Can you make a chair with a hammer, nails and a saw? Sure. Will it be a very good chair? Well sure, it might hold you up, but it won't be intricately carved or a fantastic design. Learning is like that.
You give a child a little bit of knowledge; let's call it some tools in a toolbox. You give them some math, some reading, some science, sometimes you give them more of one thing than another. You expect them to use their tools; use that theoretical hammer of math to bang away at some equations. But there is more to learning than just the basics. You need to provide more than just a hammer if you want your kids to build anything other than a rudimentary table and chair.
Oh, so you're not a carpenter .... well, let's say you are an artist and you endeavor to give your child the love of art and show them how to use an artist's tools to create a masterpiece. Would you start by giving them your top of the line watercolors and a handmade brush of the best quality? Or, would you give them some finger-paint and then introduce tempra paints, watercolors, acrylics and oils when they have explored the possibilities of finger-paints and found them lacking and they want a challenge. But what if your child is past finger paints and not quite ready for the next ‘step up'? Oh, the joy of homeschooling! You can tailor the pace of learning and the introduction of new tools to the rate that your child is at.
Learning is a bit like having this vast buffet of tools and knowledge at our fingertips. We introduce bits and pieces and allow the child to assemble them through the years. We have to remember though that learning is a life-long process. There is no end date to learning. Our society has norms that say that at 18 you graduate from school and then you get a degree and therefore graduate from college. But, does learning stop there? What if your doctor never tuned his skills, investigated new ideas, kept up with the medical field? I sure wouldn't trust him to have learned enough to treat me.
When you approach learning as a life-long investment, you see learning tools a little differently. Maybe it's not so important to teach grammar for 12 years, it doesn't really change from the basic tool you started off with. Mathematics however is like a Swiss Army knife - you think you've reached the end of the tool and out pops another implement to use. Can you expound on science and history? Yes, both change, both have new information that becomes available all the time, both are thought provoking and reflective (What if the sun was just a few thousand miles farther away from our solar system? What if Japan hadn't attacked Pearl Harbor?) What about art, music, language arts, and all the other subjects that come up on a daily basis? Look at the tools in your kit, pull out what you need, find better tools to challenge your children, dust off some pieces in there that haven't been used in a while, and go read about some new tools to use in learning - heck, even better, invent your own tool and use it to teach something new to your children. Teach them that sometimes the right tool for the job isn't readily apparent and they may have to search for it; allow them to be inquisitive, ask questions, try it on their own and come up with ideas that might work (or might not.)
You might be surprised at the creative masterpiece they present to you.