As students and I reviewed a multi-step math problem today, I compared the problem to Jimmy Kimmel's story about his son's birth and surgery.
I told students that it was the systematic work of the nurses and doctors that saved the child's life. If the nurse and doctors had not been attentive to detail, the child would not have survived.
Then I told them that learning math, in part, is learning to think and act systematically. Then we applied that thinking to solving the problem.
It's often not natural for children to think systematically. It takes practice to read with detail and act systematically. We practice all kinds of coding systems to aid systematic problem solving and work in math.
Kimmel noted the genius of science and medicine last night. Then his guest, Dr. Oz, gave us a historical context of the amazing life-saving surgery Kimmel's son had, a surgery not available when many of us were born.
Teaching math is teaching thinking and problem solving--teaching math is helping students to learn how to organize, analyze, synthesize, and make sense of the world around them. That is one reason why math is such an amazing subject to teach.