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1. “Fake It Until You Make It”: Participation and Positioning of a Bilingual Latina Student in Mathematics and Computing

   https://doi.org/10.1177/01614681221104106  

   Celedón-Pattichis, Sylvia ; Kussainova, Gulnara ; LópezLeiva, Carlos A. ; Pattichis, Marios S. ( May 2022 , Teachers College Record: The Voice of Scholarship in Education)

   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 Pimore »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.« less
2. What I Wish My Instructor Knew: Navigating COVID-19 as an Underrepresented Student - Evidence Based Research

   Sealey, Zaniyah V. Lewis ( July 2021 , ASEE Virtual Annual Conference Content Access)

   In March 2020, the global COVID-19 pandemic forced universities across the United States to immediately stop face-to-face activities and transition to virtual instruction. While this transition was not easy for anyone, the shift to online learning was especially difficult for STEM courses, particularly engineering, which has a strong practical/laboratory component. Additionally, underrepresented students (URMs) in engineering experienced a range of difficulties during this transition. The purpose of this paper is to highlight underrepresented engineering students’ experiences as a result of COVID-19. In particular, we aim to highlight stories shared by participants who indicated a desire to share their experience with their instructor. In order to better understand these experiences, research participants were asked to share a story, using the novel data collection platform SenseMaker, based on the following prompt: Imagine you are chatting with a friend or family member about the evolving COVID-19 crisis. Tell them about something you have experienced recently as an engineering student. Conducting a SenseMaker study involves four iterative steps: 1) Initiation is the process of designing signifiers, testing, and deploying the instrument; 2) Story Collection is the process of collecting data through narratives; 3) Sense-making is the process of exploring and analyzing patterns of themore »collection of narratives; and 4) Response is the process of amplifying positive stories and dampening negative stories to nudge the system to an adjacent possible (Van der Merwe et al. 2019). Unlike traditional surveys or other qualitative data collection methods, SenseMaker encourages participants to think more critically about the stories they share by inviting them to make sense of their story using a series of triads and dyads. After completing their narrative, participants were asked a series of triadic, dyadic, and sentiment-based multiple-choice questions (MCQ) relevant to their story. For one MCQ, in particular, participants were required to answer was “If you could do so without fear of judgment or retaliation, who would you share this story with?” and were given the following options: 1) Family 2) Instructor 3) Peers 4) Prefer not to answer 5) Other. A third of the participants indicated that they would share their story with their instructor. Therefore, we further explored this particular question. Additionally, this paper aims to highlight this subset of students whose primary motivation for their actions were based on Necessity. High-level qualitative findings from the data show that students valued Grit and Perseverance, recent experiences influenced their Sense of Purpose, and their decisions were majorly made based on Intuition. Chi-squared tests showed that there were not any significant differences between race and the desire to share with their instructor, however, there were significant differences when factoring in gender suggesting that gender has a large impact on the complexity of navigating school during this time. Lastly, ~50% of participants reported feeling negative or extremely negative about their experiences, ~30% reported feeling neutral, and ~20% reported feeling positive or extremely positive about their experiences. In the study, a total of 500 micro-narratives from underrepresented engineering students were collected from June – July 2020. Undergraduate and graduate students were recruited for participation through the researchers’ personal networks, social media, and through organizations like NSBE. Participants had the option to indicate who is able to read their stories 1) Everyone 2) Researchers Only, or 3) No one. This work presents qualitative stories of those who granted permission for everyone to read.« less
3. From Students to Cofacilitators: Latinx Students’ Experiences in Mathematics and Computer Programming

   https://doi.org/10.1177/01614681221104104  

   LópezLeiva, Carlos A. ; Noriega, Gabino ; Celedón-Pattichis, Sylvia ; Pattichis, Marios S. ( June 2022 , Teachers College Record: The Voice of Scholarship in Education)

   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.

   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.

   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 Raspberrymore »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.

   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 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.

   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.

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4. A model of students’ conceptions of equivalence.

   Wladis, C. ; Offenholley, K. ; Sencindiver, B. ( July 2021 , Proceedings of the 44th Conference of the International Group for the Psychology of Mathematics Education)

   Inprasitha, Maitree ; Changsri, Narumon ; Boonsena, Nisakorn (Ed.)

