Learning is a Balancing Act

In learning a new topic, or designing a curriculum, decisions must be made.  How much time is available for the learning tasks?  What is the scope of what is to be learned?  That is, the content and curriculum.  But just as important is to learn according to a balance between understanding, procedure, and skills.  These can be divided by time and effort devoted to each. As shown in Figure 1 all three are shown as equally balanced.

Figure 1

Each of these is important almost in a competitive way.  Avoid any one or two of them and essentially nothing of value can be learned.  As a math professor, I often hear the lament, “I understand the material; I just can’t solve the problems.”  Imagine if your doctor says something similar, “I understand you have an intestinal problem, I just don’t know how to treat it.”  Or the airline pilot who says, “I have my pilots license, I’ve just never flown this kind of plane.”  In each of these the learning was not balanced as it should be.   How silly these sound; how rediculous, society does not license doctors or pilot that do not have the balance.  But the schools?  That is another story.    

We hear of teachers that can solve fraction problems (procedure and skill) but can’t explain what they’ve done and why. We hear of students that can multiply 12 x 13 (skill) , but don’t understand what it means. Nowadays,  we hear a lot about is inquiry based learning.  This means the student more-or-less discovers their own knowledge as they learn.  Let’s focus on math.   Up until a few years ago when procedures and skills were reintroduced (NCTM talking points) we heard so many comments that students couldn’t do anything. They were involved with the understanding math concepts and not enough to apply them except in simple “toy problems.”

Now imagine a medical school based completely on the inquiry method.  Medical students sort of learn about organs and what they do, discovering functions in their own experiments, developing their own procedures, leaving established medical procedures and skills lacking.  Of course, no one wants this doctor to fix their illness. 

Let’s focus now on problem solving and what the triad of understanding, procedure, and skills means.  We do this through examples.  Problem solving is the meat and potatoes just about every profession from science to accounting to practice of the law.   Note even the word “practice” applied in the legal and medical professions means the application of “procedures and skills,”  the understanding component apparently is a given.

A.    Mathematics: Optimization problems.

Understanding:  To see or understand what the problems is, what is to be optimized, how the problem components interrelate.
Procedure: What procedures should be used to solve the problem, to set up the key equations, and to make ready the problem for solution.
Skills: To carry out procedures.  In this component, the skills to handle in an efficient manner all that needs to be done, whether to use calculus, graphing, tables, etc, and the computational and possibly algebraic fluency required.

B.    The Law: Making the Will

Understanding:  To understand what the client wishes to bequeath, and the law involved in interpreting the written document
Procedure: The structure of the will, the order of statements, the style to guarantee that no arbitrariness can be interpreted amongst the provisions.
Skills: The actual construction of the will, the language, key points to avoid misunderstanding and avoid legal disputes.  You surely don't want your lawyer consulting with a "Making a Will for Idiots" book or using simple will-making software. You want, you demand, an expert at all aspects of the will.

C.   Flying a commercial jet

Understanding:  Understanding basic principles of aerodynamics, and how the various airliner controls affect flying conditions.
Procedure: The hundreds of airline cockpit controls, the order in which to apply them, how they interact, and what to do in emergencies.
Skills: The actual flying skill that will maintain the aircraft in flight – and on takeoff and landing.  This usually implies many near reflexive abilities that are applied automatically as needed.  This is something akin to “touch.”  After all, the pilot can’t look up procedures or skill in the manual as the plane flies along.  

For each learning environment, the proper balance of these big three, understanding, procedure, and skills in order that the desired results are obtained.  It is the proper balance that varies across all learning topics.  I surely wish some educators were not so entirely swept away by a single pedagogy or teaching style that address just one of these.