2021 American Collegiate Mathematical Contest in Modeling
Question F checks the pulse and temperature of higher education
Reproduction of the original title:
What does it mean for a country to have a healthy, sustainable higher education system? What questions matter? Is it cost, opportunity, equity, funding, value of a degree, quality of education, level of research, exchange of ideas from some of the brightest minds in the world, some, all of the above, or something else?
The higher education system is an important element in a country's efforts to further educate its citizens beyond the required primary and secondary education, and as such, is both an industry in itself and a source of trained and educated citizens for the country's economy. When we look around the world, from Germany to the United States, from Japan to Australia, we see the approaches to higher education in various countries that not only educate their own students, but also attract large numbers of international students every year. Each of these countries’ higher education systems has its strengths and weaknesses, and after the adjustments the current pandemic requires, countries have an opportunity to reflect on what works and what works better. However, change is often difficult. The institutional reforms needed to advance any system require long-term implementation of policies in order to create a healthier and more sustainable system.
In this subject, you will develop a model to measure and assess the health of the higher education system at the national level, to determine a healthy and sustainable state considering the national higher education system, and to propose and analyze a set of policies that will A country moves from its current state to your proposed healthy and sustainable state.
Specifically, you are asked to:
develop and validate a model or set of models that will enable you to assess the health of any country's higher education system;
apply your model to several countries, and then, based on your analysis, Choose a country whose higher education system has room for improvement;
Come up with an achievable and plausible vision for your chosen country’s system to support a healthy and sustainable higher education system;
Use your model to measure current The health of the system, and a proposed healthy, sustainable system for your selected country;
Propose targeted policies and implementation timelines to support migration from the current state to your proposed state;
Use your models to shape and/or assess the effectiveness of your policies;
Discuss the real-world impact (eg, on students, teachers, schools, communities, countries) of implementing your plan during the transition period and in the end state, acknowledging that change is a difficult reality.
Overview of the overall solution process (abstract)
Education is the cornerstone of national development and human progress at all ages. Therefore, each country is committed to developing its own higher education. Our research develops a model to assess the health and sustainability of higher education systems. Countries such as Australia and the United States are analyzed, and policies for improvement are given.
In Task 1, we constructed a higher education health assessment model. Based on three basic dimensions, we selected 14 indicators such as the gross enrollment ratio of higher education and the number of international students. Through principal component analysis, we obtained the main indicators of four dimensions: quality of higher education, scale of higher education, contribution of higher education and sustainability. In addition, we obtained the contribution of each dimension as 34.608%, 26.239%, 16.223% and 11.938%, respectively, and the weights of 14 indicators. Finally, we classify the health system of higher education into 5 levels and apply it to 8 countries including Australia.
In Task 2, we drilled down on sustainability, which is the first level indicator. First, by introducing logistics models into our work, we define sustainable trends in higher education systems. A time-series ARIMA model is then used to predict the health and sustainability of the system in the future. Finally, the judgment flowchart on sustainability (as shown in Figure 5) is summarized and applied to eight countries to analyze their sustainability.
In Task 3, the state of higher education in Australia is analyzed in detail. Based on the analysis in Task 2, we find that Australia has good potential for improving its tertiary health system score, but lacks sustainability. Then, we analyzed Australia's current higher education system from the perspective of time and country, and drew three conclusions. Accordingly, we put forward five targeted recommendations and set a timetable for implementing each recommendation in 2021\u2030.
In Task 4, we analyzed the impact of our policies along four dimensions: individual, university, society, and state, in transition and in the final state. At the same time, the process of policy implementation is obviously a game between all parties. Therefore, we discuss the game between the state, the university, the individual and the society.
As a result, we discovered the reality that making these changes is difficult. In addition, we also analyze the sensitivity of indicator weights. Finally, we evaluate the strengths and weaknesses of the developed model.
Model assumptions:
1. Assume that the domestic political structure of each country is relatively stable, and the economic development is stable.
2. Assume that education is equal in all countries, and men and women can equally receive national education.
3. The selected indicators can explain the factors that affect the higher education system.
4. The country changes its policies with the aim of increasing GDP.
Question restatement:
Each country's higher education system has its strengths and weaknesses, and we need to develop mathematical models to measure and evaluate the health of a country's higher education, and propose and then analyze a set of corresponding education improvement policies. The team was given the task of
developing a set of mathematical models to assess the health of higher education in the country. Select several countries for analysis.
Analytical assessment of the sustainability of higher education systems.
Select a country for detailed analysis and propose a healthy and sustainable higher education system with corresponding policies and implementation timelines.
Evaluate suggested strategies and discuss the impact of the strategies.
Model establishment and solution Overall paper thumbnail
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Part of the program code: (code and documentation not free)
clear all;
clc;
temp = xlsread(’ab’);
k=2;
A = temp(:,k);
B = diff(A);
figure(1)
autocorr(B)
figure(2)
parcorr(B)
x(1:5,k-1) = A;
w = B;
n = 35;
s = 1;
m1 = length(A);
for i = s+1:m1
y(i-s) = x(i) - x(i-s);
end
ToEstMd = arima(’ARLags’,1,’MALags’,1:1,’Constant’,0);
[EstMd,EstParamCov,LogL,info] = estimate(ToEstMd,w);
w_Forecast = forecast(EstMd,n,’Y0’,w’);
yhat = y(end) + cumsum(w_Forecast);
for j = 1:n
x(m1 + j,k-1) = yhat(j) + x(m1+j-s);
end
x
import numpy as np
import pandas as pd
def loadDatadet(infile):
f=open(infile,’r’)
sourceInLine=f.readlines()
dataset=[]
for line in sourceInLine:
temp1=line.strip(’\n’)
temp2=temp1.split(’\t’)
dataset.append(temp2)
return dataset
infile=’data.txt’
infile=loadDatadet(infile)
k=0.0017
tmp=0
normal=77
n=100
j=0
all=[]
writer=pd.ExcelWriter("output2.xlsx")
while j < 20:
a=60
al=[a]
i=0
while i < n:
p=float(infile[j+30][i])+float(infile[j+31][i])+k*(a-normal)+tmp
a = a*(1-p)
i=i+1
if p>0.05:
tmp=0.01
if p<-0.05:
tmp=-0.01
else:
tmp=0
print(’a’+str(i)+’:’+str(a))
al.append(a)
all.append(al)
j+=1
data=pd.DataFrame(all)
data.to_excel(writer,’page_1’,float_format=’%.5f’)
writer.save
writer.close()