I thought this was bogus as soon as I read about it; Alex Tabarrok is on the case:
Frankly I suspect that this study was intended to confuse the media by conflating “low-income” with “below the poverty line”. Indeed, why did this study grab headlines except for the greater than 50% statistic? It is very easy to find official numbers of the number of students in poverty according to the federal poverty standard. Here is what the National Center for Education Statistics says about school-age children and poverty (most recent data):
In 2012, approximately 21 percent of school-age children in the United States were in families living in poverty.
The number of school-age children living in poverty today is relatively high and not surprisingly did increase with the 2008 recession and its aftermath (green line in figure below – the numbers here differ slightly from NCES but the time line is longer). But recent numbers do not look like especially remarkable compared to the history.