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The purpose of this paper is to highlight issues related to students' personal inferences that arise when students verbally explain their justification for calculus statements. We conducted clinical interviews with three undergraduate students who had taken first-semester calculus but had not yet been exposed to formal proof writing activities through undergraduate mathematics courses. We analyzed these students' verbal justification of four statements, each of which described a different relationship between two quantified variables in calculus contexts. In this paper, we document students' personal inferences that were evoked in their justifications and discuss how they are similar to or different from the logical inferences that have been accepted and practiced by the mathematics community for mathematical arguments. [For the complete proceedings, see ED630210.]

From mathematics education, a great variety of studies have focused on analyzing the presence of digital technology from different points of view. Those who work with proof and argumentation have resisted presenting results with a technological component, due to the idea of formality associated with those terms, which has increased the existing tension between the theoretical and empirical nature of mathematics. Taking into consideration that with the presence of environments such as dynamic geometry software (DGS) the student can access to dynamic representations, we seek to understand the impact of the interaction with these representations on the arguments proposed by the students. For this, we carried out an exploratory and descriptive study whose results show that the interaction with dynamic representations provides students with validation tools different from those on paper. [For the complete proceedings, see ED630210.]

This paper describes the conceptions about complex numbers that a group of university students has, these were built from the application of an activity sequence centered on these numbers. This sequence is based on the APOS theory, some aspects of semiotic representation theory, and the use of digital technology. Particularly, both the general results of a pretest and a posttest are shown and compared. Additionally, the example of a student is analyzed to show evidence of how the mental structures and mechanisms that define the students' conceptions are built through the implementation of the sequence. The results show how the activity sequence allowed students to coordinate algebraic and geometric processes on complex numbers to improve their conceptions. [For the complete proceedings, see ED630210.]

In this proposal, we share research that explores the potential benefits of a novel Making experience within mathematics teacher preparation that we hypothesized would inform the pedagogical and curricular thinking of prospective teachers of elementary mathematics (PMTs). That experience had PMTs exploring at the intersection of content, pedagogy, and design to digitally design, 3D print, and share an original manipulative with a child to promote their mathematical thinking. We share several vignettes of our research that aim to discern some of the potential benefits the experience might offer PMTs. These take a variety of theoretical and methodological approaches at the intersections of teacher knowledge, identity, pedagogy, and design. Implications of our findings for teacher preparation and professional learning are provided throughout the paper and in its conclusion. [For the complete proceedings, see ED630210.]

The development and use of learning trajectories is a body of research that has made enormous contributions to the field of mathematics education, offering insight into the teaching and learning of topics at all levels. Simultaneously, the work of building learning trajectories can benefit from explicitly adopting an anti-deficit stance, incorporating ways to center student voices from an asset-based perspective. In this paper I propose two related constructs to support this work: decentering and second-order models. In decentering, researchers work to set aside their own knowledge to understand students' reasoning as viable. This can support models of student mathematics that position student thinking as rational, powerful, and productive. I provide one example of the work of decentering and discuss ways to build learning trajectories that emphasize students' strengths and competencies. [For the complete proceedings, see ED630210.]

Mediated Field Experiences (MFEs) provide teacher candidates (TCs) structured opportunities to unpack and enact core teaching practices, gain mathematics content and pedagogical knowledge, and reflect critically on mathematics teaching and learning. In this paper we present findings from a multi-institutional descriptive pilot study that investigates the impact of MFEs on TC learning. TCs reported that they (1) deepened their understanding of the targeted core teaching practice(s), (2) developed a vision of ambitious mathematics teaching, (3) recognized the importance of cultivating a positive classroom learning community, and (4) increased their confidence when teaching after their completion of a one-term course implementing MFEs. [For the complete proceedings, see ED630060.]

