Mathematics Standards

NCTM released the Curriculum and Evaluation Standards for School Mathematics (1989) as a comprehensive effort to establish a framework to guide the reform and improvement

in the quality of school mathematics. The document, as well as the subsequent release of The

Professional Standards for Teaching Mathematics (1991), the Assessment Standards for School Mathematics (1995), and the Principles and Standards for School Mathematics (2000) presented

a vision of what mathematics curriculum should include in content and emphasis.

The mathematical standards presented by NCTM represented an effort to guide reform movements of schools as they would be able to measure revision efforts against the standards. Standards have been adopted by organizations to meet three main criteria: to ensure quality, indicate goals or expectations, and promote change. For NCTM, all three reasons were cited to have equal importance (NCTM, 1989). Standards were created to protect teachers and students from inferior products and define what was important to teach. The Commission on Standards for School Mathematics appointed by NCTM in 1986 was charged with completion of two critical tasks: develop a vision of mathematics literacy, and create a set of standards for mathematics instruction and learning.

A core belief that the NCTM standards were built upon was that all students should have a common foundation of challenging mathematics, regardless of whether the children would enter the workforce after high school or pursue further study in mathematics and science (NCTM, 2000). All students were further defined to include specific groups of children:

1. Students who have been denied access in any way to educational opportunities as well as those who have not

2. Student who are African American, Hispanic, American Indian, and other minorities as well as those who are considered to be a part of the majority 3. Students who are female as well as those who are male

4. Students who have not been successful in school and in mathematics as well as those who have been successful (p. 4)

Central to the position was that all children needed to learn more and that they often learned differently. In order to meet the needs of the children, the nature of mathematics and

mathematics instruction needed to be significantly changed. Heterogeneous groups with structures in place to provide appropriate support through differentiated instruction were sought over typical homogeneous groupings (NCTM, 2000). Tracking systems in mathematics in the middle school prohibited large numbers of students from experiencing skills and knowledge necessary for access to future opportunities (Beane, 1990; Wheelock, 1992). Systems that did not permit the equal opportunity and equal treatment of all children, excluding certain groups of children from challenging, comprehensive mathematics, could no longer be tolerated.

The call for reform of mathematics instruction suggested that new goals were needed. The shift of industrialized societies to that of an information dependent society called for transformation of curriculum and the aspect of mathematics in order for students to become productive citizens. The information age no longer permitted instruction in which mathematics was nothing more than a set of arbitrary rules and procedures to be memorized (Davis & Hersh, 1981). Schools were also cautioned to avoid the push to standardize tasks that avoided risks and experimentation in order to emphasize the basic skills computation and memorization of facts (Cohen & Ball, 1999). The curriculum standards created for each grade level expressed five general goals for all students: 1) learn to value mathematics, 2) become confident in their ability to do mathematics, 3) become mathematical problem solvers, 4) learn to communicate mathematically, and 5) learn to reason mathematically (NCTM, 1989). Inherent within each of the goals was the focus on authentic problem solving opportunities. Problem solving needed to be the focus of school mathematics through independent activities, small group, and whole class experiences in which students and teacher have opportunities to read, write, and discuss mathematics. Problems should be a mixture of open ended and formulated questions that offered challenges to students without frustration. The innovative ideas presented within the goals and

standards regarding curriculum and instruction were a radical departure from inherited ideas and practices of traditional mathematics instruction (Cohen, 1989).

The Curriculum and Evaluation Standards (NCTM, 1989) identified curriculum

standards for students in groups; Kindergarten though fourth grade, fifth through eighth grade, and ninth through twelfth grade. Although each category had standards that were specific to that age group, the standards had been presented to have been a continuous program from kindergarten through twelfth grade. Principles and Standards for School Mathematics (NCTM, 2000) maintained the grade categories, however, revised the standards by combining some of the topics while drawing increased attention to others.

Mathematics curriculum for middle level students needed to be an exciting, useful, and creative area of study that could be appreciated and enjoyed by all students (NCTM, 1989, 2000). The middle school years typically were when students began to develop concepts of themselves as learners, influenced by areas of motivation, attitude, and interest. These concepts helped shape future mathematical endeavors resulting in certain employment opportunities later in life. The mathematics curriculum needed to engage students in the middle grades classroom in thoughtful activity tied to their emerging intellectual abilities as they move from concrete to more abstract reasoning (NCTM, 2000). The standards focused on expanding student knowledge in the areas of numbers, computation, estimation, measurement, geometry, statistics, probability, patterns and functions, and concepts of algebra. Inclusion of concepts of algebra and geometry were included purposefully to push the middle grades program for all students beyond the preoccupation with number concepts. Most math textbooks place the chapters of probability, geometry, algebra, and statistics at the end of the book, most likely to be skipped by teachers as the end of the year always arrived too quickly. The result was a curriculum that constantly

rehashed the same concepts students have seen year after year. The strands of algebra and geometry needed to be highly interconnected within the remainder of the curriculum producing a coherent curriculum that effectively organized and integrated important mathematical ideas that were worth the time and attention of students. Curricular coherence was identified as an integral part of the Third International Mathematics and Science Study (TIMSS). Researchers found that Japanese lessons were designed around one central idea that was then carefully developed and extended. American lessons tended to include several topics that were not closely related or well developed (National Center for Educational Statistics, 1999). A clearly defined curriculum that was articulated across grade levels permitted teachers to work with children to increasing levels of sophistication and depths rather than continued duplication and repetition of efforts resulting in a curriculum that was dull, irrelevant, and unchallenging.