Search for: All records

There are strong motivations to implement integrated STEAM activities that engage with key ideas in mathematics. In integrating mathematics with other STEM disciplines, however, epistemic tensions can emerge. Rather than attempting to suppress, avoid, or adjudicate these tensions, we propose a strategy of “epistemic rekeying,” in which epistemic tensions are offered as provocations for students to create playful and artistic responses. This approach takes epistemic tensions seriously and makes them accessible to young learners. We give the rationale for this approach and describe settings where students’ creativity suggested its potential to us. 

This article illustrates a pedagogical approach to integrating models and modeling in Geometry with mathematics teacher-learners (MTLs). It analyzes the work of MTLs in a course titled “Computers, Teaching, and Mathematical Visualization” (or “MathViz”), which is designed to engage MTLs in making mathematics together. They use a range of both physical and virtual models of 2-manifolds to formulate and investigate geometric conjectures of their own. 

Many block-based programming environments have proven to be effective at engaging novices in learning programming. However, most offer only restricted access to the outside world, limiting learners to commands and computing resources built in to the environment. Some allow learners to drag and drop files, connect to sensors and robots locally or issue HTTP requests. But in a world where most of the applications in our daily lives are distributed (i.e., their functionality depends on communicating with other computers or accessing resources and data on the internet), the limited support for beginners to envision and create such distributed programs is a lost opportunity. We argue that it is feasible to create environments with simple yet powerful abstractions that open up distributed computing and other widely-used but advanced computing concepts including networking, the Internet of Things, and cybersecurity to novices. The paper presents the architecture of and design decisions behind NetsBlox, a programming environment that supports these ideas. We show how NetsBlox expands opportunities for learning considerably: NetsBlox projects can access a wealth of online data and web services, and they can communicate with other projects. Moreover, the tool infrastructure enables young learners to collaborate with each other during program construction, whether they share their physical location or study remotely. Importantly, providing access to the wider world will also help counter widespread student perceptions that block-based environments are mere toys, and show that they are capable of creating compelling applications. In this way, NetsBlox offers an illuminating example of how tools can be designed to democratize access to powerful ideas in computing. 

This dissertation is organized around three articles concerned with ideologies and how they are reproduced or contested when preservice teachers model complex spatial phenomena. Each article is designed to stand alone, but when taken together, they trace how ideologies are reproduced within objects (ex. maps, models, and physical spaces) and through social and technical interactions (ex. talk between participants or talk between participants and an objects) as preservice teachers reason about spatial phenomena like racial segregation and urban heat island effect. 

STEM integration holds significant promise for supporting students in making connections among ideas and ways of thinking that might otherwise remain “siloed.” Nevertheless, activities that integrate disciplines can present challenges to learners. In particular, they can require students to shift epistemological framing, demands that can be overlooked by designers and facilitators. We analyze how students in an 8th grade mathematics classroom reasoned about circles, across math and coding activities. One student showed evidence of shifting fluently between different frames as facilitators had expected. The dramatic change in his contributions gauge the demands of the activities, as do the contributions of other students, who appeared to work within different frames. Our findings have relevance for the design and facilitation of integrated STEM learning environments to support students in navigating such frame-shifts.