Educator Effectiveness

Memorandum on the revised Mathematics Curriculum Framework

Background

In accordance with the Massachusetts Education Reform Act of 1993, the Board and the Department of Education review on a timely basis all of the curriculum frameworks. The purpose of revisions is to ensure that these statewide guidelines are useful to schools and districts and reflect accurate content. The first framework on mathematics was adopted in 1995. I am pleased to present for your approval a draft of the revision of this document.

Public Input

This new draft has evolved from a lengthy process of review, beginning with the work of the Mathematics Revision Panel (January 1999 to November 1999). After that committee completed its work, voluminous public comments were received from PreK-12 teachers and administrators from a range of school districts in Massachusetts, and from mathematicians from many universities. Further revision of the 1995 document was based on these comments as well as on the National Council of Teachers of Mathematics' October 1998 draft of its Principles and Standards for School Mathematics, critiques from the field on the 1995 standards, and current research and critical comment in mathematics education.

Summary of Revisions

This new draft of the Mathematics Curriculum Framework presents:

• Clearer and more specific learning standards so that teachers at all levels will know what they are expected to teach. The skills and concepts are carefully designed to show a clear developmental sequence through the grades. The many PreK-12 teachers and administrators who attended Department-sponsored working groups in January and February guided the precise wording and developmental placement of these standards.
• Narrower gradespans. Within each strand, the standards are grouped by pairs of grades: PreK-K, 1-2, 3-4, 5-6, 7-8, 9-10, and 11-12. Because there are now more gradespans, this document contains more standards than the 1995 document.
• Division of the standards for the secondary grades into two sections: one section showing standards for integrated mathematics courses from grade 7 to 12; the other showing the standards for three single discipline courses-algebra I, geometry, and algebra II-regardless of the grade level (8, 9, 10; or 9, 10, 11) at which these courses might be taught.

The 1995 standards were clarified and articulated in narrower gradespans because a central criticism of these standards by the field after 1995 was their lack of clarity and grade level specificity. The division of the standards for the secondary grades into two sections is an organizational response to the comments of a large number of secondary school mathematics teachers who wish to continue offering single discipline courses to many of their students; these courses, in their judgment, are developmentally more demanding than the integrated mathematics textbooks now being purchased and used in many high schools. To respect these teachers' judgments, the document divides the secondary grades into two sections in order to provide the basis for two assessment options at the end of grade 8-one based on the integrated standards for grades 7 and 8, the other based on the standards for algebra I. Not all students in grade 8 are developmentally ready for a formal algebra I course. The document gives local school districts the flexibility to address their educational level appropriately, with a grade 8 MCAS test option based on the integrated standards for grades 7 and 8.

On the other hand, it is imperative that Massachusetts continue to advance mathematics education and encourage schools to continue providing a "gateway" grade 8 algebra I course for the many students who are developmentally ready for it, and to increase that number. As the US Department of Education indicated in a recent report, we need to "provide all students the opportunity to take algebra I or a similarly demanding course…in the 8th grade." Approximately 30% of our grade 8 students are now taking algebra I in grade 8, but many more could be prepared for it. Our goal ought to be a doubling of that number within four years. By providing two assessment options at the end of grade 8, the document will give schools the opportunity to construct a variety of curricular sequences and configurations at the secondary level to meet their students' needs.

Exactly how do the standards in this document differ from those in the 1995 document? They differ in five ways. (1) A few 1995 standards have been eliminated. (2) Many 1995 standards have been strengthened or clarified to make their intentions clearer to teachers and assessors. (3) Some 1995 standards have been moved to a different strand at the same grade level. (4) Some 1995 standards have been placed at a different grade level. (5) Some standards have been added, chiefly to provide standards for the newly formed gradespans and to address content that is normally taught in a mathematics curriculum but was not made explicit in the 1995 document. Overall, the substantive differences between the two documents are minimal. It is important to note that where there are changes in the standards for gradespan 9-10, student scores will not be based on the changed standards in the next several years but will be phased in over time.

Next Steps

This document does not include the criteria for evaluating instructional materials and programs and many of the explanatory or illustrative materials that were in the 1995 document, such as classroom vignettes and teacher notes. It will be expanded to include the criteria for evaluating instructional materials and programs and some classroom vignettes, teacher notes, and other illustrative pedagogical material before final publication. I will establish a process to encourage educators in the field to contribute fresh classroom material. In the meantime, we urge teachers to continue using the 1995 document for these purposes. I also want to examine the new NCTM document when it is released in April to determine if any changes in our own document are in order before final publication.