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Power and identity in immigrant parents’ involvement in early years mathematics learning

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This study examined immigrant parents’ involvement in early years mathematics learning, focusing on learning of multiplication in in- and out-of-school settings. Ethnographic interviews and workshops were conducted in an urban city in Japan, to examine out-of-school practices of immigrant families. Drawing from sociocultural theory of learning and the concept of appropriation (Wertsch, 1998), the role of power and identity was examined in relation to children’s appropriation of an informal multiplication method that was taught by their parents. An intergenerational analysis, between immigrant parents and their children, revealed heterogeneous perspectives towards appropriation. Immigrant parents in this study framed their involvement in their children’s early years mathematics learning in relation to their positional identities and the pressures to conform to the mainstream practices of their host country. During their early years of schooling, students in this study were already aware of academic tracking in the school and were aware of what was believed to be legitimate in school mathematics learning. The significance of diversifying mathematics curriculum and pedagogy was discussed to affirm the knowledge and identities of immigrant students and families.
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Power and identity in immigrant parentsinvolvement
in early years mathematics learning
Miwa Aoki Takeuchi
1
#Springer Science+Business Media B.V. 2017
Abstract This study examined immigrant parentsinvolvement in early years mathematics
learning, focusing on learning of multiplication in in- and out-of-school settings. Ethnographic
interviews and workshops were conducted in an urban city in Japan, to examine out-of-school
practices of immigrant families. Drawing from sociocultural theory of learning and the concept
of appropriation (Wertsch, 1998), the role of power and identity was examined in relation to
childrens appropriation of an informal multiplication method that was taught by their parents.
An intergenerational analysis, between immigrant parents and their children, revealed hetero-
geneous perspectives towards appropriation. Immigrant parents in this study framed their
involvement in their childrens early years mathematics learning in relation to their positional
identities and the pressures to conform to the mainstream practices of their host country.
During their early years of schooling, students in this study were already aware of academic
tracking in the school and were aware of what was believed to be legitimate in school
mathematics learning. The significance of diversifying mathematics curriculum and pedagogy
was discussed to affirm the knowledge and identities of immigrant students and families.
Keywords Mathematics learning in and out of school .Parental involvement .Identity.Power
1 Mathematics learning in out-of-school contexts
Global population mobility has contributed to a growth in the number of immigrant students in
schools internationally. For example, in the United States, 21% of households reported using
languages other than English (United States Census Bureau, 2013). In Canada, 20% of the
population reported speaking a language other than official languages at home (Statistics
Canada, 2012). Certain areas of England are becoming more linguistically diverse: London
had the highest proportion (22.1%) with people speaking languages other than English as their
Educ Stud Math
DOI 10.1007/s10649-017-9781-4
*Miwa Aoki Takeuchi
miwa.takeuchi@ucalgary.ca
1
Werklund School of Education, University of Calgary, EDT 840, 2500 University Drive NW,
Calgary, AB T2N1N4, Canada
This is a pre-print of: Takeuchi, M. A. (2018). Power and identity in immigrant parents’
involvement in early years mathematics learning. Educational Studies in Mathematics, 97 (1),
39-53. doi: 10.1007/s10649-017-9781-4
main language (Office for National Statistics, 2013). In Japan, where the study introduced here
was conducted, some industrial areas are becoming ethnically and linguistically diverse, as
represented in the percentages of registered immigrants 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
immigrants.
The Organization for Economic Co-operation and Development (2013) reported that
immigrant studentsperformance in mathematics was lower than their native peers in many
countries, although the gap between immigrant students and native students was smaller in
Canada, Australia, New Zealand, and Macao-China. This report also revealed that the second
generation of immigrant students performed lower than the first generation in certain countries
such as the United Kingdom and New Zealand. In order to make mathematics learning
accessible to all students, there is a need for research examining curriculum and pedagogy
that are responsive to immigrant studentsprior knowledge and backgrounds. Taken in this
context, the purpose of this research is to highlight mathematical resources that immigrant
students access at home and understand how power and identity influence appropriation and
the use of those resources at school.
Investigating the connection (and disconnection) between childrens out-of-school practices
and their school learning is especially significant for immigrant students, whose practices can
be different from the norm assumed in school learning and hence whose competence can be
invisible in school contexts (Baker, Street, & Tomlin, 2003; Civil & Planas, 2010;deAbreu&
Cline, 2005). As previously identified, immigrant studentsmathematical performance can be
shaped by valued practices at home (Guberman, 2004).
