Mathematical model reveals parental involvement can 'immunize' students from dropping out

In fact, new mathematical modeling from Arizona State University, Northeastern Illinois University, and the University of Texas at Arlington documents the exact statistical tipping point when positive parental influence -- found to be the leading indicator of academic performance and whether or not a student will eventually graduate -- is effectively neutralized by negative peer influence.

Anuj Mubayi, now an assistant professor with ASU's School of Human Evolution and Social Change and ASU's Simon A. Levin Mathematical, Computational and Modeling Sciences Center, initiated this research while teaching in Chicago after he and a colleague visited a local high school with a higher average dropout rate than 95% of the city.

The raw data for the study came from a 2013 survey sampling of 125 students at this particular school, Mubayi says. Areas of focus included teaching effectiveness, the role of school demographics, the impact of peer and parental influences, and academic performance.

Based on these factors, variables such as parental involvement were categorized as high, medium or low , while academic involvement was rated as passing, vulnerable or failing. Social influences from peers was also measured on a sliding scale and was determined by asking students to identify their friends' academic performance and interest levels, as well as their exposure levels to peers who had already dropped out of school.

"In this instance, more than 50% of students reported their friends thought that school was a 'waste of time,'" Mubayi says.

Once organized and categorized, the data was eventually applied in a mathematical method that shares some traits with SIR-type modeling. This approach had been previously used by Mubayi and his collaborators as well as others in tracking the spread of social and biological problems, such as alcoholism or infectious disease.

"The underlying premise of this study was that social behaviors can spread interpersonally through social interactions and influences, as well as through contextual influences in high-risk settings, just like infectious diseases can," Mubayi says.

So, can parents really "immunize" their children against dropping out just by being more involved in their education? The answer is yes, but only to a point.

That's because if a student with high parental involvement hits a moderately high range of negative influence from peers (in this study, 0.8 on the horizontal axis), their risk of failing and dropping out begins to trend upward on a similar trajectory as those students whose parents display much lower levels of engagement (in this study, 0.4 on the horizontal axis)

If any student begins to falter academically as a result of either or both influences, time is really of the essence, Mubayi adds. "Our study showed that once performance drops to a certain point, later increases in positive parental influence are no longer enough to reverse the trend and may even make things worse as the student rebels."

While providing some initial insights into the importance of positive parent/child interactions and early encouragement for vulnerable students, the question of how to more broadly protect and grow propensity towards academic success remains a complex one.

For now, Mubayi's team, which currently includes Bechir Amdoni (NEIU), Marlio Paredes (University of Puerto Rico at Cayey), and Christopher Kribs (UTA), plan to expand their study to more schools in order to understand these influences in a wider spectrum of educational environments.

"There's been a big gap in research-funded education policies and, as a result, those that have been implemented have fallen short in many neighborhoods," Mubayi says. "Our study also revealed more half of dropouts do not live with their parents, so there are also social, economic, and emotional factors that we must consider to address these issues more holistically."

Mubayi is also working the problem from another angle as the co-director of a well-renowned undergraduate summer training program called the Mathematical Theoretical Biology Institute (MTBI). This ASU program, which has received two presidential awards, was initiated by mathematician Carlos Castillo-Chavez some 21 years ago and focuses on improving dropout rates for college students while promoting graduate programs in STEM disciplines.

The full study "Why do students quit school? Implications from a dynamical modelling study" can be viewed here in the Royal Society journal Proceedings A.