Fact Sheet

A Brief History of Math Instruction

A Brief History of Math Education in the United States (1900–present)

Since 1900, there have been three major approaches to mathematics education in the United States…

TRADITIONAL MATH (1900–1957+)

Basic skills learned by continuous practice of basic algorithms (drill). Basic skills are seen as the building blocks of mathematical thinking.
Assessment based on standard pencil and paper testing.
Teacher–directed: lecture, demonstration, question and answer.
Students work independently most of the time.
Discrete content: separate courses for Algebra 1, Geometry, Algebra II, and Trigonometry.

Traditional Math dominated math instruction in the 20th century until September of 1957 when…

Change came to the USA...

The launch of Sputnik in October, 1957, forever changed mathematics education in the United States. The cry went out across the land: Our children are behind in math and science.

NEW MATH (circa 1960)

Basic skills learned by application of mathematical laws, not by practicing algorithms. Assessment based on standard pencil and paper testing.
Teacher–directed: lecture, demonstration, question and answer.
Students work independently most of the time.
Content: A logical and rigorous curriculum that requires understanding and application of mathematical principles at all stages of the learning process, from first grade to college. Set Theory is the centerpiece of study.

New Math replaced Traditional Math in America’s classrooms. New Math eventually self–destructed because no one but mathematicians can learn math that way.

It gave way to the short–lived “Back–to–Basics” movement, which sought to pick up the pieces of the New Math debacle. “Back–to–Basics” tried to swing the pendulum so far back that there was an outcry that our children were engaged in “drill” at the expense of “thinking.” This outcry provided an opportunity for another group to emerge. Enter Reform Math…

REFORM MATH (circa 1975)

Practice of basic skills are de–emphasized in favor of “self–paced” and "constructed” learning. Assessment is based on portfolios, projects, rubrics, observation, and self–reflection, as well as written tests.

Student–directed: “constructivist” activities, where the student “discovers” and creates mathematical constructs from activities and experiences supervised by the teacher. The teacher is no longer “the dispenser of knowledge.” Rather, the teacher is a “learning facilitator.”

Students work in cooperative learning groups much of the time.

Integrated content: Algebra 1, Geometry, Algebra II, and Trigonometry are integrated into a series of classes rather than being distinct courses of study. Emphasis is on “real– world” problems. Reform Math places great importance on the self-esteem of the student.
Reform Math has stumbled in the eyes of many educators because of its lack of emphasis in developing basic skills in a timely fashion. Chaos has resulted for both educators and students due to the ever-changing goals and teaching methods used over the past 50+ years.

Let’s take a look at some of the results…

From the Los Angeles Times (1997):

“Since World War II, math instruction in the United States has changed course time and again --- with little improvement in test results.”

1967: Five-year study of 12 Western nations finds U.S. 13-year- olds & high school seniors far behind those in other countries. New Math is blamed.

1988: A 17-nation comparison shows America’s best students, the top 5%, last in algebra and calculus . “Back-to-Basics” is blamed.

1996: The Third International Mathematics and Science Study, comparing students in 41 countries, finds U.S. eighth- graders below average. Reform Math is blamed.

Here is a poignant joke from the Internet:

Teaching Math in the 1950s (Traditional):

A logger sells a load for $100. His production cost is 4/5 of the price. How much is his profit?

Teaching Math in the 1970s (New Math):

A logger trades a set “L” (of lumber) for a set “M” (of money). The cardinality of set “M” is 100. The cardinality of subset “C” (his cost) is 20 less than “M”. What is the cardinality of set “P” (his profit)?

Teaching Math in the 1990s (Reform):

A logger sells a load for $100. Her production is $80 and her profit is $20. Your assignment: underline the number 20.

In the years since Sputnik, the mathematics community has been deeply divided on several key issues.

How much should we drill and “memorize”?

How do we teach Problem Solving?

When should we use manipulatives & calculators?

What about learning styles & ability groups?

How do we know when a child has learned?

How do we deal with self-image and self-esteem?

These are not easy questions…

The current “Math Wars” is a clash between Traditional and Reform approaches to math education, as they struggle for dominance in the educational mainstream. Many schools and schools districts are using both approaches.

Time will tell which approach, or combination of approaches, will best serve our children’s and society’s needs.