algorithm can be also understood as: (χ-5)×10+(y-
5)×10+(10-χ)×(10-y)=xy (where x and y are respective factors of multiplication).
Figure 1. May’s finger multiplication method (showing 8×9).
1. Product A: ((3+4)×10)
2. Product B: 2×1
3. Product A + Product B is
equal to the product of 8×9
RETHINKING BODIES 15
May explained that she learned this finger multiplication method from her parents. When
I interviewed her parents, May’s mother explained to me that she would not encourage her
children to use this method at school because using fingers would be considered illegitimate at
school. Instead, May’s mother told her children to memorize the multiplication table with the
mainstream method taught in Japanese schools. May, herself, also reported that she would not
use the finger multiplication method during mathematics quizzes or openly at school, because
she thought that only computation strategies taught by the teacher were legitimate. In fact, when
I first observed May’s use of fingers for computation, she was hiding it under her desk. In this
process, May’s body was abjected (Butler, 1993).
In the school context, multiplication operation skills were treated as one of the significant
milestones in the early years mathematics curriculum that impacted students’ relationships with
mathematics at school (such as a “slow mathematics learner”) (Takeuchi, 2018). For a student
like May who moved from another country and did not engage in a single “mainstream”
technique, narrowly defining what is legitimate at school can constrain her capability. This is
evidenced by May’s narrative when she explained how she would hide her informal finger
multiplication method during quizzes at school. May’s story tells us how the informal
mathematics knowledge she embodied came to be unintelligible and subjugated through the
formal school curriculum and pedagogy that she experienced.
Story of Karim
Now let us introduce Karim. Karim was a student I (Takeuchi) met during my
ethnographic study in an urban city of Canada. Karim was originally from Afghanistan. Before
coming to Canada, he lived in refugee camps in Pakistan, with his family. He spoke Farsi at
home to communicate with his parents and spoke English to communicate with his older brother
RETHINKING BODIES 16
and sister. Karim was receiving ESL support and attended ESL classes during language arts and
The Programme for International Student Assessment (PISA) by the Organization for
Economic Co-operation and Development (OECD) examined the academic achievement gap
between immigrant students and non-immigrant peers in mathematics, language arts, and
science. A recent report revealed that immigrant students’ performance in mathematics was
lower than their native peers in many countries (OECD, 2013), although the gap between
immigrant students and native students was smaller in Canada, Australia, New Zealand and
Macao-China. In Canada, second-generation immigrant students outperformed their native peers.
However, a local assessment provides a different picture. For example, a provincial assessment
of Ontario, the province with the largest immigrant population in Canada, indicated academic
streaming in mathematics (Education Quality and Accountability Office, 2013). The majority of
ELLs who pursued the university preparatory mathematics courses (i.e., “academic
mathematics”) met the provincial standard for mathematics. Yet, among ELLs who stayed in the
mathematics courses that emphasized practical application (i.e., “applied mathematics”), only
35% of them met the grade-level expectation. Local school boards in Canada, such as the
Toronto District School Board (TDSB) conducted a study to grasp the picture of schooling and
academic achievement gaps focusing on students from lower socioeconomic status and certain
backgrounds. For example, the scores obtained by the students from Afghanistan indicated their
challenges in reading, writing, and mathematics in school contexts (Brown, Newton, & Tam,
2015). Also in the report, the tendency for students from Afghanistan to pursue “applied
mathematics,” compared to “academic mathematics” was noted. In the case of Karim, Ms.
Wilson and the ESL teacher both mentioned his limited and discontinuous prior schooling and
RETHINKING BODIES 17
lack of progress he was making. The report focusing on the students from Afghanistan in
Canadian school contexts indicates systemic and socioeconomic challenges experienced by
During my school visits, in some days, Karim looked quite engaged; he was seated front
and centre and passionately raised his hands when the teacher posed a question to the whole
class. On other days, he looked less energetic and disengaged. He was sometimes located to sit
alone at the back of the classroom, staring down at his desk or looking out the window (Figure
2). During group work, he was occasionally on the receiving end of authoritative interactions —
his ideas were often denied without valid mathematical justification or he was excluded from the
conversation in the formal space of school (Takeuchi, 2016). The teacher was constantly looking
for ways to engage Karim by changing around the location he is positioned in the classroom. For
example, if the teacher observed Karim being excluded from the group, she separated him from
the group and provided him with individual support.
Figure 2. Karim’s position in the classroom
Note. Karim (farthest left) is working alone, facing the window.
RETHINKING BODIES 18
The Mathematics knowledge surfaced through Karim’s gesture.
As mentioned above, in the interactions with teacher-assigned peers, Karim’s ideas were
often denied without valid mathematical justification or he was excluded from the conversation.
