The California Mathematics Framework

In many of the discussions about changes in the math program in Palo Alto schools, you may have heard references to the "Mathematics Framework." If you are not familiar with that term, this article will provide a little background on what the framework is and what it says.

What is the California Mathematics Framework?

The California Department of Education publishes a series of documents called frameworks for each major subject area -- English, math, science, history, etc. These documents describe the vision of the State Board of Education for teaching these subjects in California public schools. The frameworks are advisory documents -- there is no legal requirement that schools must follow the frameworks. Similarly, there is no funding that is dependent upon a district adhering to them.

The document dealing with mathematics, entitled Mathematics Framework for California Public Schools, was last published in 1992, and is a major revision of the previous edition, published in 1985. In many ways, the framework concentrates more on how to teach mathematics than on what to teach. When discussing issues of curriculum content, the framework makes frequent reference to a document published by the National Council of Teachers of Mathematics (NCTM) entitled Curriculum and Evaluation Standards for School Mathematics.

The Palo Alto school district has made the decision to follow all of the framework documents, including the Mathematics Framework. Many of the changes that have parents so concerned are exactly the changes being pressed by the Mathematics Framework.

What does the Mathematics Framework say?

The framework analyzes mathematics education by dividing it into eight "strands" which run through all grades levels: functions, algebra, geometry, statistics and probability, discrete mathematics, measurement, number, logic and language. Along with these strands, and viewed as tying them together, the framework speaks of ten "unifying ideas" which vary from grade to grade. These include such concepts as proportional relationships, patterns, multiple representations, etc.

The real thrust of the framework, however, is in its recommendation for changes in the way that mathematics is taught. Some of its main recommendations are:

How do we know that these changes will work?

To be blunt, we don't. As the Framework itself states, "the ideas in this Framework have not been implemented all together on a wide scale". There is not even agreement on how to measure whether the Frameworks are succeeding or not. Proponents of the framework argue that since we are de- emphasizing memorization of basic skills, we should de-emphasize testing them. Critics of the plan feel strongly that fluency with basic math skills is important and must be tested.

What is the relationship of the framework to the education reform movement?

By any measure, the framework is a direct product of the education reform movement. Along with embracing all of the reform movement themes, the framework has a sweeping revolutionary tone in its call to throw out the old and bring in the new. In its very first sentence it bluntly states: "Publication of the 1992 Mathematics Framework for California Public Schools answers a call ... to change what mathematics we teach, how we teach it, and to whom." It then goes on to state "This Framework is devoted to change," and "The time for small scale experiments is past. We know what is required."

In addition, many of the changes advocated by the frameworks seem to follow a much broader social agenda than that needed just to improve mathematics education. "Mathematics instruction can be connected to society by a conscious choice of contexts for problems that illuminate the mathematics side of social issues." There is no mention of who decides on the "correct" answer to these social math problems.

Finally, many of the recommendations given in the Framework seems to address problems that are not pertinent to Palo Alto. "Progression through the mathematics curriculum is an unfulfilled promise for the majority of California's students." However, over 95% of all Palo Alto students complete four years of high schools math. For 7th through 12th grade, it states that "shallow courses, which emphasize repetition and low-level skills, must be replaced...." However, there are no such courses in Palo Alto.

How does the CLAS test relate to the frameworks?

There is direct relationship between the mathematics framework and the now defunct CLAS test. In simple terms, the CLAS test measures what the framework teaches. Many reformers lament that falling test scores are not meaningful because we are using old tests that don't measure all the good things that the framework is supposed to teach. However, everyone realizes that assessment drives curriculum, and therefore, the reform movement needed a new test. This test would de-emphasize assessment of basic skills, and emphasize issues dealing with mathematical "empowerment." The result was the CLAS test.

Can I get a copy of the Mathematics Framework to see for myself?

The frameworks are published in 8.5 x 11 softcover format by the California State Department of Education. The Mathematics Framework runs just over 200 pages and may be ordered by calling 1-800- 995-4099. The cost is $6.75 plus shipping. Credit card orders are accepted. Delivery is generally within 3 days to a week. (Ordering a copy of the frameworks by phone is one area where Sacramento actually seems to work well.)