Mapping Middle School Math

Math Skills are Interrelated

Math reflects a series of ~300 interrelated skills that span a student’s mathematical learning—from the time they master basic numeracy in the lower elementary school grades through Algebra.

For example, when a seventh-grade student learns about Operations with Rational Numbers, the instruction builds upon predecessors from prior grades, including Understanding Integers and Rational Numbers (sixth grade), Operations with Decimals (fifth and sixth grade), and Operations with Fractions (fifth grade).

That is just one example from Teach to One’s Major Concept Map, which visually illustrates the relationships between mathematical concepts, providing an expansive, nonlinear view of how mathematical concepts build on each other. At the same time, the map communicates the mathematical coherence amongst concepts by grouping sequential, topically-related concepts into “segments.”

Each concept enables deep thinking about big ideas and core mathematical content. The visual connections between the concepts allow teachers and students to examine the interrelated nature of mathematics and how a student’s year-long learning plan can be shaped.

“The mathematical relationships reflected in the Teach to One skills map are very much in line with the current state of educational research, as well as my own experience. The map itself is a formidable asset on the broadest spectrum, between kindergarten and 12th grade, and I encourage educators, policymakers, and researchers to use it to guide their practice and decision-making.

– Neil Heffernan, Worcester Polytechnic Institute