NCTM vs. Common Core

¶ … Grade 1 Math Standards in North Carolina

NCTM vs. Common Core

The most readily apparent distinction between the content and process standards for grade 1 math as outlined by the North Carolina Teachers of Mathematics (NCTM) standards and the North Carolina Common Core state standards is primarily one of scope.

Comparison of Content and Process Standards.

The Common Core state standards are currently much broader in scope, ranging well beyond the a focus on addition and subtraction to include a beginning exploration of geometry and principles and techniques of measurement. Additionally, the Common Core state standards extend performance expectation in the areas of addition and subtraction to addition operations within 100 and subtraction of multiples of 10.

The North Carolina Teachers of Mathematics (NCTM) standards tend to center around addition and subtraction operations, but it also articulates some specific performance expectations for commonly used fractions (1/4, 1/3, and 1/2) and grouping principles (such as sharing equally and equal groupings) that require basic understanding of multiplication and division. The NCTM standards appear to hover in the realm of understanding whole numbers, ordinal numbers, cardinal numbers, place value, and a base-ten number system.

A corollary emphasis in the Common Core state standards focuses on an understanding of whole numbers and place value within the frame of numbers up to 100. Indeed, the Common Core state standards do focus on numbers up to 20, and in the place value performance standards, stress the importance of children learning that numbers from 11 to 19 consist of both a ten and some ones.

The Promise of North Carolina Standards for Mathematics

Both the North Carolina Teachers of Mathematics (NCTM) standards and the North Carolina Common Core state standards show promise for effective instruction of mathematics to students in first grade. An emphasis on understanding mathematics concepts through exploration of different models and manipulation of objects to demonstrate operations and numerical relationships offer motivational and varied opportunities to students. In the Common Core state standards, in particular, the standards are designed to ensure that children understand the fundamental relationships between numbers and are not left with only a rudimentary ability to complete operations.

Many of the state standards appear to have an iterative nature, which is critical to learning more advanced skills and concepts. Through performance standards design, the two systems have developed a system of conceptual nesting rather than simply relying on the more conventional system of learning tiers. Too often, in previously employed standards for mathematics performance, students advanced through their demonstrations of mathematical reasoning by moving from one tier to the next presumably more advanced tier. For instance, first graders needed to demonstrate that they could count to 100 before they began addition, or the like. The point is that the performance standard categories were treated as discrete teaching and learning units. The approach taken by the North Carolina Teachers of Mathematics (NCTM) standards and the North Carolina Common Core state standards is integrative -- the standards do not assume that children will achieve an understanding to the numerical relationships in their instructional units. Rather, the performance standards are designed to deliberately draw and teach those relationships by coming at the constructs from any different perspectives and practical exercises.

The mathematics performance standards are part of a larger whole designed to encompass the learning requirements for students across their K-12 educational experience. These new clear and consistent state standards have been thoughtfully aligned with the expectations of higher education and the workplace. The current standards are contiguous with earlier versions of state standards, an important consideration for efficacious institutional effort in teaching and for the motivation of students. In other words, no lost time and no wasted effort results from the adoption of the new state standards.