• Communications of Mathematical Education
• /
• v.25 no.2
• /
• pp.403-430
• /
• 2011

The purpose of the study was to investigate how the use of graphing calculators influence on forming students' mathematical concept of algebra, students' mathematical connection, and attitude toward mathematics. First, graphing calculators give instant feedback to students as they make students compare their written answers with the results, which helps students learn equations and linear inequalities for themselves. In respect of quadratic inequalities they help students to correct wrong concepts and understand fundamental concepts, and with regard to functions students can draw graphs more easily using graphing calculators, which means that the difficulty of drawing graphs can not be hindrance to student's learning functions. Moreover students could understand functions intuitively by using graphing calculators and explored math problems volunteerly. As a result, students were able to perceive faster the concepts of functions that they considered difficult and remain the concepts in their mind for a long time. Second, most of students could not think of connection among equations, equalities and functions. However, they could understand the connection among equations, equalities and functions more easily. Additionally students could focus on changing the real life into the algebraic expression by modeling without the fear of calculating, which made students relieve the burden of calculating and realize the usefulness of mathematics through the experience of solving the real-life problems. Third, we identified the change of six students' attitude through preliminary and an ex post facto attitude test. Five of six students came to have positive attitude toward mathematics, but only one student came to have negative attitude. However, all of the students showed positive attitude toward using graphing calculators in math class. That's because they could have more interest in mathematics by the strengthened and visualization of graphing calculators which helped them understand difficult algebraic concepts, which gave them a sense of achievement. Also, students could relieve the burden of calculating and have confidence. In a conclusion, using graphing calculators in algebra and function class has many advantages : formulating mathematics concepts, mathematical connection, and enhancing positive attitude toward mathematics. Therefore we need more research of the effect of using calculators, practical classroom materials, instruction models and assessment tools for graphing calculators. Lastly We need to make the classroom environment more adequate for using graphing calculators in math classes.

• Journal of Korean Philosophical Society
• /
• v.145
• /
• pp.91-117
• /
• 2018

This paper aims to clarify the similarities and differences between the Zhouyi and artificial intelligence. The divination of the Zhouyi is rooted in the oldest system of human knowledge, while artificial intelligence stands at the cutting edge of modern scientific revolution. At first sight, there does not appear to be any association that links the one to the another. However, they share the same ground as seen from a semiotic standpoint because both of them depend on the semiotic system as a means of obtaining knowledge. At least four aspects can be pointed out in terms of similarities. First, artificial intelligence and the Zhouyi use artificial language that consists of semiotic signs. Secondly, the principle that enables divination and artificial intelligence lies in imitation and representation. Thirdly, artificial intelligence and the Zhouyi carry out inferences based on mathematical algorithms that adopt the binary system. Fourth, artificial intelligence and the Zhouyi use analogy as a means of obtaining knowledge. However, those similarities do not guarantee that the Zhouyi could arrive at the scientific certainty. Nevertheless, it can give us important insight into the essence of our civilization. The Zhouyi uses intellect in order to get new information about the unknown world. However, it is hard to know what kind of intellect is involved in the process of divination. Likewise, we do not know the fundamental character of artificial intelligence. The intellect hidden in the unknown subject is a mystic and fearful existence to us. Just as the divination of the Zhouyi inspires the sense of reverence toward the supernatural subject, we could not but have fear in front of the invisible subject hidden in artificial intelligence. In the past, traditional philosophy acknowledged the existence of intellect only in conscious beings. Nonetheless, it becomes evident that human civilization ushers into a new epoch. As Ray Kurzweil mentioned, the moment of singularity comes when artificial intelligence surpasses human intelligence. In my viewpoint, the term of singularity can be used for denoting the critical point in which the human species enters into the new phase of civilization. To borrow the term of Shao Yong(邵雍) in the Northern Song Dynasty, the past civilization belongs to the Earlier Heaven(先天), the future civilization belongs to the Later Heaven(後天). Once our civilization passes over the critical point, it is impossible to go back into the past. The opening of the Later Heaven foretold by the religious thinkers in the late period of Joseon Dynasty was a prophecy in its own age, but it is becoming a reality in the present.