I'll reply to a homeschooling example with another homeschooling example. The reason I'm not sure that the underlying Psychology Today blog article
http://www.psychologytoday.com/blog/freedom-learn/201003/whe...
cited in this submitted blog post gets things right is that children's readiness to learn this or that is surely influenced by early childhood experiences, and the role of an education (parent at home or teacher in school) is to serve up those experiences.
My wife the music major who is a piano teacher by occupation used to play counting and adding games with dice with our oldest son when he was little. I the Chinese major who was then working mostly as a translator and language teacher began guiding him through the excellent Miquon Math materials
http://www.keypress.com/x6252.xml
as he reached typical first-grade age. My son took to math an something fun, not tedious, and eventually at fourth-grade age enrolled in the EPGY math distance learning courses.
http://epgy.stanford.edu/courses/math/elem.html
He enjoyed those, and spurted ahead to finishing the EPGY algebra course by the end of his fifth grade school year. By then he had also tested into the University of Minnesota Talented Youth Mathematics Program (UMTYMP),
http://mathcep.umn.edu/umtymp/
his first taste of somewhat conventional classroom instruction in any subject.
Our son of two non-mathy parents has gone on to do a lot of summer programs in math
http://www.dcu.ie/ctyi/files/Overseas%20Summer%20Brochure.do...
http://cty.jhu.edu/summer/catalogs/os/osmath.html#game
http://www.mathpath.org/newspapers/Colorado.Springs.Gazette....
http://www.math.ohio-state.edu/ross/
and upper-division study of math as a dual-enrollment student at our state university. He is awaiting the last bit of college admission and financial aid news before deciding where to enroll for a double major in math and computer science.
To sum up, I'm not sure that homeschooling parents, or any parents, have to decide "not to sweat it" if a child hasn't learned much math yet. Maybe it's time to do activities that are supportive for learning math.
Our second son's strongest personal interest is literature--he loves to participate in National Novel Writing Month
http://www.nanowrimo.org/
but he applies his highly visual brain (very different from his older brother's "natural" way of approaching math) to learning math, and he is right on track to learn algebra at eighth-grade age, and rather more thoroughly than most students in Minnesota do. My two younger children (one boy, one girl) are also enjoying the Miquon Math and the Singapore Primary Mathematics materials that their older siblings used before them, well known for encouraging children to "use their noggins," as one homeschooling parent described them.
P.S. I grew to recover my childhood liking for math so much while observing my oldest son's study of math that I am now an elementary math teacher by occupation.
http://www.ecae.net/category/saturday-school/