The Common Core calls for greater focus in mathematics. Rather than
racing to cover many topics in a mile-wide, inch-deep curriculum, the
standards ask math teachers to significantly narrow and deepen the way
time and energy are spent in the classroom. This means focusing deeply
on the major work of each grade as follows:
- In grades K–2: Concepts, skills, and problem solving related to addition and subtraction
- In grades 3–5: Concepts, skills, and problem solving related to multiplication and division of whole numbers and fractions
- In grade 6: Ratios and proportional relationships, and early algebraic expressions and equations
- In grade 7: Ratios and proportional relationships, and arithmetic of rational numbers
- In grade 8: Linear algebra and linear functions
This focus will help students gain strong foundations, including a
solid understanding of concepts, a high degree of procedural skill and
fluency, and the ability to apply the math they know to solve problems
inside and outside the classroom.
2) Coherence: Linking topics and thinking across grades
Mathematics is not a list of disconnected topics, tricks, or mnemonics;
it is a coherent body of knowledge made up of interconnected concepts.
Therefore, the standards are designed around coherent progressions from
grade to grade. Learning is carefully connected across grades so that
students can build new understanding onto foundations built in previous
years. Each standard is not a
new event, but an extension of previous learning.
3) Rigor: Pursue conceptual understanding, procedural skills and fluency, and application with equal intensity
Rigor refers to deep, authentic command of mathematical concepts, not
making math harder or introducing topics at earlier grades. To help
students meet the standards, educators will need to pursue, with equal
intensity, three aspects of rigor in the major work of each grade:
conceptual understanding, procedural skills and fluency, and
Conceptual Understanding: The standards call for conceptual
understanding of key concepts, such as place value and ratios. Students
must be able to access concepts from a number of perspectives in order
to see math as more than a set of mnemonics or discrete procedures.
Procedural skills and fluency: The standards call for speed
and accuracy in calculation. Students must practice core functions,
such as single-digit multiplication, in order to have access to more
complex concepts and procedures. Fluency must be addressed in the
classroom or through supporting materials, as some students might
require more practice than others.
Application: The standards call for students to use math in
situations that require mathematical knowledge. Correctly applying
mathematical knowledge depends on students having a solid conceptual
understanding and procedural fluency.