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.