Understanding how a concept works means having a deep comprehension of the underlying principles and mechanisms that govern it. Being able to solve a problem, on the other hand, refers to the ability to apply that understanding in a practical way to find a specific solution. In other words, understanding is the foundation for problem-solving.
Yes, it is possible to solve a problem without fully understanding the concept behind it. This is often seen in rote learning, where a person memorizes a set of steps to solve a problem without truly understanding the rationale behind those steps. However, this approach may limit the person's ability to apply the concept in different scenarios or to adapt to new problems.
Understanding the underlying principles is crucial in problem-solving. It allows for a deeper understanding of the problem and the ability to apply the concept in various situations. It also enables a person to identify and troubleshoot errors or mistakes in the problem-solving process.
Both understanding how something works and being able to solve a problem are valuable skills. However, understanding the principles behind a concept can be more valuable in the long run as it provides a strong foundation for problem-solving and the ability to adapt to new situations.
To improve understanding of a concept, one can engage in active learning methods such as summarizing, explaining it to others, and applying it in different contexts. Asking questions and seeking clarification can also help in gaining a deeper understanding of a concept.