Understanding The Concept Of Fractions And Teaching Research

In the late1980s, a seminar was held in Paris with the theme of the history of fraction". In the seminar, many mathematicians which were from different countries launched a deep discussion about the origin and development of fraction; the concept and meaning of fraction; and the relationship between fraction with other disciplines, such as the economy, literature and music. In China, fraction teaching is placed in a very important position. Many front-line mathematics teachers study the teaching objectives and the difficulty of fraction. They have carried out a detailed instructional design, and actively participate in innovating who tried to help students build complete systems of fraction. Thus, which knowledge of fraction should be taught to students, teachers how to help students understand fraction, how to make an innovation to fraction instruction become an issue of this research.This study sort out by collecting the development of fraction in China, Babylon, ancient Egypt, ancient Greece, India and Western countries, and record the process from the early text notation, counsel notation, notation hieroglyphics, cuneiform notation wait to the modern fraction.While arranging the concept of fractional construct theory, the factors of fraction which affect students’ learning and definitions. Through content analysis for compulsory mathematics curriculum standards and two versions textbooks, in order to sort out the structure of the fraction and content presentation features. Through observation to record the teaching of fraction and list advantages and disadvantages. Finally, based on the above to write out of the work sheet and suggestions, which hope teachers improve the fraction teaching.The study found the results in fraction teaching as follows. First, the fraction model which guide students to understand is single. Mostly is physical model of the line model and rarely involve geometry model. Second, learning contexts mostly are fragmented picture, which lacking of new ideas. Third, it lacks the history of fraction. Fourth, it is lacks the learning of identification between "quantity" meaning and the "number" means. Fifth, it lacks the diversification of fraction. The difficulty in students’ fraction learning as follows. First, fraction concept is unclear. Second, the unit "1" concept is unclear. Third, the "average" concept is unclear; fourth, the two meanings of fraction are not clear. Therefore, this study gives some suggestions to improve teaching and help student eliminate difficulty, improve learning efficiency.