The Study Of Category, Structure And Distribution About Algebra Word Problem

Algebra word problems are of great significance for students to experience mathematical reality and application as they are particular type of problems in whch quantitative relations are embedded in various realistic situations. Problems falling into the same category have the same situational structure or quantitative structure. Students are generally required to form propriate problem schema for a given type of problems with similar problem structures in order to successfully solve them. Appropriate schema allows students to represent problems correctly, and improves their abilities of problem-solving. Therefore, investigating problem categories and structures not only contributes to teaching and learning, but also lays a scientific foundation for mathematical curriculum design and test construction. Currently, there are mainly two fundamental approaches to the classification of algebra word problem:problem structure analysis and cognitive schema analysis.Analyzing problem structure can establish relationship between problem features and cognitive schema, and integrate these two approaches. However, there is no research that has been done in the field to systematically investigate the category and structure of algebra word problem domestically and abroad.This thesis systematically investigated the categories, structures and distributions of algebra word problems over the domain and compared the variations and changes of such problems across time and countries, based on a large pool of algebra word problems collected from three versions of teaching materials in Shanghai since the1980s of the20th Century. Specifically, longitudinal changes of the categories and distributions of the algebra word problems over the1980s,1990s and the21st century were studies, so as differences and similarity between textbooks of shanghai and California. This thesis combines the classification framewok of Mayer(1981) and the notation network system of Shalin&Bee(1985). After selection, coding, building item bank and analysis, conclusions are as follows:1. There are1392algebra word problems in49teaching materials that meet the selection criteria. Among which, there are7families,42categories,118templates,406modifications. Structural chart for each of the406modifications is given in the appendix of this thesis.2. There are8families,30categories,86templates in California teaching materials and the modifications are far fewer than Shanghai. The importance degree of different problems types in both nation can be observed from distributes of families, categories and templates.3. Generally speaking, problems in20th century version are more complex, complexity change is larger as grades get higher.4. With regard to problem category, straight rate family and time rate family represent two important subsets of algebra word problems. With the passage of time, there are more kinds of categories and templates. As to problem structure, complexity degree decreases in the order of1980s,1990s, and21th century version of textbooks. Range of complexity is increasing from1980s to21th century, then to1990s version.Finally, results are analyzed and discussed, the universality of research methods is verified, also its limitations is summarized.