In this theme, the authors explore potentially foundational research tools which might aid future mathematics curriculum reform efforts. From these chapters, we highlight several key considerations: (1) Considering contexts as systems can make important choices stand out; (2) The integration of teachers into efforts is a factor in success those efforts; (3) Enhancing communication across commun...

We derive an analytic expression for the mechanical pressure of a generic one-dimensional model confined active Brownian particles (ABPs) that is valid all values Peclet number Pe and confining scenarios. Our reproduces known scaling bulk with Pe^2 while in strong confinement scales Pe. results are very well reproduced by simulations ABPs 2D. use formula to calculate both work performed engine ...