This study proposes a software system for determining gaze patterns in on-screen testing. The system applies machine learning techniques to eye-movement data obtained from an eye-tracking device to categorize students according to their gaze behavior pattern while solving an on-screen test. These patterns are determined by converting eye movement coordinates into a sequence of regions of interest. The proposed software system extracts features from the sequence and performs clustering that groups students by their gaze pattern. To determine gaze patterns, the system contains components for communicating with an eye-tracking device, collecting and preprocessing students' gaze data, and visualizing data using different presentation methods. This study presents a methodology to determine gaze patterns and the implementation details of the proposed software. The research was evaluated by determining the gaze patterns of 51 undergraduate students who took a general knowledge test containing 20 questions. This study aims to provide a software infrastructure that can use students' gaze patterns as an additional indicator of their reading behaviors and their processing attention or difficulty, among other factors.