Going Back to Conceptual Understanding When Needed.
When a student or a team is struggling with how to do something it is often valuable to ask them to take a step back and consider the bigger picture around the concept. This can feel counterintuitive for teachers and may even feel unhelpful for students at times. Consider the following analogy. If I bring a specific problem of isolated knee pain to my doctor, I may be annoyed at him or her for suggesting that I need to change to an anti-inflammatory diet. I may not recognize that my doctor is actually trying to support my long term health over my short term pain. Similarly if a student is struggling with the steps of solving a system of equations, and his or her teacher suggests they take a step back and review what is true about each equation, why the problem is putting the equations together in the first place, and what each axis or point mean in terms of the context, the student may not immediately understand or appreciate this approach. Nevertheless, Principles to Action (NCTM 2014) tells us that we must build procedural fluency from a place of conceptual understanding. This means that conceptual understanding and procedural fluency can not be taught in isolation. Connections between the concepts and the procedures they support must be made transparent for deep and lasting understanding to occur. When we direct a student’s thinking back to the big ideas of the mathematical concept, the procedures begin to make sense and no longer seem like a meaningless list of steps to memorize. Keep in mind that conceptual understanding and procedural fluency are both important and working with both can help students understand how one supports the other.