The plan would erase an 11 percent pay gap suffered by teachers, Harris says.

Some studies have linked higher teacher pay with better student outcomes.

Higher pay could draw new workers into teaching at a time when many schools are struggling to recruit new teachers.

The teaching profession is in crisis, and presidential hopeful Kamala Harris has a plan: Provide teachers with a salary increase of $13,500 each to ensure a middle-class wage — and lure new workers into the profession.

Her proposal comes at a time when teachers across the country are going on strike, protesting issues ranging from low pay to crowded classrooms. Education experts support Harris' plan, saying it could narrow the pay gap that they say scares off some workers from pursuing a career in education.

Even though the U.S. economy has largely recovered from the Great Recession, America's public schools are still struggling to recover their financial footing. State funding for public K-12 schools remains lower than before the recession in a number of states, including five where teachers have gone on strike in the last year. And in 42 states, teachers are earning less than they did during the 2009-10 school year.

At the same time, Harris' proposal may only go so far. Her plan focuses on federal funding, while local taxpayers provide the bulk of funding for the country's 100,000 schools. And those buildings are suffering from another funding problem: chronic deferred maintenance to the tune of half a trillion dollars.

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Teaching as a "viable career"

Providing a pay bump for educators could help solve some retention issues, says Catherine Brown, senior fellow at the Center for American Progress Action Fund. The Center for American Progress is a left-leaning public policy research organization.

Harris' proposal would put teaching "on an equal footing with other professions and make it a viable lifelong career," Brown told CBS MoneyWatch. "There is a lot of evidence that teachers leaving the profession has a detrimental impact on student outcomes."

Teachers are leaving education at an alarming rate, with 4 of 10 departing the profession within five years, the National Education Association has found. And the teacher shortage is due to problems long before educators step into the classroom: Colleges report a more than 20 percent decline in students completing education degree programs, with college students citing the field as an undesirable career.

Harris told "CBS This Morning" on Tuesday that boosting pay would help fix the latter issue. "We want that student who is excelling in chemistry and biology that they will pursue their passion of teaching children instead of worrying about how they are going to pay off their student loans and going to a pharmaceutical company," Harris said. "We want the mathematicians to teach math instead of going to Wall Street because they got to pay off their bills."

Bigger money problems

But at the same time, the woes afflicting America's school systems reach far beyond teacher pay. Elementary, middle and high schools across the country are struggling with inadequate upkeep and a lack of new facilities, with an annual $46 billion shortfall in necessary funding, according to a report from the National Council on School Facilities and other education groups.

The deferred investment in the schools that America's 50 million students attend each school day may be as much as $542 billion, the National Council on School Facilities found.

The poor physical state of some public schools have even spurred lawsuits, with a group of Detroit students suing last year, arguing that crumbling infrastructure violated their constitutional right to an education. The students alleged "slum-like conditions" conditions such as mold, leaking sewage and inoperable bathrooms and water fountains, as well as overcrowded classrooms, hindered their ability to learn.

Given these widespread problems, the question might be whether Harris' proposal goes far enough to remedy the problems facing America's public schools.