Across the country, the way mathematics is taught in the classroom and in textbooks has been changing notably. Classrooms are often organized in small groups where students ask each other questions and the teacher is discouraged from providing information. Students may even take tests in groups, if they have tests at all. The use of blocks and other "manipulative" objects has extended well beyond kindergarten and can now be found in many algebra classes. Meanwhile, the students practice their fundamentals less and less. Time consuming projects and essays that involve very little mathematics are the rage. Calculator use is growing and taking away expectations for student learning. Textbooks, if the students have them at all, are full of color pictures and stories, but not full of mathematics. The books often don't even give explicit definitions or procedures. That would be "telling" and the new idea is for students to discover all of mathematics for themselves. Many of these programs don't even teach the standard algorithms for the operations of arithmetic. Long division is a devil that is to be beaten into extinction - and if they manage that, multiplication will be next.
Along with the emphasis on non-traditional methods, we are offered a lot of rhetoric about higher order thinking and problem solving. There have been countless diatribes that rant about the evils of repeated practice and remembered facts and a steady stream of self-endorsements of the new directions. The selling of the so-called reform has been well-rehearsed by its proponents over the last decade. Replete with glossy promotions, the new new math is long on salesmanship but short on mathematics.
Indeed, although there are many variations in the methods of these new programs, they have one clear characteristic in common - they are all weak in mathematics. The expectations for our students are seriously undermined. And, as the mathematics is leeched out of the textbooks, the opportunity for our students to learn is withering away.
This problem is not unique to elementary school mathematics and it is not just confined to the four operations of arithmetic. The new methods and low content levels are present in many high school programs and even in college calculus.
The deterioration in the curriculum materials has been quite dramatic over the past several years. It has also been accompanied by a deterioration in the mathematics achievement of incoming college students, those who will be the math teachers of tomorrow.
Now we are faced with an inadequate supply of teachers who are really qualified to teach mathematics, with new curriculum materials that lack the content our students need, and with poor achievement compared to our international competition, all wrapped in glowing rhetoric about the new directions in mathematics education.
There is a very real possibility that our children will suffer as a result of these unverified curriculum designs.
See What is Changing in Math Ed? for a further description of these changes.
The so-called reform movement in mathematics education has roots buried deeply in the history of education in America. However, the pressure to move in this direction was solidified when the National Council of Teachers of Mathematics (NCTM) first released their Standards documents containing much of the philosophy behind the Whole Math movement in 1989. These documents do not provide content standards as the name might suggest. Instead, they focus on the promotion of theories about how math should be taught.
For more information on the role of NCTM in this process see:
These substantial changes have spread throughout California. For example:
This pattern in California is now being repeated around the country.
The deterioration of mathematics education provoked parents to take issue with the position taken by the 1992 Framework, and especially with the way these methods are implemented in textbooks in use around the state. Dr. Wayne Bishop, of CSULA, provides a well-reasoned critique of the 1992 Framework.
In March of 1995, given wide-ranging concerns about the quality of public education in California, State Superintendent Delaine Eastin announced that she was forming two task forces, one in math and one in reading, to examine state policy and the Frameworks. But, the math task force fell short of asking for a revision of the math Framework. It did make strong recommendations for a renewed emphasis on basic skills and assessment.
In September of 1995, Delaine Eastin announced that she would ask the State Board of Education to work on a supplement to the 1992 math Framework. But, merely adding a supplement to the 1992 Framework would not be sufficient to remedy the problem. This position was well argued by the only mathematician to ever serve on the State Board of Education, Dr. Henry L. Alder, in his Presentation to the State Board of Education of December 7, 1995.
Public hearings on all of the Frameworks ran from December 1995 to April of 1996. A special State Assembly Hearing on Math Education was held March 14th, 1996. On March 18th, 1996, plans to begin a revision of the Framework immediately were announced.
On September 12th, 1996, the State Board of Education approved a Mathematics Program Advisory that stresses balance in the content and methods of mathematics instruction and restores an emphasis on basic skills, computation, and rigor. The advisory is for distribution to all districts in the state.
On November 8th, 1996, the State Board of Education appointed a new Curriculum Framework and Criteria Committee to come up with a new Mathematics framework. This committee began meetings in January, 1997. On September 5th, 1997, a new Mathematics Framework draft from the Mathematics Curriculum Framework and Criteria Committee was released for review.
On Dec. 11th, 1997 the State Board of Education approved The California Mathematics Academic Content Standards for Grades K - 12. The new standards set high goals for achievement with sufficient year-to-year detail to guide implementation, earning them a #1 rating. Rigorous new Mathematics Standards were adopted in San Diego on Feb. 10th, 1998.
In the spring of 1998, statewide assessments in mathematics achievement returned to California in the form of the STAR tests.
After more than a year, the Curriculum Commission released their revised Mathematics Framework Draft on September 17th, 1998. On Oct. 18th, 1998, the Curriculum Commission voted to approve the draft and pass it on to the State Board of Education.
On December 10, 1998, the California State Board of Education unanimously approved a new Mathematics Framework.
In the spring of 1999, statewide assessments in mathematics achievement were repeated. This time, the augmented STAR tests included additional items written specifically to match the California standards.
On June 10, 1999, the State Board approved new Math Textbook Adoptions designed to support achievement under the new state standards. Finally, districts can use AB2519 funds to buy new textbooks to replace "fuzzy" math.
On January 10th, 2001, the California State Board of Education Adopted Mathematics Programs that are aligned with the new standards and framework. There is still a long way to go and there is still resistance from those who put us in this position in the first place. However, there is the hope that better materials will arrive in the classrooms soon.