Common Core Math

The Common Core Math data set is a collection of fine-grained Micro-outcomes covering Grades 9–12, mapped into a graph model with prerequisite relationships between Micro-outcomes. It was developed as part of the Mapping Lab's research on COVID-19 educational continuity.

The Model

Common Core Standards are deliberately broad — a single Standard often bundles several distinct skills. As a first step, our subject matter experts decomposed each Standard into more specific learning statements we call Micro-outcomes. For example, the Standard CCSS.MATH.CONTENT.7.G.B.4 — Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle — yields three distinct Micro-outcomes:

  1. State the formulas for the area and circumference of a circle.
  2. Use formulas for the area and circumference of a circle to solve problems.
  3. Give an informal derivation of the relationship between the circumference and area of a circle.

This decomposition enables meaningful prerequisite relationships to be drawn between entities. We can now precisely state that State the formulas for the area and circumference of a circle is a prerequisite to Use formulas for the area and circumference of a circle to solve problems — a relationship that would be impossible to express cleanly at the Standard level.

The data set has three types of entities and two types of relationships:

  1. Grade Band (e.g. Grades 6–8, Grades 9–12)
  2. Standard (e.g. CCSS.MATH.CONTENT.7.G.B.4)
  3. Micro-outcome

Micro-outcomes are connected via has-prerequisite-of relationships. Micro-outcomes are grouped under Standards, and Standards under Grade Bands, via has-parent-of relationships. The resulting graph model looks like:

Common Core network model ontology

How we created the data set

Our team of subject matter experts with graduate degrees in mathematics examined each Standard to decompose it into Micro-outcomes and to draw prerequisite relationships between them. Determining whether Micro-outcome A is a prerequisite to Micro-outcome B requires careful domain judgment — this process was carried out manually and iteratively, with review cycles to ensure accuracy and consistency.

Applications

The mapped structure makes it possible to query the graph for questions that are impossible to answer from a flat list of Standards. For example:

  • Which Micro-outcomes are downstream of a Standard that was disrupted during COVID-19?
  • How many grade levels are affected if a student misses instruction in a given topic?
  • What is the minimum remediation path to get a student back on track?

These questions underpinned our COVID-19 disruption analysis, described in detail on the COVID-19 Impact page and in our paper.

Interactive Common Core map showing prerequisite relationships

Publication

Huang, L., Bicol, A. and Willcox, K., Modeling COVID-19 disruptions via network mapping of the Common Core Mathematics Standards, ASEE, 2021.

Getting access   To gain access to this data set, please contact us at mapping@oden.utexas.edu.