First, schooling at home can allow the child to follow more of their own interests compared to traditional schooling. This self-direction can result in motivation that is internal instead of external. Researchers Ryan and Deci have found that internal motivation can result in enhanced performance, persistence, and creativity.
Also, Utman found that a focus on the opportunity for learning and the development of competence (typically found in homeschooling) leads to better task performance than does a focus on displaying high levels of ability (typically found in traditional schooling). Tasks include word memorization, reading comprehension, pattern recognition, and creative writing.
This does not mean that homeschooling automatically produces better results. In a review of homeschooling research, Kunzman and Gaither found that compared to traditional schooling, homeschooling generally results in increased verbal skills and decreased math skills. Other studies have found more positive academic benefits of homeschooling, but can suffer from flawed methodology such as non-random samples.
For those concerned about higher education, Kunzman and Gaither also found that homeschooled applicants are accepted at roughly the same rates as their conventionally schooled peers.
This research supports a decision to homeschool, but best evidence for me is my son's own happiness and love of learning.
-Mike Matessa
References
Kunzman, R., & Gaither, M. (2013). Homeschooling: A comprehensive survey of the research. Other Education, 2(1), 4-59. (http://www.othereducation.stir.ac.uk/index.php/OE/article/view/10/55)
Ryan,
R. M., & Deci, E. L. (2000). Self-determination theory and the
facilitation of intrinsic motivation, social development, and
well-being. American psychologist, 55(1), 68. (http://home.ubalt.edu/tmitch/641/deci_ryan_2000.pdf)
Utman, C. H. (1997). Performance effects of motivational state: A meta-analysis. Personality and Social Psychology Review, 1(2), 170-182. (http://www.selfdeterminationtheory.org/SDT/documents/1997_Utman_PSPR.pdf)