The correct answer is A. Is.

1. Is: This option is correct because "The teacher, as well as his students" is a phrase where "the teacher" is the primary subject. The phrase "as well as his students" does not affect the number of the main subject, which is singular ("the teacher"). Therefore, the verb should be singular, "is."

2. Have been: This option is incorrect because "have been" is a plural form and would not agree with the singular subject "the teacher."

3. Are: This option is incorrect because it is a plural form. Since the main subject is singular ("the teacher"), the verb should also be singular.

4. Were: This option is incorrect because it is the past tense plural form. The sentence is referring to the present continuous action, so the present tense singular "is" is appropriate.

Summary:

- A. Is is the correct choice because it matches the singular subject "the teacher" and correctly reflects the present continuous action described in the sentence.