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On teaching mathematics to gifted students: some enrichment ideas and educational activities

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.