Dilemma in Teaching Mathematics

The challenge in mathematics education is finding the best way to teach mathematics. When students learn the reasoning and proving in mathematics, they will be proficient in mathematics. Students must know mathematics before they can apply it. Symbolism and logic is the key to both the learning of mathematics and its effective application to problem situations. Above all, the use of appropriate language is the key to making mathematics intelligible. In a very real sense, mathematics is a language. Proficiency in this language can be acquired only by long and carefully supervised experience in using it in situations involving argument and proof. Mathematics is essentially a structured hierarchy of proposition forged by logic on a postulation base. However, nowadays, the teaching of mathematics is more on focusing the mathematical procedures. Students learn variety of problem-solving in mathematics and then on its application. In addition, the teaching of mathematics is moving towards the use of mathematics in the real world. This method is said to motivate students to learn mathematics and enable them to transfer this knowledge in their daily live and future career. There are beliefs that due to the current over-emphasis on problem-solving and applications, students who enjoy working the problems in high school math, and hence decide that they like mathematics and want to major in it, find that the nature of the subject changes abruptly when they encounter the proof courses. They are bewildered and dismayed. Their previous problem-solving courses did not prepare them for this abrupt changed. Is argument and proof in the applications-problem centered domain of school mathematics being postponed, suppressed and downgraded? Are we sacrificing the essence of mathematics in order to motivate students to learn and appreciate mathematics? In this paper, the authors will discuss on this issue.