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This NSF IUSE project incorporates instructional materials and techniques into introductory programming identified through educational psychology research as effective ways to improve student learning and retention. The research team has developed worked examples of problems that incorporate subgoal labels, which are explanations that describe the function of steps in the problem solution to the learner and highlight the problem solving process. Using subgoal labels within worked examples, which has been shown effective in other STEM fields, is intended to break down problem solving procedures into pieces that are small enough for novices to grasp. Experts, including instructors, teaching introductory level courses are often unable to explain the subgoal-level processes that they use in problem solving because they have automated much of the problem solving processes after many years of practice. This intervention had been tested in programming for a few hours of instruction and found effective. The current project expands upon that work. 

The explicit breaking of the axial symmetry by quantum fluctuations gives rise to the so-called axial anomaly. This phenomenon is solely responsible for the decay of the neutral pion π⁰into two photons (γγ), leading to its unusually short lifetime. We precisely measured the decay width Γ of the${\pi }^0\to \gamma \gamma$process. The differential cross sections for π⁰photoproduction at forward angles were measured on two targets, carbon-12 and silicon-28, yielding$\mathrm{\Gamma }\left({\pi }^0\to \gamma \gamma \right)=7.798\pm 0.056\left(\mathrm{stat}\mathrm{.}\right)\pm 0.109\left(\mathrm{syst}\mathrm{.}\right)\mathrm{ eV}$, where stat. denotes the statistical uncertainty and syst. the systematic uncertainty. We combined the results of this and an earlier experiment to generate a weighted average of$\mathrm{\Gamma }\left({\pi }^0\to \gamma \gamma \right)=7.802\pm 0.052\left(\mathrm{stat}\mathrm{.}\right)\pm 0.105\left(\mathrm{syst}\mathrm{.}\right)\mathrm{ eV}$. Our final result has a total uncertainty of 1.50% and confirms the prediction based on the chiral anomaly in quantum chromodynamics.