Case study Based on Ogane's Problem-solving Process

Abstract

In the 1980s, there were problems in the teaching of problem-solving in mathematics in the former Soviet Union, such as formulaic solutions and a lack of emphasis on teaching mathematical thinking. Therefore, Oganesian believes that in the traditional education system and in a large number of mathematical teaching practices, the role of mathematical exercises in developing students' mathematical level is limited. Mathematical exercises are difficult to test students' other aspects of mathematical development and ideological education factors. Introducing new teaching models is an urgent need for teaching mathematical problem-solving. Based on this, Oganesian proposed four steps for solving problems in his book "Teaching Methods for Primary and Secondary School Mathematics": understanding the problem conditions-developing a solution plan - implementing the solution plan - researching the obtained solutions. The article takes the "theorem for determining the perpendicularity of a straight line to a plane" in mathematics as an example, and analyzes its application based on the process of solving problems using the Oganesian method. By introducing mathematical problems into the Oganesian phase problem-solving process, gradually solving problems, delving into the vertical relationship between lines and planes, and analyzing their significance and role in practical applications. Assist students in cultivating thinking methods and problem-solving strategies for mathematical problem-solving systems, guide them to solve mathematical problems more deeply and accurately, enhance the problem-solving ability of mathematical learners, and optimize their thinking logic.