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
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
The real thrust of the framework, however, is in its recommendation for
changes in the way that mathematics is taught. Some of its main
- It pushes for a major change in emphasis. This includes a de-emphasis on
practicing basic skills and an increase in "questioning", "writing",
"discussion", and "cooperative work".
- It declares that "calculators are the 'electronic pencils' of today's world
.. costing much less than students' textbooks," and recommends that four
function calculators be issued to all kindergartners. Once the students have
these calculators, there should be a decrease in rote memorization, so that
students in 2nd and 3rd grade can "learn the addition and subtraction facts
and some of the multiplication and division facts through their many
encounters with numbers."
- It strongly discourages tracking, counseling that schools should "Maximize
time spent by students in heterogeneous groups. Minimize time spent in
tracked or special-ability groups."
- It promotes a changed role for the teacher, saying that the new approach
"requires teachers to do more coaching and facilitating and less telling..."
- It discourages testing, and promotes portfolios, "authentic assessment,"
and "holistic scoring rubrics" in their place.
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
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
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.)