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Topic

A Topic is a defined unique area of knowledge and combined together to form a topic list.

  • Topics are the fundamental building blocks for defining relationships between different units of knowledge.
  • A topic should be as specific as possible to avoid overlapping knowledge domains. (i.e. specific, clear, unambiguous).
  • All topics have the same significance. There is no predetermined hierarchy.
  • A topic is referred to differently depending on its relationship to another other topic.

Types of Topics

An Atomic Topic is a topic that is self-declared as a smallest knowledge domain.

  • Good Examples: addition, subtraction
  • Bad Examples math, arithmetic
flowchart BT

topic[/topic\]
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A Group Topic is a topic with defined subtopics.

  • Each subtopic directly represent proficiency in a subspace of the group topic.
  • Full proficiency in all subtopics indicates full proficiency in the group topic.
  • Grouping topics provides an abstraction mechanism for organic growth of the knowledge domains without exhaustive early definitions, both higher (more general) and lower (more specific).
flowchart BT

topic[/arithmetic\]
subtopic1[/addition\] --> topic
subtopic2[/subtraction\] --> topic
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A Subtopic is a topic representing proficiency in a subspace of a single group topic.

  • Topics DO NOT share subtopics.

A Pretopic, is a topic referenced as a prerequisite in order to begin building proficiency in the current topic.

  • Proficiency in a pretopic does NOT indicate proficiency in the topic requiring it.
  • Any topic can be a pretopic.
  • A topic may be used as a pretopic by multiple other topics.
flowchart BT

topic1[/addition\]
topic2[/subtraction\]
pretopic[/numbers\]

pretopic -.-x topic1
pretopic -.-x topic2
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Tips

  • Use abstraction to clarify seemingly overlapping domains (i.e. same words but different context)

  • A Group's dependencies should ideally be at a similar abstraction "layer of knowledge". This avoids a group topic with a very large number of subtopics.

  • Group topics enable the knowledge space to expand. For example:

    • Grow Higher - Create a new topic by combining existing subtopics. This defines higher-order ability.
    • Refactor - Replace a set of subtopics with a new group topic defined by the same subtopics.
    • Go Deeper - Create new topics then add them to an existing atomic topic, converting it into a group topic.

Detailed Example

Below is a simple example mapping the increasing proficiency from simple numbers to basic math proficiency.

Note

The below is for illustration only. It is NOT intended to be an accurate representation.

flowchart BT

numbers[/"numbers"\]

%% Abstraction 1
  addition[/"addition"\]
  subtraction[/"subtraction"\]
  multiplication[/"multiplication"\]
  division[/"division"\]

  arithmetic[/"arithmetic"\]
  addition --> arithmetic
  subtraction --> arithmetic
  multiplication --> arithmetic
  division --> arithmetic

  numbers -.-x addition
  numbers -.-x subtraction
  numbers -.-x multiplication
  numbers -.-x division

%% Abstraction 2
  algebra[/"algebra"\]
  variables[/"variables"\] --> algebra
  constants[/"constants"\] --> algebra
  expressions[/"expressions"\] --> algebra
  single-variable-eqs[/"single variable equations"\] --> algebra

  arithmetic -.-x single-variable-eqs
  arithmetic -.-x expressions

%% Abstraction 3
  math[/"math"\]
  algebra --> math
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What does this graph say?

  • The addition topic requires understanding the numbers topic before beginning.
  • The arithmetic topic is understood if addition, subtraction, multiplication, and division are understood.
  • The expressions topic requires understanding the arithmetic topic before beginning.
  • The algebra topic is 50% understood if the variables and constants topics are understood, but not the expressions and single variable equations topics.