She decided then to take a second trip to a planetarium. When they arrived, a college-level lecture was taking place. Hesitant, she took her boy in. Jacob immediately began reading the slides, and when the professor asked a question about the density of Mars' moons, Jacob answered the question -- correctly.
"At that point, my view changed, and I realized that his mind is remarkable," Barnett said. "He understood complex concepts. My outlook for his future was completely changed."
Today, Jacob is now working towards a PhD. at Indiana University-Purdue University Indianapolis (IUPUI). Several IQ tests have been administered on him, and Barnett said that it's been concluded that he can't be measured, so he is always given the top number.
Speaking with ABCNews.com, he said that when he entered grade school, he was already hoping to be beginning algebra.
"In kindergarten, I knew that it was for kids to play and develop social skills," he said. "By first grade, I thought we'd do some mathematics -- algebra. Then, in second grade, still no algebra. They told me not until high school. So, I guess this came out of my desire to learn more mathematics."
Jacob, at one point, came home from school and sat inside a square bookcase. His mother, fearing that he was beginning to regress, called a psychologist.
"She said he's deeply bored. She said if you don't find what you did, you're going to lose him," Barnett said.
She started taking Jacob to more planetarium visits. At a point, after attending lectures, he was told he could join classes. One was on Saturn. Another was on electromagnetism. Jacob aced them all, and began moving towards his advanced degree at an accelerated pace.
Barnett credits his success to putting her son in as many rich situations as she could find.
"If you find the passion in a child and tap into it, that will become what their drive," she said. "And if somebody had drive, they can accomplish anything."
Barnett's memoir, "The Spark: A Mother's Story of Nurturing Genius," was released in April.