Over the last three decades, many mathematics departments began to offer introduction to proof courses. However, research on student learning and curriculum design work is only now emerging. In particular, very little mathematics education research has focused on the teaching and learning of logic leading to proof techniques. We (Dr. Kyeong Hah Roh and I) have run a long series of exploratory teaching experiments studying how students reflect on and refine their use of mathematical language. From these experiments, we have identified some key ways that conventional approaches to logic do not meet students where they begin. More importantly, we have developed new task sequences supporting an alternative formulation of the logic of statements. This new approach unifies set theory, logic of statements, and beginning proof techniques. In this talk, we shall give a quick tour of the teaching sequence highlighting the motivating research findings, the resolutions to those challenges, the core ways of reasoning we now seek to foster, and the novel research findings that have emerged within the new approach. Finally, I will share about a new grant project that is expanding this instructional unit to a full introduction to proof curriculum. 

Research shows inequitable participation patterns are pervasive in mathematics classrooms. Thus, an important consideration for mathematics instructors is promoting participation by students with historically marginalized backgrounds. Existing literature often focuses on identifying and countering mathematics instructors’ implicit biases against minoritized students. However, redressing inequitable participation patterns requires changing social practices, and looking beyond individual minds. In this talk, I discuss interactional challenges associated with inviting minoritized students to the conversational floor during whole-group discussions. Based on a fine-grained study on classroom interaction, I offer “knowledge in interaction” as an important consideration when we work to disrupt inequitable patterns of participation.

As a part of the Student Engagement in Mathematics through an Institutional Network for Active Learning, or SEMINAL network, the Math Department at the University of Maryland, College Park (UMCP) has continued to work towards implementing active learning in a redesign of its Precalculus course. As a gatekeeper course, our team has sought to evaluate how active learning can better support all students in being successful in Precalculus. The overall goals of the redesign include: building on existing active learning resources; phasing in active learning materials/strategies into different versions of the course; coordinating the instruction and development of active learning materials/strategies; adapting active learning materials/strategies based on local data; and receiving support from on-campus resources and the SEMINAL network. In this presentation, I will share practical examples of our implementation and success with active learning, including findings from a recent analysis of instructor and student data that explored active learning framed in terms of the classroom norms of the Precalculus course. I will also discuss the nuanced findings related to the role student-centered (active learning) versus instructor-centered classroom norms may play in supporting the above-mentioned student outcomes.

Researchers have found that undergraduate mathematics classes taught using active learning are not consistently equitable, despite numerous studies demonstrating that active learning can increase student learning and reduce achievement gaps. These findings highlight the need for a deeper understanding of the relationships between active learning, equity, and inclusion. In this talk, I will explain how a critical perspective can help explain apparent inconsistencies in existing research findings. The majority of this talk will focus on sharing research about inclusive and equitable mathematics learning environments across secondary and postsecondary contexts to describe core components and attempt to paint a picture of how equitable mathematics instruction looks, feels, and sounds. I will close with the theoretical argument that active learning is a necessary but insufficient condition for mathematics learning communities to be inclusive and equitable.

Virginia, like many U.S. states, is beginning to recognize the need for understanding how best to serve linguistically minoritized students. In this presentation, I will discuss the ways teacher and researcher beliefs about language and linguistically minoritized young people shape mathematics classrooms. Specifically, I will share some of my learnings as a teacher-researcher in bilingual elementary classrooms.

In this talk, we will discuss examples from a mathematics methods course where pre-service teachers were working in a context linguistically unfamiliar to them. Additionally, we will watch classroom videos of multilingual students engaging in learning mathematics. These videos will serve as a point of departure for unpacking instructional strategies needed in teacher preparation that highlight the knowledge and understanding that multilingual students bring to the classroom.

Historically, derivatives are often introduced via a sliding secant line, but many students tend to forget the dynamic imagery and only have static images of the derivative (Zandieh, 2000). In this talk, I report on an alternative to introducing the derivative concept that is based on quantities as covarying. The results indicate that students can build a conceptual meaning for the limit definition of derivative that is productive and useful for future mathematical learning.