Mathematically Correct
Background:
An effective educational program needs to have clearly defined goals as to what students should know, understand and be able to do, as well as a plan that effectively guides instruction to the levels defined by the standards.
Late in 1997 California adopted a comprehensive set of Mathematics Standards. Early in 1998, San Diego City Schools adopted a comprehensive set of Mathematics Standards largely aligned with the California Standards. Both documents contain substantial detail about what students should know, understand and be able to do at every grade, but they lack any prescription as to how students should be taught.
California has since adopted a State Mathematics Framework that discusses possible instructional strategies linked to the state standards at each grade. The Framework recognizes that some students are behind the level of the standards and contains material and suggestions to focus instruction at those topics of greatest importance to preparing lagging elementary students to succeed in Algebra as eighth graders.
In the two years since the adoption of the California and San Diego Mathematics Standards, San Diego City Schools has failed to develop a systematic program to educate San Diego students to the level of the standards. Indeed, it has been the expressed policy of the district and the Institute for Learning that efforts would be concentrated on "literacy" rather than math. On June 6, 2000, the Institute for Learning released the first public draft of the San Diego City Schools K-12 Mathematics Framework.
Description of the Draft Mathematics Framework
The Framework presented to the pubic consists of 6 pages: A title page, an introductory page, one page entitled "Mathematical Content" and two pages entitled "Mathematical Process."
The introduction asserts alignment of the Framework to the district standards and also asserts the following:
The Mathematics Content section is one page long and is divided into four strands, each presented as single short paragraph: Number Sense and Operations, Functions and Algebra, Measurement and Geometry, and Data Analysis, Statistics and Probability. No item contains reference to specific grade levels or courses, nor does any item refer, except in the broadest sense, to any understanding, knowledge or skill expected of students.
The Mathematics Process section is divided into 7 strands, each represented by one short paragraph: Quantitative Literacy, Computational Fluency, Problem Solving, Using Representations, Using Reason and Proof, Communicating, and Making Connections. None of these topics are specifically related to classroom practice in any grade or course, nor are any of these linked to specific applications or skills.
Critique
As a document to guide student success in gaining the understanding, knowledge and skills described in the California or San Diego Mathematics Standards, this framework is a failure. The goals stated are broad and far reaching platitudes, e.g. "students can engage in tasks for which the solution is not known in advance" and "analyze situations in mathematical terms," but lack any detail regarding exactly what should be covered at any year and how it should be presented. Only the complete lack of specificity amid the overarching statements of this framework supplies any justification for the claim that this document aligns or converges with any other standards or framework document. Like an inkblot test, someone can attach whatever meaning he desires to the elements of the framework.
This complete lack of detail renders the document void of practical meaning. The material in this framework is sufficiently shallow and lacking in specificity as to make it unusable as a guide to classroom instruction, teacher training, or parental aid to students. There are as many classroom practices consistent with this framework as there are teachers, or there are as few as Institute for Learning staff declare in private meetings. A second grade teacher trying to develop in his students understanding of the how and why of multidigit addition and subtraction and use of that knowledge in problem solving receives no guidance from this document. A fourth grade teacher trying to help her students catch up to the level of the standards and prepare them for algebra in grade 8 receives no guidance from this document. A fifth grade teacher looking for help in figuring out an optimal order to present various topics receives no guidance from this document. An algebra teacher trying to help her students understand the quadratic formula, its derivation and use receives no guidance from this document. A pre-calculus teacher trying to prepare his students for college-level math receives no guidance from this document. A committee trying to decide among textbooks receives no guidance from this document.
The broad, vague nature of this framework removes significant accountability and public review of district instructional practices and the practices of the Institute for Learning. This document represents the only opportunity for the board, the public and teachers to discuss openly the nature of mathematics instruction in the district and to set policy on mathematics instruction. Once this framework is approved as district policy on math instruction, the actual details of teacher training and instructional practice are removed from public scrutiny. Framework-aligned instructional practice will become whatever the Institute for Learning trainers say it is. Teachers will have no document to look to for guidance prior to review by Institute for Learning personnel, and no clear defining document against which to appeal a negative review.
Recommendations
This document is sufficiently flawed that it should be rejected outright by the Board of Education. The board then has two options. 1) The board can specify that a new framework will be written and that it should contain grade by grade descriptions of various potentially effective instructional practices that relate to mastery of the standards. In addition, the new framework should contain descriptions of strategies for remediating those students who have fallen behind, with special emphasis on preparing elementary students to be prepared to pass algebra in grade 8 and emphasis on strategies for those students who need more substantial interventions. Once such a document is developed, it should then be carefully examined to determine if the array of instructional practices are likely to be effective. Only then should the framework be accepted. 2) The board could vote immediately to adopt the California Mathematics Framework as the San Diego City Schools Mathematics Framework. This second option has the significant advantage that it allows the district to adopt a document meeting all of the criteria outlined above immediately, without further waste of district funds or time. This option is strongly recommended.