An Investigation Of Proportional Reasoning Among Shanghai Junior High School Students

The knowledge of "Rate and Ratio" runs through the totally compulsory education, as well as the daily life. "Proportional Reasoning"is an important thinking process by using algebraic method to solve ratio problem. However, many students and adults fail to finish the proportional reasoning because of their absence of the concept of rate and ratio.According to the level classification of test items by Hart,K.M(1981) and the initial investigation, we have defined the classification into 3 levels to have a comprehensive understanding of the proportional reasoning ability of middle school students in Shanghai,such as the levels of proportional reasoning, the response types when facing the ratio problem, the strategies of solving ratio problem, the factors of the proportional reasoning.After data statistics and the analysis of data, we have found the following conclusions:Firstly, about one third of the students have reached a high level of proportional reasoning. The Grade six students perform worse than other grades significantly, while the period of Grade seven maybe a critical opportunity to improve.Secondly,The students who take part in this research have a good performance because they have the sense of proportional reasoning in many instances. However, the distribution of the four kinds of response type is unbalanced. The continuity of the response is not very good when they are answering the items, especially the students of Grade six.Thirdly,The main strategies which students use in the test are:complete ratio, partly ratio, add or subtract, qualitative strategy, guess. The students who apply complete ratio in typical test items are no more than a third of all the students, means the absence of the experience to solve the ratio problem. Students tend to use "internal ratio" instead of "alternative ratio" facing whatever task types, especially the students of Grade six. One of the main mistakes students make is the perversion of the "unit rate". On the other hand, the students are used to comparing the absolutely figures,which means the incomplete understanding of the four quantities in the proportional equation, while considering "digit" instead of "quantity".Lastly, The students’ ratio problem solving is impacted by the Problem situation, task types, the base of acknowledge of students.