A large part of that comes with them journalling their feelings, reactions, opinions, and honest talk about Math.
I found this great link from Joanne Griffin that includes 101 Math Journal Topics. You can download the .DOC from her website here.
But here are some examples of work and the honest, sometimes brutal, answers you can get from their Math journalling.
Believe it or not, your Math curriculum can very well we swayed by your students honest reactions to their Math learning. It isn't just as simple as saying, "This is what you need to learn and there's only one way to do it."
If you want to reach every student in your classroom, they need to be able to have an avenue to share their thoughts, opinions, and especially feelings about Math.
I have one student who absolutely despises Math, most because we do the occassional worksheet or textbook work. He can't concentrate and when he does and can't understand a question, he shuts out Math and begins to either distract others or even complain he's not good at Math when he is actually one of my best students.
Incorporating Math Games this year has made the dialogue between my students and myself alot more open and engaging because I told them specifically I rather not give them worksheets or pencil and paper work because games can help them practice everyday in a fun way. Some of my students would sometimes rather do a Cross-Number Puzzle for their Math Centre instead of a game and will frequently ask me if they can.
But I wouldn't have known this if the dialogue hadn't been opened via their Math Journals. They feel safer and more confident to ask me if they can do either pencil or paper work or if they can play games.
Having that safe atmosphere for learning and having fun at the same time is a great way to foster a positive learning environment!