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As an undergraduate education student, I was challenged to write my personal mission statement that would help me define myself as a teacher. I don't recall the entire statement, but I know that it included something along the lines of "helping students think critically about mathematics." Looking at this from an experienced perspective, I'm not convinced that I knew what critical thinking was, let alone how to help my students become critical thinkers. With time, I've come to understand that there is no one way to accomplish this task, but there are strategies we can implement that will help students develop these skills.

From a very young age, children learn and develop using all their senses. As infants they are surrounded by the stimulation of shape, color, lines, numbers, patterns, and textures. By the time they reach preschool, they are engaged in stories and imaginative pursuits that build on these sensory explorations. Thanks to the materials they have explored in their first five years, children already have a strong foundation for mathematics when they start kindergarten.

When working with math teachers at any level, one of the complaints I've heard over and over begins with the phrase, "If they only knew their facts..." Fluency with basic facts, however, is only one part of a bigger picture, and I always encouraged teachers to think about the conceptual foundation they were building rather than how quickly students can rattle off some facts. As we consider the increased emphasis on rigor, we need to keep in the back of our minds what rigor is: a balance between conceptual understanding, application, and procedural fluency.