   In mathematics education, much research has focused on studying how students think about the equals sign, but equality is just one example of the larger concept of equivalence, which occurs extensively throughout the K-16 mathematics curriculum. Yet research on how students think about broader notions of equivalence is limited. We present a model of students’ thinking that is informed by Sfard’s theories of the Genesis of Mathematical Objects, in which she distinguishes between operational versus structural thinking (e.g., 1995), which we conceptualize as a continuum rather than a binary categorization. Sfard also describes a pseudostructural conception, in which the objects that a student conceptualizes are not the reification of a process. We combine Sfard’s theory with a categorization of the source of students’ definitions, where stipulated definitions are given a priori and can be explicitly consulted when determining whether something fits the definitions, while extracted definitions are constructed from repeated observation of usage (Edwards & Ward, 2004). We combine these theories with inductive coding of data (open-ended questions, multiple-choice questions, and cognitive interviews) collected from thousands of students enrolled in a range of mathematics classes in college in the US, to generate categories of students’ thinking around equivalence. We seemore »this model as a tool for analysing students’ work to better understand how students conceptualize equivalence. With this model we hope to begin a conversation about how students tend to conceptualize equivalence at various levels, as well as the ways in which equivalence is or is not explicitly addressed currently in curricula and instruction, and what consequences this might have for students’ conceptions of equivalence.« less
5. A Sociocultural Perspective on Beginning Teachers Enacting Reasoning and Proving Practices

   Weingarden, M. ; Buchbinder, O. ( January 2022 , Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education)

   Karunakaran, S. S. ; Higgins, A. (Ed.)

   The critical role of teachers in supporting student engagement with reasoning and proving has long been recognized (Nardi & Knuth, 2017; NCTM, 2014). While some studies examined how prospective secondary teachers (PSTs) develop dispositions and teaching practices that promote student engagement with reasoning and proving (e.g., Buchbinder & McCrone, 2020; Conner, 2007), very little is known about long-term development of proof-related practices of beginning teachers and what factors affect this development (Stylianides et al., 2017). During the supervised teaching experiences, interns often encounter tensions between balancing their commitments to the university and cooperating teacher, while also developing their own teaching styles (Bieda et al., 2015; Smagorinsky et al., 2004; Wang et al., 2008). Our study examines how sociocultural contexts of the teacher preparation program and of the internship school, supported or inhibited proof-related teaching practices of beginning secondary mathematics teachers. In particular, this study aims to understand the observed gap between proof-related teaching practices of one such teacher, Olive, in two settings: as a PST in a capstone course Mathematical Reasoning and Proving for Secondary Teachers (Buchbinder & McCrone, 2020) and as an intern in a high-school classroom. We utilize activity theory (Leont’ev, 1979) and Engeström’s (1987) model of anmore »activity system to examine how the various components of the system: teacher (subject), teaching (object), the tasks (tools), the curriculum and the expected teaching style (rules), the cooperating teacher (community) and their involvement during the teaching (division of labor) interact with each other and affect the opportunities provided to students to engage with reasoning and proving (outcome). The analysis of four lessons from each setting, lesson plans, reflections and interviews, showed that as a PST, Olive engaged students with reasoning and proving through productive proof-related teaching practices and rich tasks that involved conjecturing, justifying, proving and evaluating arguments. In a sharp contrast, as an intern, Olive had to follow her school’s rigid curriculum and expectations, and to adhere to her cooperating teacher’s teaching style. As a result, in her lessons as an intern students received limited opportunities for reasoning and proving. Olive expressed dissatisfaction with this type of teaching and her desire to enact more proof-oriented practices. Our results show that the sociocultural components of the activity system (rules, community and division of labor), which were backgrounded in Olive’s teaching experience as a PST but prominent in her internship experience, influenced the outcome of engaging students with reasoning and proving. We discuss the importance of these sociocultural aspects as we examine how Olive navigated the tensions between the proof-related teaching practices she adopted in the capstone course and her teaching style during the internship. We highlight the importance of teacher educators considering the sociocultural aspects of teaching in supporting beginning teachers developing proof-related teaching practices.« less