One of the problems I find with mathematics education is that we seamlessly morph the introductory numeracy lessons of ‘counting’ and ‘arithmetic’ into the subj

One of the problems I find with mathematics education is that we seamlessly morph the introductory numeracy lessons of ‘counting’ and ‘arithmetic’ into the subject of ‘mathematics’, without ever stopping and telling kids ‘okay, now you can count, we’re going to start doing something different called ‘mathematics’.’ Mathematics is about examining things and understanding their essence - what statements can we make about all such things? How can we prove that? How can we use that to figure out other things? But nobody ever tells kids that - they think they’re just in ‘advanced counting’ lessons. I wonder whether a split in curriculum could help - similar to English language/literature. Mathematics needs a ‘numeracy’ program that starts in kindergarten and covers the mechanical ‘how numbers work’ stuff… then a separate mathematics program that starts in middle school and teaches reasoning and proof. Start with geometry.