Going for broke: a multiple case study of brokerage in education

Although the central role of educational intermediaries that can connect research and practice is increasingly appreciated, our present understanding of their motivations, products, and processes is inadequate. In response, this multiple-case study asks how and why three large-scale intermediaries—Edutopia, the Marshall Memo, and Usable Knowledge—are engaging in brokerage activities, and compares the features of the knowledge they seek to share and mobilize. These entities were deliberately chosen and anticipated to reveal diversity. Multiple data sources were analyzed based primarily upon Ward’s knowledge mobilization framework. These entities contrasted widely, especially in relation to core knowledge dimensions, enabling us to identify two distinct brokerage types. To conclude, theoretical (how to conceptualize brokerage) and practical (how to foster interactive knowledge exchange) implications are presented. This study also reveals certain innovative mobilization approaches, including skillful use of social media and the production of videos depicting how and why to adopt particular strategies

Complexity-optimal and Parameter-free First-order Methods for Finding Stationary Points of Composite Optimization Problems

This paper develops and analyzes an accelerated proximal descent method for finding stationary points of nonconvex composite optimization problems. The objective function is of the form $f+h$ where $h$ is a proper closed convex function, $f$ is a differentiable function on the domain of $h$, and $\nabla f$ is Lipschitz continuous on the domain of $h$. The main advantage of this method is that it is "parameter-free" in the sense that it does not require knowledge of the Lipschitz constant of $\nabla f$ or of any global topological properties of $f$. It is shown that the proposed method can obtain an $\varepsilon$-approximate stationary point with iteration complexity bounds that are optimal, up to logarithmic terms over $\varepsilon$, in both the convex and nonconvex settings. Some discussion is also given about how the proposed method can be leveraged in other existing optimization frameworks, such as min-max smoothing and penalty frameworks for constrained programming, to create more specialized parameter-free methods. Finally, numerical experiments are presented to support the practical viability of the method