Loki Rucca sits at a picnic table on a recent sunny day, happily pulling small squares printed with math questions from a wooden box.

The 5-year-old takes one that asks "6 + 2 =" and ponders for just a moment before rummaging in the box for a square printed with the number 8, which she uses to answer the question. She smiles, and reaches for another question square.Loki is one of an estimated two million children in the United States who are being taught at home rather than being enrolled in a public or private school.From 2007 to 2010, the number of children home schooled increased by an estimated 7 percent, according to a study by Dr. Brian D. Ray of the National Home Education Research Institute."Most indications are that the homeschool population has grown absolute terms during the past three to five years. This study shows there were an estimated 2.040 million kindergarten through twelfth grade homeschool students in the United States in the spring of 2010, with high confidence that the true number lies between 1.734 and 2.346 million," he wrote.The home schooling numbers do not include the growing numbers of children who are enrolled in cyber charter schools, which are state-approved and considered public schools. Cyber charter schools are different from cyber schooling, which can mean simply using a computer to download educational materials.Learn-at-home optionsStudents can learn at home through traditional home schooling, with parents as teachers, or through enrollment in one of the 16 cyber schools that now operate in the state since they were allowed in 1997. Some school districts, including Palmerton and Jim Thorpe, have their own cyber school programs in an effort to keep students and tax dollars. Cyber students use home computers to link to their virtual schools.Cyber schools are paid for by each student's home school district, with the amounts assessed by using a formula based on per-student spending. For example, Tamaqua's projected cost for 2012-13 is $625,000, said Business Manager Connie Ligenza.Home schooling, on the other hand, is not taxpayer funded, and parents are free to teach their children as they wish, providing their children are able to meet state educational goals.Families choosing either option who were interviewed for this story said they also make sure their children are involved in various group activities.Some home schooling families follow a set curriculum provided by their home district or through an accredited home schooling organization, such as the century-old Calvert School. Others are more free-form, like Loki's family. Her mother, Amber Moyer, says she researched several home school programs, but finally decided to create her own, based on Montessori principles.Some families opt for "un-schooling." That approach leaves learning in the child's hands. It involves no tests, formal sessions or curriculum. There is no required reading or structure.State law requires that a home schooled child's progress be reviewed annually by a qualified evaluator. Standardized tests are required for children in the third, fifth and eighth grades, and parents must keep a portfolio that includes some of the child's work and a log of reading material.Both home schooled and cyber schooled students can receive diplomas. Ray, of the National Home Education Research Institute, also found that "home schooled student achievement test scores are exceptionally high. The mean scores for every subtest (which are at least the 80th percentile) are well above those of public school students."Why home or cyber school?"I think more and more parents are realizing that they have a choice in how they educate their children. And the reasons are different for every family," says Nancy Gauvreau, an organizer of the Schuylkill County Homeschool Group.Those reasons include protecting their children from bullying; having school officials misdiagnose learning conditions; low academic standards; too much pressure to score well on tests and too much emphasis on standardized testing; or wanting more time with their children."And some just knew all along, right from birth, that they wanted to homeschool as part of their family's values or lifestyle, or because they felt, for various reasons, that their kids would be better off at home. These are all just regular people with their kids' best interests at heart," Gavreau says.She cites her own young daughter's experience of long hours at a desk, with little play time and reprimands for talking."I was thinking, 'There's gotta be something more than this'," Gavreau says."I wanted my kids to enjoy learning. To read lots, finish what they started, have a say in what they wanted to learn about, to be imaginative, creative, thinking, individual people. I envisioned field trips, good books, hands on projects to supplement what we were learning, time for questions and answers and exploring rabbit trails, free time to do our own thing."And when I thought about avoiding the peer pressure and bullying and other negative factors so prevalent in schools today, and more time with my husband who did have a sort of odd schedule, I did the research, joined the group I'm now the organizer of, pulled my daughter out right after her PSSA'S in March of 2009 and never looked back."For Jody Walker, cyber schooling gives her daughter Bridget a safe haven from bullying. The last straw was broken when a gang of bullies posted online a video of Bridget being attacked.Bridget, 16, of Tamaqua, now learns via Commonwealth Connections Academy. She completes her required 28 hours a week by logging on four or five times a day. She also works offline. Her mother, who was given her own log-in password, is able to keep current on all facets of Bridget's academic work."I go on twice a week and log her attendance," Walker says. "I'm able to see her grades, her attendance, her lessons.""It's not too hard to understand, and it's kind of fun," Bridget says.For Amber Moyer and her husband Rocky LoPresti, of Owl Creek, the decision to home school their children, who include 2-year-old Tomorrow and 8-month-old Enoch, in addition to Loki, was easy."We started out attachment parenting, and because of that, it seemed a natural extension to keep them at home with us through school age," Moyer says. "At 5, I wasn't prepared to leave her (Loki) with people I didn't know for extended periods of time. Not having someone else raise my child for eight hours a day was the underlying reason (for home schooling)."Loki is beginning to read, and it is obvious that she enjoys math. Home schooling allows children to learn at their own pace, and in their own unique manners, Moyer says.Georgiana and Marc Wakefield, also of Owl Creek, also have three children Shaila, 5, Terran, 2, and 14-month-old Noah. They are home schooling Shaila, and plan to continue with Terran and Noah."The biggest reason was that I wanted Shaila to excel in the areas she needed to excel in, and not be held back by someone else or get lost in a large group," she says.Wakefield creates her own learning programs and materials, based on her children's needs and interests.Her favorite aspect of home schooling?"Being with them. Being able to take field trips all the time, being able to go see different things during the week," she says. "On Saturdays she has gymnastics, and on Sundays, she does arts and music with her father."Support for home schoolersOne good home school resource is

http://www.homeschoolfacts.com/index.php. The website includes a listing of support groups, state laws, and curriculum sources."With all the information available at our fingertips today, it's easy to go online and find tons of information and articles and support groups and Meetup groups," says Gavreau. "To connect with other home schoolers and find yourself thinking, 'This isn't so crazy. If they can do this, I can do it, too.' And it just becomes more and more mainstream."