From Counting to Calculus: Weaving Mathematical Connections

Many curricular frameworks for teaching mathematics tend to be only a list of mathematics topics to be learned, with no clear elaboration of key ideas or organizing principles.  Because of this, students may not be taught to integrate mathematical ideas, which causes gaps in their knowledge and limits their understanding.  The Quantile® Framework for Mathematics, used in conjunction with the Common Core State Standards for Mathematics (CCSSM), helps teachers identify key connections and provide ways to ensure that students gain a comprehensive understanding of mathematics.

Mathematics is hierarchical and lends itself to learning progressions.  Development of mathematical concepts depends on a student’s understanding of prerequisite concepts.  Learning progressions are curricular frameworks that provide sequencing and guide teachers on proportional use of instructional time.  The CCSSM lend themselves to the development of learning progressions because they provide critical areas for instruction.  The CCSSM aligns content across K-12 so new material clearly builds upon concepts learned previously.

The Quantile Framework for Mathematics and its taxonomy provides a unique way to support the implementation of the CCSSM and address individual student needs by reporting both student ability and difficulty of concepts on the same scale—the Quantile scale.  The taxonomy of the Quantile Framework comprises approximately five hundred skills and concepts called QTaxons.  Each QTaxon is linked to related QTaxons, and these groupings form a knowledge cluster.  Knowledge clusters form a tightly woven web that encompasses the mathematics learned from kindergarten through high school.  By using information about student mathematical ability, the difficulty of the mathematical concepts, and the relationship among mathematical concepts, teachers can effectively target instruction for their students.

For a more detailed description, be sure to check out our latest white paper: Weaving Mathematical Connections from Counting to Calculus: Knowledge Clusters and The Quantile® Framework for Mathematics

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