  Many mathematicians find mathematics aesthetically beautiful and even
comparable to art forms such as music or painting. On the other hand, every
year a great number of school students leave mathematics with total
disillusionment and bitterness, without ever witnessing any beauty in it. In
this work, we give some strategies to teach mathematics, especially to gifted
students and to instill a love of mathematics in them. We will describe an
integrated approach to teaching mathematics where students are introduced to
more advanced, more elegant and more beautiful aspects of the subject early.
The proposed integrated approach takes advantage of the fascinating
interconnections between various subfields of mathematics, and even borrows
from advanced topics such as number theory and topology. Combining the teaching
of computer programming with the teaching of mathematics is another key focus
of this work. This opens up the door to explore, not only the beautiful topics
such as fractals, computer math art and computer graphics in general, but also
real-life applications resulting from computer simulations in engineering and
physics and other natural sciences. We will also discuss the use of
storytelling, explorations and experimenting, puzzles and creative problem
solving etc., to make learning interesting for students. It is important to
show students that the `true' essence of mathematics goes beyond the dry
procedural drill of learning arithmetic. Students must be provided with the
opportunities to experience the `aha moment' resulting from the joy of solving
a difficult problem, or from the understanding of a deep concept with complete
clarity. We will discuss several strategies, and provide many examples to
illustrate how this could be achieved, taking into account the emotional and
psychological aspects of mathematical cognition and learning.
