The question in the title mostly covers the question I want to ask. After seeing a number of questions here on ME and having taught/TA'd a number of introductory math classes, I wonder what people thing the essential skills high school should teach students in terms of math. It might be interesting to see what both what math major type people think is necessary and what just general population think is necessary. To limit the question though, let's say that we care what people who teach STEM based math (for non US, that's essentially the non-humanities based academics disciplines) think. What would you like your incoming students to have learnt in high school?

The question in the title mostly covers the question I want to ask. After seeing a number of questions here on ME and having taught/TA'd a number of introductory math classes, I wonder what people think the essential skills high school should teach students in terms of math. It might be interesting to see both what math major type people think is necessary and what just general population think is necessary. To limit the question though, let's say that we care what people who teach STEM based math (for non US, that's essentially the non-humanities based academics disciplines) think. What would you like your incoming students to have learnt in high school?