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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.

In the current U.S. context, it is relevant to disseminate research that portrays in detail how bilingual teachers create challenging and safe mathematics learning environments for emergent bilinguals. It is critical to identify pedagogical approaches that foster emergent bilinguals' participation in mathematics conversations and discourse practices where language is considered a pedagogical resource. This is possible when teachers understand that young Latino/a students come to school with a wide range of cognitive and linguistic tools, which they can use to help them make sense of problems posed in the classroom. Using case study methodology, we define and provide a detailed portrayal of a bilingual kindergarten teacher´s mathematics pedagogical practices. Specifically we discuss: (a) the use of authentic "mathematics stories," (b) the integration of multimodal representation of problem solving, and (c) collective thinking and representation of problem solving solutions. In addition, we analyze how the teacher fosters practices that use language as a learning resource. Finally, we argue that these practices promote a mathematics discourse community and that pedagogy of confidence, care, and understanding is at the core of this teacher's instructional approach.

The Research Committee focuses on several systemic barriers that have impeded the equitable development of students' mathematics knowledge, including school and school-system structures that foster the social reproduction of inequity. To develop an equitable context for all students to learn mathematics, the Research Committee posits that we need to change beliefs about students, about particular groups of students, about how students learn, and about grouping students.

In this commentary, the authors explore how mathematics education research and the decisions mathematics education researchers (MERs) make to include (or not) an equity lens are not just choices; rather, they are political acts. MERs must take a hard look at themselves as human beings shaped by the political landscape of their different histories and experiences and understand how these histories and experiences affect their choices as researchers to question, understand, and ultimately transform mathematics education into a more clearly anti-oppressive and equitable human experience. For this to take place, MERs suggest being willing to enter a brave space in which some of their assumptions are questioned. MERs argue that addressing equity necessitates an intentional, collective, and professional responsibility that is taken up by all mathematics educators in multiple ways, levels, and settings. What is asked of the MER community is not new or easy, but it is necessary to gain transformative traction on this long-standing, thoroughly documented, and seemingly intractable problem of inequity in mathematics education.

This commentary focuses on reflections involving the special issue on Teaching and Learning Mathematics and Computing in Multilingual Contexts and the important role that Teachers College Record has played in fostering creative interdisciplinary collaborations among researchers, graduate students, teachers, K-12 students, and parents. A discussion is included on how participating as a Guest Lead Editor of this special issue afforded opportunities to learn more about projects that integrate mathematics and computing as well as transformations that have impacted the work we do in our respective fields. Multilingual contexts contribute much to our understanding of global perspectives on mathematics education. Taking up a memorable moment that involved such a context, I discuss future directions for the Teachers College Record as we consider reaching to multilingual audiences. [ABSTRACT FROM AUTHOR]

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.

An introduction to the journal's special issue on Teaching and Learning Mathematics and Computing in Multilingual Contexts is presented.

This study investigated Spanish-speaking kindergarten students' participation in mathematical discourse as they solved and discussed a range of word problems. Specifically, we draw upon sociocultural perspectives on mathematics learning to frame mathematical discourse and to examine specific teacher and student actions that seemed to support the development of mathematical discourse over the course of the kindergarten year. Data sources included pre- and post-task-based clinical interview assessments and weekly (videotaped) observations of problem-solving lessons. Findings demonstrated ways that teachers supported and students appropriated discursive habits such as using more precise mathematical language, explaining solutions in ways that referenced actions on quantities in the problem, and using multiple visual representations to mediate communication. In addition, the findings point to the critical role the teacher plays in supporting the development of students' mathematical discourse. [ABSTRACT FROM PUBLISHER]

This study explores opportunities to learn mathematics problem solving for Latina/o students in 3 kindergarten classrooms in the southwest. Mixed methods were used to examine teaching practices that engaged Latina/o students in problem solving and supported their learning. Findings indicate that although students in all 3 classrooms showed growth on pre-/postassessment measures, students in Ms. Arenas's classroom outperformed students in the 2 other classrooms. More time spent on problem solving; exposure to a broader range of problems involving multiplication, division, and multiple steps; and consistent access to students' native language, Spanish, distinguished Ms. Arenas's class. [ABSTRACT FROM AUTHOR]

The purpose of this 18-month case study is to highlight the successes and challenges that an ESL/mathematics teacher encountered as she made a shift from traditional mathematics curriculum to a standards-based curriculum as part of a statewide systemic initiative. The study was conducted in an urban, public middle school in Central Texas that served predominately low-income Latina/o students. The participant of this study was a middle school teacher who taught mathematics to English language learners in a self-contained classroom, which meant that 6th- through 8th-grade students were in the same classroom. Data sources included interviews, participant and nonparticipant classroom observations, fieldnotes, and documents. Three themes emerged from the data: (1) professional development opportunities and collaboration with a mainstream mathematics teacher, (2) change in teaching practices, and (3) equity issues. Findings indicate that this ESL/ mathematics teacher valued the professional development opportunities and collaborations with the mainstream mathematics teacher that supported her implementing a standards-based curriculum. The teacher also reflected on how her teaching changed by implementing units of the Connected Mathematics Project. However, a challenge she encountered with equity issues was the mismatch between the 6th-grade curriculum and the self-contained ESL classroom that consisted of 6th- through 8th-grade students. Other challenges were the lack of resources in the students' native language and the time needed to translate the curriculum materials. Implications and recommendations are discussed in relation to mathematics reform efforts in ESL classrooms. [ABSTRACT FROM AUTHOR]

This case study investigates a professional development initiative in which a first-grade bilingual teacher engages in learning and teaching Cognitively Guided Instruction, a framework for understanding student thinking through context-rich word-problem lessons. The study explores (a) the impact of classroom-based professional development on a teacher's understanding of teaching mathematics to Latina/o students, and (b) issues of language and culture with which the teacher grapples while engaged in reflecting on students' mathematical thinking. Our findings show that ongoing reflection, collegial conversations, and analysis of students' work enhanced teacher's understandings of students' mathematical learning, and of practices that provide students opportunities to solve contextualized mathematics problems, to communicate their solutions, and to represent their thinking. [ABSTRACT FROM AUTHOR]