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University Ideological and Political Learning Model Based on Statistical Memory Curve Mathematical Equation

Publié en ligne: 15 Jul 2022
Volume & Edition: AHEAD OF PRINT
Pages: -
Reçu: 17 Feb 2022
Accepté: 13 Apr 2022
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Format
Magazine
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2444-8656
Première parution
01 Jan 2016
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2 fois par an
Langues
Anglais
Introduction

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.

Research Methods
Theoretical basis for the summary of the college ideological and political classroom

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):

Figure 1

Ebbinghaus forgetting curve

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].

Selection of forgetting curve fitting function

Ebbinghaus uses a logarithmic function to describe the forgetting curve, and the mathematical formula given is formula (1): 100×a(logt)b+a {{100 \times a} \over {{{\left( {\log \,t} \right)}^b} + a}} However, in Ebbinghaus' paper, there is no mention of using other functions to fit the forgetting curve, that is, the fitting effect of other functional models on forgetting experimental data is not compared. This made more and more psychologists later, more mathematical models are proposed for the fitting of forgetting curves, more than 100 functions have been proposed to fit the forgetting curve, among them, the most famous ones are logarithmic function, exponential function, hyperbolic function, and power function. The corresponding mathematical formula is as follows:

Logarithmic function: m=a×lnt+b m = - a \times \ln \,t + b

Exponential function: m=a×eb×t m = a \times {e^{ - b \times t}}

Hyperbolic function: m= m = \ldots

Power function: m=a×tb m = a \times {t^{ - b}}

The power function is more suitable for describing the Ebbinghaus forgetting curve than other candidate functions. Therefore, the power function is selected to fit the forgetting curve, and the obtained mathematical formula is the formula: m=M×Δtβ m = M \times \Delta {t^{ - \beta }} Among them, m is the amount of memory retention, dimensionless; M is the memory coefficient constant, dimensionless; Δt is the time interval, in min; β is the memory decay coefficient, dimensionless.

Definition of Adaptive Memory Model

Definition 1: Select the power function as the mathematical formula for the forgetting curve: m = M × Δtβ, where m is the memory retention amount, M is the memory coefficient constant, Δt is the time interval, and β is the memory decay coefficient.

Definition 2: The three gradient constants of the memory decay coefficient β0 of the initial forgetting curve are: C0 = 0.4307, C1 = 0.2038, C2 = 0.1056. Before learning, obtain the user's initial awareness of the content (unknown, vague, aware), and thus determine the initial memory decay coefficient β0: Don't know, β0 = C0; vague, β0 = C1; know, β0 = C2.

Definition 3: Memory threshold Mc=M2 {M_c} = {M \over 2} , m > Mc is remembered material, m < Mc is forgotten material. When the amount of memory mt = Mc at a certain time t, the review (ie the test) is arranged.

Definition 4: The test result fd is right and wrong: Do wrong, fd = 0; do right, fd = 1. The test result fd will be used as the feedback control signal, together with the memory decay coefficient βi of the current forgetting curve, the next forgetting curve decay coefficient βi + 1, βi + 1 = f(βi, fd) is determined together. The selection of the adaptive control function f only needs to be reasonable, for example, it can be constructed according to a reasonable memory cycle time planning Table.

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 β0 after learning new words for the first time, according to Definition 1 and Definition 3, the moment t0 when the user reviews the word for the first time can be solved by the following equations: M×Δtt0β0=M2 M \times \Delta t_{{t_0}}^{ - {\beta _0} = {M \over 2}} t0=Δt0+t {t_0} = \Delta {t_0} + t Which is Δt0β0=2 \Delta t_0^{{\beta _0} = 2} At time t, when review is required, the set of review moments for them is: {ti|tit} \left\{ {{t_i}|{t_i} \le t} \right\} Select the content to review according to the following formula: min{ti|tit} \min \left\{ {{t_i}|{t_i} \le t} \right\} After the review (ie the test) at time t, the test result fd is obtained, the next forgetting curve attenuation coefficient βi + 1 is calculated by the following formula: βi+1=f(fd,βi,t) {\beta _{i + 1}} = f\left( {fd,\,{\beta _i},\,t} \right) According to Definition 1 and Definition 3, the next review time t+1 is solved by the following equations: {M×Δti+1βi+1=M2ti+1=Δti+1+t \left\{ {\matrix{ {M \times \Delta t_{i + 1}^{ - {\beta _{i + 1}} = {M \over 2}}} \hfill \cr {{t_{i + 1}} = \Delta {t_{i + 1}} + t} \hfill \cr } } \right. Which is: {Δti+1βi+1=2ti+1=Δti+1+t \left\{ {\matrix{ {\Delta {t_{i + 1}}^{{\beta _{i + 1}}} = 2} \hfill \cr {{t_{i + 1}} = \Delta {t_{i + 1}} + t} \hfill \cr } } \right.

Results analysis and discussion

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:

Figure 2

Comparison of the average memory times of various types of content

Figure 3

Comparison of average memory times

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.

Conclusion

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.

