The journal Other Education has just published an article Rob Kunzman and I wrote together titled, “Homeschooling: A Comprehensive Survey of the Research.” It is the culmination of years of work by both of us compiling every piece of research on homeschooling ever written, culling through them all to select the best material, organizing them into coherent categories, and writing up the results.
Several months ago I reviewed Joseph Murphy’s excellent book Homeschooling in America: Capturing and Assessing the Movement, which is a very thorough review of the scholarly literature. Our article is not nearly so long as Dr. Murphy’s book and thus it lacks some of the detail he provides. Anyone interested in homeschooling research should read his book cover to cover and keep it on the shelf for frequent reference. But despite its length and depth of coverage, there are some topics and a few key studies Dr. Murphy leaves out, and he sometimes fails to differentiate between high and low quality studies or between studies published recently and those published decades ago. I think our article provides even more breadth and does a better job discriminating between sources. Plus you can download it for free! Do so here.
A second, fully revised edition of my 2008 book Homeschool: An American History, was published in March of 2017. 
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Homeschooling Research Notes 