Learning mathematics means having conceptual understanding of mathematical big ideas.  This is important at all levels of study.  Students should be able to see relationships between numbers, use those numbers and their relationships to solve problems, and to explain their thinking.

So, how do we provide students with opportunities to explore and build mathematical ideas?  Try establishing a classroom routine that includes time for Number Talks and Mental Math Strings.  Number Talks and Math Strings are one way to develop mathematical reasoning while promoting teacher-student and student-student classroom discourse.  Number Talks and Math Strings also help students to make sense of numbers, number relationships and number operations.

Another effective curriculum is the Contexts for Learning Units.  These replacement units help students explore a specific mathematical idea using one or two problems within a relevant context.  For example, in the unit The Teacher's Lounge, fourth and fifth grade students are asked to determine how many students should be put into each group if there are 100 students and 13 chaperones for an upcoming field trip.  After solving the problem, students share their thinking by creating a poster, viewing their peer's work during a gallery walk, and participating in a class discussion of strategies.  The Contexts for Learning Units provide excellent opportunities for students to develop their understanding of concepts.  

It is extremely important to ask effective questions when promoting mathematical discourse in your classroom.  Discourse happens throughout the school day.  Our goal should be to deepen student thinking so that students expand their skills and abilities.  Try asking, "Does that strategy always work?" or "Can you make a model to show that?"   Effective questions help students to explore math concepts in a deeper and richer way.