In this presentation, we will present findings from a research study that investigates the ways preservice teachers of Color make sense of their racialized experiences as learners of mathematics as children and how this impacts their intentions for their future math teaching.

Research on pre-service teachers’ discussion practices have focused on decompositions of practice into subskills, while acknowledging the role of context, identity, and relationships. We analyzed 66 elementary preservice teachers’ (PTs’) framing and orchestrating moves in a mixed-reality custom simulated discussion after problem-solving. PTs used five launching moves: gathering information about student processes, focusing on problem features, task and non-task oriented social interactions, and partner talk. PTs used five orchestrating moves: eliciting, probing, orienting to peers’ contributions, making contributions, and social moves. We argue PTs’ moves are motivated by more than the mathematical goals of the discussion.

Of the many challenges in shifting towards inquiry-oriented instruction from a lecture-based approach is understanding the role of the teacher in this new paradigm. One aspect of that role involves navigating novel classroom authority dynamics as students bear more authority to create and justify mathematical ideas. Supporting teachers as they navigate this shift is one of the many roles of effective professional development (PD). I present results from a case study of one PD facilitator’s authority as he worked to support instructors’ inquiry-oriented instruction (IOI). These results suggest  the impacts of facilitators’ beliefs and teaching experiences on long-term professional development. Additionally, I present a preliminary analysis of the phenomenon in the first study through the lens of positionality and discuss possible applications to graduate student professional development.

Dominant narratives about who can do what kind of mathematics shapes how people view themselves and each other in mathematical spaces and influences who gets viewed as competent. Scholars have argued that students whose backgrounds and experiences conflict with identities that are often perceived as having “high status” in mathematics may be excluded from being viewed as competent in proof spaces specifically. Questions worth exploring related to these ideas are: Do storylines that emerge from student interactions as they engage in small group proof activity influence perceived mathematical status? If so, how? In this talk I will share some ongoing work that my colleague, Dr. Tenchita Alzaga Elizondo (UTRGV), and I have been doing to investigate these questions in the context of an intro to proof course using inquiry-oriented activities. I will discuss how we have been thinking about the connections between mathematical status, storylines (and positioning), and equity in small group interactions. I will also share initial findings from an analysis using positioning theory that examined a small group interaction between three students, Abigail (white woman), Alison (white woman), and Justin (white man) as they worked together on constructing a proof.  

In this talk, we will look at the two recent studies we conducted on the graduate teaching assistants’ (TAs’) use of students’ work in teaching. In the first study, we examined the types of the errors that the TAs identified from students’ written work, their plans to address them, and implementation of their plans in class. Our results show that TAs often did not identify the most frequent errors students made, which reflected well-documented difficulties from the literature; the errors TAs identified were mainly procedural in nature; specific details of students’ work were mainly included in procedural errors, and the level of specificity of students’ work was generally consistent but showed some drops when going from identifying to planning, then to teaching. In the second study, with a different group of TAs, we investigated how they interpret students’ work and plan to address them in teaching based on approaches to address students’ misconceptions discussed in the literature: viewing them as simply incorrect thus to be retaught regardless of students’ thinking behind them, viewing them as a reflection of students’ flawed ideas to be confronted and replaced, and viewing them as resources for future learning to be refined and reorganized. Our analysis shows that while TAs’ interpretations were often sufficiently rich to support using student misconceptions as resources for future learning, none of their plans used them in this way. Rather, most TAs’ plans were aligned with asking students to revisit their work without further planning afterwards, or confronting and replacing. Our results suggest that professional development could be designed to help TAs use students’ errors in teaching to promote students’ learning in general and convert TAs’ rich interpretations into plans for using student misconceptions as resources for future learning in particular.

During the seminar, Dr. Aguilar will be sharing his experience in integrating state-of-the-art technologies like Mixed-Reality Simulations (MRS) to enhance the preparation of elementary pre-service teachers in orchestrating and fostering mathematical discussions to elicit, assess, and question students. In addition, it will be shared the opinions and perspectives of in-service teachers toward the use of MRS as professional development tool to strengthen their mathematical pedagogical skill in the mathematics classroom.

Activities related to mathematical proofs (i.e., reading, presenting, and constructing proofs) are notoriously challenging for college students. On top of applying advanced logico-mathematical knowledge, these activities require students to process and operate on a substantial amount of information. Failure to successfully navigate the incoming stream of information may result in cognitive overload and impede one’s ability to make progress on the task. In this talk, I will present the model for measuring the hypothetical cognitive load associated with the proving activities. Drawing on this model, I show how an undergraduate student, David, could use his hands to overcome the cognitive load he experienced when reading a proof of the Two-Color Theorem. The findings suggest that in the absence of other modes of offloading (e.g., using pen and paper, figurative materials, or technology), hand gesturing may serve as a powerful and convenient offloading mechanism.

The notion of ‘belonging’ has exploded recently in education and psychological discourse. However, belonging has also long been undertheorized and oversimplified, preventing scholars and educators from turnkeying the notion into a tool for understanding and addressing inequity in mathematics classrooms and shifting teachers’ pedagogical practice therein. In this talk, I elaborate on my journey of understanding belonging through various theoretical lenses as well as through the lived experiences of Black and Brown adolescents in secondary mathematics classrooms. Armed with this theoretical and practical insight I discuss the development of a multi-dimensional framework of belonging that appraises the instructional and interpersonal patterns of secondary (grades 5 thru 10) mathematics classrooms and how I have leveraged this tool to support mathematics teachers in developing culturally competent and responsive mathematics instruction.

In this study using data collected from students and instructors from several first semester calculus classes, difference equations models were created to model the changes in students' deep/shallow mindset over the course of the semester.  Using these models we conjecture how different subgroups' deep/shallow mindset of the class are affected by different instructor-student interactions throughout the semester.  We find that students' perception of confidence in the material has an important effect on their mindset, as well as time spent on material outside of the normal curriculum.