Is there some kind of consensus on the determinant factors of education achievement? There is quite a bit of literature on the economics of education. One of the most debated aspects of it arises when estimating the achievement of the student (usually in the form of standardized test scores). Which are the most relevant inputs? Which are not?

A few usual suspects are:


Parent's education
Teacher "quality", which is by itself an issue. Sometimes it is represented by years of experience, majors acquired, certification, test scores, etc. 
School inputs
Peer effects
Teacher absenteeism
The list goes on...
There is no solid consensus on the inputs that go into educational achievement or attainment. The list of variables is vast and varied. 

One of the most common applications of this is attempting to calculate the returns to education - i.e. the average increase in income that results from one additional year of schooling.

I myself have performed research on this topic in grad school, and a good reference is:


Bronars, Stephen G., and Gerald S. Oettinger. “Estimates of the return to schooling and ability: Evidence from sibling data.” Labour Economics 13.1 (2006) : 19-34. http://www.sciencedirect.com/science/article/pii/S0927537104000983


In my research there were many variables that were statistically significant:


age
gender
race
marital status
union membership
year at time of measurement
number of siblings
religious beliefs
opinion on sex ed in schools
opinion on national educational spending
opinion on education as catalyst for racial/class divides


Most researchers in this area agree that parental involvement is one of the main determining factors for a child's educational outcome. The difficulty is in quantifying this and other subjective data such as teacher quality and peer effects. This is one of the main issues in the field now - figuring out how to statistically measure non-numerical variables. The opinion variables I mentioned above are from national social surveys and are an attempt to quantify these subjective things. Specifically, my data came from the General Social Survey (GSS) available here: http://www3.norc.org/GSS+Website/