Educators and researchers throughout the world are seeking ways to promote inclusion and reduce social and educational inequalities for refugee, immigrant, and marginalized children and families (Allexsaht-Snider, et al., 2017; European Commission, 2013; Gadsen, et al., 2009). There is a call to innovate in creating learning spaces that account for the wide range of knowledge families draw on in authoring roles for themselves in supporting their children’s learning and schooling (Calabrese Barton, et al., 2004; Flecha & Soler, 2013). At the same time, there is a need for robust theoretical perspectives to help educators, researchers, parents, and children to re-conceptualize notions of inclusion and exclusion and challenge the ways in which refugee and immigrant families and children have been positioned as marginalized in educational settings.

The objective of our research is to elucidate new theoretical perspectives for imagining and conceptualizing family engagement from the standpoint of borderland identities. We see this as powerful way to rethink the learning of immigrant children and families as well as way to creating new learning spaces and experiences. For this purpose, we investigate the ways mathematics learning and knowing is experienced and could be experienced when bilingual immigrant children and families, along with educators, engaged in mathematics learning together in a series of family workshops. We center our analysis on the theoretical notions of the mestiza by Anzaldúa and the outsider-within by Collins as a way of thinking about identities, ways of being, experiences, learning, and positions in regard to knowledge of parents and children in this unique learning space. To this end, we focus on the following research questions: 1) How do the notions of the mestiza and the outsider-within allow us to conceptualize the ways of being and knowing of borderland identities as a more powerful way to understand the education of people who are immigrants? 2) How do the notions of borderland identities allow us to re-conceptualize the ways immigrant children and families are being positioned in educational settings and through family engagement?

In light of these questions we position our research in the context of two different theoretical frameworks.  We draw on two feminists of color, Anzaldúa and Collins, because they allow us to uncover the relations between knowledge and identity as well as the power dynamics that envelope knowledge; they help us see the contextual nature of knowledge and how it is impossible to see any standpoint as unquestionable (Delanty and Strydom, 2003). We examine the ideas by Collins and Anzaldúa as we see in them possibilities for understanding the ways of being of Latino children and families in an informal mathematics learning context; they allow us to imagine new possibilities that go beyond inclusion for immigrant children and families around the world. A specific example of this is the way Anzaldúa constructs the mestiza consciousness, which offers a way to see the world and the ways of being of immigrant with borderland identities that is generative. This way of being of the mestiza goes beyond needing to belong to just one culture or assimilation, it accepts a complex way of being in which it is possible to belong to more than one culture and be in more than one world, to be in the borderlands. Anzaldúa’s words are transformative in the sense that they turn such identities into powerful ways of being.

Our research began as we designed a series of workshops called Familias Aprendiendo, originally conceptualized as a space for Latino families with parents whose dominant language was Spanish. They were a response to Cristina's experience with exclusionary English only policies in local schools and her perspectives on the beliefs about language in those contexts, where speaking languages other than English is seen as a significant disadvantage, particularly for people who do not belong to the dominant culture. Consequently, we focused on creating opportunities to reinforce Spanish and bilingualism as valuable learning resources. The workshops alternate between family sessions and sessions in which parents and children work separately, with a main focus on mathematics, but we also discuss other ideas concerning education and schooling, such as language and language acquisition. During family sessions, parents and children work together on creative projects related to mathematics. The children work in another room on mathematics activities set in stations during the parent sessions. Parents take part in whole group conversations about the activities they engaged in during the family sessions and concerns parents have around their children's education. We collected data through the role of a participant observer and practitioner researchers, reflecting together as we debriefed each session with families and planned subsequent sessions. We also recorded highlights of conversations with parents in summary charts during the conversations and audio-recorded some group discussions. Finally, we interviewed parents after the workshops about their experiences. Data were generated and analyzed taking an "interpretative/hermeneutic" approach, with a focus on meaning and understanding. By drawing on both hermeneutics and the feminist theories developed by Anzaldua and Collins, we were able to question taken for granted notions about knowledge and language in the context of mathematics learning with families and children. Hankins (2013) explains that "Hermeneutics as method involves a reading and interpretation of some kind of human text" (p. 8). Consequently, we enriched our understandings through the in-depth analysis of events rendered into text generated as data in our study. Written events were carefully analyzed within their own boundaries and in relation to others as a way to gain insight into how immigrant children and families are being positioned in educational settings and through family engagement.

For Collins (1986) self-definition is a process that entails challenging the political processes of knowledge validation that are intrinsically external and carry stereotypical images in them. She understands self-valuation entails stressing the content of self-definition, replacing externally created images with authentic ones that come from others with a shared identity. The workshops are a space of self-definition and self-valuation for families in the sense that they are a space claimed by parents to see in a new light their role in the education of their children and their children's mathematics ability. Having a peer group with other parents who shared their cultural background and language, as well as the shared experience of the workshops, allowed for parents to reinforce this process of self-definition, to reinforce the new ways in which they were seeing their roles as parents and their children as able mathematics learners. In fact, we saw in the opportunities to build community the necessary movement from self-definition, to self-valuation. Other conceptualizations of borderland identities as well as the data from the family workshops allowed us to see them as a space that served as a complement and counterpoint to the experiences parents and children were having in school. The non-evaluative nature of the workshops gave space for the parents to shift the focus of learning away from the pressures and concerns imposed by others and focus on what they were noticing about their children as learners. The workshops created a space in which parents share with each other their own narratives of learning, for themselves and for their children, providing narratives and images for each other to learn from and imitate, allowing the parents to assume their identities in new ways and transform themselves.

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