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Leah Yates Duke University Master of Arts in Teaching |
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Critical Analysis of State and National Standards for Mathematics
As our nation evolves into an era where mathematical understanding is essential to the success of the individual in the workplace, as a consumer, and as an everyday problem solver, mathematical education is also evolving to help students prepare for their future. The general consensus among the National Council of Teachers of Mathematics’ Principles and Standards for School Mathematics and the Standards of North Carolina is that it is no longer acceptable for students to simply memorize mathematics. Traditionally, students have been taught to do mathematics, but not to explore mathematics. The central goal of each set of standards is to encourage students to become curious learners who maintain flexibility of thought and a genuine understanding of the content. I believe that educators in the state of North Carolina are continually striving to meet these goals, but that they also recognize that such an idealistic math program takes time to cultivate and implement.
According to the National Council of Teachers of Mathematics, the role and purpose of Standards is to ensure quality, indicate goals, and to promote change. The Principles and Standards for School Mathematics provides a foundation for high-quality mathematics education. The ten Standards presented by the Principles and Standards for School Mathematics are divided into two groups: The Content Standards, and The Process Standards. The Content Standards include: Number & Operations, Algebra, Geometry, Measurement, and Data Analysis & Probability. These are areas of content that the National Council of Teachers of Mathematics feels are absolutely vital to a good mathematics foundation. The Process Standards include: Problem Solving, Reasoning & Proof, Communication, Connections, and Representation. The Process Standards provide strategies for learning and using mathematics effectively. The Principles and Standards for School Mathematics outlines each of these content areas in terms of the overall expectations of what students should learn from each area. The Principles and Standards for School Mathematics also provides suggestions for teaching and exploring each of the content areas in a classroom setting. This is what makes the Principles and Standards for School Mathematics such a compelling resource for teachers.
The Standards of North Carolina support the notion that each student should be equipped with the knowledge that is necessary to be productive citizens in our technological society. Each student should possess a fluency in mathematics that promotes efficiency, accuracy, and flexibility in developing strategies and solving problems. The six goals of the North Carolina standards are that students develop: efficient problem solving skills, a strong background of mathematical concepts and skills, connections between mathematics and other disciplines, the ability to use technology to solve problems, the ability to communicate mathematics effectively, and a positive attitude towards mathematics. The Standards of North Carolina provide a very detailed list of competencies necessary for successful mastery of each content area as well as encourages teachers to change the classroom environment to promote higher levels of success. Unfortunately, they do not provide teachers with suggestions for effectively teaching these competencies. This is the main difference between the National Council of Teachers of Mathematics’ Principles and Standards for School Mathematics and the Standards of North Carolina. This difference makes the Principles and Standards for School Mathematics a more valuable resource in terms of effective teaching and the Standards of North Carolina a valuable resource in terms of detailed competencies necessary for success.
Each set of standards should be a necessary part of every math teacher’s repertoire of educational resources. Together, they provide the math teacher with a solid foundation of concepts, competencies, and methods for promoting educational success. I personally will use them everyday to help create a more structured and innovative learning environment for my students. With today’s ever changing technology, students need to excel in problem solving and creative thinking. Both sets of Standards strongly support this philosophy. The National Council of Teachers of Mathematics and the state of North Carolina both take a firm stand that it is no longer acceptable for students to have faith in their teacher alone. They must have the proof that only genuine exploration and discovery of mathematics can provide. Mathematics is a language and as with learning any language, it is not enough to simply memorize words; one must be able to speak the language in order to be truly fluent.