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Calculus has long been known as a “gateway course” to STEM fields in postsecondary education. To address this issue, researchers in the Math Department at Mountain State University (pseudonym) designed a model of complementary instruction that features peer-facilitated workshops where Calculus I students work in groups on inquiry-oriented, groupworthy tasks. The purpose of this multiple-case study is to seek answers to the question, "How do undergraduate Calculus I students experience and navigate their learning of calculus in the parallel spaces of coursework and inquiry-oriented complementary instruction?" The findings of one case study are presented here and include characterizations of the different forms of agentive participation afforded to students in each of the two spaces, as well as their complementary nature relative to learning calculus with understanding. Implications for dismantling the persistent barriers imposed by calculus on access to postsecondary STEM fields are also discussed. 

An Educational CAD Model Library (CAD Library) is being developed by collaborating educational associations affiliated with the National Technology Leadership Summit coalition. The CAD Library’s Curators’ Council has developed descriptive metadata fields that will be associated with each educational object published in the library. These fields are designed to facilitate search and discovery of objects by teachers who are increasingly well positioned to use these objects in their instruction due to the increasing presence of school-based makerspaces and the 3D printers, digital die cutters, and other fabrication tools. The publication of these metadata standards makes them available to the members of the educational associations participating in the development of the CAD Library and to other relevant stakeholders for feedback to inform ongoing revisions. 

This work seeks to understand the emergent nature of mathematical activity mediated by learners’ engagement with multiple artifacts. We explored the problem solving of two learners as they aimed to make sense of fraction division by coordinating meanings across two artifacts, one being a physical manipulative and the other a written expression of the standard algorithm. In addressing the question, “How do learners make sense of and coordinate meanings across multiple representations of mathematical ideas?” we took an enactivist perspective and used tools of semiotics to analyze the ways they navigated the dissonance that arose as they sought to achieve harmony in meanings across multiple representations of ideas. Our findings reveal the value of such tool-mediated engagement as well as the complexity of problem solving more broadly. Implications for learning mathematics with multiple artifacts are discussed.