Understanding the concept of limit in college students with computer

• Main Authors: Szu-Hui Wu, 吳思慧
• Other Authors: Sou-Yung Chiu
• Format: Others
• Language: zh-TW
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/60809987732961088675

博士 === 國立彰化師範大學 === 科學教育研究所 === 97 === The purpose of this study is to investigate the university students’ cognition of the limit concept with the assistance of computer. The research is divided into three aspects. We adopt classroom observation and teaching experiment method to investigate the learning and understanding of the subjects. We collect the experimental reports, questionnaires and the protocols of student in their problem-solving and interview. The psychological perspective of the information process theory was used to conduct the qualitative research analysis. In the first aspect, we investigate students’ realization of the function limit through the programs of Maple, the subjects are from two classes in J-University. The findings show that students can build the dynamic limit concept with the numerical and graphic representation, but it’s still hard to cross to the formal definition. In the second aspect, we inspect students’ concept of the limit in the problem-solving activity of Taylor expansions with Maple. Under the guidance of worksheet, we explored how students made connections between the “approximation” and “limit”, and then, reconstructed the informal and formal limit concept. The findings show that: First, based on their rough concept of approximation, the beginners did learn the Taylor topic and think actively to inquire the meaning of “approximation”. Second, following the guidance of worksheet, the sophomores recognized abstract representation in the definition, and reconstructed the informal and formal limit concept. However, the learners still had the difficulty to internalize the definition. In the third aspect, we investigate students’ understanding the “differentiability” of two-variable functions with Java interactive modules. The finding shows that students can learn these advanced concepts meaningfully and confidently as they reasoned in visual way, and then, successfully combined the graphic representation with their algebraic expressions of concepts. They could aware and clarify the misconceptions through this learning environment. And this friendly program can afford to promote group cooperation, meaningful mathematical talk. Thus students’ potentials can be developed. Summarily, in the above three aspects, this research affirms that it facilitates the understanding of university students in limit concept with the representations of computer. Finally, we identify some requirements for improving the efficiency of computer integrating into teaching.