Here are some simple proposals which would make Monteverde Vecchio a more liveable neighborhood. Many have to do with automobiles and the damage they have done and continue to do to our cites, but others are more generally about public space and civic behavior.
Via Carini isn't really too far from the centro storico of Rome but getting there can be an oddysey.
On foot: The walk down the steps to Via Garibaldi can be pleasant but it is not short. By Porta San Pancrazio it means risking ones life crossing traffic, walking in the middle of the street past illegally parked cars. If you walk down Via Dandolo to catch the tram even the sidewalk has been taken over by cars now.
By bike: it's a nice ride down the hill, but getting up is another story.
By public transportation: The wait for the 75/44/or 870 can last close to an hour, far more than the time needed to reach the center on foot. What's worse, there is no schedule to help you decide whether or not to wait. The routes themselves are long and slow, The 870 regularly gets stuck at the Bambin Gesu' due to autos parked illegally everywhere within 250 meters of the hospital. The others get stuck on entering Viale Trastevere or crossing the Lungotevere when the intersection becomes clogged with cars ignoring the red lights. Finally, the routes are quite limited, requiring a change to the tram (not even at the same stop) and subsequent wait to get to Largo Argentina, the Pantheon, or anywhere near Piazza Navona.
By car: perhaps the easiest option, it is no slower than the bus once you are aboard but without the uncertain wait, discomfort and restricted route. As long as parking is cheap in the blue zone and tolerated almost everywhere else use of private cars is encouraged.
By scooter. Hands down the easiest, if not safest or cleanest, way to get to the center and back. But not for everyone, children and elderly for example.
Without recourse to major public works like escalators or funiculars, great improvement would be possible by acting simultaneously on two fronts: penalizing private traffic and improving public transit.
a. Penalizing use of the private auto. It would be enough to actually enforce laws on the books, fining and towing cars parked illegally or blocking traffic crossings. The incentive to use one's car would disappear overnight as its cost skyrocketed.
b. Respect the schedules of the existing bus routes first of all, and post them clearly. Then gradually increase their frequency and rationalize the routes. The 75 should start at Largo Oriani with a real capolinea, connected by stairway to Stazione Quattro Venti below. The 870 and 44 just need to run on reasonable, reliable schedules.
c. Some new ideas to consider. Italo Insolera suggests an electric minibus that would cruise the neighborhood and make stops at Villa Pamphillj. This could connect Trastevere with the Villa too. A "scala mobile" from Fratelli Bandiera to Piazza Ippolito Nievo would make the 8 tram much more accessible. Another bus could take Via delle Fornaci, connecting Monteverde to St. Pietro, and then take Corso Vittorio to Largo Argentina.
Whatever routes are designed, they should not be dictated by the problems of congestion caused by traffic outside the school. Rather that traffic must be penalized, encouraging parents to walk with their kids or use the bus to get to school.
Actually, a city-sponsored school bus would make most sense. Rather than facilitating traffic outside schools and at major intersections as they do during rush hour, the municipal police should relentlessly fine drivers for violations, be they double parking, parking at bus stops, going through red lights and blocking intersections. The results: more money for the city in the short term and greater respect for the law and fluidity of traffic in the long term.