This paper discusses teachers' critical knowledge needs for assessing the pedagogical potential of educational apps and similar software. A central point is that such software often have clearly identifiable features and functions that either support or hinder learning, depending on how they are implemented in the digital medium. Because these types of features, such as multimodality or automated feedback, are unique to digital technologies (they do not appear in traditional or "analogue" education material such as textbooks) I refer to them as the "Integral Digital Values" (IDV). Here, different IDV are discussed and sorted under three main headings: (i) Representation - how the software deals with representing the learning content in different modalities (i.e. what the student can see on screen in terms of visual, verbal, auditory information), (ii) Interactivity - how the student-software interaction works in terms of generating meaningful actions and feedback (i.e. what the student can or cannot do with the content), and (iii) Social Agency - how the software presents the student's social position by enabling and promoting different roles or approaches to the learning tasks (e.g. by using digital characters in different student/peer/mentor roles). Authentic examples of using different software applications in the classroom illustrate how an understanding of IDV can help identifying both pedagogical benefits and pitfalls in the design of educational software. Future research may address the role of IDV for existing evaluation rubrics and its incorporation into related theoretical frameworks, such as teachers’ TPACK.