What Is Mathematics?
The National Council of Teachers of Mathematics (NCTM), the world’s largest organization devoted to improving mathematics education, is developing a set of mathematics concepts, or standards, that are important for teaching and learning mathematics. There are two categories of standards: thinking math standards and content math standards. The thinking standards focus on the nature of mathematical reasoning, while the content standards are specific math topics. Each of the activities in this booklet touches one or more content areas and may touch all four thinking math areas. The four thinking math standards are problem solving, communication, reasoning, and connections. The content math standards are estimation, number sense, geometry and spatial sense, measurement, statistics and probability, fractions and decimals, and patterns and relationships.
Often, people equate mathematics with arithmetic. Arithmetic is concerned with numbers. When considering the mathematics curriculum, many people focus on computational skills and believe that they constitute the full set of competencies that students must have in mathematics. Traditionally, the major emphasis of the K-8 mathematics curriculum has been to teach children arithmetic – how to add, subtract, multiply, and divide whole numbers, fractions, decimals, and percentages. Mathematics involves more than computation. Mathematics is a study of patterns and relationships; a science and a way of thinking; an art, characterized by order and internal consistency; a language, using carefully defined terms and symbols; and a tool. Teachers and other educators working together to improve mathematics education must explore a broader scope of mathematics.
“A mathematician is a blind man in a dark room looking for a black cat which isn’t there.” – Charles Darwin This is the first of at least three chapters discussing the philosophy of mathematics. The philosophy of mathematics is at a crossroads right now. There are two major camps building. On one side are the old school mathematicians who see mathematics as a foundation of science. On the other side is a small but growing group of scholars made up of cognitive psychologists, linguists, and neural biologists (and some mathematicians as well) who see mathematics as a function of the brain. While a comprehensive philosophical definition of mathematics is not really possible, philosophers have been working on it for millennia without success, these new neurobiological/ linguistic/ cognitive theories show promise in helping us understand how we learn and understand math. If we better understood how the brain handles math, we could find approaches to teach math more effectively.
Mathematics as a formal area of teaching and learning was developed about 5,000 years ago by the Sumerians. They did this at the same time as they developed reading and writing. However, the roots of mathematics go back much more than 5,000 years. Throughout their history, humans have faced the need to measure and communicate about time, quantity, and distance. The Ishango Bone (see ahttp://www.math.buffalo.edu/mad/ Ancient-Africa/ishango.html and http://www.naturalsciences.be/expo/ishango/ en/ishango/riddle.html) is a bone tool handle approximately 20,000 years old.
