Abstract:

Understanding the heterogeneous pathways that students take through content to gain mastery of a topic or skill is a longstanding goal of the educational enterprise. Mapping these differential learning pathways has been discussed at least as early as 500 BCE (FN) with many solutions to the problem being suggested. In the modern era learning paths have been derived through a wide range of methods including expert opinion (Phillips & Wong, 2010), error analysis (Brown, Quinn, & others, 2006), skill analysis (Fischer & Farrar, 1987), sequential pattern analysis (Cen, Koedinger, & Junker, 2006) and Q-matrices (Barnes, Bitzer, & Vouk, 2005).

Learning pathways are an essential tool in standards-based or competency-based education and are a necessary component of any automated personalization system such as intelligent tutoring systems. A known pathway allows student progress to be estimated, students to be differentiated based on progression and specific interventions to be designed to aid students at different stages or branches of the path. This mapping enterprise has been greatly aided by the advent of the internet and mobile computing. The ease with which data can be collected within educational platforms has ballooned allowing for greater granularity in mapping learning paths. For example, large-scale mapping efforts using online games, such as those of Andersen. et al. (2013), have provided insight into differences across nations and education systems.

Building on the mapping techniques of both Q-matrices and error analysis the following research classifies students according to the error patterns they produce as they answer a sequence of questions. However, in addition to considering the sequence, we also consider how different sequences impact students differentially. We have developed a method (transitive item networks) based on probabilistic longitudinal network analysis (Snijders, Van de Bunt, & Steglich, 2010) to extract preferred question order from a set of questions that are randomly given to students. In this way, we can make visible the structure of the underlying knowledge required to master the content. For example, if question A contains required knowledge to answer question B, then receiving question A before B will more often lead to students being correct than receiving question B before A. In this paper the theory behind the analysis is explained. It is then applied to both a simulated data set from an online academic question and answer platform, Brainly, in which students ask and answer each others’ questions. Students receive questions randomly within this system and the hope is that the derived question pathways will be able to aid suggesting which question a student should answer next, or which question they might be on the cusp of asking.

Keywords:

Learning pathways, item networks, learning progression, stochastic network analysis, online education.