When I was in the seventh grade we were expected to be able to extract square and cube roots -- arithmetically, on paper. We were required to memorize all of the counties and county seats of Illinois (where I was in school). We began geography in the third grade; I learned then (among other things) that Malaya was a pennisula, Australia was an island, where Baffin Island was, and something about the people that lived there.

In high school I took two years of Latin, two years of algebra, a year of plane geometry (with a bit of other geometries tossed in at the end), a semester of trig, a semester of analytic geometry, a semester of typing, four years of history (US, Western Europe, World, Western Hemisphere), a year of chemistry, a year of biology, a year of physics, four years of PE (which for various reasons I never did take), driver's ed, four years of religion (Catholic school), four years of grammar and literature, and public speaking.

We were REQUIRED to memorize things from second grade on through 12th. As a result I can memorize folk songs and other things and my memory is pretty good.

It didn't seem to harm me any. And I can add, subtract, multiply and divide fractions.