The United States is blessed to have many excellent schools, including hundreds of fantastic high schools, such as those that recently received recognition from Newsweek. And our high schools as a whole deserve credit for helping to push America’s graduation rate to all-time highs.

However, there is still an enormous gap between the aspiration of America’s students and parents and the quality of education our public school system is providing. Put simply, almost all young people today want to go to college (including technical colleges), but only about a third are graduating with the reading and math skills to be successful once on campus.

Not all of the blame for that chasm can be placed at the door of high schools. Too many students are reaching the ninth grade who are barely literate and numerate. Still, at a time when student achievement is rising at the fourth and eighth grade levels, but not in twelfth grade, it’s fair to ask whether our high schools are doing all they can to help teenagers make real academic progress while under their care.

Part of the problem is that most of our cities continue to house huge, impersonal, monolithic high schools that offer students neither choices nor rigor. But it doesn’t have to be this way. Over the past decade, New York City implemented an aggressive initiative to create hundreds of small schools, some with a college-prep focus, and others with a more technical orientation. An independent study found astonishing results, especially in terms of graduation and college enrollment rates.

The Common Core standards, currently in place in more than forty states despite much political backlash, should help many more students arrive in the ninth grade on track and on a trajectory for success in college and career. Let’s make sure our high schools are structured to finish the job.