I have opted to answer this question in combination with Question 11, as they are related.
There is certainly a perception that certain elementary schools are more favorable than others with regard to parental involvement, PTO financing, specific teaching styles, and other factors. Conversation with parents bears this out, with stories about discouragement form principals and few PTO members.
The perception that parents have of a school is determined by several factors, including neighborhood and family demographics, particular teachers at the school, the individual principal, and any special programs that the school may have. This has resulted in some schools being overpopulated, while others are under populated. Districts have been redrawn is a way that borders on defying common sense.
One way to make the schools more equitable would be to offer attractive programs at all the schools. One example would be the use of a Montessori-like or developmental education option within the school. Another might be to expand the linkage with Tufts to all schools.
There are also several ways that schools can be differentiated while providing equitable education to all students. This is only possible with a true choice program that allows parents to choose amongst the four schools on an even basis.
This could be accomplished by narrowing the districts to proximity zones, eliminating districting altogether, or reserving a substantial percentage of out of district seats.
Another approach to make sure that each school is equitable is to monitor differences in test results and to seek out, listen to, and act upon anecdotal information from parents, students and staff about what is perceived to be good or bad at each of the schools.
The district should also stress city-wide fund raising and earmark outside grants to those schools with a less affluent parent group.
Finally an interesting approach would be to require teachers to spend one year out of every five or six years at another school to learn different approaches, and to bring fresh insights to the a school.