Proceedings of the Annual Meeting of the Cognitive Science Society

An important aspect of mathematical and computational thinking is algorithmic thinking––the analysis of systems, algorithms, and natural processes. A fundamental skill in algorithmic thinking is estimating the growth of functions with increasing input size. In this study, we asked 178 participants to estimate values of seven common functions in algorithmic analysis [log(n), sqrt(n), nlog(n), n^2, n^3, 2^n, n!] to understand their intuitive perception of their growth. Their estimates were fit against the actual values for all functions. Participants showed a linearization bias: sublinear functions were best fit by a linear function, and superlinear functions were best fit by a cubic (i.e., polynomial) function, even those that grow much faster (e.g., n!). In addition, participants estimated logarithmic functions least accurately. These results provide insight into how people perceive the growth of functions and set the stage for future studies of how to best improve people's reasoning about functions more generally.