Previous studies examining non-dominant studentspractices in and out of school contexts
have challenged a deficit perspective towards non-dominant students and have collectively
highlighted non-dominant peoples and communitiescompetence in collective practices that
involve mathematical tools (Baker et al., 2003; Brenner, 1998; Civil, 2007; Gonzalez,
Andrade, Civil, & Moll, 2001;Nasir&Hand,2008;Saxe,2012; Saxe & Esmonde, 2005;
Taylor, 2009). These studies foreground mathematical competence and Bfunds of knowledge^
(Moll, Amanti, Neff, & Gonzalez, 1992, p.133), which have traditionally been neglected in
school contexts. Seminal works in this area have provided ethnographic accounts of the
practices in which children from non-Western countries engage. Ethnomathematics studies
have challenged an ethnocentric perspective on the development of mathematics and offered
emic accounts of mathematics linked to local historical and cultural practices (Ascher, 1994;
DAmbrosio, 2006).
Studies in this area have taken into consideration historical contexts and systemic changes
affecting mathematics practices outside the school. For example, historical and longitudinal
accounts of the Oksapmin peoples 27-body-part counting system illuminate how the counting
system has been reproduced and altered along with the shift in political, economic, and educational
macro systems in Papua New Guinea (Saxe, 2012;Saxe&Esmonde,2005). Taylors(2009)
analysis of low-income African American childrens purchasing practices in the United States
demonstrated the direct influences of macro system(such as concentrations of poverty and taxation
policies) on the practices in which these children engage. Nasir and Hand (2008)compared
studentspractices in mathematics classrooms and basketball games, and highlighted practice-
linked identity as one of the significant layers of practice that supported studentsengagement.
The current study further develops this vein of research by examining whether and how
Takeuchi M.A.
immigrant studentsin- and out-of-school mathematics learning experiences can be integrated
by focusing on the role of power and identities.
This research also furthers the current body of literature on immigrant parentsparticipation
in mathematics practices. Previous studies on this topic have highlighted immigrant parents
mathematics knowledge and resources that were embedded in their cultural practices (Civil,
2007; Willey, 2008). This line of research has also pointed out some of the conflict and
struggles that immigrant parents experience (de Abreu & Cline, 2005; Civil & Bernier, 2006;
Crafter, 2012; Gorgorió & Abreu, 2009). This study adds a new cultural and historical context
that can reveal how power and mathematics learning are intertwined locally. By providing an
intergenerational perspective on both immigrant parents and their children, I shed light on how
parents and children differently appropriated an informal mathematics method. In response to
the call by Gutiérrez (2013) for a sociopolitical turn in mathematics education, the current
study examines the role of power through the analysis of cultural and historical practices
surrounding the appropriation of informal mathematics knowledge. With regards to power, de
Abreu and Cline (2007) revealed the process of social valorization wherein different kinds of
mathematics (e.g., Brazilian peasant mathematics and school mathematics) are valorized or
devalorized with reference to social classification. Set in the context of an urban city in Japan
that is gradually becoming linguistically and ethnically diverse, this study examines how
power and positional identities influenced early years mathematics learning for Filipina
immigrant mothers and their children living in Japan.
2 Theoretical framework: Power and positional identities in appropriation
of cultural tools
In this study, I highlight immigrant studentsappropriation of out-of-school resources and
practices for mathematics learning. By appropriation, I refer to the categorization made by
Wertsch (1998), as explained below. One of the central tenets of sociocultural theory is that
human learning is mediated by technical and psychological tools including languages and
culturally specific ways of approaching mathematics (Vygotsky, 1978). These tools are
cultural; they are created, shared, and used in collective practices. Vygotsky maintained that
the use of these cultural tools is first developed as an interpsychological process between
people and later internalized into an intrapsychological process within a person.
This idea of internalization was later elaborated by Wertsch with careful attention to the
tension between cultural tools and learners as active agents. Wertsch distinguished between
mastery, appropriation, and resistance of cultural tools. Mastery is described as knowing how to
use cultural tools, whereas appropriation is defined as Bmaking a cultural tool onesown^(p.
145). Resistance relates to power and is considered to occur when agents distance themselves
from particular cultural tools or when they perform actions with cultural tools under a forced
circumstance. For example, in Wertschs study, Estonians mastered the official and dominant
account of Estonias history of joining the Soviet Union learned in school and exhibited their
understandings in forced situations, such as exams. However, they resisted appropriation of the
official historical account and viewed it as someone elses history. Highlighted in Wertschs
study is how identity and power are strongly tied with appropriation of cultural tools. Polman
(2006) further elaborated on the aspect of identity development in the process of appropriation
and maintained that agents take up certain cultural tools while simultaneously creating
possibilities for kinds of person one can be in the future.