This paper reports on a study of learners' use of immersive spatial diagrams to make arguments about three-dimensional geometric figures. Immersive spatial diagrams allow learners to use the movement of their bodies to control their point of view, while immersed in three-dimensional digital renderings. We present analysis of two pairs of pre-service elementary teachers' argumentation about the shearing of pyramids, using the ck¢-enriched Toulmin Model of Argumentation (Pedemonte & Balacheff, 2016) to link the affordances of immersive spatial diagrams to the learners' mathematical reasoning. We share how one pair of learners took points of view bending beside and standing within the pyramid to describe how the space inside is transformed without reference to one- or two-dimensional components of the representation. [For the complete proceedings, see ED630060.]

Prompting people to estimate climate change numbers before showing them the true value can shift learners' attitudes and conceptions. Yet, interventions created for such a learning experience are not easily accessible to the general public. The purpose of this preregistered study was to address this research gap by developing and testing an openly accessible online intervention that presents participants with novel numbers about climate change after they estimate those numbers. An experimental online study design was used to investigate the impact of the intervention on undergraduate students' climate change understanding and plausibility perceptions. Findings revealed that posttest climate change knowledge was higher among those randomly assigned to use the app compared with those assigned to a control condition, and that supplementing this experience with numeracy instruction was linked with more robust gains. [For the complete proceedings, see ED630210.]

There is a popular myth that mathematical creativity is a trait possessed by a small group of people. This is perpetuated by the lack of understanding of what influences mathematical creativity, especially in the classroom. In particular, professional mathematicians often name aesthetic experiences as a critical aspect of their mathematical creativity. Therefore, this study examines aesthetic dimensions of episodes of student creativity from the high school classroom. Several types of aesthetic experiences arose across the episodes. Students were motivated to take creative action by experiences of mystery or discomfort. Furthermore, in some instances, taking a creative action was accompanied and propelled by a sense of craziness or satisfaction. [For the complete proceedings, see ED630210.]

Unpacking middle school students' mathematical relationships is important as a step towards improving mathematical relationships. In this study, 500 middle school students drew personifications of mathematics. We examined these personifications of mathematics for insight into their relationships with mathematics. Using constant comparative methods, we present various ways the middle school students personified mathematics. Negative relationships were personified with terrible beasts, abusers, authoritarians, and pests/nuisances. Positive relationships were personified with best friends and nature. Some personifications supported both positive and negative relationships or were neutral relationships. Reflecting on these personifications point to components of positive relationships with mathematics that we should support and confronts ways we may be perpetuating negative relationships with mathematics. [For the complete proceedings, see ED630210.]

Using data from teaching experiments and theories from quantitative reasoning, we built second-order accounts of students' mathematics with regards to how they conceived rate of change through operating on existing quantities. In this report, we explain three different ways STEM undergraduates structurally conceive rate of change as they constructed mathematical models for real-world scenarios. [For the complete proceedings, see ED630210.]

We report on a research study conducted within a transition-to-proof course for mathematics majors at a large public university. Within the course, students explored famously unproven conjectures and reflected on how their perspectives of mathematics changed through this exploration (if at all). In this report we share students' takeaways from the project. For instance, some students experienced mathematics as a creative subject for the first time, as they tried their own methods to solve the conjectures; other students reflected on developing a greater understanding of the behind the scenes work of mathematicians that goes into mathematical creation. We also report on the subjective emotional experiences of the students, which ranged from frustration from being unable to find patterns to enjoyable exploration. [For the complete proceedings, see ED630210.]

When mathematics educators work towards making mathematics more relevant, they often think about including more real-world applications into mathematics lessons. But what happens when a lesson is devoid of real-world contexts? In what ways can students find it relevant? This study explores how high school students perceived relevance when they were asked to describe their experiences during decontextualized mathematics lessons. Students highlighted how they found certain characteristics of the lessons to be useful in their learning and how they perceived relevance through different feelings experienced in the lessons. This, in turn, broadens our understanding of what relevance means to students. [For the complete proceedings, see ED630210.]

