STANDARD COURSE OF STUDY

PHILOSOPHY

North Carolina public schools have the challenge to provide all students with the mathematical knowledge, skills, and confidence they will need to compete in a technology-oriented workforce and to be informed citizens.  With national standards, research in learning, and the increasing role of the federal government in education, there is an emerging consensus about the essential elements of mathematics content and instruction. 

The North Carolina Mathematics Standard Course of Study is organized in five strands or goals for K-8: Number and Operations, Measurement, Geometry, Data Analysis and Probability, and Algebra.  (Geometry and Measurement are combined for grades 9-12.)  The objectives for each goal progress in complexity at each grade level and throughout the high school courses.  The curriculum has been designed around key ideas that should not be piecemealed into incidental details that address low-level skills.  Success in mathematics integrates knowledge, conjecture, and facility with a variety of mathematical concepts.  The goal of mathematics instruction should be to produce learners who comprehend concepts, operations, and relationships in mathematics as well as proficiency in computation and the application of those concepts.

The early grades focus on building a strong understanding of number and fluency with mathematics to solve problems.  Fundamental to these skills is knowledge of number facts, the computational processes, and the appropriate use of each operation.  Together with an emphasis on using mathematics to solve problems, elementary students will build a depth of understanding enabling them to apply the content in a variety of contexts.

Middle grades content will highlight rational numbers and algebraic thinking.  Students will develop fluency in solving multi-step equations and modeling linear functions.

High school courses are designed to give students the skills and knowledge required for their future.  Algebraic and geometric thinking and applied mathematics are essential for all students.

Fluency in mathematics is an expectation for all students.  Fluency incorporates three ideas: efficiency, accuracy, and flexibility.  Students can get bogged down with procedures and calculations that lead to errors.  They become efficient as they develop strategies that are manageable, understandable, easily carried out, and generate results that solve problems.  Students must develop an accurate knowledge of number facts and number relationships in order to reason and solve problems well.  Flexibility is the product of studentsí successful experiences with problems using a variety of strategies and the analysis of the strategies to determine their efficiency and accuracy.

Mathematics has its own language, and the acquisition of specialized vocabulary and language patterns is critical to a studentís understanding and appreciation of the subject.  Students need to use correctly the concepts, skills, symbols, and vocabulary identified in the standards set in this document.  Students should talk about mathematics and use the language to verify solutions to mathematical problems.

Problem solving and reasoning are stressed throughout the goals at each grade and in every course.  The development of problem-solving skills is a major goal of the mathematics program.  Experiences in problem-solving processes should permeate instruction.  Problem solving should be integrated early and continuously into each studentís mathematics education.  Students need a wide range of skills and strategies to use as a tool for representing and solving a variety of problems.

Mathematical modeling is an important technique used to build understanding of abstract ideas.  Teachers need to expose students to physical representations that help develop understanding of abstract concepts.  Early years should include work with manipulatives to help form a sense of number, and work with geometric shapes and patterns facilitates the development of spatial reasoning.  In later studies, students will generate algebraic expressions, another form of modeling, which represent physical, social, or natural phenomena and help them make predictions.

One of the challenges facing education today is the development of effective mechanisms for informing teachers about this research so that they can transform the learning environment in their classrooms.  Research shows that students develop mathematical competence and power by engaging in solving meaningful problems.  Beginning in the earliest grade levels, students should use their own knowledge and experience, working alone, in pairs, and in small and large groups, to solve challenging tasks.  They should be expected to communicate their thinking with pictures, numbers and words.  Teachers should encourage students to question one another when an explanation doesn't make sense to them.  This problem-centered approach to learning mathematics will enable students to take greater responsibility for their own learning, to develop essential communication and decision-making skills, and to understand the fundamental concepts of mathematics, all of which will be critically important to them.

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