  In this paper we discuss how teaching of mathematics for middle school and
high school students can be improved dramatically when motivation of concepts
and ideas is done through the classical problems and the history of
mathematics. This method improves intuition of students, awakens their
curiosity, avoids memorizing useless formulas, and put concepts in a historical
prospective. To illustrate we show how diagonalizing quadratic forms, elliptic
integrals, discriminants of high degree polynomials, and geometric
constructions can be introduced successfully in high school level.
