The ideological and political discipline of the university has undergone many curriculum reforms, now, it ushered in a new round guided by the fundamental task of “Lide and cultivate people”, basic education curriculum reform based on subject core literacy [1]. In this process, the teaching goal has realized the transition from “double base” to “three-dimensional goal”, and then to “core literacy”. No matter how the teaching goals change, the construction of an efficient classroom will be the eternal focus of teachers, because improving the quality of classroom teaching is the main starting point to achieve the goal of educating people. In order to build an efficient ideological and political classroom in high school, it is inseparable from the careful polishing of each teaching link by teachers [2]. A high-quality high school ideological and political class, it not only needs the wonderful classroom introduction of “Fresh Head”, but also the rich and substantial content explanation of “Pork Belly”, it is even more necessary for the “leopard tail” to wrap up a powerful class summary. Among them, class introduction and class summary, although they only occupy a small amount of time in the classroom teaching process, but they are all indispensable and important links, which will directly affect the effect of classroom teaching. For those who do not review in time after class, as time goes by, the amount of forgetting increases, the relative memory retention is also less. This requires teachers to complete the teaching task in the classroom, in order to guide students to review the knowledge learned in class in a timely manner, in order to strengthen memory, avoid the occurrence of later large-scale forgetting [3]. Some researchers will use the mathematical equation of memory curve, using mathematics to describe the objective world is an important means of scientific research and technological development. Mathematics was once thought to play a role in biology equal to zero, but by the 20th century, mathematics had played an ever-increasing role in biology. Emerging disciplines such as quantitative genetics and quantitative ecology were born one after another, it marks that the ancient discipline of mathematics has become an important tool for biological research [4]. Ecological mathematical model studies how to use mathematical language and mathematical tools to describe ecological phenomena and laws, some conclusions are drawn through mathematical logical reasoning, these conclusions are then used to explain, predict ecological phenomena and discover new laws. Any biological system, whether it is a population, biome, ecosystem, or biosphere, both survive for a limited time, it is only stable during this time. Extinction or migration of species indicates a loss of stability. In the process of ecological succession, one ecosystem is gradually replaced by another. It can be said that the surrounding world is a stable and coordinated sum of forms, its development is the replacement of these forms, this replacement is a process of transferring between forms and ideas in a short period of time. The ecosystem evolves from the initial stage of birth to the mature stage, within species, between species, communities and habitats are more closely linked, the ability to maintain nutrients is enhanced, and the resistance to external disturbances is increased. At this time, the population number fluctuates little, the intraspecific structure and quantity within the community are relatively stable, and the interspecific connections are close, ecosystems are basically in a self-sustaining stable state. Although the period of ecosystem stability is not necessarily long, but stability remains an essential feature of ecosystem survival. The study of stability can not only reveal the ecological laws of populations, communities, and ecosystems, moreover, for the protection of human beings, the construction of ecological environment and the improvement of environmental conditions, prevent the degradation of existing ecosystems, provide scientific countermeasures to solve the restoration and reconstruction of degraded ecosystems. In order to effectively carry out the practical work of ideological and political education for college students, many experts and scholars have carried out a series of fruitful research work, and achieved certain results. Murre J et al. started from five aspects: Educator, educational object, educational content, educational method and educational context, constructed an evaluation index system for the effectiveness of ideological and political education for college students, however, the system is complex and the index weights are not quantitatively given [5]. Lewis A et al. took the effectiveness of postgraduate online ideological and political education as the research object, targeted establishment of the evaluation index system [6]. Yao, Wenbin et al., the overall effectiveness evaluation index system of ideological and political education in colleges and universities has been constructed, in order to evaluate and guide the school's ideological and political education [7]. On the basis of current acting skills, the author proposes, research on university ideological and political learning model based on the mathematical equation of statistical memory curve, the intelligent memory model is further discussed, the power function is selected to fit the Ebbinghaus memory curve, and the correctness of the mathematical model of memory is established, and for the deficiencies of the intelligent memory model in adapting to the memory situation of each user, an adaptive control system with a reference model is introduced. According to the user's actual test results and review time, as a feedback control signal, combined with a reasonable memory cycle time planning table, in order to determine the next memory curve attenuation coefficient, thus, the intelligent vocabulary memory model is improved into an adaptive memory model. The results show that while not affecting the memory effect, using the intelligent memory model, the number of memories is reduced by 37.12% compared with the New Oriental memory method, using the adaptive memory model reduces the number of memories by 43.35% compared to the New Oriental memory method. The experimental results show, the adaptive memory model further saves 6.31% of memory times compared to the intelligent memory model, not only has good adaptability to each user's memory situation, but also further improves memory efficiency.

High school ideological and political classroom summary, it is an important link in the ideological and political classroom teaching process in high school, its design has its theoretical basis. The design of the summary link of the high school ideological and political classroom, its theoretical basis can be sought from modern associationist psychology and cognitivist learning theory. Among them, the “Ebbinghaus Forgetting Curve Theory” (the mathematical theory of memory curves) in modern associationist psychology, it can provide theoretical support for the summary of high school ideological and political classroom [8].

