The more I wrote though, the more I realized that separates the concepts too much. A hammer is a tool and most people don't pick it up unless they need to hammer in a nail. Most people don't think about hammers, where they come from, or how they are made, unless they are interested in making hammers. However, hammers are also made of the same metals from which many other things are made. Hammers have a history that ties into every era of the world, which is directly related to what materials and process was used to make them and who made them- blacksmiths or factories.
Like with everything, even the tools are interconnected to everything else in the world. So yes, math is a tool, but that doesn't make it separate from the interests that require its use. That's what schools say- that you need to acquire the tools in order to be able to follow the interest. In real life, the tools are inherently part of the interest. You gather them AS you experience the interest. Then you use the tools you gathered to deepen and widen the interest and as it is expanding, so are your tools. It's an ever changing, ongoing process.
So why do we tend to view math as “basic math” and “higher math” if math is everywhere and inherent in every interest? Why divide it that way? Well, because that is the way schools divide it. First you learn 2+2, then division, multiplication and fractions. You only learn "higher math" if you succeed in the lower levels. Otherwise you're told you're "just not a math person," and by the time you enter high school you've already decided that because you're just not a math person, you'll have to go into a field of work that doesn't require higher math.
That's so sad! Math teachers will say "math is everywhere in the world," but kids don't really learn to see it, because no one points it out and connects it to this nebulous concept called "math." Or they do learn the ideas and concepts, but they don't realize it has anything to do with the math they do on paper at school, and they don't have the terminology for it unless and until they reach a "higher math" class.
Because of our own schooled backgrounds, most unschooling parents like myself aren't able to see the math in everything. Sure I do fine using fractions when I cook with the kids, or helping them divide the box of 12 icecreams into equal portions for each of them, or noticing that my 8 year old can tell you that at 7:50 it's 10 minutes until 8:00. Even things like degrees, angles, and some algebra have come up. We do that kind of math all the time.
what it meant.
So I found an interesting resource for really seeing the math everywhere called Moebius Noodles. (I had to look up what moebius means too). I'm reading the book right now. It isn't unschooling, but it's not a normal curriculum either. A lot of math curriculums try to "make math fun," which usually translates into taking the same old arithmetic problems and dressing them up with cartoon characters, and creating games that still revolve around arithmetic. Moebius Noodles is all about seeing that "mathematics is fundamentally about patterns and structures, rather than 'little manipulations of numbers.'"
The Moebius Noodles books says:
"Children have more imagination than it takes to do differential calculus. They are frequently all too literate like logicians and precise like set theorists. They are persistent, fascinated with strange outcomes, and are out to explore the “what-if” scenarios.....children are required to develop their mathematical skills rather than being encouraged to work on something more nebulous, like the mathematical state of mind. Along the way the struggle and danger are de-emphasized, not celebrated – with good intentions, such as safety and security. In order to achieve this, children are introduced to the tame, accessible scraps of math, starting with counting, shapes, and simple patterns. In the process, everything else mathematical gets left behind “for when the kids are ready.” For the vast majority of kids, that readiness never comes. Their math stays simplified, impoverished, and limited. That’s because you can’t get there from here. If you don’t start walking the path of those exotic and dangerous math adventures, you never arrive.
It is as tragic as if parents were to read nothing but the alphabet to children, until they are “ready”
The book has games, but they are games that demonstrate how concepts normally only discussed in algebra, geometry, trigonometry or calculus classes are very present in the real world in things that kids do every day.
I'm really looking forward to using this book, not as a curriculum for them, but as a way for me to learn more about math in the real world so I can point it out to them when they are interested as we go about our daily lives. And we'll play the games the way we play all games- when they are interested, for as long or short a time as they'd like.