Final answer:
Students who know one definition for a word or use it in one context have contextual knowledge, which can be expanded through cognitive understanding and various methods such as the semantic way, systemic way, and knowledge by acquaintance.
Step-by-step explanation:
Students who know one definition for a word or can use the word in one context are said to have contextual knowledge. This type of knowledge involves understanding a word based on a single, often surface-level, definition or use-case, similar to what might be found in a dictionary. For a more profound and versatile comprehension of a word, it is necessary to explore beyond this limited view, engaging with the word in various contexts and developing a sense of how its usage and meaning can change depending on the situation. Cognitive understanding, in contrast, concerns the ability to use language within the realm of statements that are true or potentially true or false, which involves a deeper engagement with the nature of knowledge itself.
Navigating the complexity of language and knowledge, one can consider different methods of analysis, like the semantic way of knowing, which emphasizes learning the meaning of words through definitions; the systemic way, centered on understanding systems of words or symbols, their relationships, and operational rules within domains like mathematics and geometry; and knowledge by acquaintance, which comes through direct experience and perception, allowing an individual to be directly aware of, and thus know, something.