Graphing for Learning and Teaching

id: 1764946663
Date: Dec. 5, 2025, 2:58 p.m.
Author: Donald F. Elger

Goals
- Catalyze learning or teaching by using graphs.
- Build high quality graphs, especially for topics that are difficult to learn
- Describe graphs.
- Recognize the value of graph and become a person who routinely uses them for teaching, learning, explaining, and thinking
Graphs (Network Diagrams)
- A graph refers to a network diagram like this one
- A graph also refers to a typical x-y plot like we use in math or science. But, this page refers to graphs in the context of network diagrams.
- Graphs as network diagrams are taught in computer programming, math, and information technology courses.
What
- Graphing means representing knowledge as nodes connected by relationships.
- A graph can show causes, dependencies, similarities, contrasts, interactions, and feedback loops.
- Graphs differ from lists, trees, and tables because they show many-to-many relationships instead of one-to-many.
- This makes graphs ideal for topics that are complex, interconnected, or hard to grok.
- Core idea: Graphing works because it is the natural language of the brain. When you graph, you stop fighting how the brain organizes knowledge and start working with it.
Why
- The brain stores knowledge as a network of connected ideas.
  - Nodes are concepts.
  - Edges are associations and relationships.
- Graphs mirror how neural networks represent meaning, so learning feels more natural and less effortful.
- Graphs reduce cognitive load by offloading structure from working memory onto the page.
- Graphs increase understanding by showing the deep relationships that lists and trees cannot capture.
- Graphs support better recall by creating many retrieval paths for each idea.
- Graphs help detect:
  - Missing ideas
  - Contradictions
  - Weak connections
  - Misconceptions
- Graphs support meaningful learning, not just memorization.
How to Excel
- Start with a topic you want to understand or teach.
- Identify the key concepts.
- Place concepts as nodes.
- Draw arrows to show relationships.
  - causes
  - depends on
  - interacts with
  - contrasts with
  - leads to
  - consists of
- Add linking phrases to make relationships explicit.
- Expand outward to reveal the full structure of the idea.
- Check for clarity:
  - Does each node represent a clear idea?
  - Is each relationship accurate and meaningful?
  - Are important interactions missing?
  - Are any relationships ambiguous or vague?
- Revise the graph until the structure feels obvious and intuitive.
- Use the graph for explanation, teaching, or further learning.
Examples of When to Use Graphs
- Understanding systems
  - ecosystems
  - democracies
  - economies
- Understanding processes
  - chemical reactions
  - feedback loops
  - learning models
- Understanding complex concepts
  - power
  - motivation
  - fairness
- Mapping relationships across many categories
  - beliefs, norms, values
  - causes and consequences
  - evidence and conclusions
Summary
- Graphs align with the brain’s natural architecture.
- They externalize the hidden structure of understanding.
- They reveal relationships that linear formats hide.
- They reduce cognitive load and deepen comprehension.
- They turn information into meaning.
- When you graph, you work with the brain instead of against it.