My definition is grounded in three assumptions about learning. First, learning can be inert. Whithead North, introduced this term in to describe the knowledge that can be expressed by learners, but they have no idea what it means or how it should be interpreted or applied. In my experience as a science and math teacher (and also a student in these fields), there are some in schools who believe that “finding the roots of quadratic equations” is a useful thing to teach. I maintain that is inert knowledge unless the student can recognize quadratic shapes (on paper, screen, and physical objects) and unless they can recognize when it is necessary to find the roots.
Second, learning comprises both “things” we can observe and “things” we cannot observe. Some of what we think is an observation of learning (e.g. answering questions on a test) may not be valid and reliable measures. The more types of methods educators deploy in observing learning, the more likely they are to observe learning. There are also many things that are relevant to learning that cannot be observed unless we look very carefully and ask the correct questions.
Third, the opposite of inert learning is deeper learning, and deeper learning is a multidimensional phenomenon. What exactly these dimensions are, how they were derived and developed, and their existence is open to debate, but or my operational definition of deeper learning is based on results that is usable, flexible, questioned, and improved. Further, it is grounded in autonomy; the learner perceives themselves to be able to use it, they actually can use it, and they feel they are positioned to use it.