He was sometimes physically positioned at the corner of the classroom by himself as seen in
Figure 2. This used to be Karim’s positional identity observed occasionally in mathematics
classrooms. During my participation in Karim’s mathematics class over an academic year, there
was a moment in which I noticed a change in the way he participated as well as a shift in his
“positional identity” — which refers to “the day-to-day and on-the-ground relations of power,
deference and entitlement, social affiliation and distance with the social-interactional, social-
relational structures of the lived world” (Holland, Skinner, Lachicotte Jr, & Cain, 1998, p. 127).
This happened in mid-April. The following episode depicts how such shift came to light. In this
episode, Karim’s positional identity shifted in a subtle but significant manner.
In this introductory lesson to fractions, the teacher drew multiple shapes divided into
equal pieces, where some pieces were coloured in. Students were asked to name a fraction that
corresponded to the coloured pieces relative to the whole. After a series of similar interactions,
the teacher drew a rectangle divided equally into four pieces, with three pieces colored. The
teacher expected the answer to be 3
During this exchange, the teacher was sitting in a rocking chair and was drawing shapes
on a flip chart. Students were sitting on the floor as a group and their bodies were therefore not
bounded to desks (Figure 3). Karim was sitting just in front of the teacher and was able to make
his body visible to others. This position or positional identity was in stark contrast to a more
marginalized position that he occupied in the classroom (Figure 2). When the teacher asked the
RETHINKING BODIES 19
students to name a fraction showing the rectangle, Karim said “two out of eight.” He then
immediately corrected himself and said, “six out of eight.” The teacher, surprisingly repeated
what Karim said, “six out of eight?” And she encouraged Karim to show where he saw six
eighths. Karim pointed at how he saw a way to divide a rectangle into two equal parts; this
gesture pointed out the equivalence between 3
4 and 6
8 (Figure 4). The teacher acknowledged and
took up Karim’s contribution while saying “you’re very clever,” and took it up as the lesson of
equivalent fractions by adjusting the original lesson plan. The teacher went beyond the
curriculum expectation for the particular grade (the local curriculum did not require a lesson on
equivalent fractions for Grade 4) and opened up the space for meaningful discussions.
Figure 3. Classroom configuration during introductory fraction lesson.
RETHINKING BODIES 20
Figure 4. Karim gesturing the invisible line (indicated with dots) and showing how he
sees the equivalence between 3
4 and 6
Note. The invisible line is halving the rectangle.
In this interaction, Karim’s bodily interactions with the object (that was expected to be
interpreted in a normative way) queered the object. Going back to Ahmed’s (2006) account on
queering, this moment illustrates “how the strangeness that seems to reside somewhere between
the body and its objects is also what brings these objects to life and makes them dance” (p. 163).
What was overlooked in the rectangle representation of fractions got noticed and started to
mobilize with a simple yet meaningful gesture of drawing a line halving the rectangle. In fact,
Karim’s answer was not what the teacher expected — but nonetheless the teacher praised
Karim’s idea as a vital contribution. Karim did not yet have the words to describe what he
discovered, that is “equivalent fraction.” However, he was able to “show” the concept by
gesturing. Instead of discounting what Karim showed, by affirming his contribution, the teacher
provided a new language, a new concept, and new positioning in this interaction.
At the beginning of this interaction, when Karim said “six out of eight,” some of his peers
whispered, “it’s four” and tried to dismiss his contribution. However, when Karim showed how
RETHINKING BODIES 21
the equivalence between 3
4 and 6
8 simply drawing the invisible line to divide the rectangle, his
peers said, “ohhhh”, sounding surprised. The teacher took up Karim’s gesture of the “invisible
line” and let the class compare two rectangles showing equivalent fractions. By taking up
Karim’s contribution, the teacher not only moved beyond narrow mainstream mathematical
expectations, but also leveraged Karim’s positional identity into someone who can contribute to
mathematical discussion. Karim tweaked the original rectangle model to a model that can
possibly highlight other concepts related to fraction such as the division or multiplication of
fractions. In other words, Karim’s gesture brought forth otherwise unnoticed affordance of the
rectangle model. In North America, a frequently-used representation of fractions used in the
school context and textbooks is a circle model, which is often associated with pizza; however,
the circle model does not afford reasonable representation of numerical operations, especially
division or multiplication, with fractions (Watson & Mason, 2005). Just before this episode, the
teacher also used the circle model of fractions. In his subtle gesture, Karim showed a way to
advance the discussion mathematically with the alternative representation through this tweaks
(e.g., equivalence of fractions visually, and potentially other more advanced numerical
operations with fractions). In this sense, Karim’s gesture could be read as the disruption of the
dominant representation of fractions. The teacher acknowledged the central position that Karim
took in this interaction by making his body more visible to others and thus opened up his
Rather than treating learners as human capital or disembodied entities, from the
perspective of human capabilities, we shed light on learner bodies. Drawing from the integral
theoretical perspective of sociocultural theory with queer theory and critical race theory, we
RETHINKING BODIES 22
conceptualized learner bodies as cultural and historical—and also the locus of negotiation of
norms and power. By rethinking May and Karim’s learner bodies in this light, we are able to
better appreciate their vulnerable yet valuable mathematical contributions. Both May and Karim
used their bodies in non-normative ways to engage with mathematics. May’s finger
multiplication represents embodied actions that contradict normative standards for engaging in
mathematics, yet it could serve as tools that enable these learners to participate in mathematics
discourse. By challenging the norms associated with the stabilized marginality he occupied in the
classroom and mobilizing his body, Karim tweaked the given representation of fractions and
brought forth its otherwise unnoticed mathematical affordance, through his use of gesture. Their
stories highlight the need to reconceptualize learner bodies within the context of STEM
education so that we honour the contributions and practices of all students, especially those
historically left to the margins. These stories call for designing learning environments that value
the whole learner and prompt to rethink STEM education as a tool for capitalist enterprise and
reimagine it as a place for building human capability.