Power and identity in immigrant parentsinvolvement in early years...
While there has been a growing collection of literature laying out the relations between
identity and learning, I draw on the definition of positional identities by Holland, Skinner,
Lachicotte, and Cain (1998), which considers the role of power and hierarchy in the process of
shaping and developing identity. Positional identities are defined as Bthe 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 et al., 1998,p.
127). Positional identities are shaped through ones access to spaces, activities, speech genres,
and voices, which are all embedded in the power relations that are also produced and
reproduced in moment-by-moment interactions. Holland et al. contrast the positional identities
with figurative identities which Bhave to do with the stories, acts, and characters that make the
world a cultural world^(p.127). While figurative identities are Babout signs that evoke
storylines or plots among generic characters^(p.128), positional identities are Babout
acts that constitute relations of hierarchy, distance, or perhaps affiliation^(p.129).
These two types of identities can be intertwined but this paper will focus more on
positional identities. Analyzing both parent and student data will provide insights into
how a particular cultural practice and resource were, or were not, appropriated and
maintained across generations among transnational families and how power and
identity influenced this process.
3 Methods
This project was conducted in an urban city of Japan that is increasingly becoming linguis-
tically and ethnically diverse. In this study, my analysis draws from three types of data: (1)
semi-structured individual interviews with 12 Filipina women who were living and raising
children in Japan, (2) semi-structured individual interviews with nine elementary school-aged
children of the women whom I interviewed, and (3) post-interview workshops with the women
and their children who participated in the interview. Because the focus of the analysis was on
elementary school curriculum, I excluded child interviews with older grade students. However,
I included all 12 interviews with parents as they reflected their interactions with their children
when the children were still young. Interview questions for parents included participants
stories of coming to and living in Japan, participantspractices related to mathematics and
language teaching at home, and participantsexperiences with schools in the Philippines and in
Japan. Interview questions for children included their experiences of school learning, parent-
child communications at home, and out-of-school mathematics learning. Mathematical prob-
lem solving (computation problems and word problems) was also part of parent and child
interviews. Interview questions were shaped through my ethnographic observations in the
participantscommunities and schools. Each parent interview lasted approximately 90 min and
each child interview lasted approximately 45 min. All the interviews were audio-recorded and
workshops were video-recorded.
All the parent participants were multilingual. Ten participants answered Tagalog as their
first language and two of them answered Bikol as their first language. All the participants
answered they were comfortable in English as their second language because they received
education for subjects such as mathematics and sciences in English. Except for two partici-
pants, they all answered that they felt comfortable communicating orally in Japanese but were
not comfortable with reading and writing. The majority of the participants felt more comfort-
able speaking in English and chose to conduct the interviews in English. Interviews and
Takeuchi M.A.
workshops were mainly conducted in English. If Japanese was used, I translated all quotes into
English. Another person who was fluent in Japanese and English confirmed the translations.
The majority of child participants (seven children) were born in Japan. Two children were
born in the Philippines. All the child participants were enrolled in Japanese public schools, at
the time of this study. For six of the child participants, with one Japanese parent and one
Filipino parent, the main home language was Japanese. For the other three participants, the
main home language was Tagalog. All the interviews with child participants were conducted in
Japanese. After conducting individual interviews, workshops were organized based on the
themes that emerged from those interviews. For the purpose of this paper, I focused on part of
the workshop data and I included two of the workshop sessions and 152 min of video recorded
data. In the Findings section, Iprovide narratives that capture the details of the workshop
interactions.
The analysis focused on two central themes discussed earlier: (a) appropriation of cultural
tools (Wertsch, 1998), and (b) positional identities (Holland et al., 1998). Of all the out-of-
school practices identified through ethnographic interviews and workshops, this article focuses
on the informal finger multiplication method as one example of what these children learn at
home. This finger multiplication method will be explained in further detail in the following
section. Analysis was centered around two main research questions. The first question focused
on whether and how participants appropriated a finger multiplication method. The second
question focused on how participantsidentities were embedded in relations of power,
deference, and social affiliation/exclusion in relation to mathematics learning. Cross-case
analysis and coding were conducted by using the qualitative analysis software MAXQDA
(Verbi GmbH, Berlin, Germany). I analyzed both the commonalities and differences among
participants.