Isomorphism and homomorphism appear throughout abstract algebra, yet how algebraists characterize these concepts, especially homomorphism, remains understudied. Based on interviews with nine research-active mathematicians, we highlight new sameness-based conceptual metaphors and three new clusters of metaphors: sameness/formal definition, changing perspectives, and generalizations beyond algebra. Implications include a way to articulate a conceptual purpose for homomorphism beyond its relationship to isomorphism: namely, as a tool for changing perspectives when problem-solving. [For the complete proceedings, see ED630210.]

Gaining insight into how one's noticing shapes decision making can enable a teacher to reflect on how they frame, interpret, and respond to classroom activity and disrupt the influence of dominant ideologies. Working in the context of teacher education, we conjectured that systematically analyzing and reflecting on their own noticing can enable preservice teachers (PSTs) in mathematics to develop more equitable practices. Using data from summative assignments in a course on advancing equitable teaching, we investigate how PSTs use lenses of equitable teaching to make sense of their noticing and develop conceptions of equity. Analysis reveals that PSTs engaged in meaningful reflection and adopted terms from the course but avoided discussing the sociopolitical dimensions of instruction. These findings have implications for course design and facilitation in the context of developing PSTs' noticing for equity. [For the complete proceedings, see ED630210.]

Flipped instruction has been flaunted as a pedagogical strategy that supports improved learning and retentive abilities of students. Nevertheless, one of the twin challenges reported in the literature, students' failing to complete preparatory work, impedes the efficacy of the model. Thus, learners' motivation and attitude to work are essential for the successful implementation of the constructivist learning-centric approach. Yet very few studies have examined the connections between students' motivation and achievement goals in flipped instruction. To address the current gap, this study investigated the relationship between students' motivation beliefs, flipped method, and achievement in precalculus using pre- and post-course surveys collected from 32 undergraduates. Both motivation beliefs and flipped instruction influenced academic achievement positively in the course and were moderated by students' efforts. [For the complete proceedings, see ED630210.]

Teacher candidates bring many beliefs and interpretations of mathematics teaching and learning at the start of their teacher preparation coursework (e.g. methods courses, field experiences, assessment). Well-prepared beginning teachers in many instances requires programs and designed experience to breakdown unproductive beliefs and/or improve dispositions to align to best practices and equitable dispositions for the teaching and learning of mathematics. Our study focused on developing and validating two rubrics to evaluate teacher candidates' talk during live discussion forums in the first month of their initial teacher preparation program coursework with the intent to inform to varying degrees, where teachers candidate talk is situated (or not) in alignment to foundational readings and productive beliefs. Early validity evidence for rubric use is presented with suggestions for informative use and practice. [For the complete proceedings, see ED630210.]

Research suggests that preservice teachers enter teacher education with predominantly negative dispositions towards mathematics. We present a case study of an approach to supporting the development of positive mathematics teaching identities among students in a middle-level math methods course. Our findings suggest that engaging in narrative reflection in tandem with collaborative problem solving in a mathematical discourse community over time helped students to transform their relationships with mathematics and forge positive mathematics identities. Providing opportunities for students to share and work through their vulnerabilities was critical to this process. Our findings illustrate a promising approach for teacher educators to support the development of positive mathematics teaching identities in preservice teacher education. [For the complete proceedings, see ED630210.]

This study examined how the social interactions that mathematics teaching assistants (TAs) have within their institution influenced their professional identity development as early-career undergraduate instructors. We drew on a sociocultural perspective of professional identity development in higher education to examine TAs' interactions with students, faculty, and other TAs. We qualitatively analyzed five mathematics TAs' responses to semi-structured interviews and found that some dimensions of their identities were more frequently situated within specific relationships, while others were evident in multiple relationships. Overall, the social interactions were sites for professional identity development. Identity is a complex construct, and a better understanding of how professional identity is developed can inform higher education institutions on ways to support positive identity development of future mathematics instructors. [For the complete proceedings, see ED630210.]

