This one might be obvious but it was still amazing to me how many of my students had the prior knowledge necessary to have higher-level conversations about math-specific topics. Instead of worrying about lower level skills and taking days to teach a math class how to properly graph a scatter plot, today my students interviewed each other, collected data, and plotted points without flinching. One of the most difficult concepts - how to set up correct intervals for each axis - was a breeze to them. Last year I spent two weeks making sure every student knew how to set up a graph so that all points would be plotted.

Again, I am not certain where this disconnect comes from - I am just noticing it thoroughly. The major outcome for me means that my classes can complete more interesting activities (I think) because we are not bogged down in the basic skills.

This might seem like an advertisement for the basic skills movement in mathematics but I don't think it is, mainly because when I talk to my students about how they intuitively understand these concepts they explain it rationally, using real examples, and without difficulty. For someone who learned a skill through rote memorization, he or she would not be able to answer in the same way (at least that is what I think). 

So how do we make sure kids in neighborhood high schools master the prior knowledge before they are too far behind? Isn't that the questions. Creating supporting structures from pre-K through college is definitely a good idea (here's looking at you, Harlem Children's Zone) but I think we need to do this on a public school-scale. I just hope we don't get bogged down in the politics of it all.