Efficient egg drop contests: How middle school girls think about algorithmic efficiency

In this basic interpretative qualitative study, middle school girls with no formal experience in algorithmic reasoning, abstraction, or algebra were interviewed individually in order to help understand and explain how they think about algorithmic efficiency. A contextually relevant problem (determining the maximum height an "egg-drop contraption" could be dropped without breaking) was described to the students who were then asked 1) to come up with the most efficient solution they could to the problem while describing their thinking for the interviewer; and 2) to determine, from a choice of three solutions proposed by the interviewer, which is the most efficient. Students were found to have varying degrees of success in solving the problem or picking the most efficient solution. The most successful recognized the salient features of the problem and used them to generate possible solutions. The least successful were unable to understand the abstractions inherent in the problem. Students recognized that the most efficient of three proposed solutions may depend on the instance of the problem (where the contraption actually failed). They also understood that there was a "best" solution in general, and chose the solution that had the best worst-case scenario. Compared to college students studied previously using similar algorithmic reasoning problems, middle school girls appeared to perform similarly. They were able to demonstrate sophisticated computational thinking skills while suffering from some of the same algorithmic thinking limitations as older students.