Beyond PEMDAS: Teaching Students to Perceive Algebraic Structure

Evidence shows that transforming expressions is a major stumbling block for many algebra students. Using Sfard's (1991) theory of reification, I highlight the important roles that the process of parsing and the notions of subexpression and structural template play in competent expression transformation. Based on these observations, I argue that one reason students struggle with expression transformation is the inattentiveness of traditional curricula to parsing, subexpressions, and structural templates. However, simply refocusing attention on these ignored aspects of algebra will not alone ensure that students avoid common pitfalls. After examining evidence that students are very prone to overgeneralize, I argue for a connectionist view of how people's minds work when they are learning algebra. Utilizing these additional insights, the instructional strategies I ultimately recommend are strategies that focus on structure, but in ways that will make structure a winning competitor for student attention

Strategies and performance of the CMS silicon tracker alignment during LHC Run 2

The strategies for and the performance of the CMS silicon tracking system alignment during the 2015–2018 data-taking period of the LHC are described. The alignment procedures during and after data taking are explained. Alignment scenarios are also derived for use in the simulation of the detector response. Systematic effects, related to intrinsic symmetries of the alignment task or to external constraints, are discussed and illustrated for different scenarios