Search for: All records

In this report, we share the design of a year-long professional development program for university math instructors that we developed and refined as the Anti-deficit Learning and Teaching Project (Adelante). The program is a community learning project wherein minoritized students, STEM peer mentors, and math instructors (graduate students and instructional faculty) build relationships as they share their knowledge and experiences with race, gender, and mathematics. Culturally relevant pedagogy (Ladson-Billing, 1995) frames the goals of the community learning in terms of deep mathematical knowledge, cultural knowledge, and sociopolitical consciousness. The program activities are inspired by the Funds of Knowledge for Teaching project (Moll et al., 1992) wherein teachers are offered opportunities to build meaningful relationships with students and their communities. An anti-deficit perspective (Adiredja et al., 2020) guides the learning experience for all participants. Not only are minoritized students assumed to have cultural and intellectual assets for learning, but the project also aims to dismantle deficit master narratives (Solórzano & Yosso, 2002) about these students and their capacity to learn. Instructors worked on explicitly challenging deficit narratives about their students as they engaged in the program’s activities. The project also takes an anti-deficit approach to instructor development, focusing on their individual growth and agency, joy in teaching, and mental health. We also position ourselves as learners to the experience and wisdom of the staff and students at the university cultural centers. The core activities for the PD engage teachers to: (a) participate in five PD meetings on anti- deficit teaching and Inquiry Based Learning (IBL) teaching method; (b) lead a five-day math summer bridge workshop in Pre-Calculus, Calculus I, II, Vector Calculus, or Linear Algebra immediately following the meetings; (c) participate in critical conversations about race and gender in STEM with students at the cultural centers; (d) conduct a semi-structure interview with one of their students from the summer workshop about their STEM experience; and (e) participate in group reflection meetings debriefing their experience in the activities. Preliminary analysis of two of the three cohorts of participants found that most instructors developed a more humanizing approach to their teaching and their students (Gutiérrez, 2018). IBL helped instructors to explicitly challenge deficit narratives about minoritized students in the classroom, wherein most observed their students engaging in deep mathematical reasoning. Interviewing one of their students also shifted deficit narratives that developed in the classroom for some instructors. The workshop served as a space to try out previously learned teaching ideas (student centered teaching) without constraints from curriculum and assessments. Doing so reinvigorated many instructors’ passion for teaching, especially those who are more experienced. 

Teaching professional development (TPD) in collegiate mathematics has expanded over the last few decades. Providers of TPD, people who organize and facilitate professional learning about teaching, are at the center of this growth. Yet, little is known about who Providers are and what they do. To better understand the national landscape of Providers of TPD within university mathematics departments, this report shares data from a national survey where respondents were Providers. The focus here is on findings from survey questions asking about characteristics of Providers and the “providees” with whom they work, along with formats, topics, and activities used in TPD. Results suggest that Providers value active, learner-centered instructional methods promoted by research and policy. However, in the TPD itself, formats, topics, and activities commonly used by Providers may preach but not regularly practice activity-based methods. 

In this poster we illustrate how stewardship, a particular kind of leadership, in the complex system of mathematics instructional development requires decentering and interconnecting. This theory development for professional growth of faculty agents for change expands on earlier work describing how instructional practices used by providers of teaching-focused professional development in seminars about teaching (for graduate students) could be beneficial both for learning high-powered approaches to teaching of undergraduate mathematics and for building a foundation for future change-agent work. Here we move one level up and present an analogous argument about practices for stewards who are teaching about teaching about teaching. The poster illustrates the multilevel system with an expanded model that incorporates learning objectives for provider professional learning and the instructional practices of such professional learning in ways that showcase (and teach about) decentering and interconnecting. 

Studies show that Research-Based Instructional Strategies (RBIS) help students learn, however their adoption has been slow. The Teacher Centered Systematic Reform Model (TCRM) is a general model for organizing enablers and barriers to adoption of new teaching methods that includes departmental, personal and teacher thinking factors. We used the TCRM model as a framework to assess the amount of formal lecture reported by 634 mathematics instructors in their undergraduate courses. Regression analyses found that instructors who participated in Project NExT (a professional development workshop) during their early careers were less likely to use lecture than non-participants. Other significant predictors of lecture less included evaluation expectations emphasizing active teaching methods, involvement in equity and diversity efforts, and prior experience with RBIS. Factors with a positive correlational association with lecture included evaluation efforts by departments where lecture was expected. Results confirmed some prior models in different disciplines. 

Learning to interpret proofs is an important milepost in the maturity and development of students of higher mathematics. A key learning objective in proof-based courses is to discern whether a given proof is a valid justification of its underlying claim. In this study, we presented students with conditional statements and associated proofs and asked them to determine whether the proofs proved the statements and to explain their reasoning. Prior studies have found that inexperienced provers often accept the proof of a statement’s converse and reject proofs by contraposition, which are both erroneous determinations. Our study contributes to the literature by corroborating these findings and suggesting a connection between students’ reading comprehension and proof validation behaviors and their beliefs about mathematical proof and mathematical knowledge base. 

This paper presents six categories of undergraduate student explanations and justifications regarding the question of whether a converse proof proves a conditional theorem. Two categories of explanation led students to judge that converse proofs cannot so prove, which is the normative interpretation. These judgments depended upon students spontaneously seeking uniform rules of proving across various theorems or assigning a direction to the theorems and proof. The other four categories of explanation led students to affirm that converse proofs prove. We emphasize the rationality of these non-normative explanations to suggest the need for further work to understand how we can help students understand the normative rules of logic. 

Mathematicians often use set-builder notation and set diagrams to define and show relationships between sets in proof-related courses. This paper describes various meanings that students might attribute to these representations. Our data consist of students’ initial attempts to create and interpret these representations during the first day of a paired teaching experiment. Our analysis revealed that neither student imputed or attributed our desired theoretical meanings to their diagrams or notation. We summarize our findings in two vignettes, one describing students’ attributed meanings to instructor-provided set-builder notation and the other describing students’ imputed meanings to their personally-created set diagrams to relate pairs of sets. 

This study explores how instructional interventions and teacher moves might support students’ learning of logic in mathematical contexts. We conducted an exploratory teaching experiment with a pair of undergraduate students to leverage set-based reasoning for proofs of conditional statements. The students initially displayed a lack of knowledge of contrapositive equivalence and converse independence in validating if a given proof-text proves a given theorem. However, they came to conceive of these logical principles as the teaching experiment progressed. We will discuss how our instructional interventions played a critical role in facilitating students’ joint reflection and modification of their reasoning about contrapositive equivalence and converse independence in reading proofs.