Both stories also prompt us to examine the design of equitable learning environments in
STEM education. Design of the environment is powerful — in a sense that can either challenge,
perpetuate or create inequity in education settings. Panopticon, a prison architecture, designed by
Jeremy Bentham that Foucault (1980) depicts, is a vivid example of the power of design. With
carefully designed use of light and locations of prison cells and a guard, this design produced
self-policing, self-monitoring, and self-control, just with (imagined) gaze. Similarly, the ways in
which school curriculum, school architecture, classroom settings, and locations of a teacher and
students all influence strongly the ways in which power produces its effects at the level of
knowledge but also at the level of desire.
RETHINKING BODIES 23
In the case of Karim, the material re-organization of the classroom allowed him to engage
his body in the communication of mathematics, allowing the class to see his mathematics
competence. The teacher rearranged the classroom space so that students were not bounded by
desks and with this rearrangement, Karim was able to better mobilize his body and through
which, normative mathematical representation was queered. In the case of May, the
mathematical reasoning she embodied was unrecognized or even disciplined in the classroom
space and by the rigid curriculum — with consequences for possible marginalization of her
reasoning, her body, and possibly herself. May carefully monitored the ways she used her body
to engage with mathematics. That is, she hid her finger multiplication method to fit into the
mainstream mathematical practice of performing number operations. She tactically used the
method, monitoring legitimate and illegitimate bodily acts in the classroom.
In school contexts, there is still a deeply-rooted assumption that mathematical thinking
has to be “a pure mental activity — something immaterial, independent of the body, occurring in
the head” (Radford, 2009, p.111). STEM education tends to be treated as politically neutral
though it is inherently political and ethical, and discourse in STEM education can value certain
bodies more than others (as demonstrated in Philip, Gupta, Elby, & Turpen, 2018). The
assumptions about political neutrality and disembodied nature of learning can marginalize
certain bodies of learners and hence their associated sense of identity with STEM disciplines. By
incorporating queer theory and critical race theory, in this chapter, our attempt was to advance
the conceptualization of learner bodies as the locus of negotiation of power, desires and
emotions. Such a reconceptualization of learner bodies can lead us to reframe what is considered
as mathematics in STEM education, which is often perceived as “existing independently of the
people who do it, and independent of their bodies, senses, desires, emotions, and aesthetics —
RETHINKING BODIES 24
everything that makes a person flesh and blood” (Greer, Mukhopadhyay, & Roth, 2013, p.6).
Rethinking learner bodies and challenging the traditional framework of teaching and learning is
essential for STEM education; without which, the ways in which mathematics has been taught
and conceptualized as a discipline in school will not be mobilized or renewed.
In discussing the materialization of bodies, Butler (1993) described the paradox of the
subjectivation of bodies, where the formation of the subject is enabled or produced by the very
norm that the subject is resisting. In this sense, agency is perceived as “reiterative or
rearticulatory practice, immanent to power, and not a relation of external opposition to power”
(p.xxiii). Agency conceptualized by queer theory is located with the chain of historicity; it is a
power to “avow a set of constraints on the past and the future that mark at once the limits of
agency and its most enabling conditions” (p.174). This view of agency is insightful when we
think of our agency to reimagine STEM education. Shanahan, Burke, and Francis (2016)
maintained that “STEM education” can be best conceptualized as a boundary object. By
liberating disciplined bodies, we could exercise our agency to include abjected bodies in
traditional school mathematics and rearticulate STEM education. Such efforts have just begun.
For example, Sengupta and Shanahan (2017) assembled otherwise-dispersed bodies through the
learning environment of public computation. They demonstrated the possibility of extending the
boundary of STEM education to public experience. By rearticulating the disciplinary boundaries
afforded by STEM education, we can envisage mathematics learning which is more integral to
learners’ bodies, and which allows learners “to lead lives they have reason to value and to
enhance the substantive choices they have” (Sen, 1997, p.1959).”
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