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Abstract The Reading and Appreciating Mathematical Proofs (RAMP) project seeks to provide novel resources for teaching undergraduate introduction to proof courses centered around reading activities. These reading activities include (1) reading rich proofs to learn new mathematics through proofs as well as to learn how to read proofs for understanding and (2) reading mathematician stories to humanize proving and to legitimize challenge and struggle. One of the guiding analogies of the project is thinking about learning proof-based mathematics like learning a genre of literature. We want students to read interesting proofs so they can appreciate what is exciting about the genre and how they can engage with it. Proofs were selected by eight professors in mathematics who as curriculum co-authors collected intriguing mathematical results and added stories of their experience becoming mathematicians. As mathematicians of colour and/or women mathematicians, these co-authors speak to the challenges they faced in their mathematical history, how they overcame these challenges, and the key role mentors and community have played in that process. These novel opportunities to learn to read and read to learn in the proof-based context hold promise for supporting student learning in new ways. In this commentary, we share how we have sought to humanize proof-based mathematics both in the reading materials and in our classroom implementation thereof.  

Because the master narratives about mathematics in the US often play an exclusionary role in students’ educational experiences, educators have sought to integrate counternarratives into instruction that might disrupt these effects. As part of a larger project to develop a research-informed curriculum for undergraduate introduction to proof courses, we gathered author stories from a diverse set of mathematicians for students to read and reflect upon. To study student responses to these author stories, we synthesized a framework of the master narrative of mathematics in the US and identified how the author stories countered elements of this narrative. We then analyzed 80 student reflections from one introduction to proof course to identify whether and how students either endorsed or countered the elements of the master narrative. Our findings point to a positive, yet modest capacity for these stories as counternarratives. 

This research explores how undergraduate students interpret mathematical symbols in new contexts when reading diverse mathematical texts across various subareas. Collaborating with experts in mathematical sciences, we collected proof-texts aligned with their specialized areas. These proof-texts were presented to undergraduate transition-to-proof students who had studied logic for mathematical proof while their experience of proofs in advanced mathematics topics was limited. Task-based interviews were conducted outside their regular classroom. This paper examined student encounters with curly bracket symbols in a graph theory context. Our findings suggest the nuanced relationship students have with symbols in proof- texts. While possessing familiarity with certain symbols, this pre-existing student knowledge could influence their accessibility to symbols introduced in unfamiliar contexts. 

In mathematics, counter narratives can be used to fight the dominant narrative of who is good at mathematics and who can succeed in mathematics. Eight mathematicians were recruited to co-author a larger NSF project (RAMP). In part, they were asked to create author stories for an undergraduate audience. In this article, we use narrative analysis to present five polarities identified in the author stories. We present various quotations from the mathematicians’ author stories to highlight their experiences with home and school life, view of what mathematics is, experiences in growth in mathematics, with collaboration, and their feelings of community in mathematics. The telling of these experiences contributes towards rehumanizing mathematics and rewriting the narrative of who is good at and who can succeed in mathematics. 

In many advanced mathematics courses, comprehending theorems and proofs is an essential activity for both students and mathematicians. Such activity requires readers to draw on relevant meanings for the concepts involved; however, the ways that concept meaning may shape comprehension activity is currently undertheorized. In this paper, we share a study of student activity as they work to comprehend the First Isomorphism Theorem and its proof. We analyze, using an onto-semiotic lens, the ways that students’ meanings for quotient group both support and constrain their comprehension activity. Furthermore, we suggest that the relationship between understanding concepts and proof comprehension can be reflexive: understanding of concepts not only influences comprehension activity, but engaging with theorems and proofs can serve to support students in generating more sophisticated understanding of the concepts involved. 

In recent years, professional organizations in the United States have suggested undergraduate mathematics shift away from pure lecture format. Transitioning to a student-centered class is a complex instructional undertaking especially in the proof-based context. In this paper, we share lessons learned from a design-based research project centering instructional elements as objects of design. We focus on how three high leverage teaching practices (HLTP; established in the K-12 literature) can be adapted to the proof context to promote student engagement in authentic proof activity with attention to issues of access and equity of participation. In general, we found that HLTPs translated well to the proof setting, but required increased attention to navigating between formal and informal mathematics, developing precision around mathematical objects, supporting competencies beyond formal proof construction, and structuring group work. We position this paper as complementary to existing research on instructional innovation by focusing not on task trajectories, but on concrete teaching practices that can support successful adaption of student-centered approaches.