Exceptional Subitizing Patterns: Exploring Mathematical Abilities of Finnish Primary School Children with Piecewise Linear Regression

Abstract

Numerical processing competences such as the ability to enumerate small sets of dots and to compare the relative magnitudes between sets are diagnostic markers of young children’s emerging math abilities. In the FUnctional Numerical Assessment (FUNA) study, these abilities are assessed using several computer-assisted tasks, among which is a Dot Enumeration (DE) task where children determine the number of dots in a visual array. It seems that there is a natural threshold around 3 or 4 dots: below this threshold, it is possible to determine the correct number at a glance, known as subitizing; above the threshold, children must count the dots in some way. In this paper, we develop a piecewise linear regression model class for Exceptional Model Mining with various quality measures discovering subgroups of children whose subitizing curves exhibit atypical patterns. The dataset does not follow the conventional data mining representation where each individual is described with a tuple of attribute values. Rather, for each task, students perform multiple items, one after the other, taken from a larger set of items, and not necessarily in the same order. Hence, we discuss a manner (tailored to the dataset at hand) to transform this item-performance data into the flat-table form that the typical data mining task expects. Domain experts confirm that our experiments evidently demonstrate how children’s subitizing performance and counting skills are related to math abilities. Our findings provide opportunity for further development of assessment tools and intervention programs.