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[quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous]I went to high school in a state with a traditional math curriculum, but I went to college at an engineering school in New York state, so my classmates were mostly from New York State public schools which offered an integrated math curriculum.

From years of study groups and my now DH, I have a strong impression that the integrated curriculum was a whole lot weaker and less rigorous than what I learned, but also that the students who had taken a mixed up curriculum had no idea what they knew and didn't know. They couldn't identify something as algebra, statistics, trigonometry, geometry, or any particular type of math. They knew lots of random bits of stuff without knowing how it fit together or how it built on itself. Given that experience, I have a strong preference for a curriculum that builds linearly instead of jumping all over the place at random.[/quote]

You're confused. 
"algebra, statistics, trigonometry, geometry, or any particular type of math." is an artificial invention that hampers learning. Real math blends these all together.

Look at a college course catalog, and you'll see classes with names like
 
Algebraic Geometry 
Differential Geometry 
Geometric Algebra
Linear Algebra

[/quote]

I would call these blending.

Algebraic geometry shows you that algebraic solutions are equivalent to geometric solutions. Different mathematical methods that arrive at the same answer.

Differental geometry isn't exactly geometry in the traditional "you can draw it" sense. It's how to handle multidimensional spaces with calculus.

Geometric algebra is an abstract algebra. There's no geometry except for vector spaces.

Linear algebra extends algebra from a single variable to matrices. It's another level of algebra and not a combination of things. [/quote]

I was about to say the same things. Also geometric algebra is some form of Linear Algebra by other name.

There’s not a lot of “blending” in higher math. Sure there are connections and spiraling but courses are organized by overarching themes, techniques and applications, not studying everything at once. [/quote]
Geometric algebra is actually a generalization of linear algebra 
https://youtu.be/60z_hpEAtD8?si=dKh8caDIgLK4u043[/quote]

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