Symbols and Thinking

I stumbled across some notes I made years ago - easy to say, hard to implement...

Teachers sometimes ask students to think about symbols when they should be using the symbols to represent their thinking. 

1) Pose problems that ask students to think mathematically about the big ideas we are interested in.
2)  Introduce mathematical symbols and tools to represent their thinking.
3)  When the symbols have meaning for the students, then they can use the symbols as tools.

Easy!