Several of my colleagues and I were fortunate enough to travel to New Orleans for the NCTM 2014 conference. It was amazing to hear so many great presenters. There were two overall topics that resounded with me:

The importance of writing, reading, listening, and speaking math.

We need to provide students with problems that get them thinking, talking, then solving
Writing and speaking “math” is something I know to do, but need to do more of. Teacher, Beth Nickle, gave great ideas and insight into how she uses it in her classroom. She provided her full presentation here.
The second resounding topic was the fact that it so important for students to inquire. So many times we present material without giving students the chance to question, think, or talk it out. The following presenters touched on this topic:
 The team from Mathalicious provided real world lessons that are challenging, engaging, and require students to think critically. One such example, was a lesson titled “Pairalysis” in which students would figure out how many possible combinations of Nike Shoes they could design (based on the options at Nike).
 Geoff Krall – discussed how to design a problem based classroom. “Effective problembased learning classrooms adeptly foster problemsolving skills in students by steeping instructional meaning in the context of complex tasks.” In one example, he created a video for his students involving moving. He left them to the question, “Should I rent a smaller truck and take several trips or rent a larger truck and take less trips?” It was left openended, allowing the students to figure out the variables. What is needed to solve this problem?
 MathSolutions spoke of the importance of having academically productive talk in the classroom (presentation here). They showed a 3act math, which once again promotes inquiry in our students. They ended with a quote, that I think wraps it all up:
“Our goal is not to increase the amount of talk in our classrooms, but to increase the amount of high quality talk in our classrooms—the mathematical productive talk.”
We want to promote this kind of talk for our students. To get them there, we need to challenge them and get them thinking critically through engaging problem scenarios.