On several occasions, Richard Riley, Secretary of Education, has called for a cease-fire in the "math wars" that now rage across the country. Concomitantly, the National Council of Teachers of Mathematics (NCTM) and other educator groups have lashed out at the mathematics standards development in California, have continued to develop their position through the use of commercial public relations firms, and have dug themselves deeper into the trenches of their so-called "reforms." These actions do not appear to be directed at a resolution of the conflict or a resolution of the dismal state of mathematics education in America.
Whereas, Mathematically Correct finds that compromise and resolution of the "math wars" are not forthcoming; and
Whereas, Mathematically Correct seeks to promote greater mathematics achievement for our children and all of the students of America; and
Whereas, Mathematically Correct finds that the so-called "reform" movement in mathematics education has taken misguided directions that are not beneficial to the students of America;
Therefore, we hereby offer to NCTM and its offshoot organizations the following guidelines designed to promote both "math peace" and a more efficacious mathematics education for all:
1) Demand greater mathematics knowledge for teachers
The deficiencies of the mathematical background of our teachers is an embarrassment as well as a hindrance. Encouraging the placement of well-prepared teachers in secure classrooms should be the first order of business. Our universities must provide a deeper treatment of mathematics for our future teachers, and greater mathematics knowledge must be required for teacher placement.
2) Stress that standards of learning must have yearly benchmarks
Effective standards detail content-based learning objectives at least for each year/course of the curriculum. While the NCTM documents belie this approach by their use of the name "Standards" there is no excuse for not clearly directing the development and use of real standards by states and districts.
3) Admit that weak programs have resulted from following NCTM guidelines
Whether intended by the NCTM or not, seriously deficient curriculum materials have been written in the name and spirit of alignment with NCTM and now are found in many schools. This fact must be admitted and condemned, otherwise there remains defacto support of these programs.
4) Refrain from promoting any theory of learning or method of teaching
Diversity in the student population is no excuse to promote methods such as constructivism or cooperative learning over methods such as direct instruction. The well-prepared teacher is skillful in a variety of approaches and in deciding which approach to use in specific classroom situations. Any guiding document on mathematics education should avoid promoting one approach over others.
5) Encourage frequent objective tests to monitor student progress
The use of objective tests of student knowledge and skills has been much maligned. Regardless of whatever other measures are used, students should also be able to do well on these more traditional, objective indices of achievement. The importance of frequent measures of student progress necessitates the use of these valuable tools.
6) Keep the focus on mathematics
The key to success is not just making mathematics fun and interesting -- mathematics achievement will continue to require hard work. Diverting time and attention away from the mathematical focus with projects and activities that contain little mathematics is self-defeating. Similarly, skipping among unrelated topics in a misguided effort to increase interest destroys the mathematical focus.
7) Refrain from promoting heterogeneous grouping or repudiating homogeneous grouping
The use of heterogeneous grouping and disdain for homogeneous grouping is without empirical basis and may detract from the learning potential for all students. Any guiding document on mathematics education should avoid these issues.
8) Admit that arithmetic and algebra are the key elements of the early curriculum
Arithmetic and algebra have continually been stumbling blocks for many students. Rather than a reason for mathematics education to shy away from these areas, this is a reason for increasing the emphasis on and attention to these subjects. The putative changes in mathematics have been used to justify broadening the scope of math education to the point of detracting from these important areas, and their rightful emphasis must be restored.
9) Include symbolic skill-building, abstract mathematics, and repeated practice
Not all learning in mathematics must or should be based in applications. Even when the ultimate objective is real-world application, the acquisition of skills and knowledge may often require more abstract and fundamentally pure mathematical material along the way.
10) Reinstate an emphasis on proof and mathematical justification
The de-emphasis on proof and the casual approach to mathematical reasoning have been harmful to this important feature of mathematics. The gradual development of formal logic and proof must begin earlier in the curriculum and be given greater emphasis.
11) Emphasize that algorithms should be taught, understood, and used
Algorithms and operations are not evil, but in fact are techniques to be taught, understood and then used to make processes more efficient and thus make room for further advancement.
12) Delete the list of topics for de-emphasis
The NCTM "Standards" contain a list of topics for de-emphasis that has been taken to an extreme, including NSF-funded programs that eliminate these contents. Whether intended or not, the list has resulted in great harm and must be eliminated.
13) Indicate that calculators and computers should be used sparingly
The advances of technology proceed at an alarming rate, making it all but impossible to evaluate their impact on education. Introduction of these has to be assumed to place learning at risk unless it is done conservatively, including a large portion of class/curriculum/tests that do not allow technology.