Mathematical terminology is sometimes created according to conventions that are not obvious to students who will use the term. When this is the case, investigating the choice of a name can reveal interesting and unforeseen connections among mathematical topics. In this study, we tasked prospective and practicing teachers to consider: What is geometric about geometric sequences? Participants embedded their explanations within a scripted dialogue between teacher- and student-characters in a mathematics classroom, provided commentary on this dialogue, and expanded on its mathematical content. Participants most often leverage the concept of a geometric mean to explain why geometric sequences are named as such. To capture this informal arguments, we built on the work of Toulmin (1958/2003) to conceptualize and develop the Toulmin-Reversed (Toulmin-R) model. [For the complete proceedings, see ED630210.]

Mathematics teacher educators have suggested that preservice mathematics teachers' (PMTs') practices provide evidence of their Mathematical Knowledge for Teaching (MKT). In an effort to explore connections between MKT and PMTs' practices, we developed a framework that operationalizes Ball et al.'s (2008) six MKT domains in terms of approximations of practice. We then used our framework to investigate which domains were evidenced in eleven PMTs' lesson plans and how PMTs described MKT in their lesson plan reflections. We found Knowledge of Content and Teaching most evidenced and Horizon Content Knowledge least evidenced. Also, PMTs made few instances of Knowledge of Content and Students as they struggled to address students' mathematical thinking in their plans. We propose alternative forms of approximations of practice to optimize PMTs' opportunities to demonstrate and conceptualize MKT. [For the complete proceedings, see ED630210.]

Given the centrality of angle in mathematics curricula and scarcity of research in this area, we investigated 64 PTs' assimilatory domains of angularity by analyzing the angles they indicated when presented with four segments mutually sharing an endpoint. In both interview and written settings, we found PTs were more likely to recognize convex angles than reflex angles. Additionally, they were more likely to assimilate disjoint angles than angles formed via additive angular compositions. In particular, we found that PTs were unlikely to recognize full angles or additive compositions involving reflex angles. We consider future directions and implications. [For the complete proceedings, see ED630210.]

Inequities in STEM participation for people of color and women are documented extensively, often highlighting issues of representation and/or achievement. This study adds to the literature by looking at participation inequities in a high school calculus class. Equity is conceptualized as a fair distribution of opportunities for students to engage in rich mathematical experiences. Analysis of participants' dialog revealed talk about student participation focused primarily on gender patterns, even when pertaining to only one race-gender group of students (i.e., White males). Analysis of whole-class participation showed White dominance superseded male dominance; White males had the most robust opportunities to participate followed by White females, females of color, and males of color. Findings suggest participants' gender-focused discourse obscured racial inequities in classroom participation. [For the complete proceedings, see ED630210.]

Research exploring how Hispanic-Serving Institutions (HSIs) serve Latin* STEM students has largely focused on features of organizational structures (e.g., support programs), but minimally examined instruction and classroom experiences. This is an important gap to fill, especially in gateway mathematics courses, where faculty relationships and quality of instruction impact Latin* students' persistence and identities in STEM. To advance such research, this report presents findings from an analysis of how perspectives from HSI mathematics faculty and students about instruction in introductory statistics converged and diverged in terms of serving Latin* populations. We present two illustrative cases of dissonant and resonant perspectives on serving Latin* students through instruction that frames mathematical ability expansively (e.g., not limited to being fast or correct). We conclude with research and practice implications. [For the complete proceedings, see ED630210.]

This study seeks to demonstrate how knowledge and authority are linked for preservice mathematic teachers and how this link may pose a challenge for teaching mathematics for social justice. A CDA of multiple preservice class discussions is presented. [For the complete proceedings, see ED630210.]

