FIXME //These are raw notes for an eventual wiki page. Please return later.// There are a number of aspects of problem-solving that upper-division students need to be taught explicitly: * How to break up a complicated problem into smaller pieces. See the [[..:sequences:emsequence:pieces|Pieces Link]] or the {{whitepapers:problemsolving:pieces.pdf|Pieces PDF}} * Using geometric and [[..:harmonic:start|harmonic]] reasoning. Students who go fluidly back and forth between algebraic symbols and a problem's geometry are referred to as thinking "harmonically". * Recognizing what is [[..:variables:start|variable vs. constant]] throughout a problem, including during integration. * Engaging in [[..:reflection:start|reflection]] such as doing dimensional analysis, thinking about the meaning of their answer, and thinking about limiting cases.