I thought I'd write a bit about an aspect of everyday life that I've been able to appreciate more since our move to Thailand. Yesterday Alisha was commenting on the fact that our lives here don't have the same rhythm they had in the US with me going into work every day from 9:00 to dinner time. The variety in our schedule certainly takes some getting used to. But we've snatched some flexibility out of the chaos in the way that we take turns facilitating schooling throughout the week.
I've really appreciated the freedom to just follow the kids' interests and see where it takes us for the day. I am a strong believer that meaningful learning is something a student can only do on their own. To me teaching at its best is not a matter of imparting facts or opinions, but rather just asking the right questions and providing the spark that ignites curiosity, and the willingness to follow that curiosity even if it leads somewhere unexpected.
This is best exemplified in how we do math. I do my best to try to pull topics from whatever "materials of life" we have at hand. For instance, one morning a breakfast of waffles offered a perfect opportunity to talk about square numbers. This was before we had introduced them to the concept of multiplication, but with 4x4 waffles it was easy enough to count the squares one by one, then eat a layer from off the edge, then count the 3x3 waffle that remained, all the way down to a single square. Later when we did start to teach multiplication, they were able to relate it to what we did with the waffles.
With math specifically, it's important to understand that while some topics do build on earlier ones, other topics can be approached in any order you please. Some topics are often thought of as advanced simply because they are typically taught later in school, but they are not beyond the abilities of younger kids.
For instance, one day after studying some Thai, Z asked what language robots used. Since we had already done some electronics projects, I was able to explain that robots and other machines use the same electrical signals he's already seen, but they had a way to "think about" numbers using on and off as two "digits". We went on to talk about how we represent numbers using ten digits and what you would have to do if you only had two, which turned into teaching them binary representation of numbers. Eventually we got to how to represent letters and writing using numbers, which tied into earlier exercises we did using Caesar ciphers to email grandparents.
Everyday life is full of numbers, and you can find opportunities to explore them if you stay alert. But some days it can be nice to take a break from the spontaneity, since it can be a bit draining to maintain. The kids are always up for some videos as a change of pace. My personal favorite is Vi Hart's channel as her enthusiasm for the material has proven infectious. (Hexaflexagons and Fibonacci in particular are great starting points.) But we also throw some Khan Academy and Right Start Math into the mix in order to keep things more balanced and ensure we cover all the bases.
It's been striking to me how focused they can be when working through exercises that have come up through pursuing their own questions rather than just whatever happens to be next in the plan. In the case of binary the kids took to the material naturally and just ate it up. In other cases I've pulled up videos that covered a topic that they didn't fully understand, but I believe it's still beneficial every so often to expose them to something they're "not ready for" as long as you don't set unrealistic expectations. For one, it can serve as a preview to exciting things to come, but beyond that sometimes it can show you that your expectations were too low to begin with.