| In the era of advocating lifelong learning for all,"AI + Education" has become a hot research field.Intelligent Computer Aid Instruction(ICAI)system can give full play to its unique advantages.The ICAI system improves learning efficiency by providing students with personalized teaching services,reduces the burden on teachers,and explores new education models.The research on automatic solving of mathematical problems is an important branch of it.The automatic problem solving for primary school mathematics has obtained the plentiful research results.However,there are few studies on automatic solution for high school mathematics.This paper develops an automatic algorithm for solving triangle and solid geometry problems in college entrance examination mathematics.The algorithm takes the test text as the input and outputs the humanoid solution.The research content mainly includes the following three aspects:(1)Design a reasonable and efficient knowledge representation model.A knowledge representation method combining production rule representation and object-oriented representation is proposed,and a knowledge representation model is established for specific problems.The model can not only describe the mathematical objects involved,but also represent the basic formulas,theorems and human problem-solving methods.(2)Design human like problem solving algorithm.For solving the triangle problem,the synthesis method of forward reasoning and the analysis method of reverse reasoning are combined,and the relationship between the problem conditions and the solution objectives is gradually established by using state progressive reasoning.Moreover,in order to deal with the complex reasoning of multi condition combination,using the special skills of human problem-solving for reference,the reasoning rules based on expert knowledge are established to improve the generalization ability of the algorithm.About 95% of the solution accuracy is obtained in the test set.For solid geometry problems,it completely simulates human problemsolving thinking,and establishes six core functional modules: reasoning of the spatial position relationship of lines and surfaces,calculation of angles and lengths in plane geometry,establishment of coordinate systems and construction of point coordinates,establishment of auxiliary lines,the vectorized representation of geometric problems,the calculation of vectors.The design of the problem-solving algorithm fully draws on the human thinking mode,and combines the human macroscopic problem-solving strategy with the advantages of computer efficient computing.About 80% of the correct solutions were obtained on the test set.(3)Human like reasoning process display and test question similarity analysis.For solving the triangle problem,after reasoning,the algorithm starts from the solution goal,reversely traces the reasoning chain and outputs the problem-solving path map,which is helpful to intuitively understand the problem-solving process.Based on the largest common subgraph of the problem-solving path graph,the test question similarity is defined,which makes necessary preparations for the in-depth application of "AI + Education". |