In recent decades, scholars of teacher education have suggested that teacher educators (TEs) should integrate the development of prospective teachers' (PTs') knowledge with their skills for enacting teaching, characterized in the literature as pedagogies of practice. One way to operationalize pedagogies of practice is through engaging PTs in cycles of enactment and investigation (CEIs). Using an opportunity to learn (OTL) lens, this study investigated one CEI enacted in a secondary mathematics methods course. Analyzing course artifacts and final interviews, we found that the PTs had OTL in all six nodes of the CEI, that OTL differed across the nodes, and that OTL in later nodes depended on knowledge built in previous nodes. Implications include the importance of PTs engaging in all nodes of a CEI to maximize OTL about mathematics teaching practices, mathematics, students, and learning. [For the complete proceedings, see ED630060.]

We report the results of a study on informal covariate statistical reasoning conducted with 22 students (aged 16 and 18 years). We designed and implemented a task in a digital technology environment to introduce the line of best fit. The task design having elements that foresee misconceptions reported in the literature, and by focusing on four statistical ideas that we consider being central to the development of informal reasoning about the line of best fit. After having used the digital technology environment, students transitioned from viewing points of a scatterplot as individual points or fragmented into subsets to viewing the scatterplot as an aggregate from a mathematical mechanism that links them through the notion of distance from a point set to a right line. [For the complete proceedings, see ED630060.]

People often view mathematics as abstract, cold, and irrelevant to real-life, and their school experiences influence such views. In this case study, we investigated the mathematics learning experiences of two women who participated in an afterschool girls STEM club 26 years ago. We explored their experiences in and out of school and how such experiences informed their images of mathematics. Data were collected from a survey, focus group interviews, and individual interviews. Using qualitative analysis, we learned that their school mathematics experiences influenced the participants' images of mathematics. The findings also revealed the participants' continuous and discontinuous learning experiences between school and out-of-school mathematics. This study suggests creating spaces to develop curricula that bridge the gap between school and out-of-school learning experiences. [For the complete proceedings, see ED630060.]

The purpose of this project was to understand how implicit views of authority support or limit prospective elementary teachers' (PTs) mathematical activity of justifying and to understand how the experience of justifying might support a development of an internal source of authority. In this case study of 18 PTs, we coordinate an analysis of (1) their responses to two justification tasks and (2) interview transcripts in which they discuss their experiences in learning to justify. Preliminary results indicate ways in which their views of authority limited their reasoning about mathematics by not recognizing their own sense-making and supported a sense-making exploration of mathematics that was freeing and empowering. These results provide mathematics teacher educators with insight to help them identify and address limiting views of authority and leverage productive views of authority. [For the complete proceedings, see ED630060.]

This study examines the nascent forms of political conocimiento demonstrated by elementary preservice teachers before and after a series of activities designed to engage them in thinking critically and quantitatively about the impacts of different grading systems. In reflections about their learning, the preservice teachers most frequently raised considerations related to knowledge with students and communities, followed by political knowledge. Many of the preservice teachers anticipated using their new knowledge in the near future to understand the implications of their professors' grading systems and in the more distant future to design grading scales in their own classrooms. A few reflections showed awareness of the tensions involved in grading systems, potentially a sign of developing Nepantla, while others evidenced more binary thinking. [For the complete proceedings, see ED630060.]

To support productive struggle, prospective secondary mathematics teachers (PTs) need to elicit and respond to students' mathematical ideas in ways that focus on those ideas and that position students to build on those ideas. Using the Teacher Response Coding framework (Van Zoest et al., 2021) we analyzed PTs' responses in three rehearsals of instruction. We identified significant differences in the natures of responses in one rehearsal compared to the other two. Using a Levels of Constraint framework based on findings of Kavanagh et al. (2020) we compared structures of the rehearsals and developed hypotheses regarding which aspects of structure might account for differences in PTs' responses. [For the complete proceedings, see ED630060.]

