Learning Graph for Geometry
This section contains the learning graph for this textbook. A learning graph is a graph of concepts used in this textbook. Each concept is represented by a node in a network graph. Concepts are connected by directed edges that indicate what concepts each node depends on before that concept is understood by the student.
A learning graph is the foundational data structure for intelligent textbooks that can recommend learning paths. A learning graph is like a roadmap of concepts to help students arrive at their learning goals.
At the left of the learning graph are prerequisite or foundational concepts. They have no outbound edges. They only have inbound edges for other concepts that depend on understanding these foundational prerequisite concepts. At the far right we have the most advanced concepts in the course. To master these concepts you must understand all the concepts that they point to.
Here are other files used by the learning graph.
Course Description
We use the Course Description as the source document for the concepts that are included in this course. The course description uses the 2001 Bloom taxonomy to order learning objectives.
List of Concepts
We use generative AI to convert the course description into a Concept List. Each concept is in the form of a short Title Case label with most labels under 32 characters long.
Concept Dependency List
We next use generative AI to create a Directed Acyclic Graph (DAG). DAGs do not have cycles where
concepts depend on themselves. We provide the DAG in two formats. One is a CSV file and the other
format is a JSON file that uses the vis-network JavaScript library format. The vis-network format uses nodes, edges and metadata
elements with edges containing from and to properties. This makes it easy for you to view and edit the learning
graph using an editor built with the vis-network tools.
Analysis & Documentation
Learning Graph Quality Validation
This report gives you an overall assessment of the quality of the learning graph. It uses graph algorithms to look for specific quality patterns in the graph.
- Graph structure validation - all concepts are connected
- DAG validation (no cycles detected)
- Foundational concepts: 8 entry points
- Indegree distribution analysis
- Longest dependency chains
- Connectivity: percent of nodes connected to the main cluster
View the Learning Graph Quality Validation
Concept Taxonomy
In order to see patterns in the learning graph, it is useful to assign colors to each concept based on the concept type. We use generative AI to create about a dozen categories for our concepts and then place each concept into a single primary classifier.
- A concept classifier taxonomy with approximately 12 categories (+/- 1 or 2)
- Category organization - foundational elements first, course capstone project ideas last
- Balanced categories (3% - 17% each)
- All categories under 30% threshold
- Pedagogical flow recommendations
- Clear 3-5 letter abbreviations for use in CSV file
- A Miscellaneous (MISC) category is sometimes added
Taxonomy Distribution
This reports shows how many concepts fit into each category of the taxonomy. Our goal is a somewhat balanced taxonomy where each category holds an equal number of concepts. We also don't want any category to contain over 30% of our concepts.
- Statistical breakdown
- Detailed concept listing by category
- Visual distribution table
- Balance verification