As the primary professional organization for teachers of mathematics in grades pre-K–12, the National Council of Teachers of Mathematics (NCTM) has the responsibility to provide broad national leadership in matters related to mathematics education.
In meeting this responsibility, NCTM has developed a set of standards for school mathematics that address content, teaching, and assessment. These standards are guidelines for teachers, schools, districts, states, and provinces to use in planning, implementing, and evaluating high-quality mathematics programs for prekindergarten through grade 12.
The NCTM Standards are based on a set of core beliefs about students, teaching, learning, and mathematics.
We believe the following:
- Every student deserves an excellent program of instruction in mathematics that challenges each student to achieve at the high level required for productive citizenship and employment.
- Every student must be taught by qualified teachers who have a sound knowledge of mathematics and how children learn mathematics and who also hold high expectations for themselves and their students.
- Each school district must develop a complete and coherent mathematics curriculum that focuses, at every grade level, on the development of numerical, algebraic, geometric, and statistical concepts and skills that enable all students to formulate, analyze, and solve problems proficiently. Teachers at every grade level should understand how the mathematics they teach fits into the development of these strands.
- Computational skills and number concepts are essential components of the mathematics curriculum, and a knowledge of estimation and mental computation are more important than ever. By the end of the middle grades, students should have a solid foundation in number, algebra, geometry, measurement, and statistics.
- Teachers guide the learning process in their classrooms and manage the classroom environment through a variety of instructional approaches directly tied to the mathematics content and to students' needs.
- Learning mathematics is maximized when teachers focus on mathematical thinking and reasoning. Progressively more formal reasoning and mathematical proof should be integrated into the mathematics program as a student continues in school.
- Learning mathematics is enhanced when content is placed in context and is connected to other subject areas and when students are given multiple opportunities to apply mathematics in meaningful ways as part of the learning process.
- The widespread impact of technology on nearly every aspect of our lives requires changes in the content and nature of school mathematics programs. In keeping with these changes, students should be able to use calculators and computers to investigate mathematical concepts and increase their mathematical understanding.
- Students use diverse strategies and different algorithms to solve problems, and teachers must recognize and take advantage of these alternative approaches to help students develop a better understanding of mathematics.
- The assessment of mathematical understanding must be aligned with the content taught and must incorporate multiple sources of information, including standardized tests, quizzes, observations, performance tasks, and mathematical investigations.
- The improvement of mathematics teaching and learning should be guided by ongoing research and by ongoing assessment of school mathematics programs.
Changing mathematics programs in ways that reflect these beliefs requires collaborative efforts and ongoing discussions among all the stakeholders in the process. NCTM stands ready to work with all those who care about improving mathematics education for all students. Through such dialogue and cooperative efforts, we can improve the mathematical competence of the students in mathematics classes across the continent.