The purpose of this study is to investigate three elementary preservice teachers' (PSTs') conceptions of and reflections on the role of perseverance in mathematics. This study presents findings regarding the PSTs' perseverance conceptions, student interactions, and the PSTs reflections from a two-week summer math camp in which they assisted in teaching elementary student campers. Additionally, this study used an analytic framework based on a corpus of literature to capture how the preservice teachers' conceptions, interactions, and reflections aligned with each other and with current and relevant research recommendations. [For the complete proceedings, see ED630060.]

This paper presents selected findings from an assessment of university students' moment-by-moment reading of mathematical proof. This method, adapted from an assessment of narrative reading validated by psychologists, yields novel insights into the strategies students use to construct meaning for the equations in a proof text. In particular, we present evidence that novice readers constructed meanings for the equations using mathematical practices familiar from non-proof oriented courses -- substituting and solving for variables -- while more experienced readers drew upon practices native to proof-oriented mathematics -- inferring properties of quantities. We refer to these as computational and inferential orientations, respectively. We interpret this mismatch of practices in terms of Systemic Functional Linguistic's notion of textual metafunction and briefly discuss its implications for proof-oriented instruction. [For the complete proceedings, see ED606531.]

To better understand how to support high school students' engagement, advancements in research methods that provide greater understandings of malleable factors of engagement and conditions that affect students' engagement are needed. In this conceptual paper, we introduce four dilemmas that researchers need to navigate to study secondary students' engagement with mathematics: How can we concurrently capture engagement in-the-moment and at scale? What counts as a moment or experience? What sorts of experiences could be engaging? Whose perspectives on the experience should be privileged? We propose approaches for navigating these dilemmas in the context of a current research project. [For the complete proceedings, see ED606531.]

Increasingly, mathematics is being positioned as a tool to support students' understandings of social (in)justice and their own unique social positioning in the world. To this end, this study analyzes the impact of curricular reform efforts in an elementary mathematics content course. The course focused on fractions and statistics, and the course content was taught through tasks designed to support prospective teachers in understanding and critiquing the world. The authors found that through the course, prospective teachers' content knowledge increased and their knowledge of the world's demographics and social inequities increased. [For the complete proceedings, see ED629884.]

Mathematics teaching is an inherently social activity, highly dependent on the lived experiences of its members. Drawing on sociocultural perspectives, we explore the mathematical lives of Latinx paraeducators to better understand the ways in which their backgrounds might influence their attitudes toward mathematics and mathematics teaching. Eleven paraeducators participated in the study that used interviews, artifacts, and informal observations to document their lived experiences, particularly in regard to mathematics. The evidence suggests that aspects of their personal narratives, particularly family, home culture, and personal hobbies and interests, had important influences on many of the participants. Implications on the social aspects of mathematics teaching and the need for relevance are provided. [For the complete proceedings, see ED629884.]

Research in mathematics education has overlooked creativity in mathematics, partially because of a lack of an accepted definition of mathematical creativity. The present study investigates elementary pre-service teachers' (PSTs') conceptions of creativity in teaching and learning mathematics. Data were collected using observations and semi-structured interviews with nine PSTs and analyzed using thematic analysis. PSTs' conceptions of mathematical creativity included using multiple approaches to solve problems, designing mathematical tasks from scratch, making learning challenging but not impossible, and exercising independence in learning. Implications of these results are applicable to teacher preparation programs, and they suggest a need for more research on the nature of experience(s) that shapes PSTs' conceptions of mathematical creativity and how to develop it. [For the complete proceedings, see ED629884.]

In this study, we investigated two students', ages ten and eleven, emotions while they engaged in mathematical problem solving. During three task-based interviews, the students explored parts of the unsolved problem the Graceful Tree Conjecture. While they were engaged in the interviews, they self-identified the emotions of frustration and joy they were feeling using the Wong-Baker Scale. The students displayed the interplay of the emotions of frustration and joy or which we consider to be productive struggle. A descripted case of Georgia is included to describe her emotions while problem solving. [For the complete proceedings, see ED629884.]

