The main purpose of this chapter is to introduce students to the ongoing revolution in school mathematics or what has popularly been referred to as the "reform movement". Of course the guiding force behind this movement has been NCTM and the standards documents. For most preservice teachers, the vision of the Standards is quite different than their own experiences. The five chapters that follow this one will create the foundational ideas for good teaching in a constructivist environment. Those chapters are to be seen in the context of the revolution that has been going on since 1989.
This chapter explains briefly how the reform movement began with the Curriculum and Evaluation Standards for School Mathematics, followed by the Professional Standards for Teaching Mathematics and the Assessment Standards for School Mathematics. Considerable attention is given to the content of Principles and Standards for School Mathematics.
Also discussed are the influences of comparative studies (NAEP and TIMSS), state-level standards, and curriculum materials.
NCTM and the three Standards Documents
Throughout the course, students need to be able to hear you mention NCTM and understand that is the organization that has the most influence on what happens in school mathematics.
Principles and Standards for School Mathematics is so important that all teachers and prospective teachers should be familiar with what it says and have read at least relevant important sections. The text helps students see how Principles and Standards fits into the context of the preceding three standards documents by updating the Curriculum Standards and incorporating the big ideas of the Professional and Assessment standards documents. The chapter includes a statement and brief discussion of each of Principles and Standards six principles for school mathematics. The five content standards are listed but not described. You should encourage students to examine Appendix A, which contains the five content standards and grade-level expectations for all four grade bands. The five process standards are each described briefly.
As you discuss the Principles and Standards Document, it would be good to point out the NCTM notes (indicated by an icon) that are found throughout the text. One hope is that students will be curious to see a more complete discussion of a topic and will look up these quotations in the document itself. NCTM no longer makes the full document available on the website to non-members. The short summaries that are available are substitute for reading the actual Standards. However, I do not believe that the summaries are adequate.
The Professional Standards for Teaching Mathematics is also introduced briefly. It is useful to draw attention to the five shifts in teaching that are mentioned in the introduction to that document. These will be strange for your students in the beginning of the semester. Perhaps a poster or bulletin board with these ideas would be a profitable linking device to refer to throughout the semester. Note that the goals from the seven Teaching Standards are found in Appendix B in the back of the text.
The Assessment Standards are also briefly introduced as a completion of the trilogy of Standards documents. Chapter 6 discusses each assessment standard and all four of the purposes for assessment that are found in that document. It is useful to point out that the main theme of assessment in the mathematics education today is the blending of assessment with instruction. To that end, assessment must become an integral part of teaching, not something done after students have been taught. Note also that students will initially confuse assessment to mean evaluation - only one component of an assessment program. You may want to point this out in the few minutes you spend with students on this chapter.
You will not be able to adequately help your students understand Standards documents in any one class or by having them read any chapter in this book. The task at this early juncture in the course is to heighten students' awareness of the Standards and permit you to refer to them as you travel through your course. The following points are significant, even to the novice:
It is important to help teachers know that Principles and Standards is not a curriculum but a statement of what is important in school mathematics. Most likely your own state or province has standards with which teachers must be familiar. You may want to have students contrast the NCTM standards with those at the state/province level.
Other Influences on School Mathematics
Since the early nineties, the pressures influencing school mathematics have become much more complex. The TIMSS data has caused much of the concern with the popular press pointing out that most industrialized countries significantly outperform U.S students in mathematics and science. At least 20 countries performed better than the United States which found itself in a group of 14 countries in the middle of the pack. U.S fourth-grade students did much better comparatively than did those at the eighth grade and high school level. The National Assessment of Educational Progress (NAEP) offers us ongoing indications of what American students are learning. This data suggests that while we continue to show improvement, we are not near where we want to be. Both TIMSS and NAEP are referred to at various times throughout the book.
Pressures on teachers from state testing programs and the requirements of NCLB are having a significant influence on what is happening in mathematics classrooms. It is difficult to make general statements concerning these influences across states. Students will undoubtedly have heard of NCLB in their general curriculum course.
Finally, the power of the textbook being used in the classroom cannot be ignored. The text points out that there are a number of "standards-based curriculums" that have been developed with NSF and other monies. These programs are more in alignment with the NCTM Standards. A listing of the three elementary and five middle school programs can be found at the end of the chapter. You may want to use some of the "excerpts" from either Investigations or Connected Mathematics that can be found in every chapter in section two.