4 Findings: Power and hierarchy affecting in- and out-of-school
mathematics learning
In this section, Ipresent findings obtained from both the interviews and workshops. First, I
introduce the mainstream/formal and informal multiplication strategies that child participants
encountered in in- and out-of-school contexts. Then, I connect participantspositional identi-
ties that affected appropriation of informal multiplication method. Subsequently, I describe
whether and how child participants appropriated the informal method, drawing from the
interviews and the workshops.
4.1 Informal and formal multiplication strategies: Finger multiplication method
and Kuku
Participants used both the informal and formal multiplication methodsfinger multiplication
method and kukuin the process of solving mathematical problems in the interview. The
following informal method was observed when participants were solving a single-digit
multiplication of numbers between six and nine (e.g., 9×9). Using two hands (each hand
represents one factor), five is represented by the closed hand and any number above five is
represented by the number of open fingers (e.g., nine is four fingers open; Fig. 1is a
participants representation of 9×9). Participants add the number of open fingers in each hand
and multiply this number by ten (product A; e.g., in the case of 9×9, participants calculated
Power and identity in immigrant parentsinvolvement in early years...
(4 + 4)× 10). Then, the participants multiply the number of closed fingers in each hand
(product B; e.g., in the case of 9×9, participants calculated 1×1). The final multiplication
product is calculated by adding the above products A and B.
This finger multiplication method can be also extended to the multiplication of numbers
between 11 and 15. The closed hand represents ten and the open fingers represent the number
above ten. First, add the number of open fingers in each hand and multiply this number by 10
(Product A; in the case of 14 x 14, participants calculated (4 + 4) x 10). Second,
multiply the numbers of open fingers in each hand (Product B; in the case of 14 x
14, participants calculated 4 x 4). The final product is calculated by adding 100,
Product A and Product B (see Fig. 2).
Parent participants explained that the finger multiplication method was learned outside of
school and used mainly to deal with the pressure in the school to complete computation
quickly. For instance, Irene
1
said, BWhen we were at school and then we were doing some
tests...that needs to be quick.^Parent participants acquired this method from various sources:
family members, friends, and at school. Child participants acquired this method exclusively
from their parents. Neither parent nor child participants could identify the origin of this finger
multiplication. Three parent participants stated that the method had spread throughout their
communities in the Philippines. There is a record indicating that this finger multiplication was
commonly used in Florence, Italy (Ball, 1888). This finger multiplication is also known as
BRussian or French peasant algorithm^(Davis & Preciado Babb, 2015;Gray,2001). However,
it has not been recorded in English how the method came to spread in some communities in the
Philippines.
In contrast to the informal finger multiplication method, there is a formal method to
memorize a multiplication table, which is taught in the Japanese school system. In Grade 2,
the Japanese mathematics curriculum (the official course of study) covers multiplication of
single digit numbers and requires students to recite the entire multiplication table between one
and nine. Students use a culturally specific recitation method called kuku, which is a language-
driven rhythmic chant (Ministry of Education, Culture, Sports, Science and Technology,
2008). Similar rhythmic chants for multiplication are commonly observed in Asian countries.
The Japanese version of kuku is considered to have originated in China, and there is a historical
archive recording the use of kuku in the tenth century in Japan. Children learn this kuku either
Fig 1 A parent participants finger multiplication method (9×9)
1
All the participantsnames are pseudonyms. These names were chosen from the same language as the
participantsreal names.
Takeuchi M.A.
at school or at home from their family members. In the case of immigrant students in this
study, their encounter to kuku tended to be only at school.
4.2 Parentspositional identities and home practices
I will first describe the positional identities of Filipina mothers in this study by focusing on the
reasons why they came to Japan and their language policies at home. As introduced below,
these positional identities influenced these parentsdecisions on how they displayed their ways
of engaging in mathematics, including finger multiplication. These positional identities also
influenced how their children would be involved in various home practices (such as engaging
in international currency conversions and calculating international time differences). Women
in this study came to work in Japan and the majority (10 of 12 participants) stayed in Japan
after marrying Japanese men. Filipino is one of the major and the fastest growing ethnic groups
in Japan. Since the late 1970s, Filipina women have been coming to Japan to fill the bride
shortage in farm village areas, to work as entertainers in urban cities, and, more recently, to
work as nurses, caregivers and English language teachers and tutors. All of the
Filipina mothers I interviewed said that they were from a big family of lower
socioeconomic status and that financially supporting their family was their main
motivation for coming to Japan.
