Improving teachers' mathematical knowledge and their capacity to use it to do the work of teaching is crucial in developing students' mathematical proficiency.
- Adding It Up1
Content for the IMAGES program covers five different strands:
These strands were chosen to be consistent with international (TIMSS: the Third International Mathematics and Science Study), national (NAEP: the National Assessment of Educational Progress), and state standards and expectations.
Because teachers need to know material that reaches beyond the level of the geometry and measurement that they themselves are teaching, IMAGES includes content beyond grades K-5, in support of what students will need to know in subsequent years. In designing this publication, determining how to present the K-5 student expectations posed a dilemma, as the NCTM standards are divided pre-K-2 and 3-5, while many states have traditionally required assessments at grades 3, 5, and 8. In order to be teacher-friendly, IMAGES clusters content for grades K-3 and 4-5 to help guide teachers for state benchmark assessments.2
It is crucial that a teacher creates and follows a coherent curriculum; simply adding a few geometry and measurement activities is not sufficient. Students best understand this geometry and measurement content when their teacher integrates it within mathematics and relates it to other disciplines and information that students already know. A teacher can do this through overlapping and clustering geometry and measurement content areas, both across strands and within a single strand. (more information on clustering)
Each content strand refers to grade-appropriate activities and lesson plans, which are provided in detail in Instructional Activities and Lesson Plans. To explore how the IMAGES content strands correlate to state standards for assessment, refer to Appendix A, which lists, by content strand, those standards that apply to various sample state standards.
This content chapter is meant to provide models for teachers to use in creating and adapting their own original lessons, incorporate the content of geometry and measurement, and also expand the framework of the state standards and the NCTM Principles and Standards for School Mathematics.
This chapter presents the following components for each of the five content strands:
A note on language: While some state standards seem to use the terms "figure" and "shape" interchangeably, IMAGES consistently uses the term "geometric shape."