ARE HOMESCHOOLERS PREPARED FOR COLLEGE CALCULUS?: Math Achievement

Summary: Christian P. Wilkens and Carol H. Wade teach in the Department of Education and Human Development, College at Brockport. Gerhard Sonnert and Philip M. Sadler teach in the Science Education Department, Harvard-Smithsonian Center for Astrophysics, Harvard University. As the title implies, the authors investigate the preparation and success of homeschooled students in college calculus. 

Research on the academic achievement of homeschoolers is often anecdotal, biased, and politicized. It suffers from small sample sizes and a large percentage of the population that only homeschools for several years. These design flaws make it difficult to find studies that have reliability and generalizability, but the authors do cite two studies that they found to be good enough quality. The first is by Belfield, who found that homeschoolers taking the SAT scored slightly better on the verbal section and slightly worse on the math section than expected. The second is by Qaqish, who found that homeschoolers taking the ACT scored slightly lower than expected on the math section.

The authors use data from the 2009–2010 Factors Influencing College Success in Mathematics (FICSMath) survey to gain an understanding of homeschoolers’ success in tertiary calculus, the first single-variable calculus course taken at the college level. Of the 10,492 students from around the country who completed the FICSMath survey at the beginning of their calculus course, 190 (2.1% of the sample) were homeschooled for a majority of highschool. The survey included students from 134 institutions, which were stratified by size and 2-year versus 4-year colleges. The homeschooled students tended to be whiter and have better-educated parents than their public-schooled peers, but the authors did control for these variables (and others) in their model.

The FICSMath survey found no significant differences in SAT/ACT math scores by school type. As for calculus scores, the mean grade of public-school students was 80.6% and the mean grade for homeschool students was 87.2%. Even though homeschoolers had the highest average of any school type, it did not reach statistical significance because of the low number of homeschoolers in the sample. Rather than school type, the most powerful predictor of calculus success seemed to be SAT/ACT math scores.

The authors recognize that there are a number of limitations with their findings. First, the study does not have much generalizability because there is an obvious selection bias towards people who are successful in mathematics. Students who did not take calculus, who did not go to college, or who did not graduate from high school are not included in the sample. Also, the FICSMath dataset is based on student surveys, and it subject to all the typical limitations of surveys.

So to answer the main question of whether homeschooled students are prepared for college calculus, students who homeschooled earned higher grades than students from other school types. This is despite the fact that they come from similar demographic backgrounds as students from other types of schools. Why could this be? Only further investigation might give an answer.

Appraisal: The first thing to say is that it’s wonderful when a researcher (or team of researchers) uncovers a dataset that can provide new insight into homeschooling, as is the case here with the FICSMath survey.  That the results call into question previous studies finding a slight homeschooler disadvantage in math is even more intriguing.

As the authors readily acknowledge, their findings have limited significance for the broader discussion of homeschooling achievement. They are plagued by the same issues that affect many homeschool studies. It is certainly interesting that homeschoolers did better than public-schooled students by approximately 7% in Calculus, but that does not mean that homeschooling caused students to have stronger math skills. Without a better understanding of the homeschooling population as a whole, rather than just the high-achieving students who enroll in a college calculus course, it is impossible to make any generalizations about homeschooling as such.

However, their findings are consistent with several other studies by Snyder, Cogan, and Gloeckner and Jones on the high success-rates of homeschool students in college.  It seems that for these students at least, the finding of Belfield and Qaqish, not to mention older studies by Frost and Morris (in 1988) and Ray and Wartes (in 1991) and a more recent study by Coleman (2014), all of which likewise found that homeschoolers scored a bit lower than expected in math, do not apply.  At the elite level, homeschoolers are indeed prepared for college Calculus.

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