July 25-28, the Mathematics Standards Study Group (MSSG) organized by Roger Howe, was a group of 12 mathematicians. These 12 mathematicians gave advice on the revision of state math standards. Here is the third section that includes curriculum advice:

**III. Advice for Revising School Mathematics Standards and Curriculum**

The design of school mathematics standards and curriculum is a very complex, intellectually challenging task. We offer the following advice about this task.

.... A.

**States should seek out the best mathematical thinkers from schools, higher education and the**

*private sector*to serve on committees to design school mathematics standards and curriculum.The outstanding credentials of members of such committees must reflect the intellectually challenging nature of designing of school mathematics standards and curricula. If mathematics education is to be given a high priority by states and they want expert guidance, then we believe that states would be well advised to follow the model used by the federal government, which turns to the National Academy of Sciences for expert advice. The Academy assembles panels of the nation’s experts on a topic. These panels are chosen free of input from governmental officials or interest groups.

Such an expert panel for school mathematics would ideally be composed of distinguished scholars in mathematics and in mathematics education, along with representatives from the schools where the instruction occurs-- practicing teachers-- and representatives from companies and institutions who employ graduates-- mathematical experts from the private sector. The expertise of these groups is needed to design a focused, incremental curriculum, as outlined in the previous section, and to resolve conflicting objectives, e.g., simplicity and age-appropriateness versus mathematical correctness and completeness.

.... B.

**State mathematics programs have been redesigned too often. For help in developing more effective, stable mathematics programs, states are advised to draw heavily on successful mathematics programs in other countries, which have been gradually refined for many years.**

All countries seek to teach their young people good mathematical skills and reasoning. It stands to reason that the experiences of other countries can be an important resource for U.S. standards developers. In virtually all commercial and intellectual activities, successful strategies incorporate the best ideas of others and then extend them. So it should be with school mathematics.

**A number of East Asian countries have well documented track records of educating students who excel in mathematics at all levels**in international comparisons, most recently in the Trends in International Mathematics and Science Study (TIMSS).

**These countries have school mathematics curricula that are widely judged to be effective and of high quality. We urge U.S. standards developers to use these successful East Asian mathematics curricula as a valuable resource in their work.**

.... C.

**Greater precision and clarity are needed in the language in mathematics standards.**

Terms like ‘reasoning’ and ‘understanding’ are used so extensively and in such general ways in many mathematics standards that they have lost meaning. Most standards documents use phrases that not only are vague but assume some context or additional information that is not explicitly stated. An example is the statement in one state’s standards about examining the “relationship between perimeter and area” of common geometric figures. The reality is that while some common geometric figures, e.g., a square, have such a relationship, many do not, e.g., an acute triangle. An example of mathematically incorrect reasoning appears in a standard directing students to use technology to show that rational numbers can be expressed as terminating or repeating decimals and irrational number as non-terminating and non-repeating decimals. While it is desirable to discuss the differences between rational and irrational numbers, this is a good example of a situation where technology is useless.

We believe that mathematicians have a natural role to play in polishing the language in standards, because they are experts in precise mathematical communication. For example, they could reformulate the flawed standards language mentioned in the previous paragraph to accurately communicate the intent of the standards writers. Also see A. above for our advice about an expert panel including mathematicians to design mathematics curriculum and standards.

.... D.

**Mathematics should arise in instruction in other school subjects in order to reinforce and apply learning in mathematics classes.**

Proficiency in mathematics now ranks at the top of educational priorities along with proficiency in reading and writing. Reading and writing are developed in instruction in an array of different subjects. The same needs to be true for mathematics. Mathematical reasoning and problem-solving should be an integral component of school instruction in the sciences, in the same way that reading and writing are. In addition, work with displaying and interpreting graphical data should be part of social science instruction.

This recommendation applies to instruction in elementary school as well as middle school and high school. In elementary grades there is usually one teacher for all subjects, who in theory can integrate mathematics across the curriculum.

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