A new perspective on the teaching design of mathematical problem solving: from the perspective of inspiring students to generate mathematical concepts

For math problems of considerable difficulty, such as the final questions in the college entrance examination, a crucial instructional objective in the design and classroom implementation of mathematical problem-solving teaching is to inspire students to develop appropriate mathematical concepts based on the specific characteristics of the problem at hand. Mathematical concepts play an organizing role among a series of math problem-solving teaching objectives. Mathematical methods originate from the standardization and concretization of mathematical concepts, and mathematical creative thinking first requires the generation and transformation of mathematical concepts. Mathematical concepts are behavioral instructions for operating on information in math problems, it is only through the execution of these conceptual directives that the problem-solving subject can formulate effective solution strategies.