This study investigates the effects of a technology methods course containing a unique collaborative design experience on prospective elementary and secondary mathematics teachers' technological beliefs, computer algebra system (CAS) beliefs, and technological pedagogical content knowledge (TPACK). Overall gain scores on all three instruments were statistically significant. Moreover, gender and level (elementary vs. secondary) were statistically significant predictors of TPACK gain scores. However, the influence of level on TPACK gain score was different for female prospective teachers (PTs) than male PTs. Even in the case of low gain scores PTs displayed beliefs that were aligned with productive uses of technology in the classroom. PTs showed greater gains on knowledge subdomains associated with technological knowledge than on technology free subdomains (e.g., pedagogical content knowledge). [For the complete proceedings, see ED629884.]

Mathematics majors, including future secondary teachers, should understand the work of pure mathematicians and the crucial role proof plays for the discipline of mathematics. Beyond the textbook proofs seen in most transition-to-proof courses, we conjectured that students might develop a deeper understanding of the discipline of mathematics and proof if they had the opportunity to do mathematical research--to try and prove an unsolved conjecture. As an added component of our transition-to-proof course, we designed an intervention so that students researched the Twin Primes conjecture or the Collatz conjecture. Students wrote reflections about their research and described how their perceptions of mathematics were influenced by the research. We analyzed the reflections and sought to understand how the students' views of mathematics and proof were enriched, if at all, through research on unsolved conjectures. [For the complete proceedings, see ED629884.]

This study employed hierarchical linear modeling to investigate the student- and school-level factors associated with the secondary mathematics achievement of English language learners (ELLs) and non-ELL students among a nationally representative sample of ninth graders in the United States. While certain characteristics, such as socioeconomic status, attitudes and interest in mathematics, and school engagement and belonging were predictive of access to and achievement in mathematics for both student groups, the direction and relative magnitude of the predictors differed. School-level variables, such as whether the school was public or private and administrator perceptions of school climate, were only predictive of mathematics grade point average (GPA) for non-ELLs. Implications of the findings are discussed. [For the complete proceedings, see ED629884.]

Most teacher preparation programs require prospective teachers (PTs) to engage in early field experiences (EFEs) prior to completing required coursework. These EFEs, however, may lack meaningful connections to course content and provide limited opportunities to experience the demands of classroom teaching. In this paper, we share evidence from the implementation of a novel kind of EFE, the "University Teaching Experience" (UTE) model, where secondary mathematics PTs receive mentoring from teacher educators (TEs) as they teach in a undergraduate mathematics course Findings reveal the importance of both guidance from TEs and observations of peer teaching for PTs learning in EFEs. [For complete proceedings, see ED581294.]

Efforts to enhance the aesthetic impact of mathematics lessons must account for the role of teachers in shaping the unfolding mathematical content of their enacted lessons. In this paper, we draw from Dietiker (2015) to describe differences in the mathematical stories of the enacted lessons of two veteran teachers teaching the same lesson. We identify connections between these differences and the variations in student experiences as illustrated by visible student reactions. [For the complete proceedings, see ED583608.]

We analyzed 5th grade students' interactions with one computer-based modeling simulation to examine how they defined and prioritized variables in a dynamically simulated environment. Results revealed that exposure to the simulation environment helped students visualize continuous motions, interpret the different quantities present in the model, and connect how variables related to each other. Additionally, students became more precise and systematic in adjusting the variables to explore the problem, test hypotheses, and achieve desired outcomes. [For the complete proceedings, see ED606556.]

