Research On Mathematical Exercise Understanding And Application Algorithms Based On Formulae

In recent years,intelligent education platforms use artificial intelligence technology to recommend suitable content to users,playing an increasingly important role in our daily life.In this circumstances,how to better understand the exercises and establish an accurate exercise model plays an importance role for improving the quality of exercise recommendation and teaching efficiency.A good exercise representation can reflect the inspection purpose and calculation logic of the exercise,and reflect the relationship between the similarities and prerequisites of the exercise.Through the analysis of actual data,we observe that simply relying on the stem text to represent the exercise cannot fully and accurately reflect the purpose of the exercise.However,the formula of the exercise is the symbolization of the problem-solving logic,and contains rich mathematical logic information.Therefore,the formula is of great value for obtaining an accurate representation of the exercise.A lot of research has been done in academia around exercise representation,but there are still many problems.Specifically,the current exercise representation model has two main deficiencies:(1)it only pays attention to the information of the question stem,ignoring the importance of the exercise formula;(2)it does not consider the prerequisite relationship.These two shortcomings limit the performance of current exercise representation models.To this end,this paper designs two deep exercise representation models that integrate formula information and question stem information,which can reflect the similarities and prerequisites relationship of exercises.The specific contributions of the paper are as follows:(1)A set of systematic mathematics exercise datasets was constructed,including2358 exercises(covering 24 concepts)for similar exercise retrieval task;370 exercises(including 70 templates and 60 prerequisite rules)for prerequisite relationship judgment task.(2)For similar exercise retrieval scenarios,a exercise representation model which fuse information of formula and question stem text is proposed.In this model,the deep semantic context representation of the numbers in the question stem,which reflect the mathematical logic,is aggregated in a bottom-top manner through the formula-based tree neuron network,so the problem stem and formula information are fused to obtain the problem representation.The experimental results show that AUC of binary classification is improved by 0.04 compared with the baseline model,and the Precision@1,Precision@5 and Precision@10 of retrieval task are improved by 0.02,0.04 and 0.05 respectively.The results of multi-angle analysis of exercises also show that the exercise representations obtained by our model can correctly reflect the mathematical logic of exercise.(3)For the task of judgment of the prerequisite relationship between the exercises before the exercise,a model based on the node attention mechanism of the formula tree is proposed.By comparing the formula tree structure and tree node representation of the two exercises,the model perceives the semantics and the calculation logic,and then uses the attention mechanism based on the formula tree node to fuse the perception results and then determine whether there is a mathematical logic prerequisite relationship between the two exercises.The experimental results show that AUC of binary classification is improved by 0.16 compared with the baseline model,which verifies the effectiveness of the model.The understanding and application model of mathematical exercises based on formulas designed in this paper is of great significance to promote the research progress of intelligent education.