If you were to envision the mathematics elementary school students should learn, what would they look like? What habits and attitudes do you think mathematically proficient students have?

In my opinion too often math at elementary schools is seen as a memorization skill where students regurgitate numbers quickly rather than being able to understand and apply the rules of math. As long as students only see the 'right' and 'wrong' of an answer without being able to explain the why, then they do not understand math they only "know it".
Students need to be exposed to the reasons behind the math, how it helps us to learn from what we can see/measure. Students have their own questions and need to learn how math can help them solve these. Things as simple as 'Do you want to be a millionaire? Then how much do you have to make every -week or month or year- to become one in a set number of years.' Then combine this with all the possible ancillary questions and you have students working through all kinds of pertinent self directed questions. They do the work but don't see it as 'assigned work' it is rather work in their own self interest.
Not all math can be reduced to this level of simplicity but in the early years it often can. Later on teachers have to learn to ask better questions to help keep up an interest in math. Basics have to be understood and we need to be taught that more than one path leads us to the correct answer. The diversity of paths is what needs to be encouraged so that we can all grow. As teachers we need to find these paths and not be stuck on just one of them.

My idea for a great vision of elementary school math would be to gain a foundation of the numeracy skills that kids will need throughout their lives. This would include basic mastery of addition, subtraction, multiplication, and division—without needing to use a calculator for simple calculations.
Another great vision for elementary school math would be to foster curiosity to learn more about math; to develop a love of numbers and the patterns that they form and to appreciate the logic behind each sum.
A mathematically proficient student should have an attitude of precision and determination when it comes to solving problems. They need to get into the habit of checking and double checking their work, paying attention to detail and thinking logically.