A Conversation on Teaching

To Begin

graeme fawcett @graeme EN

educate: [verb] to teach someone over a period of time

==[

A series of facts, presented in the right order can be used as a teaching method.

First, establish the context by framing the discussion. Framing facts can be presented in any sequence by definition as they contribute to the starting position, not the vector. Care should be taken not to overload, as attention is limited and the act of establishing a baseline position is crucial. If the framing is too vague, you and your collaborator will not start from the same place. Crossed vectors meet once, collaboration requires parallel lines.

Then a series of facts, presenting in an order carefully curated to reinforce connection. Provide the first to establish the vector A -[an idea]-> B. Ensure the correct conclusion is reached, provide a confirming fact and the next target, B -[a corollary]->C. Repeat

]==>

context engineering: [verb] to teach someone over a period of time #engineering #mathematics #ai

A Reply

1h Three plus or minus five @ThreeSigma@mastodon EN

@graeme

Wow is that not how education works….

The Question

1h graeme fawcett @graeme EN

@ThreeSigma I'm curious to know what you mean.

It might not be how the traditional broadcast method of teaching via lecture functions, but as a means of transferring verified information across a boundary, it seems to be sufficient.

What were your office hours to you if not a vehicle for collaborative learning?

The Reply

1h Three plus or minus five @ThreeSigma@mastodon

@graeme Education is not a transfer of information.

Education fosters thinking, and in higher ed it trains disciplinary thinking. Ideas are given less than facts. Most people learn ideas inductively, not deductively, especially when being introduced to a discipline. Skills and thinking are learned by iteration and practice and feedback.

Office hours were of course collaberative: which means the student talks to the teacher, which is not in your model.

The Teaching Moment

Dec 18, 2025, 10:55 AM · 0boosts · 0quotes · graeme fawcett @graeme EN

@ThreeSigma I fear, my friend, that we are talking past each other on similar vectors.

"Education fosters thinking" - this is the vector we're establishing. Thinking is a progression of ideas, the vector frames them. Our job is to provide the framing

"Ideas are given less than facts" - that's the entire thesis. My apologies for choice of word, I had understood it's use in the feedback loop implied the suggestive qualities of the facts being provide - they're being given in a sequence to guide the receiver towards understanding. The medium converts "a thing that is known to be true, especially when it can be proved" to "a plan, thought or suggestion, especially about what to do in a particular situation".

"Most people learn ideas inductively, not deductively" - again, the whole point of the thesis. We're leading someone to a conclusion by providing the information in a predefined order, with gates ensuring comprehension before proceeding.

"Skills and thinking are learned by iteration and practice and feedback" - that's what we do once the conversation is over. We have to establish the vector first. Crossed vectors meet once, if you don't start from the same place your paths will only ever meet on a singular piece of output. If your goal is collaboration though, then this up front work becomes crucial to sustained, aligned output.

"Office hours were of course collaborative: which means the student talks to the teacher"

""" Provide the first to establish the vector A -[an idea]-> B. Ensure the correct conclusion is reached, provide a confirming fact and the next target, B -[a corollary]->C. Repeat """

"Ensure the correct conclusion is reached" is the very feedback mechanism you're describing whereby the student talks to the teacher.

The information transfer is just the means by which we establish the vector. Teaching happens when we're collectively traveling it

North

slots:
- context:
  - Teaching conversation demonstrates the innuendo philosophy in practice - vectors,
    parallel alignment, collaborative learning
  slug: prompt-engineering-by-innuendo

East

slots:
- context:
  - Teaching conversation articulates the vector metaphor; this node shows it's mechanistically
    true
  slug: vectors-all-the-way-down
- context:
  - Related teaching reflections
  slug: toodles-teaching-moment