By principles, National Council of Teachers of Mathematics (NCTM) means particular features of high-quality mathematics education. Meanwhile, standards describe the mathematical content and processes that students should learn. The six principles for school mathematics address overarching themes :
1. Equity. Excellence in mathematics education requires equity-high expectation and strong support for all students. Mathematics can and must be learned by all students. This principle demands that expectation for mathematics learning be communicated in words and deeds to all students. School have an obligation to ensure that all students participate in a strong instructional program that supports their mathematical learning. High expectation can be achieved in part with instructional program that are interesting for students and help them see importance and utility of continued mathematical study for their own futures. Well documented examples demonstrate that all children, including those who have been traditionally underserved, can learn mathematics when they have access to high-quality instructional programs that support their learning. Achieving equity requires a significant allocation of human and material resources, especially the professional development teachers.
2. Curriculum. A curriculum is more than collection of activities: it must be coherent, focused on important mathematics and well articulated across the grades. An effective mathematics curriculum focused on important mathematics that prepares students for continued study and for solving problems in a variety of school, home, and work setting. Mathematics comprises different topical strands that highly interconnected. A coherent curriculum effectively organizes and integrates important mathematical ideas so that students can see how the ideas build on, or connect with, other ideas, thus enabling them to develop new understanding and skills. Learning mathematics involved accumulating ideas and building successively deeper and more refined understanding. Without a clear articulation of the curriculum across all grades, duplication of effort and unnecessary review are inevitable.
3. Teaching, effective mathematics teaching requires understanding what students know and need to learn and then challenging and supporting them to learn it well. Students learn mathematics through the experiences that teachers provide. Thus, students’ understanding of mathematics, their ability to use it to solve problems, and their confidence in, and disposition toward, mathematics are all shaped by the teaching they encounter in school. The improvement of mathematics education for all students requires effective mathematics teaching in all classrooms. Teaching mathematics well is a complex endeavor, and there are no easy recipes for helping all students learn or for helping all teachers become effective. To be effective, teachers must know and understand deeply the mathematics they are teaching and be able to draw on that knowledge with flexibility in their teaching tasks. They need to understand and be committed to their students as learners of mathematics and as human beings and be skillful in choosing from and using a variety of pedagogical and assessment strategies. In addition, effective learning requires reflection and continual efforts to seek improvement.
4. Learning, students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge. Learning mathematics with understanding essential. One of the most robust findings of research is that conceptual understanding is an important component of proficiency, along with factual knowledge a procedural facility. Learning with understanding also makes subsequent learning easier. Mathematics makes more sense and is easier to remember and to apply when students connect new knowledge to existing knowledge in meaningful ways. Well-connected conceptually grounded ideas are more readily accessed for use in new situation.
5. Assessment. Assessment should support the learning of important mathematics and furnish useful information to both teachers and students. Assessment should be more than merely a test at the end of instruction to see how students perform; rather, it should be an integral part of instruction that informs and guides teachers as they make instructional decisions. Assessment should not merely to students; rather, it should also be done for students, to guide and enhance their learning. Assessment should reflect the mathematics that students should know and be able to do; enhance mathematics learning; promote equity; be open process; promote valid inference; be a coherent process.
6. Technology. Technology is essential in teaching learning mathematics, it influences the mathematics that is taught and enhances students’ learning. Electronic technologies – calculator and computers – are essential tools for teaching, learning, and doing mathematics. They furnish visual images of mathematical ideas, they facilitate organizing and analyzing data, and they compute efficiently and accurately. They can support investigation by students in every area or mathematics, including geometry, statistic, algebra, measurement, and number. Technology should not be used as a replacement for basic understanding and intuitions; rather, it can and should be used to foster those understanding and intuitions.