Confirmation of Mathematical Knowledge

The internet is changing the world, as everyone must know on some level, but not many people seem to be talking about in my experience, at least. I’m quite confused as to why not…

In my latest attempt to become certified to teach in public schools, I encountered a lot of resistance to deviation from the traditional drill-style approach to math instruction. Part of the problem is that most math educators are very over-worked and feel they have to be more concerned with making the current way of doing things run smoothly than with experimenting with new ideas (even though that’s the only way progress ever happens). But another part is that people seem unaware, or just not to care much, about how the internet changes society’s approach to knowledge.

As the following table explains, there are three stages: 1. authority  2. personal experience  3. understanding of the social application. The printing press and books allowed a huge increase in the second level, as all of a sudden people could learn to read for themselves and experience culture on their own time, rather than through staged rituals and performances. The internet is allowing an equivalent increase in the third level. Rather than having to confirm everything through individual experience, the internet exposes us to multiple sources of authority, allowing us to confirm knowledge by using our judgment to decide which source of authority to trust. This is a far more efficient method of gathering and confirming knowledge than the second stage, which itself was far more efficient than stage 1.

How People Confirm Knowledge

based on:

example:

when it first started to become a dominant/mainstream form for confirming knowledge within society:

Stage 0

instinct

“I’m hungry” “I’m horny” “I’m hurt”

when animals evolved a large enough brain to be aware of sensations.

Stage 1

authority (awareness of the concept)

Tribalism, “Thou shalt not”

with the invention of language

Stage 2

personal experience (awareness of personal applications)

“I like to eat at Wendy’s”, “I like Virginia Woolf’s novels”

with the invention of the printing press

Stage 3

personal judgment: often based on differentiated experiences from multiple sources (awareness of social applications)

“My favorite fast-food restaurant is Wendy’s, because Wendy’s has the best internet access.” “My favorite novelist is Virginia Woolf, because her novels remind the reader of the value of the non-human world.”

with the invention of the internet

Math education lends itself to computers and electronic presentation, so will be one of the first fields to go through this transformation.

SRC: http://academic.mu.edu/peressini/documents/proof-rel.pdf

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