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Numbers and languages are present around the world. While mathematics is deemed as universal, communities around the world have developed mathematical practices that align with their specific context and needs. Rooted in an Indigenous epistemological framework, this manuscript presents a dialogue among four co-researchers and teachers retelling their experiences teaching and learning Mesoamerican numbers in both monolingual (Spanish) and bilingual (Ixil and Spanish) contexts. With a strong desire to learn about and reconnect with the forces of Indigenous mathematical thought and language that move within the teaching and learning of these numbers, the authors collectively reflected on their "tellings" of prior work. It is worthy of note that these reflections on teaching and learning processes of naming Mesoamerican numbers, their symbols, and numerical values help realize that these concepts are more fully animated when presented in contexts that are onto-epistemologically relevant.

Background/Context: Computer programming is rarely accessible to K-12 students, especially for those from culturally and linguistically diverse backgrounds. Middle school age is a transitioning time when adolescents are more likely to make long-term decisions regarding their academic choices and interests. Having access to productive and positive knowledge and experiences in computer programming can grant them opportunities to realize their abilities and potential in this field. Purpose/Focus of Study: This study focuses on the exploration of the kind of relationship that bilingual Latinx students developed with themselves and computer programming and mathematics (CPM) practices through their participation in a CPM after-school program, first as students and then as cofacilitators teaching CPM practices to other middle school peers. Setting: An after-school program, Advancing Out-of-School Learning in Mathematics and Engineering (AOLME), was held at two middle schools located in rural and urban areas in the Southwest. It was designed to support an inclusive cultural environment that nurtured students' opportunities to learn CPM practices through the inclusion of languages (Spanish and English), tasks, and participants congruent to students in the program. Students learned how to represent, design, and program digital images and videos using a sequence of 2D arrays of hexadecimal numbers with Python on a Raspberry Pi computer. The six bilingual cofacilitators attended Levels 1 and 2 as students and were offered the opportunity to participate as cofacilitators in the next implementation of Level 1. Research Design: This longitudinal case study focused on analyzing the experiences and shifts (if any) of students who participated as cofacilitators in AOLME. Their narratives were analyzed collectively, and our analysis describes the experiences of the cofacilitators as a single case study (with embedded units) of what it means to be a bilingual cofacilitator in AOLME. Data included individual exit interviews of the six cofacilitators and their focus groups (30--45 minutes each), an adapted 20-item CPM attitude 5-point Likert scale, and self-report from each of them. Results from attitude scales revealed cofacilitators' greater initial and posterior connections to CPM practices. The self-reports on CPM included two number lines (0--10) for before and after AOLME for students to self-assess their liking and knowledge of CPM. The numbers were used as interview prompts to converse with students about experiences. The interview data were analyzed qualitatively and coded through a contrast-comparative process regarding students' description of themselves, their experiences in the program, and their perception of and relationship toward CPM practices. Findings: Findings indicated that students had continued/increased motivation and confidence in CPM as they engaged in a journey as cofacilitators, described through two thematic categories: (a) shifting views by personally connecting to CPM, and (b) affirming CPM practices through teaching. The shift in connecting to CPM practices evolved as students argued that they found a new way of learning mathematics, in that they used mathematics as a tool to create videos and images that they programmed by using Python while making sense of the process bilingually (Spanish and English). This mathematics was viewed by students as high level, which in turned helped students gain self-confidence in CPM practices. Additionally, students affirmed their knowledge and confidence in CPM practices by teaching them to others, a process in which they had to mediate beyond the understanding of CPM practices. They came up with new ways of explaining CPM practices bilingually to their peers. In this new role, cofacilitators considered the topic and language, and promoted a communal support among the peers they worked with. Conclusions/Recommendations: Bilingual middle school students can not only program, but also teach bilingually and embrace new roles with nurturing support. Schools can promote new student roles, which can yield new goals and identities. There is a great need to redesign the school mathematics curriculum as a discipline that teenagers can use and connect with by creating and finding things they care about. In this way, school mathematics can support a closer "fit" with students' identification with the world of mathematics. Cofacilitators learned more about CPM practices by teaching them, extending beyond what was given to them, and constructing new goals that were in line with a sophisticated knowledge and shifts in the practice. Assigned responsibility in a new role can strengthen students' self-image, agency, and ways of relating to mathematics.