Opportunities matter when it comes to students' math attitudes and performance. Over two semesters, across treatment sections of college algebra students, we implemented a set of dynamic computer activities linking animations and graphs. Across all sections, we administered a fully online survey of students' attitudes toward math. Using mixed methods, we analyzed students' attitudes toward math and their performance on a course final exam. At the end of each semester, we found statistically significant differences between treatment and comparison students' perceived competence toward math. Furthermore, treatment students outperformed comparison students on the course final exam, with statistically significant differences on an item linked to the dynamic computer activities. When students have opportunities to interact with dynamic computer activities, it can impact their math attitudes and course performance. [For the complete proceedings, see ED606556.]

Participation in mathematics classrooms has received considerable attention in previous research. Scholars have emphasized researchers' and teachers' perspectives on what it means to participate. I draw on sociocultural theories of learning to explore both students' and a teacher's perspectives on participation. I describe a participatory research study where a Spanish immersion third-grade teacher and I collaborated to elicit students' perspectives on mathematics class participation. Data generation included multi-method focus groups with the students, and an interview with the teacher. Drawing on social semiotics as an analytical framework, findings suggest that there were two connotations of participation in this classroom: While the teacher's connotation characterized participation mainly as quantifiable, observable student talk attributable to individual children, students' connotation characterized participation mainly as qualifiable, amorphous, diverse and focused on the social. I argue that developing mathematics teaching that is inclusive of diverse ways of participating involves learning about students' perspectives on participation. [For the complete proceedings, see ED606556.]

This study examines how preservice teachers select standards, plan tasks, and develop a full lesson plan focused on a social justice context. While traditional studies of this topic involve scholars examining completed lesson plans, this study is unique in that audio data was recorded to capture the types of discussions preservice teachers engaged in while completing social justice lesson plans. Findings indicated that PSTs used keywords to map standards onto elements of the social justice context, that they vacillated between selecting a standard and developing an appropriate task, and that they treated the social justice context as a fixed scenario. I will share examples along with implications for how mathematics teacher educators can better support PSTs as they navigate this complex process. [For the complete proceedings, see ED606556.]

Researchers have investigated how teacher feedback contributes to students' learning, yet there is insufficient research into the connection between teacher feedback and student happiness, which is linked to engagement, socio-emotional well-being, and ultimately academic achievement. We coded lesson transcripts from elementary teachers to determine emergent patterns between types of teacher feedback and average student self-reports of happiness in mathematics. We found teachers to employ specific feedback more than general feedback. In addition, feedback for effort and ability accounted for a small percentage of feedback. Findings suggest that student happiness is linked to specific combinations of feedback dimensions. [For the complete proceedings, see ED606556.]

This research report will discuss mathematics specialists and the way in which they communicate ideas of equity and social justice within a master's program that leads to a state endorsement in mathematics education leadership. Many mathematics specialist programs focus on developing their mathematical content knowledge for teaching, but these specialized leaders also need to learn about curriculum, assessment, pedagogy, and leadership for school change. This research describes one mathematics specialist program's initial efforts in developing mathematics teacher leaders who take action within their K-12 school contexts. Preliminary findings suggest that the mathematics specialists within this program are aligning their views of equitable mathematics instruction with Principles to Actions (National Council of Teachers of Mathematics, 2014) and the Teaching for Robust Understanding Framework (Schoenfeld, 2015). Implications for the program are that we are still exploring how to incorporate these ideas and facilitate critical conversations as teacher educators within our classrooms. [For the complete proceedings, see ED606556.]

As the field of professional development for mathematics graduate students evolves, there is a need for research studies that examine how mathematics graduate students develop as teachers. This study aims to fill this gap in the research by studying mathematics graduate students' experiences with teaching as they progress through their graduate programs. Mathematics graduate students were recruited from a large university mathematics department. They were responded to surveys and were interviewed semi-annually for two or more years. We analyzed their responses using thematic analysis and a framework that captured their development as teachers. In this report, we describe a framework for teachers' development and context and methods of the study. We present findings on how the framework elucidated mathematics graduate students' development as teachers and illustrate obstacles to their development. [For the complete proceedings, see ED606556.]