A Study On Understanding Levels And Teaching And Learning Strategies Of Operation Of Rational Numbers

Nowadays there exists an active exploration on mathematical education both home and abroad. One of the focal points is to emphasize the importance of "learning mathematics with understanding." In order to do so, it is necessary to know what is "understanding", how many levels there are in the whole understanding system and how many students there are in each of the understanding level. In fact, we do not have clear perception of students' understanding situation, understanding levels and limitations, therefore, effective teaching and learning strategies are not taken.Taking operation of rational numbers as the carrier, this paper starts the research right from the study on multiplication of decimal, division of fraction and multiplication of rational numbers and studies the "understanding levels of operation of rational numbers and the teaching and learning strategies that matches them." In detail, three aspects are taken into consideration. They are 1) what understanding level can students reach? 2) Why does that happen? 3) What would be the effective teaching and learning strategies, based on the specific understanding levels of students?The investigating procedure is as follows. First of all, choosing the testing schools and classes, then attending the classes, making records of them, interviewing teachers after classes and conducting mini-teaching tests over some parts; after that, handing out questionnaires towards both teachers and students and conducting interviews based on the results of questionnaires; finally, analyzing the obtained data both quantitatively and qualitatively. To be more detailed, the quantitative research consists of the encoding of the questionnaire results, the inputting of data and analyzing of these data with SPSS software. On the other hand, the qualitative research is to analyze specific classroom teaching and interview.Through the research mentioned above, the following conclusion is obtained.Firstly, students' understanding on the operation of rational numbers is limited and there exists different levels in the whole understanding system. 1) There do exist different levels within students' understanding on the meaning of operation. As far as the multiplication of decimal and division of fraction are concerned, it is easiest for students to understand the translation from real world situation or spoken symbols to written symbols. Then comes the translation from written symbols to spoken symbols. And then comes the linguistic explanation of the meaning of operation. The hardest to obtain is the translation from spoken symbols to pictures. 2) There are different levels and...