If you are observing a student, it would be good to get a sense of the student. Look at his or her academic performance and written evaluations. If you have the ability you should also look at his or her test scores. It would also be good to get the opinion of past teachers and others who have had interaction with the student in view.

When you are observing the student, you should try to form an independent opinion. Do not allow what has been stated by others to give you a conclusion. This is an important point. Also write down your observations. Look for things like, body language, habits, and attention span. Also see how the student responds to people around him or her. Also keep a note of how he or she interacts with what the teacher is doing. In other words, does the student respond to visual learn or auditory learning better?

Finally, after the observation, you might want to note the following. First, what the student's response after the class? Is he or she happy, relieved, or something else? Also you might want to think of ways in which to enhance the student's learning. Good observations should have an action plan.

Basing this answer on the current trend of Differentiated Instruction as a way to help students succeed, these are the things that should be taken into consideration before, during, and after an observation of student behavior:

Before

Look for the student records. Do they show any special consideration? Most importantly, was that consideration met in a timely manner? What is the child's background? What number child does he or she make in the family (first born, middle child, youngest, twin?) Has any behavior changed recently? Are there observable behaviors that denote a significant change in the student's daily routine?

Check for student interests inventories (which the student has filled out), or any completed forms given by the teacher to differentiate instruction: What is the child's developmental level? Is the student meeting his or her lexile level? What is the student learning style and is the teacher using strategies for that student's unique needs?

During:

What interventions is the teacher using as a way to show consequences or feedback for the student's behavior? Are good actions being rewarded with feedback? How long does it take the teacher to provide a consequence? What is the first reaction of the student to consequences or feedback?

It is very important that you can determine whether the student is working at his or her academic level. If not, the behavior of a student can be greatly affected. Check for the individual academic plan for the student and what are the goals that the teacher and the student have established together.

After:

What type of consequences or feedback works best for the student's behavior? Which activities helped the student achieve success at his or her level of developmental prime? How was assessment used to differentiate the instruction of the student? Was the student given the chance to participate in his or her own goal plan? Was there a change from the beginning of the intervention to now?

The goal of observing behaviors is to detect whether the student can operate at his or her developmental level in a way that success can help the student move to a zone of proximal development. A great part of student behavior comes hand in hand with academic achievement. This is the reason why it is most important to observe and analyze behavior under the scope of academics because the school environment is he home of the student for a longer period of their social time than the home itself.  In all, it is the best way to quantify the effects of an intervention.