Ebbinghaus' forgetting curve theory The famous German psychology Ebbinghaus used meaningless syllables as material, research on oneself and others, carry out memory and forgetting experiments. After a lot of rigorous experimental tests, the following experimental data were obtained (Table 1):

The results of memory and forgetting experiments

time interval | amount of memory |
---|---|

just finished | 100% |

20 minutes | 58.19% |

1 hour later | 44.49% |

After 8–9 hours | 35.79% |

1 day later | 33.69% |

2 days later | 27.77% |

6 days later | 25.38% |

Plot these experimental data into a graph, the famous Ebbinghaus forgetting curve, as shown below (Figure 1):

Ebbinghaus Forgetting Curve Description: Human forgetting follows the law of first fast then slow, first more then less. As can be seen from the figure, the periods of faster forgetting are after 20 minutes, 1 hour and 8–9 hours, the forgetting amount accounted for 58.19%, 44.49% and 35.79% respectively. This means that if not reviewed in time, over time, the greater the amount of forgetting, the smaller the relative amount of memory retention. This requires teachers to complete the teaching task in the classroom, in order to guide students to review the knowledge learned in class in a timely manner, in order to strengthen memory and avoid the occurrence of large-scale forgetting later. This task is mainly completed by the teacher in the classroom summary, this actually emphasizes that class summaries are helping students review in a timely manner, consolidate and strengthen memory. Later, ebbinghaus further conducted memory research on meaningful syllables, and found that the more understanding of knowledge, the faster and stronger the memory. This suggests that when we memorize knowledge, we must do it on the basis of understanding. And find the inner connection between old and new knowledge, build knowledge structure or knowledge system, it helps to deepen the understanding of knowledge and improve the memory effect. This is the distinction and connection between teachers in the classroom summary or seeking knowledge, or building a knowledge network, it provides a theoretical basis, and actually lays a theoretical foundation for the design of the classroom summary [9].

Ebbinghaus uses a logarithmic function to describe the forgetting curve, and the mathematical formula given is formula (1):

Logarithmic function:

Exponential function:

Hyperbolic function:

Power function:

Definition 1: Select the power function as the mathematical formula for the forgetting curve: ^{−β}, where m is the memory retention amount, M is the memory coefficient constant, Δ

Definition 2: The three gradient constants of the memory decay coefficient _{0} of the initial forgetting curve are: _{0} = 0.4307, _{1} = 0.2038, _{2} = 0.1056. Before learning, obtain the user's initial awareness of the content (unknown, vague, aware), and thus determine the initial memory decay coefficient _{0}: Don't know, _{0} = _{0}; vague, _{0} = _{1}; know, _{0} = _{2}.

Definition 3: Memory threshold
_{c}_{c}

Definition 4: The test result _{d}_{d}_{d}_{d}_{i}_{i}_{i}_{i}_{d}

Forgetting is the basis for consolidating memory, if people can't forget those unnecessary content, then it is impossible to memorize those important materials that need to be memorized.

Using methods consistent with this biological memory property, that is the best way to remember, review when you are about to forget, the effect is the best, and it is also the most time-saving. And a natural definition of forgetting is that the amount of memory has dropped by half, this is the principle of Definition 3 to determine memory thresholds and schedule review time points. Definition 4 iteratively determines the new forgetting curve memory decay coefficient after each review, use the test results of each review as a feedback signal, dynamically determine the next forgetting curve memory decay coefficient. In this way, after repeated reviews, the self-adaptive refinement will continue, the new forgetting curve memory decay coefficient also reflects the user's memory effect more and more realistically [10].

When choosing to learn, users can be provided with sequential, disordered, and reversed learning order choices, let users choose the position effect suitable for their memory, and help users achieve the best memory effect. At time t, according to the user's initial memory of the new word, after determining the initial memory decay coefficient _{0} after learning new words for the first time, according to Definition 1 and Definition 3, the moment _{0} when the user reviews the word for the first time can be solved by the following equations:
_{d}_{i}

The intelligent memory model based on the Ebbinghaus forgetting curve, it has been used to develop the word memory software “Fudan Smart Memory” series of iOS apps, further improve the adaptive content memory model of the intelligent vocabulary memory model, apply to the App to make a version update. In this experiment, the “Fudan Smart Memory-TOEFL 1500 High-Frequency Words” App, which selected 1500 TOEFL high-frequency words as memory materials, collected test data, its user downloads have exceeded 700. At each review time point, the App arranges random interference tests on the content, including choice and dictation to test the user's memory [11]. The multiple-choice test is the correct answer word, 3 random distractions are arranged except synonyms/synonyms, the dictation test is about spelling words by listening to their pronunciation. The software divides the user's initial cognition of words into three types: Cognition, vagueness, and ignorance, the average memory times of these three types of content are counted separately, finally, the average memory times of the three types of content are comprehensively averaged, and the experimental data are shown in Table 2:

