Advances in information and communication technologies (ICT) coupled with artificial intelligence have made computer programming skills indispensable for IT majors and for an increasing number of other science, technology, engineering, and mathematics (STEM) disciplines. Like any hands-on skill, mastering computer programming requires dedicated time, patience, focus, and persistent effort. Understanding students' learning strategies as they engage in computer programming activities can reduce attrition and lay a solid foundation for a successful career in IT/STEM disciplines. This paper focuses on developing the cognitive programming engagement (CPE) scale, which builds on existing cognitive engagement measures. Self-reported data from undergraduate IT students who are learning computer programming show that CPE supports four-dimensional learning strategies: memorization, practice, analysis, and visualization, which aligns with the levels of Bloom's Taxonomy. The new scale supports confirmatory, discriminant, and predictive validity and tests on programming self-efficacy and coding grit with acceptable predictive validity. IT/STEM educators can use the scale to assess and evaluate students' learning and improve their teaching strategies.