What if we replaced high school geometry with a year of probability? I know it sounds heretical, but consider proofs. The bane of many students and teachers alike, it is vital for aspiring mathematicians to learn how to use the definitions and rules of mathematics persuasively. Proving something with the laws of probability is analougus to doing so geometrically, but considerably more intuituve. Many of the laws used in geometry are abstract and meaningless to most students, but the rules of probability are much more evident in the everyday world and therefor a better catalyst for learning how to develop mathematical arguments. I bet you can't remember the last time you used the Side Angle Side property in your life.
I do not intend to belittle geometry, but I do doubt its relevance at the high school level. Much of it can be covered in other subjects. Angle relationships, for example, are covered in precalculus/trigonometry, and the ability to use coordinate systems should be refined in many other areas (i.e. science and geography). Spacial reasoning is another wildly important aspect of learning geometry, but I would argue that students would do better to take engaging art classes to flex those muscles.
Anyway, it's likely that there are holes in my proposition and I welcome any criticism that seriously consideres my claim.
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Geometry is useful in real life, especially the trades, which people often directly enter after high school. Probability is best left to university students studying theoretical physics.
The traditional high school program was developed from experience with the learning abilities of kids at different ages. Whether sophomores are ready for probability, I couldn't say. I do believe that geometry is overdone in some ways, and I believe that the current math teaching system could be improved.
The major goal of education is teaching students to think. Geometry, with proofs, gives kids experience with lining up ideas to make a convincing argument. This is the basis of science, the law, and political discourse. Geometry is sandbox logic.
My personal recollection of statistics is a mess of Greek letters and fancy axioms and the nagging feeling that you're a sane person's soul away from having any idea what it all means. Obviously, I don't remember how probability was taught back in grade school. That said, I believe it's more important for kids to know how to arrive at logical certainty than statistical likelihood, but that they should be taught both subjects, how to use them, and how to abuse them.