HCC class lecture 2 items

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HCC classlecture 2 items
John Canny1/24/05
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Administrivia

• The class swiki is up.
• Office hours this week
• 3-4 pm Tuesday
• 4-5 pm Wednesday

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Kinds of knowledge

• Things you might overhear
• That was a beautiful proof
• Its a very elegant result
• Mathematics is an art
• But these adjectives are out of place. Surely the
  only sensible ones are e.g. correct, complete,
  short, long,
• Why do we use the first kind of adjective?

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Kinds of knowledge

• The readings contrast various kinds of knowledge
  knowledge of facts and figures vs. knowledge
  with understanding
• Knowledge with understanding included
• Conditionalization (contextualization)
• Relating to existing knowledge
• Applying in multiple contexts
• Thinking ahead (meta-cognition) about how this
  concept might be useful in future.

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Kinds of knowledge

• The readings also underscore that learning
  doesnt stop once we have the concept. What
  happens afterwards?
• We gradually automate the concept make it
  pre-attentive so we can fluidly use it.
  Structures fuse into chunks that are
  immediately perceived.
• We prioritize the new concept relative to others.
  Once we know how and when to use it, we place it
  in our bag of big ideas with a priority.

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Discussion point 1

• Contrast knowledge of mathematics with the skill
  to do mathematics.
• Mathematics (predicate logic) allows
  meta-mathematical knowledge to be represented.
  i.e. Allowable steps in a proof can be
  represented mathematically.
• Is math a good language for describing math
  skill?

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Microgenesis

• The readings only briefly mentioned
  microgenesis the evolution of an individual
  concept during learning.
• But much of the readings cover various steps
  that happen when we acquire a concept with
  understanding.

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Discussion point 2

• Pick a concept that many of you share (e.g.
  proof of the halting theorem, or understanding of
  compilation etc.)
• List some important steps that occur during
  micro-genesis.
• Give the time frame for those steps.

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Aside

• Pretty much everything you read is abstract
  knowledge.
• Your ability to understand it depends on your
  ability to connect it to existing knowledge,
  preferably first-hand.
• So dont forget to use examples from personal
  experience in the discussion.

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Discussion groups

• An ideal group size is 4-5 people. As the group
  grows, its more likely to have margins.
• Remember you have to summarize your groups
  discussion at the end.
• Elect a note-taker.

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Discussion points

• Contrast knowledge of mathematics with the skill
  to do mathematics. Is math a good language for
  describing math skill?
• List some important steps that occur during
  micro-genesis. Give the time frame for those
  steps.

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Reading for next time

• Several chapters from The Psychology of the
  Child by Piaget and Inhelder. Volunteer?
• Piagets classic description of ontogenesis in
  young children.
• Contrast this with the map of micro-genesis
  that you just built.