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The following process was used to identify standards and benchmarks for mathematics:
Identification of Significant Reports
In addition to these documents which focus solely on mathematics, Benchmarks for Science Literacy (Project 2061, 1993) contains a section entitled The Mathematical World. This section parallels and details many of the standards found in Principles and Standards for School Mathematics. Also, the New Standards Project has published three documents that report mathematics standards and benchmarks at elementary, middle, and high school levels. Those documents are: Performance Standards: English Language Arts, Mathematics, Applied Learning, Volume 1, Elementary School (1997a); Performance Standards: English Language Arts, Mathematics, Applied Learning, Volume 2, Middle School (1997b); and Performance Standards: English Language Arts, Mathematics, Applied Learning, Volume 3, High School (1997c). The Council for Basic Education has published Standards For Excellence in Education (CBE, 1998), which details mathematics content appropriate for students at the end of grades 3, 5, 8 and 12. The CBE standards are described as a "blend of state standards from Delaware, New Jersey, and Pennsylvania"(p.181).
Three documents from the International Baccalaureate Organization were also consulted: Group 5 Mathematics Guide (1993), Middle Years Programme: Mathematics (1993), and Primary Years Programme: Making it Happen in the Classroom (1996). The inclusion of the Primary Years is new with this edition.
The Third International Mathematics and Science Study (TIMSS), a large-scale, cross-national comparative study of math and science curricula, has made available to the public about two-thirds of the mathematics and science items administered to students in 1994-95. Of interest for this study were all items used for populations 1 and 2; for population 3, in keeping with the stated purpose of this study (see Process of this work), only literacy items were reviewed. The International Association for the Evaluation of Educational Achievement (IEA) published TIMSS Mathematics Items: Released Set For Population 1 (Third and Fourth Grade) (1998a); TIMSS Mathematics Items: Released Set For Population 2 (Seventh and Eighth grade) (1998b);and Released Item Set for the Final year of Secondary School: Mathematics and Science Literacy, Advanced Mathematics, and Physics (1998c).
Finally, McREL has published a study entitled A Distillation of Subject-Matter Content For the Subject-Areas of Language Arts, Mathematics, and Science (Kendall, Snyder, Schintgen, Wahlquist, & Marzano, 1999). Researchers at McREL reviewed a selected set of highly rated state standards within each subject area, examining them for common content. The McREL analysis resulted in the identification of the significant subject-area content that consistently appeared within these top rated documents.
Selection of the Reference Document
Identification of Standards and Benchmarks and Integration of Information from Other Documents
While most of the mathematics content found in the 1989 and 2000 NCTM standards documents remains very similar, the structure of the standards has been revised. The standards themselves appear to be more deliberately articulated at all grade bands, that is, content within each standards category is addressed consistently at each grade band, whereas in the 1989 set not all standards were addressed at each grade band. In addition, a clearer delineation between mathematics content standards and what NCTM calls mathematics process standards (reasoning, representation, communication, and problem solving) has brought greater clarity to the organization of the document. For reasons discussed in the Process section of this report, many of the elements identified within the NCTM standard on mathematics as reasoning were judged to be more appropriately classified under one of the standards within our thinking and reasoning category. With the exception of the content related to problem solving, which we address in standard 1, we classify the remaining NCTM process standards as more appropriately instructional guidelines, or curriculum standards, and do not include them.
For the most part, the information in the Project 2061, New Standards, and International Baccalaureate documents was integrated into the standards generated from the NCTM and NAEP reports. The one exception to this general rule was Standard 9, Understands the General Nature and Uses of Mathematics. As the title indicates, this standard deals with general awareness about mathematics and its relationship to other disciplines, particularly science. This standard was generated solely from the Project 2061 document Benchmarks for Science Literacy.
Any benchmark that addressed content closely related to a test item in the TIMSS mathematics assessment has been identified by indicating the test level of the matching TIMSS assessment item. Similarly, any benchmark that addresses mathematics content that was also identified as important in the McREL study of top standards documents has been so identified by an asterisk at the end of the citation log, which appears just above and to the right of the benchmark.