The average memory times of TOEFL 1500 high-frequency words

smart memory model | adaptive memory model | |
---|---|---|

do not know | 7.45 | 6.80 |

Vague | 4.19 | 3.81 |

know | 1.79 | 1.70 |

Comprehensive average | 5.599 | 5.999 |

Using New Oriental's memory method, each content needs to be memorized 9 times. The New Oriental memory, intelligent memory, and adaptive memory are compared for experiments, and the experimental results are shown in Figure 2 and Figure 3:

According to the experimental data: While not affecting the memory effect, using the intelligent memory model, the number of memories is reduced by 37.12% compared with the New Oriental memory method, using the adaptive memory model reduces the number of memories by 43.35% compared to the New Oriental memory method. The experimental results show, the adaptive memory model further saves 6.31% of memory times compared to the intelligent memory model, not only has good adaptability to each user's memory situation, but also further improves memory efficiency.

The author proposes, research on university ideological and political learning model based on the mathematical equation of statistical memory curve, the intelligent memory model is further discussed, choose a power function to fit the Ebbinghaus memory curve, establish the correctness of the mathematical model of memory, and for the intelligent memory model, it is insufficient to adapt to the memory situation of each user, an adaptive control system with a reference model is introduced. According to the user's actual test results and review time as feedback control signals, combined with a reasonable memory cycle time planning table, in order to determine the next memory curve attenuation coefficient, thus, the intelligent vocabulary memory model is improved into an adaptive memory model. Of course, due to the lack of research ability, lack of practical experience, limited paper length and research time, etc, there are still many deficiencies in this study. In the future, it can be applied in the summary of ideological and political classrooms, consolidate knowledge and conduct in-depth research.

#### The average memory times of TOEFL 1500 high-frequency words

smart memory model | adaptive memory model | |
---|---|---|

do not know | 7.45 | 6.80 |

Vague | 4.19 | 3.81 |

know | 1.79 | 1.70 |

Comprehensive average | 5.599 | 5.999 |

#### The results of memory and forgetting experiments

time interval | amount of memory |
---|---|

just finished | 100% |

20 minutes | 58.19% |

1 hour later | 44.49% |

After 8–9 hours | 35.79% |

1 day later | 33.69% |

2 days later | 27.77% |

6 days later | 25.38% |

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linear regression Animation character recognition and character intelligence analysis based on semantic ontology and Poisson equation Design of language assisted learning model and online learning system under the background of artificial intelligence Application of machine learning in stock selection Comparative analysis of CR of ideological and political education in different regions based on improved fuzzy clustering Action of Aut( G ) on the set of maximal subgroups ofp -groupsThe internal mechanism of corporate social responsibility fulfillment affecting debt risk in China: analysis of intermediary transmission effect based on degree of debt concentration and product market competitive advantage Study on transmission characteristics in three kinds of deformed finlines based on edge-based finite element method Asymptotic stability problem of predator–prey system with linear diffusion Research on loyalty prediction of e-commerce customer based on data mining Algebraic Equations in Educational Model of College Physical Education Course Education Professional English Translation Corpus Under the Binomial Theorem Coefficient Geometric Tolerance Control Method for Precision Machinery Based on Image Modeling and Novel Saturation Function Retrieval and Characteristic Analysis of Multimedia Tester Based on Bragg Equation Semiparametric Spatial Econometric Analysis of Household Consumption Based on Ordinary Linear Regression Model Video adaptive watermark embedding and detection algorithm based on phase function equation English Learning Motivation of College Students Based on probability Distribution Scientific Model of Vocational Education Teaching Method in Differential Nonlinearity Research on mobile Awareness service and data privacy Protection based on Linear Equations computing protocol Vocal Music Teaching Model Based on Finite Element Differential Mathematical Equations Research on threat assessment problems of island air defence system based on the leader-follower model Studying a matching method combining distance proximity and buffer constraints The trend and influence of media information Propagation based on nonlinear Differential equation Research on the construction of early warning model of customer churn on e-commerce platform Study on inefficient land use determination method for cities and towns from a city examination perspective A sentiment analysis method based on bidirectional long short-term memory networks Evaluation of ecosystem health in Futian mangrove wetland based on the PSR-AHP model A study of local smoothness-informed convolutional neural network models for image inpainting Towards more efficient control of the ironmaking blast furnace: modelling gaseous reduction of iron ores in H _{2}-N_{2}atmosphereAlgorithm of overfitting avoidance in CNN based on maximum pooled and weight decay Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Decisions of competing supply chain with altruistic retailer under risk aversion Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations The Marketing of Cross-border E-commerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory Application of Linear Partial Differential Equation Theory in Guiding Football Scientific Training The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function System Model of Shipping Enterprise Safety Culture Based on Dynamic Calculation Matrix Model The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Analysis and Research on Influencing Factors of Ideological and Political Education Teaching Effectiveness Based on Linear Equation Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model