That is old school thinking.
That sounds like the strong core skills, basic, well rounded education myself and others of my generation received before the school systems were corrupted in the 1980s and beyond.
To graduate high school we were required to take and pass at least 2 semesters each of trigonometry, geometry, general science, biology, physics, and chemistry. All of those classes fostered creative thinking and problem solving.
To update for the 21st century all you would really need is to add to that would be a few computer science classes that teach the basics of how a computer works and you would have a well rounded STEM foundation.
What are they teaching in high school today? Basket weaving?
I also think blaming standardized tests is a cop out. If schools taught a strong core curriculum they would not need to teach to the test. The kids would pass with what should be considered basic knowledge.