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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. 

This article offers the construct unitizing predicates to name mental actions important for students’ reasoning about logic. To unitize a predicate is to conceptualize (possibly complex or multipart) conditions as a single property that every example has or does not have, thereby partitioning a universal set into examples and nonexamples. This explains the cognitive work that supports students to unify various statements with the same logical form, which is conventionally represented by replacing parts of statements with logical variables p or P(x). Using data from a constructivist teaching experiment with two undergraduate students, we document barriers to unitizing predicates and demonstrate how this activity influences students’ ability to render mathematical statements and proofs as having the same logical structure. 

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.