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The year 1999 marked the 10th anniversary of the NCTM's Curriculum and Evaluation Standards for School Mathematics. It also marked the 150th anniversary of the birth of German mathematician Felix Klein, who lived from 1849 to 1925. Although the relation between these two anniversaries may not be obvious, the connection is that Klein, were he still alive today, would probably support the NCTM's Standards. As the year 2000 brings us NCTM's Principles and Standards for School Mathematics, let us look back to the year 1900 and find Felix Klein at the forefront of a movement to reform mathematics education from rote learning to more meaningful mathematical learning.
Felix Klein was an acclaimed mathematician, teacher, and administrator at the University of Gottingen in Germany in the late nineteenth and early twentieth century. The University of Gottingen was a renowned center for mathematical thinking, with a heritage that included Gauss, Dirichlet, Riemann, and others. The Gottingen tradition continued with Klein as head of the mathematics department, attracting David Hilbert and, later, Emmy Noether. As a mathematician, Klein worked in the areas of Euclidean and non-Euclidean geometry, group theory, and complex function theory. His contributions to modern mathematics are considerable, but what makes him noteworthy here is that he cared deeply about how mathematics is taught.
Felix Klein was known as a gifted teacher, and his reputation as both an instructor and a mathematician drew students from all over the world. He was elected the first president of the International Commission on Mathematical Instruction, which was established by the International Congress of Mathematicians in 1908. Cover a period of years, he gave a series of lectures for teachers and prospective teachers of mathematics in German secondary schools. These lectures formed the basis of his three-volume work, Elementary Mathematics from an Advanced Standpoint: Arithmetic, Algebra, Analysis, which was originally published in 1908. In light of the current reform movement in mathematics education, looking back and learning what such a great mathematician and teacher had to say about teaching mathematics is interesting. The parallels between Klein's approach of the early 1900s and Principles and Standards for School Mathematics (NCTM 2000) are striking.
CONCEPTUAL UNDERSTANDING THROUGH CONCRETE AND GRAPHICAL REPRESENTATIONS OF MATHEMATICS
The presentation of mathematics in schools should be...