Home language policies were indicative of Filipina womens positional identities at home.
In the households where a Filipina woman was married to a Japanese husband, participants
interviews revealed that the husband or husbands parents tended to decide the family language
practices, which were often the exclusive use of Japanese (Takeuchi, 2016). This situation was
often because their husbands or husbandsparents did not comprehend Filipino (Tagalog), the
official language of the Philippines, or other languages in the Philippines. However, some
participants reported that, even in the households where the husband understood Tagalog, the
exclusive use of Japanese was still common practice. This home language policy influenced
Filipina parentsparticipation in childrens school learning. For example, Mariel described her
involvement in her daughtersschoollearningasBI help her only in English.^
As revealed through the following interview quotes, parent participantsinvolvement in
their childrens mathematics learning was shaped through these positional identities. Parental
involvement in childrens school learning was reported as limited partially because Filipina
women in this study felt they did not know the curriculum and pedagogy in Japanese schools.
Fig. 2 Finger multiplication method for two-digit numbers (14×14)
Power and identity in immigrant parentsinvolvement in early years...
For example, in response to my question (BDid you teach mathematics that you learned?^),
Mariel said, BNo (...) Its different ways I think.^For the same interview question, Karen said:
Maybe since its all in Japanese, we dont know, really, exactly what kinds, how you
solve the mathematics. We dont understand your ways. One time, I taught my child and
he got confused. I thought, maybe it was a different way. So, its hard to teach children,
if they feel confusions. I think Japanese system, you have your own system.
In this narrative, Karens use of pronouns serves as a marker (Fairclough, 1989) to indicate
a boundary between the Japanese ways (e.g., your ways, your own system) and her ways,
through which she distanced herself from the Japanese system. This distancing from the
mainstream was also observed in the following interview excerpt from Irene. She is describing
her decision on teaching children mathematics.
Its up to them. I used to compare. I cant always tell them or demand all the things I
learned. Because life here in Japan is quite different from where I grew up. So I used to
compare but if they are okay, then its okay. They dont need to learn whatever Ive
learned.
As these interview quotes represent, many parents described the distance they felt towards
the Japanese school system. In addition, as I discussed elsewhere (Takeuchi, 2015), for some
parent participants, their positioning as a Bforeigner^or Boutsider^in Japanese society hindered
them from playing an active role in their childs school learning (as represented in one of the
participantsinterview quote, BIm Filipina and I cant offer anything as a parent because Ima
foreigner^). Sometimes, children commented that their parentsways of doing mathematics
were wrong just because it was different from the way they learned at school. For example,
Arlene and Karen both reported a difference in how a reminder is notated when computing
multi-digit division. Karen said she fought with her son over ways of computing multi-digit
division and was told by him, BMom, yours is not a right way.^Arlene also said she was told by
her children, BMom, youre wrong.^These episodes suggest that the difference between the
Japanese school way and parentsway of computation was perceived in a hierarchical manner:
The parentsways were wrong and the Japanese school ways were correct.
Similarly, taking an example of teaching the informal, finger multiplication method,
parentspositional identities also shaped the contexts of their decisions. Parent participants
in this study either chose not to teach the finger multiplication method or taught it only to the
children who were struggling in school mathematics. All the parent participants positioned the
finger multiplication method or the use of fingers as secondary to kuku, the formal memori-
zation method for multiplication tables. For example, Nicole explained that she decided to
teach the finger multiplication method at home as a Bsecret.^Karen also described that this
method was Bonly for an emergency purpose^for her children, because using fingers would be
considered to be illegitimate in Japanese schools. But because her son was falling behind
academically, Karens husband taught the finger multiplication method. While teaching this
finger multiplication method to her children, Karen said she and her husband also encouraged
their children to memorize the multiplication tables with kuku,astaughtinJapaneseschools.
Karen said, BYou should only use your mind to compute. Or you can use scratch paperbut
never fingers, because its cheating right?^She also commented, BMaybe itsnotaright
technique to use for tests.^
Similarly, Irene taught the method to her child who was struggling with computation and
memorization but not to her child who was doing well in mathematics. Regarding this point,
Takeuchi M.A.
Irene, Ryans mother, said, BIm telling Ryan this because his memory is a little bitslow. So,
I told him, You can use this one,and he said, Mommy, I think this is harderI cant. I have
to remember.^As seen in these examples, teaching or not teaching informal knowledge was
connected to how parents perceived their childrens mathematical competence and became a
locus of social valorization (de Abreu & Cline, 2007). In the following section, Idescribe how
child participants appropriated or did not appropriate the finger multiplication method.
