# Network analyses of student engagement with on-line textbook problems

## TL;DR

This paper introduces a novel network and principal component analysis approach to categorize student behaviors during online physics problem solving, revealing distinct behavioral structures and session groups.

## Contribution

The paper develops a new method combining network and PCA analysis of server logs to identify behavioral components and session groups in online textbook problem solving.

## Key findings

- Identified five behavioral components: Complexity, Linear Length, Navigation, Mutuality, Erraticism.
- Classified problem solving sessions into three main groups based on complexity.
- Discovered ten distinct behavioral structures corresponding to Schonfeld's phases.

## Abstract

Problem solving in physics and mathematics have been characterized in terms of five phases by Schonfeld and these have previously been used to describe also online and blended behavior. We argue that expanding the use of server logs to make detailed categorizations of student actions can help increase knowledge about how students solve problems. We present a novel approach for analyzing server logs that relies on network analysis and principal component analysis. We use the approach to analyze student interactions with an online textbook that features physics problems. We find five 'components of behavioral structure': Complexity, Linear Length, Navigation, Mutuality, and Erraticism. Further, we find that problem solving sessions can be divided into three over-arching groups that differ in their Complexity and further into ten clusters that also differ on the other components. Analyzing typical sessions in each cluster, we find ten different behavioral structures,which we describe in terms of Schonfeld's phases. We suggest that further research integrates this approach with other methodological approaches to get a fuller picture of how learning strategies are employed by students in settings with online features.