NCTM Standards and the Evolution of American Mathematics Education
The National Council of Teachers of Mathematics (NCTM) has played a pivotal role in shaping how mathematics is taught across the United States and Canada. By publishing a series of standards, the NCTM has sought to define a vision for school mathematics that balances conceptual understanding with practical application. From the immediate aftermath of World War II to the development of the Common Core, the organization's guidelines have often sparked intense debate between traditionalists and reformers.
Key Facts
- NCTM has issued several major frameworks, including the 1989 Curriculum and Evaluation Standards and the 2000 Principles and Standards.
- The "Math Wars" emerged from opposition to reform curricula that de-emphasized rote memorization and basic skill drills.
- The 2000 Principles and Standards introduced six core principles and ten strands to create a more balanced approach to math education.
- Curriculum Focal Points (2006) aimed to solve the "mile wide and an inch deep" problem by narrowing the focus to the most essential topics per grade.
- NCTM's work served as a foundational component for the 2010 Common Core State Standards.
Post-World War II Strategic Planning
In 1944, the NCTM developed a postwar plan to ensure that the mathematical advancements of World War II translated into lasting educational benefits. The organization identified grades 1-6 as the critical period for building foundations, with a specific emphasis on algebra, which had proven essential for military and industrial efforts during the war.
To make algebra relevant to everyday citizens, the NCTM proposed three primary strategies:
- Focus on Meaning: Moving away from a strict choice between "Drill" or "Meaning Theory," teachers were encouraged to provide the purpose behind concepts alongside sufficient practice.
- Organized Instruction: The informal teaching techniques of the 1930s—which relied on student interest—were replaced by a structured approach, reflecting the inherent organization of mathematics.
- Adaptive Practice: Teachers were encouraged to provide targeted practice to ensure student success.
For students in grades 7 and 8, the focus shifted to mastering previous concepts and preparing for high school. This was partly a response to Army reports suggesting that poor performance among recruits was due to the forgetting of basic math. The curriculum for these years focused on number and computation, everyday geometry, graphic representation, and elementary algebra. In high school, the NCTM suggested a two-track system in ninth grade: one for students pursuing advanced algebra and another for those studying general mathematics to prevent students from being held back.
The "New Math" Revolution of 1961
By 1960, the NCTM, with funding from the National Science Foundation, promoted the adoption of Modern Mathematics (or "New Math"). This movement aimed for a rapid improvement of school mathematics, culminating in the 1961 report, The Revolution in School Mathematics.
However, this era faced significant criticism. Professor Morris Kline, in his book Why Johnny Can't Add, argued that the "Modern Mathematics" label was essentially propaganda used to make traditional methods seem sterile and obsolete. Kline asserted that many school administrators adopted these programs not because they understood the scientific merits, but to appear active and alert to parents and school boards.
The 1989 Standards and the "Math Wars"
The 1989 Curriculum and Evaluation Standards for School Mathematics marked a shift toward constructivism—the theory that children build their own understanding of concepts. This approach emphasized problem-solving and conceptual understanding over the direct instruction of facts and algorithms.
Under this reform, students were introduced to algebraic concepts, such as the commutative property, as early as first grade. Rather than starting with standard arithmetic methods, students were encouraged to invent their own problem-solving methods through guided discovery. The standards also promoted equity, aiming to provide mathematical power to women and underrepresented minorities, and encouraged the use of calculators and manipulatives.
While the U.S. Department of Education praised some of these programs as "exemplary," the reform triggered the "math wars." Antireform organizations like Mathematically Correct and HOLD protested the decrease in rote memorization and basic skill practice. Critics argued that the new methods led to gaps in fundamental knowledge, though some research later indicated that students from traditional curricula entered college remedial math at even higher rates.
Refining the Vision: 2000 and 2006
To address the controversies of the 1989 standards, the NCTM released the Principles and Standards for School Mathematics in 2000. Developed through a consensus of mathematicians, teachers, and researchers, this version was seen as more balanced and less radical.
| Six Principles | Five Content Strands | Five Process Strands |
|---|---|---|
| Equity, Curriculum, Teaching, Learning, Assessment, Technology | Number and Operations, Algebra, Geometry, Measurement, Data Analysis and Probability | Problem Solving, Reasoning and Proof, Communication, Connections, Representation |
In 2006, the NCTM released Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics. This document addressed the common criticism that U.S. curricula were "a mile wide and an inch deep" by identifying only about three primary mathematical topics per grade level. Crucially, the Focal Points explicitly stated that standard algorithms should be included in arithmetic instruction, bridging the gap between reform and traditional methods.
These Focal Points eventually served as one of the key documents used to create the 2010 Common Core State Standards, which have since been adopted by the majority of U.S. states.
Frequently Asked Questions
What were the "Math Wars"?
The "Math Wars" were a period of intense conflict between proponents of reform mathematics, who emphasized conceptual understanding and discovery, and critics who believed that the de-emphasis of rote memorization and basic skill drills harmed student proficiency.
How did the 2000 standards differ from the 1989 standards?
The 2000 Principles and Standards for School Mathematics were developed through a broader consensus process and were designed to be more balanced and less controversial than the 1989 version, which was seen by some as too radical.
What is the "mile wide and an inch deep" problem?
This phrase describes a curriculum that attempts to cover a vast number of topics (sometimes between 26 and 89 per grade) without providing enough time or depth for students to truly master any single concept.
Did the NCTM eventually support the teaching of standard algorithms?
Yes. In the 2006 Curriculum Focal Points, the NCTM made it clear that standard algorithms were to be included as part of arithmetic instruction.
What was the purpose of the two-track curriculum in ninth grade?
The two-track system allowed students with a high interest in math to study algebra, while those with less interest studied general mathematics, ensuring that students were not held back by a single rigid curriculum.