Conceptual Understanding Versus Procedural Fluency.

 

I am from the days when you learned to solve mathematical problems by being fluent in knowing how to solve the types of problems.  I didn't have to know that when I solved a one step equation, I was finding a point on a line or that the number in front of the variable in the linear equation represented the slope no matter whether it was a business application or a standard y = 3x + 2 solved in isolation.

It is only since I became a teacher that I've seen these connections rather than working each topic in isolation.  So today, I'm looking at conceptual understanding versus procedural fluency.  

Procedural fluency is the ability to memorizing the steps to solve an equation and doing the computation without necessarily understanding the concept behind the math.  This is like seeing a one step equation and knowing the steps to find the unknown value without knowing what the result represents.  Learning math this way seldom allows students to make deep connections

Conceptual understanding connects the procedures with understanding the concept behind them. In other words, when a person solves a math problem they know how to solve it, why certain steps carried out, and why the approach worked. It actually requires higher depths of knowledge because of the connections being made.

In fact, deep conceptual understanding is defined as students having the ability to transfer learning or knowledge from one lesson or subject to another, to learn through trial and error, consider how to solve a problem rather than just applying a procedure, and explain the thinking that went into solving it.  This is why developing conceptual understanding is important.

It is important to know that most text books have questions that focus on developing procedural fluency  so as a teacher it is important to spend time helping students develop conceptual understanding. This can be done by readjusting questions so they more open.  For instance, rather than asking a student to find the area and perimeter of a specific 15 by 8 rectangle, ask students to find a rectangle with an area of 36 square units and a perimeter of 30 units.  The second way has students work with their knowledge of area and perimeter to determine various rectangles that meet the criteria stated. 

So when you are teaching the topic, look at ways you can change some of the problems from being strictly procedural to requiring conceptual knowledge.  Let me know what you think, I'd love to hear.  Have a great weekend.