Worries over losing deep conceptual knowledge: Better teaching in any subject, part 4

• 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

A concern some may have with facilitating learning through the inner game of meaning-as-uses is that it seems to turn everything into decomposed techniques and skills, lacking in holistic, deep, conceptual, or otherwise "meaningful" knowledge.

A moment's thought should give you comfort that that's very far from the truth.

Imagine complaining that by breaking tennis up into the various forehand and backhand techniques, players will lose sight of the holistic meaningful concepts required to understanding tennis.

I'd imagine a lot of the worry comes about from not "seeing" the holistic concepts being taught or learned when seeing only the individual techniques being learned.  Traditionally, we'd see the worksheets for practicing factoring quadratics but never see the worksheets for learning what quadratics are conceptually, or what the meaning of factoring is.  From that, we might be led to believe that there must be something wrong with worksheets or with not teaching concepts and meanings (as if we could even directly teach concepts or meanings at all).

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.

Meaning is use: Better teaching in any subject, part 2

• 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
  (forthcoming)
• Part 4: Worries over losing deep conceptual knowledge (forthcoming)

Meaning is use

Meaning as use is a philosophical concept of meaning from Wittgenstein:

"For a large class of cases of the employment of the word 'meaning' --- though not for all --- this way can be explained in this way: the meaning of a word is its use in the language" (Philosophical Investigations).

Many traditional and folk understanding of meaning explains meaning in terms of mental representations, or idealized objects in some (sometimes mathematical) objective space, etc. --- i.e. stuff in people's heads or in some Platonic ideal space that has no practical significance for teachers in the classroom.

So while we may not necessarily agree that meaning is philosophically just its use in the language, it's certainly practical to see it that way for teaching!  Because we can, as Wittgenstein urges, look and see the variety of cases in which a word is used, but we cannot look into the heads and minds of students --- and more importantly, nor can students look into the minds of teachers in learning what the teacher meant.

"So different is this new perspective that Wittgenstein repeats: 'Don't think, but look!' (PI 66); and such looking is done vis a vis particular cases, not generalizations." [1]

Meaning as discussed usually refers to meaning of words in a language, but math is no different.  Math is itself a natural language, with a grammar and semantics that's evolved in the mathematical community, used to talk about things and their relationships.  We need not look further than many science research papers wherein authors write mathematical notations and formulas, interweaved with English prose, to see how math is very much a language we can talk about things with.

If we accept that meaning (of words) comes from their use, then the meaning of a thing like a math formula is also built up from the use of it.  The proper meaning of a math formula doesn't come from the instructor explaining it, and it doesn't even come from students discussing and talking about it.  The meaning of a math formula comes from the proper use of it.

Problems with modern inquiry based methods: Better teaching in any subject, part 1

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

Problems with experiential, discovery, inquiry, and constructivist learning and teaching

In education, teachers nowadays are often taught constructivism and other modern inquiry based teaching and learning methods.  Those teaching methods purport to help educators teach children in a way that helps the kids construct their own meaning of what they are to learn.  One of the central claims is that meaning is constructed through experiencing, and reflecting on those experiences, on the basis of concepts and meanings learned previously.

By "modern inquiry based" teaching and learning methods, I mean the constellation of academic philosophies and folk understandings of experiential, discovery, inquiry, and constructivist learning and teaching methods.

What's frustrating is that the core understandings in modern inquiry based teaching and learning methods are not so much as wrong, but are just not very helpful to teachers.  Not helpful because the core pedagogical ideas basically only tell teachers that kids must learn from experiences and reflection.  Since we're not privy to see or control all the stuff that happens in the kids' heads anyway, therefore all the philosophically interesting parts of constructivism have no practical significance in the classroom.

Nuking Akonadi data to fix KOrganizer crash

I updated my Lubuntu Linux system recently and afterwards KOrganizer started to crash.  Well, not exactly crash.  More like KOrganizer refuses to work when it finds that Akonadi has stopped working.

Symptoms:  Open KOrganizer only to be greeted by a big red "X" icon and the words "The Akonadi personal information management service is not operational."  Click on the "Details" button and the "Akonadi Server Self-Test" window says I have these errors:

• MySQL server log contains errors
• Akonadi control process not registered at D-Bus.
• Akonadi server process not registered at D-Bus.
• No resource agents found.
• Current Akonadi server error log found.
• Previous Akonadi server error log found.

Here's my fix for it.