Figure 1

Ebbinghaus forgetting curve
Ebbinghaus forgetting curve

Figure 2

Comparison of the average memory times of various types of content
Comparison of the average memory times of various types of content

Figure 3

Comparison of average memory times
Comparison of average memory times

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%

Narayan S, Sidhu J S, Volberda H W, et al. From Attention to Action: The Influence of Cognitive and Ideological Diversity in Top Management Teams on Business Model Innovation[J]. Journal of Management Studies, 2020, 58(8):2082–2110. NarayanS SidhuJ S VolberdaH W From Attention to Action: The Influence of Cognitive and Ideological Diversity in Top Management Teams on Business Model Innovation [J]. Journal of Management Studies 2020 58 8 2082 2110 10.1111/joms.12668 Search in Google Scholar

Li W. Research and Investigation on Learning Experience of Ideological and Political Course for Social Science Students[J]. Region - Educational Research and Reviews, 2020, 2(4):25–29. LiW Research and Investigation on Learning Experience of Ideological and Political Course for Social Science Students [J]. Region - Educational Research and Reviews 2020 2 4 25 29 10.32629/rerr.v2i4.186 Search in Google Scholar

Comunian, R. Rethinking the Creative City: The Role of Complexity, Networks and Interactions in the Urban Creative Economy[J]. Urban Studies, 2015, 48(6):1157–1179. ComunianR Rethinking the Creative City: The Role of Complexity, Networks and Interactions in the Urban Creative Economy [J]. Urban Studies 2015 48 6 1157 1179 10.1177/0042098010370626 Search in Google Scholar

Chao G, Zhao G, Lu J, et al. A grid-based cooperative QoS routing protocol with fading memory optimization for navigation carrier ad hoc networks[J]. Computer Networks, 2015, 76(jan.15):294–316. ChaoG ZhaoG LuJ A grid-based cooperative QoS routing protocol with fading memory optimization for navigation carrier ad hoc networks [J]. Computer Networks 2015 76 jan. 15 294 316 10.1016/j.comnet.2014.11.017 Search in Google Scholar

Murre J, Joeri D, Chialvo D R. Replication and Analysis of Ebbinghaus' Forgetting Curve[J]. Plos One, 2015, 10(7):e0120644. MurreJ JoeriD ChialvoD R Replication and Analysis of Ebbinghaus' Forgetting Curve [J]. Plos One 2015 10 7 e0120644 10.1371/journal.pone.0120644449292826148023 Search in Google Scholar

Lewis A, Call J, Berntsen D. Non-goal-directed recall of specific events in apes after long delays[J]. Proceedings Biological Sciences, 2017, 284(1858):20170518. LewisA CallJ BerntsenD Non-goal-directed recall of specific events in apes after long delays [J]. Proceedings Biological Sciences 2017 284 1858 20170518 10.1098/rspb.2017.0518552449328701556 Search in Google Scholar

Yao, Wenbin, Hu, et al. Improvement of LDA model with time factor for collaborative filtering[J]. The Journal of China Universities of Posts and Telecommunications, 2019, v.26(06):57–65. YaoWenbin Hu Improvement of LDA model with time factor for collaborative filtering [J]. The Journal of China Universities of Posts and Telecommunications 2019 26 06 57 65 Search in Google Scholar

Siominski J. ON COMPARISONS OF ALGEBRAS BY USING THE ENRICHMENTAL THEORIES AND CLONING SYSTEMS[J]. Demonstratio Mathematica, 2017, 20(1):19–36. SiominskiJ ON COMPARISONS OF ALGEBRAS BY USING THE ENRICHMENTAL THEORIES AND CLONING SYSTEMS [J]. Demonstratio Mathematica 2017 20 1 19 36 10.1515/dema-1987-1-203 Search in Google Scholar

Tang D, Rong W, Qin S, et al. A n-Gated Recurrent Unit with review for answer selection[J]. Neurocomputing, 2020, 371(Jan.2):158–165. TangD RongW QinS A n-Gated Recurrent Unit with review for answer selection [J]. Neurocomputing 2020 371 Jan. 2 158 165 10.1016/j.neucom.2019.09.007 Search in Google Scholar

Abozaid A A, Selim H H, Gadallah K A K, et al. Periodic orbit in the frame work of restricted three bodies under the asteroids belt effect[J]. Applied Mathematics and Nonlinear Sciences, 2020, 5(2):157–176. AbozaidA A SelimH H GadallahK A K Periodic orbit in the frame work of restricted three bodies under the asteroids belt effect [J]. Applied Mathematics and Nonlinear Sciences 2020 5 2 157 176 10.2478/amns.2020.2.00022 Search in Google Scholar

Aghili A. arman.aghili@gmail.com University of Guilan, Faculty of Mathematical Sciences, Department of Applied Mathematics, Iran-Rasht, P.O.BOX 1841. Complete Solution For The Time Fractional Diffusion Problem With Mixed Boundary Conditions by Operational Method[J]. Applied Mathematics and Nonlinear Sciences, 2021, 6(1):9–20. AghiliA arman.aghili@gmail.com University of Guilan, Faculty of Mathematical Sciences, Department of Applied Mathematics, Iran-Rasht, P.O.BOX 1841. Complete Solution For The Time Fractional Diffusion Problem With Mixed Boundary Conditions by Operational Method [J]. Applied Mathematics and Nonlinear Sciences 2021 6 1 9 20 10.2478/amns.2020.2.00002 Search in Google Scholar

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