Background/Context: After-school programs that focus on integrating computer programming and mathematics in authentic environments are seldomly accessible to students from culturally and linguistically diverse backgrounds, particularly bilingual Latina students in rural contexts. Providing a context that broadens Latina students' participation in mathematics and computer programming requires educators to carefully examine how verbal and nonverbal language is used to interact and to position students as they learn new concepts in middle school. This is also an important stage for adolescents because they are likely to make decisions about their future careers in STEM. Having access to discourse and teaching practices that invite students to participate in mathematics and computer programming affords them opportunities to engage with these fields. Purpose/Focus of Study: This case study analyzes how small-group interactions mediated the positionings of Cindy, a bilingual Latina, as she learned binary numbers in an after-school program that integrated computer programming and mathematics (CPM). Setting: The Advancing Out-of-School Learning in Mathematics and Engineering (AOLME) program was held in a rural bilingual (Spanish and English) middle school in the Southwest. The after-school program was designed to provide experiences for primarily Latinx students to learn how to integrate mathematics with computer programming using Raspberry Pi and Python as a platform. Our case study explores how Cindy was positioned as she interacted with two undergraduate engineering students who served as facilitators while learning binary numbers with a group of three middle school students. Research Design: This single intrinsic case focused on exploring how small-group interactions among four students mediated Cindy's positionings as she learned binary numbers through her participation in AOLME. Data sources included twelve 90-minute video sessions and Cindy's journal and curriculum binder. Video logs were created, and transcripts were coded to describe verbal and nonverbal interactions among the facilitators and Cindy. Analysis of select episodes was conducted using systemic functional linguistics (SFL), specifically language modality, to identify how positioning took place. These episodes and positioning analysis describe how Cindy, with others, navigated the process of learning binary numbers under the stereotype that female students are not as good at mathematics as male students. Findings: From our analysis, three themes that emerged from the data portray Cindy's experiences learning binary numbers. The major themes are: (1) Cindy's struggle to reveal her understanding of binary numbers in a competitive context, (2) Cindy's use of "fake it until you make it" to hide her cognitive dissonance, and (3) the use of Spanish and peers' support to resolve Cindy's understanding of binary numbers. The positioning patterns observed help us learn how, when Cindy's bilingualism was viewed and promoted as an asset, this social context worked as a generative axis that addressed the challenges of learning binary numbers. The contrasting episodes highlight the facilitators' productive teaching strategies and relations that nurtured Cindy's social and intellectual participation in CPM. Conclusions/Recommendations: Cindy's case demonstrates how the facilitator's teaching, and participants' interactions and discourse practices contributed to her qualitatively different positionings while she learned binary numbers, and how she persevered in this process. Analysis of communication acts supported our understanding of how Cindy's positionings underpinned the discourse; how the facilitators' and students' discourse formed, shaped, or shifted Cindy's positioning; and how discourse was larger than gender storylines that went beyond classroom interactions. Cindy's case reveals the danger of placing students in "struggle" instead of a "productive struggle." The findings illustrated that when Cindy was placed in struggle when confronting responding moves by the facilitator, her "safe" reaction was hiding and avoiding. In contrast, we also learned about the importance of empathetic, nurturing supporting responses that encourage students' productive struggle to do better. We invite instructors to notice students' hiding or avoiding and consider Cindy's case. Furthermore, we recommend that teachers notice their choice of language because this is important in terms of positioning students. We also highlight Cindy's agency as she chose to take up her friend's suggestion to "fake it" rather than give up.

The preparation of bilingual prospective teachers (BPTs) in mathematics encompasses a challenge because many U.S.-born BPTs had limited opportunities to learn mathematics in their native language, in this case, Spanish. Consequently, BPTs feel ill-prepared to teach mathematics bilingually. This study describes the experiences of seven Latinx BPTs facing this challenge. A language socialization framework and the analysis of mathematics teaching practices through BPTs' beliefs, goals, and actions prior to and during a language shift reveal links to non- and re-negotiated Imagined Learning Communities. The relevance and necessity of teaching translingual identities and practices in mathematics education are discussed.

This paper analyzes the work developed with a group of Latina mothers in a mathematics afterschool program for a period of 3 ½ years. The analysis of the productive patterns of interaction of this group of mothers with a group of bilingual participants shows that the program's participation and activity structure closely determines the quality of the mothers' participation. We present a sequence of attempts developed to alter this structure in order to successfully capitalize on mothers' leadership roles and knowledge during intergenerational and bilingual mathematical activity. We further discuss key social processes--acknowledging mothers as facilitators, focusing on communication rather than on a specific language, and supporting mathematics performance through social interactions--that opened up a space for Latina mothers' leadership and dynamic participation during bilingual mathematical activity.

