Speaking of the "Math Wars", here's an observation I made about teaching the most basic elementary-school subjects.
When I was very young, we were taught reading by "phonics", i.e., sounding out the letters of unknown words, and then thinking about how those sounds related to words we already knew. Sometime after that, phonics was dropped for a "whole word" approach, but it seems like the pendulum might be swinging back these days.
Why do "phonics" make sense as an instructional strategy? Because our system of writing is a technology based on exactly that principle. The whole point to our alphabet is that it is phonogrammatic, i.e., written symbols represent spoken sounds. This system of writing is meant for there to be an obvious connection between what we write, and what we say. (Of course, this is totally different from logographies such as Chinese whole-word characters and Egyptian heiroglyphics, but that's an entirely different story.) In teaching a child to read, why would you not use the language tool the way it was designed to be used?
Similarly, the traditional way of teaching arithmetic is to memorize a small number of basic facts (addition and multiplication tables), and then learn fundamental written procedures for adding, subtracting, multiplying, etc., large (many-digit) numbers. More recently, we've had to deal with the "Math Wars" is which training in time-tested prodecures has been frowned upon as too authoritarian (or something). Rather, there appears to be extensive time spent in base-10-system conceptual understanding, and then inventive or creative exhortations to make up your own multifarious addition, subtraction, etc., algorithms.
Why do "procedures" make sense as an instructional strategy? Again, because our system of written numbers is a technology based on exactly that principle. The whole point to our place-value system (base-10) is that it is intended to make the specific procedures for adding, subtracting, and multiplying simple, straightforward, and consistent for everyone! Consider the history of written numbers: With ancient systems like, again, Egyptian numerals or Roman numerals, there was no way to get addition or multiplying accomplished by simple writing or mental effort. Without a fixed base system, numbers don't "line up" the way they do for us. To get any arithmetic done (including total sales or tax calculations), you had to go to a licensed counter (think: public notary) with their counting board or abacus tool for use as a mechanical calculator, and trust that the computations they did there were correct. You were entirely at the mercy of this elite, cryptic profession, just to do simple addition.
At some later point, our Hindu-Arabic numeral system was invented and made its way to the West. This system of writing numbers is meant for there to be an obvious connection between the numbers we write, and how to add and multiply them, via a specific written procedure. Kings and princes were astounded at the prospect of people being able to do arithmetic on paper, or in their head, without using an abacus as a calculator. It's like magic! It's not some kind of accident that we use a positional-number system, it was engineered that way only so that we could use a specific adding and multiplying algorithm. In teaching a child to do arithmetic, why would you not use the written number tool the way it was designed to be used?
In summary, it's fascinating that both reading & writing instruction have taken almost exactly parallel paths in the last few decades in America. In each case, they have abandoned the rationale for which the writing tool was designed in the first place. It's like showing someone a power saw for this first time and them asking them, "Can you think of something you might use this for?" To leave out the intention of the tool is to miss the whole point of it. We should play to the strengths of our writing technology, and not frustrate ourselves fighting against it.