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

###### Recibido: 17 Feb 2022
Detalles de la revista
Formato
Revista
eISSN
2444-8656
Primera edición
01 Jan 2016
Calendario de la edición
2 veces al año
Idiomas
Inglés
Introduction

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):

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): $100×a(log t)b+a$ {{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: $m=−a×ln t+b$ m = - a \times \ln \,t + b

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

Hyperbolic function: $m=…$ m = \ldots

Power function: $m=a×t−b$ 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: $m=M×Δt−β$ 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 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: $M×Δtt0−β0=M2$ 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: ${ti|ti≤t}$ \left\{ {{t_i}|{t_i} \le t} \right\} Select the content to review according to the following formula: $min{ti|ti≤t}$ \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: ${M×Δti+1−βi+1=M2ti+1=Δti+1+t$ \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:

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.

#### 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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