Facilitate learning through the inner game of meaning as uses: Better teaching in any subject, part 3

• This is part of the "Better teaching in any subject" series:
• Part 1: Problems with modern inquiry based methods
• Part 2: Meaning is use
• Part 3: Facilitate learning through the inner game of meaning as uses
• Part 4: Worries over losing deep conceptual knowledge (forthcoming)

The inner game of meaning: a lesson from tennis

A lesson from the Inner Game of Tennis (Gallwey) we might draw from is that consciously and intellectually solving the problem of "what is the instructor doing" is like a fool's errand. Because the actual problem the student is trying to solve is "how do I [the student] hit that tennis ball in that situation".  Solving the former problem may help with solving the latter, but there is no guarantee of effectiveness or efficiency.

Because of the unique cognitive and physical characteristics of each student, the solution to the actual problem is always unique anyway.  It always require each student to solve it anew.  The instructor can only point in a general direction, but the student has to go the final distance to arriving at a personalized solution.

If a student's energy is devoted to solving the problem of "what is the instructor doing", then the student will have little energy left for what is more important: solving the actual problem anew for themselves in a way that fits their own unique cognitive and physical characteristics.

How to facilitate learning proper meanings from proper uses

"Meaning is use" means that meaning comes from a variety of particular uses, and students need to look and see while teachers show the varieties of uses properly in order to learn the proper meanings from their proper uses.  But because every student brings with them a different set of prior learning and experiences, a way of conceptual thinking (and physical doing) that works for one student may not work for another.

 
It's a fool's errand for the student to try to consciously and intellectually solve the problem of "what is the teacher doing", be it in math or in tennis.  Again, the actual problem the student should be trying to solve is "how do I [the student] do X [e.g. hit that tennis ball] in that situation". Be it in math or in tennis, the solution to the actual problem is always personalized, requiring each student to solve it anew.

That's why "show, don't tell" may be a good slogan for a very good first step, but it's not enough.

Certainly, for students to learn the proper meaning of things, they must be shown proper uses (be it words, formulas, backhand with a racket, etc.), but developing a personalized solution to "how do I do X in situation Y" is a task that each particular student must solve for themselves. That's because each student has uniquely personal prior learning and experiences, all of which are trapped in their own mind, and no one but themselves have privileged access to the stuff in their head.

Therefore a good step two, for a teacher who wants to help a student learn effectively, is to figure out how to facilitate the process of the student finding a personalized solution to "how do I do X in situation Y" for themselves.

The obvious general way to facilitate that process is to expose the student to many varieties of situations that requires doing X, so the student can keep doing X until he gets into a personalized "groove" (a kind of mental habit) for doing X in a variety of situations.  Conversely, the student needs to also be exposed to many situations that requires not doing X to ensure the student learns not to do X except in the right situations.

So a part two to the slogan "show, don't tell" might be: "Make them experience it, don't just show it."

That is no excuse for tons and tons of poorly conceived worksheets though.  The key problem with traditional worksheets for practice is their lack in variety.  Worksheets are themselves just one particular situation for doing a task, and it's a very synthetic and artificial situation that has little to no similarity to the authentic real work that people do in research, commerce, industry, etc.  That doesn't mean worksheets are necessarily bad, but that they are not enough.


Summary: Two major steps to teaching for effective learning

If we must summarize, the two major steps to teaching for effective learning are:

• 1. Let students look and see, while teachers show the varieties of uses properly, in order for students to learn the proper meanings from their proper uses.
  
  
• 2.  Facilitate the process of the student finding a personalized solution to "how do I do X in situation Y" for themselves by (A) exposing the student to many varieties of authentically realistic situations that requires them to do X, so they can pick up a personalized "groove" for doing X, but also (B) exposing the student to many authentically realistic situations that requires not doing X to ensure the student learns not to do X except in the right situations.

Note that "doing X" covers a very wide spectrum of possibility, from doing a one-handed backhand with a racket, to doing a completing the squares factoring of a quadratic equation, to doing the conjugation of a verb based on gender, tense, number, etc., to doing the balancing of stoichiometric coefficients in chemical reaction equations, and so on.

There's a lot more techniques to help teachers and students in step 2, but I can't be giving away all the secrets to the inner game of learning here (or I'm just too lazy to write more at this time).