25 August 2015

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


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.

18 August 2015

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



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.

11 August 2015

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.

04 August 2015

Cognition as a Collaboration with Nature


In the previous posts' parable and examination on trust and collaboration, the group was always two or more intelligent agents.  An interesting angle to think about is to recast those person-vs-person games into a person-vs-nature story, from which we might learn that intelligence cannot figure out the world without assuming by charity that nature must be out to help it (rather than out to harm it).

This post is extremely speculative, but is an interesting thought experiment, one might say.

Consider, if an animal acts in the world only to get feedback in the form of a veto vs no-veto, as in the form of die or not-die, well that at first seems like how evolution works but it ignores a lot of information the animal receives from nature beyond die-or-not.

After all, there's no a priori reason why an animal should think that walking off a ledge should kill it, and yet it learns not to along with lots of other stuff to do or not do.  Not all of that is encoded genetically via evolution: certainly the appearance of every ledge or hilltop or predator can't all be encoded into DNA. Some basics are, of course, but much is learned once born.  How does it learn it if the only feedback it can ever get is die-or-not?

28 July 2015

Trust and Other Elements of Collaboration




In the previous post, I examined through a parable comparing two different kinds of group decision making strategies: (1) "freely" throwing out suggestions, vs (2) veto-or-not the other group member's choice.

From that, we talked about communication in terms of information content and how it affects whether we can really get to know a person better (as a friend, let's say) in what is a repeated game (as in game theory, or micro-economics).

Now, we can also talk about what it means to collaborate, not just cooperate, but arrive at decisions via collaboration.  That's what we'll talk about presently.

See, both strategies above can be cooperative.  In fact, the veto-or-not strategy could be seen as an extreme form of cooperation via deferring totally to the other party unless the choice picked is just too far outside the bounds of one's bare minimum acceptability.

Though it's cooperative, it really is another classic example of what non-collaboration looks like.  The party who engages in veto-or-not behaviour is purposefully, even if unintentionally due to ignorance, withholding information from the other parties.  That was clear in the previous post's parable where we saw how veto-or-not communicates exactly one bit of information, a true vs false, or 1 vs 0, etc.