Through a collaborative effort between a sixth-grade teacher and two university faculty, we designed an integrated unit to learn about motion and we learned that an integrated teaching and learning experience about motion is MESSY (i.e., it includes movement, engagement, social interactions, spontaneity, yikes, and yippees!). We engaged in a twofold goal process of integrating mathematics, science, and technology. First, we embedded an inquiry approach in our planning and facilitation of learning experiences. Second, students coconstructed their understandings of motion through collective inquiry. School and university faculty, as well as students, learned about inquiry, about using motion detectors to learn and teach about motion, and about how mutual respect and collaboration support productive STEM learning, teaching, and research.

In this paper, we discuss the characteristics of microaggressions based on minority language(s) as a form of discriminatory practice against non-dominant students in the mathematics context. Microaggressions are subtle, brief, and commonplace verbal, behavioral, or visual negative slights or insults toward people of color. We extend the concept of microaggression to include discrimination based on a minority language. We draw on our work with Latinas/os in the USA to demonstrate the occurrence of microaggressions in the teaching act. Revealing microaggressions based on language has the potential of creating more equitable learning environments for non-dominant students and can point to possible directions for future research and improvements in the preparation of teachers who serve non-dominant students who speak a language other than the school's official language.

This paper presents a new approach to science education that takes a path through sociocultural theory and into the ideas of Gloria Anzaldúa. We apply Anzaldúan theory to science education by illustrating it in action through various examples which explore the multidimensionality of teaching science with Latin@ students in various contexts including dual language settings. We present what it is to journey through transformation using examples from educators at various levels of science within the world of teaching science with Latin@ students in the U.S. Our examples illustrate how Latin@ students cross many cultural borders in Spanish, English, Latin@ home culture, school culture, and the world of scientific dialogue and content, and in doing so, go through tensions and transformations between dominant and non-dominant worlds, which should be acknowledged and better understood through Anzaldúan theory. Fundamentally, we present a transformative notion of Latin@ science learning as "living on the bridges" of many dialogic and cultural practices, and having to negotiate these in-between spaces, or "nepantla" ("Anzaldua and Keating in Interviews," Psychology Press, London, 2000), where Latin@ students must contend with the fragmented and sometimes painful struggle of living in racialized reality amidst the demands of a dominant culture, and where transformation and healing are possible through the path of conocimiento. We advocate for teachers to become science teacher "nepantler@s," who guide their students through "nepantla," and into a "new mestiz@" consciousness of science education.

As English-only efforts continue in the US schooling system, dual-language programs have served as attempts to preserve students' home language. An after-school, dual-language, Spanish-English, mathematics program, Los Rayos was developed in a predominantly Mexican/Mexican-American neighborhood in Chicago. As participant observers with a sociocultural perspective, we explored the linguistic and personal resources used by participating 4th grade bilingual Latina/o students. We found that students used imaginative, playful, and hybrid linguistic resources to make sense of and solve probability tasks when engaged within a zone of mathematical practice. Results challenge narrow perspectives on bilingual students' linguistic resources. Language implications are discussed.

There is a strong need in the United States to increase the number of students from underrepresented groups who pursue careers in Science, Technology, Engineering, and Mathematics. Drawing from sociocultural theory, we present approaches to establishing collaborations between computer engineering and mathematics/bilingual education faculty to address this need. We describe our work through the Advancing Out-of-School Learning in Mathematics and Engineering project by illustrating how an integrated curriculum that is based on mathematics with applications in image and video processing can be designed and how it can be implemented with middle school students from underrepresented groups.

The preparation of bilingual prospective teachers (BPTs) in mathematics encompasses a challenge because many U.S.-born BPTs had limited opportunities to learn mathematics in their native language, in this case, Spanish. Consequently, BPTs feel ill-prepared to teach mathematics bilingually. This study describes the experiences of seven Latinx BPTs facing this challenge. A language socialization framework and the analysis of mathematics teaching practices through BPTs' beliefs, goals, and actions prior to and during a language shift reveal links to non- and re-negotiated Imagined Learning Communities. The relevance and necessity of teaching translingual identities and practices in mathematics education are discussed. [ABSTRACT FROM AUTHOR]