Sorting Out Algorithms: What Makes One Better than Another?

For many years, beginning computer science students have been asked the seemingly simple question: what makes one algorithm better than another? Usually, this concept of "best-ness" is introduced with the many algorithms that are used to sort data. Thus, students are overwhelmed by the intricacies of sorting while simultaneously trying to understand one of the greatest questions in computer science. In this work we take inspiration from embodied cognition and describe a new, constructionist curriculum for approaching algorithmic efficiency. In order to help students construct understandings of both sorting algorithms and algorithmic efficiency, we present a curriculum that focuses around participatory simulations (PartSims) where students "play as" datapoints and experience sorting algorithms from an entirely different perspective. Instead of first experiencing the usual top-down approach to sorting where datapoints are manipulated by an "observer," each student follows a simple set of rules which, collectively, end in an emergent sorting algorithm. In this way, instead of talking in the abstract about the different pros and cons of sorting algorithms, students have different physical experiences across the different algorithms. With this embodied, grounded experience, students then construct for themselves metrics for comparing the different algorithms by evaluating the differences in their physical experiences. This two-week curriculum is targeted towards beginning computer science students (high-school or collegiate level) and utilizes the Parallax hackable Electronic Conference Badge and NetLogo to track the students experience in the PartSims throughout the curriculum.