4.3 Childrens appropriation of the informal multiplication method
The following stories from child participants demonstrate the discontinuity between home and
school learning, experienced especially by immigrant families. I focus on three children whose
parents taught them the finger multiplication method. May, who was in Grade 6 and had come
from the Philippines to Japan when she was in Grade 4, had repeated Grade 3 in Japan because
her Japanese language proficiency was perceived to be limited. Eric was in Grade 4 and had
come from the Philippines to Japan after finishing Grade 1. Ryan was born in Japan. At home,
none of them was exposed to the kuku method, the mainstream method taught at Japanese
schools. Child participantsinterviews revealed whether they had appropriated the finger
multiplication method. May and Eric both used the method for single digit multiplication
between six and nine. They both explained that they learned the finger multiplication method
from their parents. Ryan did not use the finger multiplication method but used the kuku
method. Findings from the child interviews demonstrate how the child participants had to
negotiate between what was considered legitimate at school and what was taught at home. For
the child participants, this negotiation meant hiding or not appropriating what was taught at
home.
The interview with Ryan indicates how computation fluency was used to classify students
academically at school. When I asked if he memorized kuku, he said he repeatedly practiced to
memorize it because he was placed in the slowest group for computation in Grade 2. The
following accounts of May and Erics use of the finger multiplication method at school
revealed how they were already aware of what was and was not considered to be legitimate.
May and Eric both mentioned that they would not use the method openly at school. Eric said
he never showed the method to school teachers. May also reported that she would not use this
method during mathematics quizzes because she thought that only computation strategies
taught by the teacher were legitimate. She provided an example of 7 + 8. Outside of the school,
she said she would usually compute addition by decomposing the number by 5 (such as 5 +
5 + 2 + 3). But in the mathematics quizzes at school, she would follow the teachersmethod,
which did not involve decomposing numbers. This example shows how these immigrant
children came to be keen observers of what was considered legitimate at school and would
strategically hide computation strategies that differed from what their teacher taught them.
The following quote from May provides a further account of how she appropriated the
finger multiplication method and used it to maneuver within a competitive school environ-
ment. When asked in the interview if she wanted to show her finger multiplication method to
the teacher, May said, BNo, I dont want to [show it to the teacher]. Everyone else is very fast
at computation. I shared this only with those who were slow [at computation].^She added,
BStudents who go to juku [afterschool cram schools] are very fast [at computation].^Attending
juku during after-school hours is common among children in Japan and even among upper-
grade elementary school students. At juku, students preview and review school subjects and
also prepare for entrance exams. Fees range between 5000 YEN and 20,000 YEN per month.
Power and identity in immigrant parentsinvolvement in early years...
As such, there can be a social class divide between those who can attend a cram school and
those who cannot. May described how she observed a gap in computation fluency, partially
resulting from inequity in access to additional educational resources. In facing this gap, May
selectively shared the finger multiplication method only with students like herselfthose who
were slower at computation and did not have access to juku. By sharing the method with other
students, May tactically used the finger multiplication method to create a context where she
could use the informal method meaningfully.
4.4 Examining the finger multiplication method through the workshop
Based on the themes that emerged from the interviews, the workshops were organized. In the
workshops, participants and I discussed different computational models for multiplication and
the base-ten (decimal system) underlying the finger multiplication method. For example, an
array model was used to highlight how whole numbers can be decomposed and regrouped (see
Fig. 3). By letting xbe one factor (represented with one hand) and letting ybe another factor
(represented with the other hand), the second way to understand the finger multiplication method
is as (x5) × 10 + (y5) × 10 + (10 x)×(10y)=xy. In addition, this finger multiplication
method can be examined by a statement of the identity: (5 + a)(5 + b) = (5 a)(5 b) + 10(a + b).
In the process of engaging in the workshops, I observed resistance from child participants to
unlearn the school knowledge, as can be seen in the following workshop narratives. Some
child participants were reluctant to learn about this method because they had not learned it at
school, as reflected in comments such as Ryans question, BDo we learn about this at school?^
The following narrative from the workshop reveals how child participants internalized the
legitimacy of school knowledge over informal knowledge.
