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Part B

The NCTM Standards
  Introduction | Standards Summary
"Because mathematics as a discipline is highly interconnected, the areas described by the standards overlap and are integrated. Processes can be learned within the content standards, and content can be learned within the process standards. Rich connections and intersections abound."

NCTM, pp 30-31.


 
 

The National Council of Teachers of Mathematics (NCTM) is a membership organization of educators dedicated to providing high-quality mathematics instruction for all students.


They are the body responsible for publishing national standards in mathematics education, and it is the most recent edition, Principles and Standards for School Mathematics, on which this course is based. The publication, which can be reviewed online at www.nctm.org, is divided into sections.

The first section comprises the principles, which underlie the entire standards project. These principles are as follows:

  • Equity
  • Curriculum
  • Teaching
  • Learning
  • Assessment
  • Technology
We encourage you to review the principles now, as they present the foundations on which the process standards, and thus this course, rest.

The document also outlines both the content and process standards for mathematics pre-kindergarten - grade 12. Here are all of the standards:

  • Data Analysis and Probability
  • Measurement
  • Geometry
  • Algebra
  • Number and Operations
  • Communication
  • Problem Solving
  • Reasoning and Proof
  • Representation
  • Connections
The first five standards are referred to as the content standards, and they outline specific mathematics concepts for each grade band. These are the subject of an online course series, Learning Math, that is parallel to this one. It is available at www.learner.org/learningmath. Learning Math has five courses, one devoted to each of the standards.

The remaining five standards, communication through connections, are the subject of this course. Each of the following sessions in the course introduces and explores one standard in detail, with a focus on implementing them in the elementary school classroom. There are three other course in the Teaching Math series, one for each of the grade bands, pre-kindergarten-2, 3-5, and high school.


As NCTM and others have noted, the power of the standards and principles comes from their integration. In the course, we highlight each process standard individually as a means to learn about them. In classroom practice, however, you will find that all the standards come together and interlock. Representation, for instance, can be a key part of problem solving. Reasoning and proof may call on connections. Nor can communication be separated out as a discrete task, but instead is embedded in all aspects of what students or teachers do in the classroom.


Workshop participants sometimes ask, "To which audience are the process standards addressed, students or teachers?" The answer is both -- students and teachers. In order to develop student skill in communication, problem solving, reasoning and proof, representation, and connections, teachers must understand and refine their own skill in these areas. In other words, the process standards are good habits for everybody. Their application in the classroom helps students learn and teachers teach. As you progress through the course, you will find some activities that focus on the classroom context, as well as other activities that focus on your own thinking and work.


As you work through the course and in your teaching practice, we encourage you to refer to the NCTM Principles and Standards on the Web or in print form.

Next  A Summary of the Process Standards

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