The correct answer is option 'A': locating patterns of error and suggesting improvement. This approach is effective because it focuses on identifying recurring errors and providing guidance for improvement, rather than simply correcting every mistake or offering vague comments. Here's a detailed explanation of why this option is the most effective:

1. Understanding patterns of error:
- By analyzing the student's writing, teachers can identify common errors that students make. These patterns could include grammatical mistakes, punctuation errors, or issues with sentence structure or organization.
- Recognizing these patterns allows teachers to provide targeted feedback that addresses specific areas of weakness in students' writing.

2. Suggesting improvement:
- Once teachers have identified patterns of error, they can provide specific suggestions for improvement. This could include explaining grammar rules, offering alternative sentence structures, or providing examples of correct usage.
- By offering clear and constructive feedback, teachers can guide students towards making meaningful improvements in their writing.

3. Avoiding the correction of every error:
- Correcting every single error in a student's essay can be overwhelming and discouraging for the student. It may also give the impression that the teacher is more interested in pointing out mistakes than helping the student improve.
- Focusing on patterns of error allows teachers to prioritize the most significant issues and provide targeted feedback, rather than overwhelming students with an excessive amount of corrections.

4. Writing detailed comments in the margin:
- Writing detailed comments in the margin of a student's essay helps provide specific feedback on areas that need improvement.
- These comments should be clear, specific, and constructive, highlighting both strengths and weaknesses in the student's writing.
- By providing detailed comments, teachers can help students understand their mistakes and guide them towards making necessary improvements.

5. Offering encouraging and summary remarks:
- In addition to providing feedback on areas that need improvement, teachers should also offer encouraging remarks to motivate students and boost their confidence.
- Summary remarks can help students understand the overall strengths and weaknesses of their writing, allowing them to focus on specific areas for improvement.

In conclusion, locating patterns of error and suggesting improvement is an effective approach for teachers to respond to and correct students' writing. By understanding common errors, providing specific suggestions, and offering both constructive and encouraging feedback, teachers can help students enhance their writing skills effectively.