Scope of Mathematics
Scope of mathematics
This article will provide an overview of the NCTM process and content standards. Educators first studying the standards may feel overwhelmed with the amount of content addressed within each grade-level span. State frameworks that dictate standards for each grade level exacerbate this situation. However, a longitudinal view will show how the same topics are developed over several years in a spiral and interconnected pattern. For example, the concepts of multiplication and division are introduced in the PreK-2 band, but fluency with these operations isn't expected until the 3-5 band. Multiplication and division skills are used in grades 6-8 with problem solving and algebraic equations and in grades 9-12 with vectors, matrices, and other advanced applications. It is critical to keep in mind that deeper study of a few topics is more important for student learning than covering dozens of discrete topics at a surface level.
Process Standards
The process standards address ways of acquiring and using knowledge and are developed across the entire mathematics curriculum. They also can be applied across other content areas and real-world problems. These processes are the "verbs" of math. The role of the teacher is to provide settings, models, and guidance for these processes to develop and to assess student skills in using these processes. The process standards are applied at every grade level and across all five content areas.
Problem solving is a major focus of the mathematics curriculum; engaging in mathematics is problem solving. Problem solving is what one does when a solution is not immediate. Students should build mathematical knowledge through problem solving, develop abilities in formulating and representing problems in various ways, apply a wide variety of problem-solving strategies, and monitor their mathematical thinking in solving problems. Problems become the context in which students develop
This article will provide an overview of the NCTM process and content standards. Educators first studying the standards may feel overwhelmed with the amount of content addressed within each grade-level span. State frameworks that dictate standards for each grade level exacerbate this situation. However, a longitudinal view will show how the same topics are developed over several years in a spiral and interconnected pattern. For example, the concepts of multiplication and division are introduced in the PreK-2 band, but fluency with these operations isn't expected until the 3-5 band. Multiplication and division skills are used in grades 6-8 with problem solving and algebraic equations and in grades 9-12 with vectors, matrices, and other advanced applications. It is critical to keep in mind that deeper study of a few topics is more important for student learning than covering dozens of discrete topics at a surface level.
Process Standards
The process standards address ways of acquiring and using knowledge and are developed across the entire mathematics curriculum. They also can be applied across other content areas and real-world problems. These processes are the "verbs" of math. The role of the teacher is to provide settings, models, and guidance for these processes to develop and to assess student skills in using these processes. The process standards are applied at every grade level and across all five content areas.
Problem solving is a major focus of the mathematics curriculum; engaging in mathematics is problem solving. Problem solving is what one does when a solution is not immediate. Students should build mathematical knowledge through problem solving, develop abilities in formulating and representing problems in various ways, apply a wide variety of problem-solving strategies, and monitor their mathematical thinking in solving problems. Problems become the context in which students develop