Showing your work, especially in fields such as mathematics, science, engineering, or any problem-solving domain, is important for several reasons:

1. Clarifies Thinking: It helps you clarify your own thought process and ensures you understand each step of your solution. By laying out your reasoning, you can more easily identify any errors or gaps in your logic.
2. Facilitates Communication: Showing your work allows others to follow your thought process, making it easier to communicate complex ideas or solutions. This is crucial in collaborative environments where understanding each other's work is essential for progress.
3. Demonstrates Understanding: When you show your work, you demonstrate not just that you found an answer, but that you understand how to arrive at that answer. This is particularly important in educational settings, where the goal is not just to get the right answer but to understand the underlying concepts.
4. Enables Error Checking: If you make a mistake, showing your work makes it easier to go back, review your steps, and find where you went wrong. This can be a powerful learning tool, helping you to avoid similar mistakes in the future.
5. Provides a Detailed Record: By documenting your process, you create a record that you or others can refer back to. This can be invaluable for long-term projects or when you need to recall how a particular result was obtained.
6. Supports Rigorous Evaluation: In academic and professional settings, showing your work allows instructors, peers, or colleagues to rigorously evaluate your approach. This evaluation is critical not just for grading or assessment, but for ensuring that solutions are valid, reliable, and based on sound reasoning.
7. Encourages Critical Thinking: The process of showing your work often requires you to critically examine each step of your reasoning, promoting a deeper engagement with the material and encouraging a more thoughtful approach to problem-solving.
8. Facilitates Learning and Teaching: For learners, seeing the detailed steps in solving a problem can aid in understanding and mastering new concepts. For teachers, detailed work from students provides insight into their understanding and misconceptions, guiding further instruction.

In summary, showing your work is a crucial aspect of problem-solving and communication, enabling clearer thinking, facilitating collaboration, ensuring a comprehensive understanding, and promoting rigorous evaluation and learning.