Wednesday, March 10, 2010
Damn, this is good!

Dept of Ed has issued a new set of standards for K-12 schools, seemingly connected to the "Race to the Top" stuff.

I've thoroughly read the math parts, and skimmed the other parts.

Everything is just about perfect! Though it's written in drab passive edu-ese, it's still clear, and the lists of goals and 'core skills' are exactly what I've always wanted to see.

Frankly, I was afraid the pressure to catch up with China and India would produce math goals designed for Oriental brains, with lots of abstraction and memorization. That would be counter to the national interest, and wouldn't work anyway. Our mix of genotypes (mainly African and European) will never match Orientals in those departments. We're better at estimating, problem-solving and organizing. During the decades when America was successful, those were the skills that took us to the top. And these new goals have returned to the direction of success!

An extract from the section on modeling:
In any given situation, the model we devise depends on a number of factors: How precise an answer do we want or need? What aspects of the situation do we most need to understand, control, or optimize? What resources of time and tools do we have? The range of models we can create and analyze is constrained as well by the limitations of our mathematical and technical skills. For example, modeling a physical object, a delivery route, a production schedule, or a comparison of loan amortizations each requires different sets of tools. Networks, spreadsheets and algebra are powerful tools for understanding and solving problems drawn from different types of real-world situations. One of the insights provided by mathematical modeling is that essentially the same mathematical structure might model seemingly different situations.

The basic modeling cycle is one of (1) identifying the key features of a situation, (2) creating geometric, algebraic or statistical objects that describe key features of the situation, (3) analyzing and performing operations on these objects to draw conclusions and (4) interpreting the results of the mathematics in terms of the original situation. Choices and assumptions are present throughout this cycle.

Just as a randomly chosen f'rinstance, a student who mastered this concept could easily see how the whole Global Warming mess is a crime.

I only wish standards like these had been in effect when I was a student in the '50s and '60s, and when I was teaching math and electronics in the '80s. Especially in the '60s, math teachers were whipsawed back and forth by competing and conflicting standards, each based on some ivory-tower asshole's pet theory.

Trouble is, new standards don't really help until teachers and textbooks implement their ideas. Some experienced teachers will be glad to have this new focus and will know what to do with it. Unfortunately, it will dissolve when it runs into the teacher-training courses at universities. Teacher training courses have always been hopelessly stupid, and recently have served nothing but Gramscian multi-culti tyranny.