Consider a typical examination question: “What are the biological kingdoms?” The expected answer is: “monera, protista, fungi, plantae, animalia.” What a learner needs in order to answer the question is mere familiarity with the terminology and correct spelling. He doesn’t have to understand the meanings of the words. A university graduate who vaguely remembers the expressions ‘laws of motion’, ‘gravity’, ‘acceleration’, and ‘mass’ is familiar with the theory of gravity and motion, but may not understand it. Familiarity with terminologies, taxonomies, or facts as unconnected trivia does not count as understanding.

Mechanically applying a set of concepts and procedures to solve textbook problems involves superficial understanding. Given the initial position and velocity of a canon ball, calculating its terminal position needs only a rudimentary understanding of the theory. Likewise, learners can successfully calculate the positions of planets in the solar system without necessarily understanding the distinction between the concepts of rotation and revolution. The vocabulary of Freudian psycho-analysis can be applied to ‘analyze’ a short story without any understanding of the human mind.

In contrast, applying the concepts and propositions of knowledge to novel and unfamiliar problems calls for conceptual understanding. Solving textbook problems in geometry does not need a conceptual understanding of points, lines, straight lines, and parallel lines. However, proving that a circle is a regular polygon in certain discrete geometries but not in Euclidean geometry does call for a conceptual understanding of the relation between points and lines.

Similarly, teasing apart the different meanings of ‘democracy’ in terms of voting, selection of representatives, self-government, and ‘swaraj’, and figuring out the differences in their consequences, calls for conceptual understanding. It calls for noticing similarities and distinctions, perceiving analogies, making connections, and unifying apparently unrelated ideas. These processes lead to a holistic grasp of the concepts, a feel for what they mean and of how they are connected to one another, and a sense of their relative significance in the larger picture.

Deeper than even conceptual understanding is critical understanding, the understanding of the evidence and arguments for and against a given concept or proposition. Critical understanding calls for an exploration of questions like: “Why should we believe that the earth revolves around the sun?” and “Why should we believe that there was a time when humans lived in nomadic bands, or in tribes of hunter gatherers?” Critically evaluating knowledge claims requires deep understanding at this level. Understanding at the deepest level is the result of a process of critical thinking, inquiry, and integration. It involves developing a sense of plausibility and of what is reasonable, a sense of relevance and of proportion, all leading to the ability to gauge or judge the acceptability of a claim within the norms and criteria that experts use.