The instructional focus for the revised standards appears to present a better balance of teacher guidance and student discovery, between concept understanding and skill mastery. Further, the consistency of the content strands across grade levels is an improvement. However, a confusing dichotomy of purpose remains. Is this a document of idealized visions to promote discussion among mathematics educators or a requisite set of student expectations?
The 2000 standards document was revised into four grade-level bands: PreK-2, 3-5, 6-8, and 9-12. The reorganized standards include six principles, five process standards, and five content standards, applied across all grade levels (see Figure 1.6). The new document begins with these sentences:
Imagine a classroom, a school, or a school district where all students have access to high-quality, engaging mathematics instruction. There are ambitious expectations for all, with accommodation for those who need it. Knowledgeable teachers have adequate resources to support their work and are continually growing as professionals. The curriculum is mathematically rich, offering students opportunities to learn important mathematical concepts and procedures with understanding. (p. 3)
This vision is compelling and challenging, especially for teachers of students with learning problems or specific mathematics disabilities. While the standards do not address special-needs learners' instructional considerations, the emphasis on "all students" should be inclusive. The equity principle comes closest to assuring access and high expectations for all students:
Excellence in mathematics education requires equity – high expectations and strong support for all students....Low expectations are especially problematic because students who live in poverty, students who are not native speakers of English, students with disabilities, females, and many nonwhite students have traditionally been far more likely than their counterparts in other demographic groups to be the victims of low expectations....mathematics must be learned by all students. (pp. 12-13)
Other specific references to students with disabilities are found solely in the principles section of the 2000 document. The equity standard reminds educators that high expectations and access are not enough, that some students will require further assistance and accommodations without inhibiting the learning of others [emphasis added] (NCTM, 2000, p. 13). Teachers are challenged to understand the strengths and needs of their students, accommodate differences, and confront their own beliefs and biases about what students are able to learn.
The 2000 standards document specifically stated its intentions to supply guidelines and goals by which local districts and materials producers can orient curriculum, teaching, and assessment efforts for decades to come (p. 6). These standards have subsequently influenced mathematics standards in most states. Some states have adopted the NCTM content standards and grade-band structure, while others have designed their own or modified the NCTM structure. For example, Colorado, Illinois, Massachusetts, and Washington State adopted the NCTM content standards. Arizona's 2003 mathematics standards combined geometry and measurement into one content standard and added structure and logic, articulating the standards by specific grade level rather than bands of grade levels. California also applied the NCTM content standards to each grade level, combined geometry and measurement, and added mathematics reasoning.
Traditionally, teachers have used the district- or state-adopted textbook as a guide for organizing the scope and sequence of mathematics study. The NCTM curriculum standards are beginning to influence textbook content because textbooks tend to lag at least ten years behind major curriculum changes. According to a survey by the National Center for Education Statistics (2003), of the twenty states selecting or recommending mathematics textbooks by 2002, all twenty based their selections on state content standards. Although most elementary texts are still organized by math topic (e.g., multiplication), integrated concepts aligned with NCTM content and process standards are beginning to appear within chapters and unit activities. Middle grades texts were evaluated by Project 2061, using specific standards-based criteria (American Association for the Advancement of Science, 2000). Of the twelve textbook series reviewed, only two included in-depth mathematics content. High school texts are either integrated or topical (e.g., algebra, geometry), based on the district's or state's approved coursework. Topical texts are beginning to include some integration across the standards but, by design, emphasize narrower applications. The teacher's materials for all current texts include curriculum matrices that reference NCTM and state standards, but the actual alignment with those standards is not always strong.
