Thin slices of head movements during problem solving reveal level of difficulty

This paper reports on the computational analysis of thin slices of video fragments showing children that solve either easy or hard mathematical puzzles. The objective of the analysis is to determine if head movements reveal whether the children consider the puzzle to be easy or hard. Our analysis method combines a facial-expression extraction method with a nonparametric classifier. Training and evaluating the classifier in a leaving-one-out cross-validation procedure on extracted head movements, we obtained a 71% correct classification rate. Children engaged in solving mathematical puzzles tend to make head movements in a prevailing orientation that depends on the experienced level of difficulty of the puzzles, i.e., vertically for easy puzzles and diagonally for hard puzzles. We conclude that (1) computational analysis methods lead to the identification of hitherto unnoticed nonverbal behaviors that reflect the perceived difficulty of mathematical puzzles, and (2) computational analysis methods can be employed in automatic tutoring systems that automatically estimate the experienced difficulty of the problems presented.