The facilitator asked Irene to introduce how she would use the finger multiplication
method to compute 6×8. Irene stood up and started to introduce in Tagalog how she used
the method. I, as a facilitator, asked Irenes child, Ryan, to translate her explanation into
Japanese. Irene explained the method in Tagalog and the participants listened to Irenes
Fig. 3 An array model to explain the finger multiplication method (8×6)
Takeuchi M.A.
explanation while looking at her. Ryan looked at me and said, BIcant translate.^Isaid,
BCant you?^and explained the method in Japanese to the child participants. After the
explanation, Ryan asked me, BDo we learn about this at school?^Irene laughed.
Because the children had been told to memorize the multiplication tables in one way (by using
kuku) at school, they were disinclined to learn any other methods and ways of thinking about
multiplication. Despite of the initial resistance, when parents taught the finger multiplication
method for single- and multi-digit multiplication at our workshop, the children who did not know
about or did not appropriate this method were amazed, as illustrated in the following narrative.
I, as a facilitator, used an example of 7×7 and let all child participants try out the finger
multiplication method. While watching the child participants trying out the method,
Irene was nodding. After a while, Ryan all of the sudden shouted BAh! Youre right
This is amazing.^I asked participants to try 8×9. Another child participant, Brian said,
BOh wow.^Ryan looked at Irene and said, BI got it.^Irene clapped her hands for Ryan.
5 Discussion and Implications
The findings presented in this paper offer insights into immigrant studentspractices and resources
for mathematics learning. Framed by sociocultural theory of learning and especially by focusing
on the concept of appropriation, this study showed how appropriation of an informal multiplica-
tion method can be a site for negotiation of power and positional identities. By examining the case
of Filipina mothers and their children living in Japan, the study offers insights into a global issue
regarding mathematics learning that immigrant students experience both inside and outside the
school. As the interview results revealed, immigrant parents framed their involvement in their
childrens learning while contending with the pressures to conform to the mainstream practices of
their host country. Some child participants came to understand what is legitimate at school and
chose a tacit strategy to maneuver competitive school contexts while also appropriating resources
at home. At the same time, the workshop findings highlight that there were other child participants
who were reluctant to learn and think about the informal multiplication method, partially because
memorization without any external tools is encouraged at school and also because they were
aware of what is legitimate and what is not at school. The fact that the curriculum required
students to learn one cultural method and teachers had to enact that curriculum in daily teaching
practices shows how students were molded into the culturally dominant computation method
through schooling. I discuss the findings presented above in relation to power and identity in
mathematics learning. I also discuss some limitations of this study and pedagogical implications.
5.1 Power and identity in mathematics learning
Highlighting the informal finger multiplication method as one of the examples of what
children learn at home, this study illustrates how a seemingly politically neutral multiplication
learning can be a space to negotiate identity and power for immigrant families. The findings
from this study contribute to advancing the sociopolitical turn in mathematics education
(Gutiérrez, 2013) by putting the issues of positional identities at the center of analysis. As
previously discussed (Baker et al., 2003; Civil & Planas, 2010;deAbreu&Cline,2005), by
prioritizing certain ways of knowing as legitimate and valued at school, school practices can
Power and identity in immigrant parentsinvolvement in early years...
suppress other ways of knowing. Because the finger multiplication method was considered to
be illegitimate in schools, some immigrant students were taught to repeatedly practice and
memorize multiplication tables with a mainstream way. Through the learning of multiplication,
students were gradually socialized to conform to the mainstream and, already at Grade 2, some
acquired the identity of being a Bslow learner,^as the interviews with child participants
suggested. At the same time, for another case, child participantsagency was highlighted in
their efforts to create a context in which this socially undervalued cultural tool could be used
meaningfully, even when parent participants were reluctant to teach the tool.
By using the concept of positional identities, this study also adds to the ongoing discussion
on parental involvement in school and childrens mathematics learning. Immigrant parents in
previous studies have tended to value their knowledge and the mathematics they learned in
their home countries (Civil, Díez-Palomar, Menéndez, & Acosta-Iriqui, 2008; Civil & Planas,
2010;deAbreu&Cline,2005). However, Filipina mothers in this study tended to undervalue
their knowledge and the mathematics they had learned. Not only the finger multiplication
method but also other mathematical knowledge they had learned in the Philippines were not
openly taught at home. This was partially due to their positional identities in Japan and their
lived history: migrating to Japan, which had economic and industrial advantages, in order to
financially support their family members in the Philippines. As such, findings from this study
adds to the discussion of social valorization (de Abreu & Cline, 2007) by highlighting how
different kinds of mathematics are valorized or devalorized with reference to social
classification.
