Knowledge Clusters

Quantile Knowledge Clusters

Quantile Knowledge Clusters harness the real power of the Quantile Framework's ability to link assessment to instruction. Within the Quantile Framework, each Quantile Skill and Concept (QSC) relates to other QSCs that are prerequisite concepts that students must understand in order to progress in their study of mathematics.

These relationships form a Knowledge Cluster. Knowledge Clusters show the connections between mathematical skills and give their relative difficulty to one another using the Quantile scale.

For example, below is the Knowledge Cluster for the math skill unit rate.  This QSC has a Quantile measure of 830Q (see diagram below).  Remember, the description plus the Quantile measure describe a QSC. This is important because teachers and students can look at the hierarchy in the mathematics content but also numerically see the relative difficulty of one skill compared to another.

The QSCs shown in green are prerequisites and should be learned before advancing to "calculating rate to make comparisons". Looking at the Quantile measures of these skills, you can see that prerequisite skills have lower Quantile measures than 830Q. Impending skills, in red, are those which depend on understanding unit rate. Looking at the Quantile measures of these skills, you can see that impending skills have higher Quantile measures. Supplemental skills, in yellow, are related to learning about unit rate but are not dependent on learning or having learned about it.


Unit Rate Diagram



The QSCs connect to each other forming an enormous web of mathematics skills and concepts related through their content and their measures. This web of content spans content from kindergarten through secondary school mathematics.