Quantitative studies on technology integration often examined general quantity of classroom technology use or teacher-reported accounts of integration practices. There is a current need for a measurement tool that links students' technology use and cognitive engagement, which will allow researchers to better illustrate how technology is woven into the learning process. The purpose of this study is to develop a scale to measure how students use technology for different cognitive tasks, following theoretical conceptions from Bloom's Digital Taxonomy and Multiple-Document Task-based Relevance Assessment and Content Extraction. We employed Confirmatory Factor Analysis, as well as both classical test theory and item response theory over three studies to validate our newly created scale. The new Cognitive Engagement with Technology (CET) scale showed good psychometric properties, item functioning, and construct validity. The CET scale can be used to triangulate students' technology use patterns with other research methods. It can also help extend past findings by taking into account how students use technology to aid in the cognitive processes of learning.