Junior High School Mathematics Application Problems

Author: Ye Yaoceng
Publisher:
Publish Date: 2003-01-01
Features: The types of applied math problems in junior high school are roughly categorized as follows:
1. Applying existing formulas and theorems directly to the quantitative relationships or formal structures presented in the practical context of the problem.
2. Using established numerical models to conduct quantitative analysis, followed by calculations or reasoning to solve the problems raised in the applied math problems.
3. For refined and processed materials, ignoring secondary factors while establishing the relationships among the retained factors as a mathematical model.
Research in modern psychology shows that for many students, the transition from abstract to concrete is no less challenging than the transition from concrete to abstract. A common difficulty students face when solving applied math problems is the inability to refine real-world problems into mathematical ones, specifically the inability to establish mathematical models (such as not being able to formulate objective functions, systems of inequalities, or systems of equations). This is closely related to the current math education system, which overly emphasizes logical reasoning while neglecting applications and disconnecting from real-world contexts.
Applied math problems are generally lengthy, involve multiple variables, and have numerous interrelated factors. Students are required to identify the essential features of a problem from a wealth of information, discern the corresponding quantitative and positional relationships, and transform the problem into a mathematical one. Therefore, solving applied math problems must first involve thoroughly understanding the problem, particularly clarifying the quantitative relationships between relevant quantities, especially the equal and inequality relationships. This is the foundation for establishing the corresponding mathematical model.
After deriving conclusions by applying mathematical methods to the formulated functions, equations, inequalities, etc., it is essential to verify whether the results align with the actual problem. The retention of approximate values should not be generalized by simple rounding but must depend on the specific requirements of the real-world context.
To support the reform of junior high school math education and cultivate students' innovative awareness and abilities; to align with the research and preparation for the reform of junior high school math exam questions, we have compiled and organized this book based on recent relevant materials, providing it as a reference for junior high school teachers, students, and math enthusiasts.