“New Math”, developed at the beginning of the computer age, was an introduction to discrete math and number theory (the mathematics of computer science). New math was primarily of interest to mathematicians, who felt that with the coming of computers, understanding discrete math would be valuable to the general public. Educators thought that the new math, with its focus on counting and sets, would be easily understood by young children. However, non-scientists came to view the new math as difficult and irrelevant, demanding a return to the traditional 500 year-old math curriculum. Remembering the controversy surrounding “New Math”, many regard math reform with skepticism.
In our technology and information age, there is genuine need for more than the traditional rote memorization of facts and procedures characteristic of the Renaissance period of history. Five hundred years ago books were in short supply, so students wrote their own school books by copying words from a lecture. Important facts were memorized and carried in human brains, for lack of other storage receptacles. Numbers, learned by scholars and used by specific trades, such as commerce, navigation, and architecture, were seldom available to the general public. Pure mathematics was reverently memorized by scholars and enshrined for its beauty rather than its utility.
Now we are surrounded by and dependent on numbers. They appear on our mailboxes, auto license plates, social security cards, airplane tickets, computers, television, newspapers, bank accounts, and ATM access codes. Numeracy is becoming increasingly important to understanding the modern world. Reform mathematics is aimed at making mathematics more understandable and useful to everyone. Through the centuries, as mathematical discoveries were made, students were asked to memorize more and more, often at the expense of taking time to understand the information they carried. Experts at the game of school developed “memorize and purge” methods to carry them successfully from exam to exam. Mathematics, a subject where thoughtful analysis is necessary for understanding, lost its meaning and utility.
Of all the subjects we require our students to take in school, math is probably the most inefficient in terms of cost to benefit ratio. In traditional high school mathematics, the average student will probably use only a small fraction of what he/she has had to learn.
The goal of reform math is to bring math into the context of the information age; to help students understand the numbers and mathematical ideas they must use daily. Math is more pervasive and important today than ever before. Most persons have and use calculators in their daily lives; many use computers in their jobs.
Calculators and computers give people computational power, but power is useless unless we know when and how to use it.
1. To understand numbers and patterns found in nature
2. To know when and how to use math tools
3. To make fast and accurate predictions
4. To grow and maintain mental power
5. To understand invisible things
6. To think logically and clearly when solving problems
7. To operate systems using profound knowledge
8. To recognize long-term causes and effects
9. To check the reasonableness of answers
10. To feel comfortable in a technological world
1. To determine whether they actually understand the mathematics or just got lucky with their calculators, or temporarily memorized a procedure, or borrowed the answers from someone else.
2. To assess their logical thinking and problem solving skills.
3. To decide how well they are able to communicate their
mathematical ideas to others.
4. To allow for independent and creative mathematical ideas that may lead to more than one correct answer to a test question. (Answers must be proved to be mathematically correct and show a logical interpretation of the question.)
5. To gain insights into student mathematical misconceptions so they may be corrected.
6. To help students to analyze and clarify their mathematical thinking.
7. To encourage students to determine the reasonableness of their answers.
1. Less memorized facts; more understanding of math applications and procedures.
2. Less time spent introducing rarely used, complex paper-and-pencil procedures that can easily be done by calculators; more formulating and defining problems for input to calculators and computers
3. Less variety of material covered superficially; more selective material covered extensively.
4. Less artificial problems with whole numbers to plug into formulas; more real-world problems and data
Information that is seldom used can be quickly looked up in a book or computer program, so it is more important to know where to find it and understand how to use it than to memorize it. Our brains usually make these decisions for us. Most things that we use frequently, we will automatically memorize over time; others will be discarded.
I would like to express my appreciation to my colleagues who have contributed to this document, for sharing their experiences, and ideas, especially Sharon Smith and Phyllis Chinn.