Incorporate Academic Standards

By actively addressing standards, whether at the state or national level, a teacher sets strong expectations for all students. Standards offer a teacher a detailed guide of the content and learning experiences that he or she should be providing students. How a teacher makes use of a standards-based curriculum is of the highest importance. Essential elements that a teacher must include when implementing a standards-based curriculum through instruction are:

classroom discourse and writing to learn mathematics
presenting mathematics skills in a problem-solving context
applying concepts to real-life situations
requiring students to justify their thinking
expecting students to use multiple representations of concepts.9

Providing guidance for a teacher, standards indicate when students are developmentally ready to learn a concept, which topics to emphasize, and when students should master a concept or procedure. Standards are also useful when choosing activities and lessons; a teacher should alter or replace an activity that, while fun (for both students and the teacher), does not address any of the standards.

Integrating NCTM and state standards

All of the activities and lesson plans included in Chapter 4 incorporate NCTM and representative state standards. Appendix A of this document provides sample state standards for mathematics that pertain to the IMAGES content for geometry and measurement. Complete standards for these states are also available online; see the Web sites.

National Council of Teachers of Mathematics, Principles and Standards for School Mathematics, pp. 52-71.