Considering that certain parental involvement at home (such as engaging in conversation
involving critical thinking) can positively influence studentsacademic engagement at school
(Galindo & Sonnenschein, 2015;Lee&Bowen,2006), it is important to understand the
positional identities of parents and their impact on parental involvement at home. This
intergenerational perspective will help design culturally responsive mathematics teaching that
can connect with studentsways of knowing mathematics, situated in their cultural and
linguistic practices (Aguirre & del Rosario Zavala, 2013; Caswell, Esmonde, & Takeuchi,
2011;Gay,2009).
5.2 Limitations
There are several limitations in the current study. First, my data draws from a relatively small
number of Filipina mothers and their children living in Japan. This methodological decision
allowed me to closely engage with them through this study, by talking with them in depth and
designing workshops with them after the interviews. At the same time, I would like to
acknowledge that the findings presented are based on this small number of participants and
gathering more stories can help to reveal diverse perspectives on the themes discussed.
Second, this study revealed the norm of mathematics learning expressed as the child
participantsreluctance to learn about or even think about mathematics behind the informal
finger multiplication method. These findings point to the significance of transforming the
cultural practices of schools to embrace diverse ways of knowing. A successful mathematics
unit reported by Civil (2007), the garden project, illuminated the possibility of bringing
parentsintellectual resources to schools when teachers view immigrant parents as academi-
cally resourceful. Booker and Goldmans(2016) participatory design research on mathematics
workshops with families highlights the significance of attending to the participantsepistemic
authority to confront institutional power. Understanding more about bridges between schools
Takeuchi M.A.
and communities would be meaningful to achieve equitable mathematics learning
opportunities.
5.3 Pedagogical implications
With regards to equity in mathematics education, recent reform movements have aimed to
promote studentsproblem solving and conceptual understanding in mathematics. In fact,
when teachers are trained to teach mathematics for understanding and use quality curricular
resources, teaching for understanding can narrow the achievement gap, as has been shown
among students in the United States (Schoenfeld, 2002). The public debate on mathematics
education between emphasizing the basics and emphasizing problem solving and conceptual
understanding has been observed in many countries and can affect the ways in which non-
dominant students access opportunities to learn. Interviews with child participants in this study
implied that acquisition of basic computation skills (in this case, memorizing multiplication
tables with a specific recitation method) was expected as a necessary step before students
moved on to problem solving and conceptual understanding. This context hindered students
from mastering and exploring various computation strategies and also restricted opportunities
for some students to challenge advanced problem solving until they had mastered basic
computation skills in a mainstream way.
The underlying assumption prohibiting the use of the finger multiplication method in the
school can be that mathematical thinking has to be Ba pure mental activity something
immaterial, independent of the body, occurring in the head^(Radford, 2009, p.111). In school
contexts, mathematics is often presented as Bexisting independently of the people who do it, and
independent of their bodies, senses, desires, emotions, and aesthetics everything that makes a
person flesh and blood^(Greer, Mukhopadhay, & Roth, 2013, p.6). Findings from this study
suggest the significance of interrogating the assumption that mathematics is a pure mental activity,
in order to enhance opportunities to learn for students who embody specific cultural tools.
This study underlines the significance of affirming and encouraging diverse strategies and
methods that students learn at home, in classroom mathematics teaching. Such classroom
practices will benefit not only non-dominant students, but all students as the ethnomathematics
literature has shown (Ascher, 1994;DAmbrosio, 2006). For example, unpacking the mech-
anism of the finger multiplication method highlighted in this study could be useful for
challenging studentsBfossilized^(Vygotsky, 1978, p. 64) knowledge with a recitation method
of multiplication and for diversifying studentsways of approaching multiplication. Diverse
ways of mathematical knowing can humanize mathematics and enrich the school mathematics
curriculum.
Acknowledgements I truly appreciate the participants in this study, who shared with me their insights and
experiences. An earlier version of this manuscript was presented at the Eighth International Conference of
Mathematics Education and Society and I am grateful for detailed comments and feedback I received there from
Dr. Julia Aguirre, Dr. Marta Civil, and Dr. Rochelle Gutiérrez. I am thankful to Dr. Lesley Dookie and Dr.
Armando Paulino Preciado Babb for their comments and feedback through our writing group.
Compliance with ethical standards
Funding This study was supported by the Grant-in-Aid for Scientific Research [Grant number: 12 J02927] by
the Japan Society for the Promotion of Science. Any opinions, findings and conclusions expressed herein do not
necessarily reflect the views of the funding agency.
Power and identity in immigrant parentsinvolvement in early years...
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