NCF 2005 aims to develop mathematical skills and knowledge that are essential for students to understand the world around them and to participate effectively in society.

NCF 2005 emphasizes the importance of understanding mathematical concepts and processes, and developing problem-solving skills. Rote memorization is not a key principle of NCF 2005.

NCF 2005 recommends a child-centered and activity-based approach to teaching mathematics. This approach emphasizes the importance of engaging students in hands-on activities and providing them with opportunities to explore mathematical concepts and processes.

NCF 2005 recommends a variety of teaching methods, including group work, project-based learning, and discovery learning. Lecture-based instruction is not a recommended teaching method in NCF 2005.

NCF 2005 emphasizes the importance of assessment for measuring student achievement, promoting learning, and providing feedback to students and teachers.

NCF 2005 recommends a variety of assessment methods, including oral tests, projects, and portfolios. Written tests are not the only recommended assessment method in NCF 2005.

NCF 2005 emphasizes the importance of using textbooks as a supplement to other teaching resources. Textbooks should not be the primary source of learning in mathematics.

NCF 2005 recommends the use of a variety of resources for teaching mathematics, including manipulatives, calculators, and computers. Textbooks are not the only recommended resource for teaching mathematics.

NCF 2005 emphasizes the importance of the teacher's role in delivering lectures, providing information, facilitating learning, creating a supportive learning environment, and assessing student achievement.

NCF 2005 emphasizes the importance of promoting problem-solving and critical thinking, and using real-world examples to teach mathematics. Encouraging students to memorize mathematical facts is not a recommended teaching strategy in NCF 2005.

NCF 2005 emphasizes the importance of problem-solving as a key skill that students need to develop in mathematics, a way to assess student achievement, and a way to engage students in learning mathematics.

NCF 2005 emphasizes the importance of using a variety of problem-solving strategies, including guess and check, working backwards, and drawing a diagram. Using a formula is not a recommended problem-solving strategy in NCF 2005.

NCF 2005 emphasizes the importance of using real-world examples to help students understand mathematical concepts and processes, see the relevance of mathematics to their lives, and develop problem-solving skills.

NCF 2005 emphasizes the importance of using real-world examples to illustrate mathematical concepts and processes, create problem-solving situations, and engage students in learning mathematics. Using real-world examples to assess student achievement is not a recommended way to use real-world examples in NCF 2005.

NCF 2005 emphasizes the importance of communication as an essential skill for students to learn mathematics, share their mathematical ideas, and develop problem-solving skills.