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Research article

Impact of gender role stereotypes on STEM academic performance among high school girls: Mediating effects of educational aspirations


  • The underrepresentation of women in STEM fields persists, despite ongoing global initiatives aimed at achieving gender equality. Gender inequality and associated biases significantly impact educational equity and academic outcomes. This research investigated the impact of gender role stereotypes on the STEM academic performance of high school girls in economically deprived regions of China, with a particular focus on the mediating effect of educational aspirations and the moderating role of grade level in promoting equity in STEM education. Using a quantitative research approach, this study surveyed 768 female students (10th–11th grade) and analyzed data using regression and moderated mediation analysis to examine the proposed relationships. Results show that gender role stereotypes and STEM academic performance have a negative correlation (β = -0.066, p < 0.05). This association is fully mediated by educational aspirations, indicating that gender role stereotypes primarily influence STEM performance by shaping students' academic aspirations [indirect effect β = 0.134, 95% CI (-0.9047, -0.0994), p < 0.001]. Specifically, stronger gender role stereotypes are associated with lower educational aspirations, which in turn lead to reduced STEM academic achievement. However, as students progress to higher grades, the negative effect of gender role stereotypes on STEM academic performance weakens, becoming nonsignificant in 11th grade. This pattern suggests that while educational aspirations serve as a critical pathway through which gender role stereotypes affect STEM outcomes, the overall influence of these stereotypes diminishes as students face increasing academic pressure and raise more resilient self-identities. This study emphasizes the necessity of addressing gender stereotypes at pivotal educational stages and advocates for specific interventions. The research presented here offers practical recommendations for policymakers and educators aimed at promoting gender equity and mitigating achievement barriers in STEM fields.

    Citation: Ping Chen, Aminuddin Bin Hassan, Firdaus Mohamad Hamzah, Sallar Salam Murad, Heng Wu. Impact of gender role stereotypes on STEM academic performance among high school girls: Mediating effects of educational aspirations[J]. STEM Education, 2025, 5(4): 617-642. doi: 10.3934/steme.2025029

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  • The underrepresentation of women in STEM fields persists, despite ongoing global initiatives aimed at achieving gender equality. Gender inequality and associated biases significantly impact educational equity and academic outcomes. This research investigated the impact of gender role stereotypes on the STEM academic performance of high school girls in economically deprived regions of China, with a particular focus on the mediating effect of educational aspirations and the moderating role of grade level in promoting equity in STEM education. Using a quantitative research approach, this study surveyed 768 female students (10th–11th grade) and analyzed data using regression and moderated mediation analysis to examine the proposed relationships. Results show that gender role stereotypes and STEM academic performance have a negative correlation (β = -0.066, p < 0.05). This association is fully mediated by educational aspirations, indicating that gender role stereotypes primarily influence STEM performance by shaping students' academic aspirations [indirect effect β = 0.134, 95% CI (-0.9047, -0.0994), p < 0.001]. Specifically, stronger gender role stereotypes are associated with lower educational aspirations, which in turn lead to reduced STEM academic achievement. However, as students progress to higher grades, the negative effect of gender role stereotypes on STEM academic performance weakens, becoming nonsignificant in 11th grade. This pattern suggests that while educational aspirations serve as a critical pathway through which gender role stereotypes affect STEM outcomes, the overall influence of these stereotypes diminishes as students face increasing academic pressure and raise more resilient self-identities. This study emphasizes the necessity of addressing gender stereotypes at pivotal educational stages and advocates for specific interventions. The research presented here offers practical recommendations for policymakers and educators aimed at promoting gender equity and mitigating achievement barriers in STEM fields.



    The novel coronavirus SARS-CoV-2 has caused a global pandemic of unprecedented viral pneumonia [1,2]. This infection is known as coronavirus disease 2019 (COVID-19) [3]. Because of the high human-to-human transmissibility, SARS-CoV-2 has spread rapidly around the world [4,5,6,7]. In mainland China, the outbreak started in December 2019, reached the peak in February and then the number of new confirmed cases decreased. On March 18, 2020, there were no new cases of infection for the first time and the economy and daily life gradually returned to normal [8,9,10,11]. In Hong Kong Special Administrative Region (SAR), the first case was reported on January 18, 2020. The outbreak peaked in late March 2020 with no new confirmed cases on April 23, 2020. However, spread of COVID-19 in the world is continuing and the outbreak is ongoing globally [12,13]. The infection has been confirmed in about 190 countries up to now. As of February 21, 2021, there have been over 110.6 million cases and 2.45 million deaths reported globally since the beginning of the pandemic. The European Region has the largest new cases and new deaths. The United States accounts for the greatest proportion of cumulative cases and deaths [14]. In China, although the epidemic has been under control, confirmed cases have been found occasionally in different places, which raised significant concerns on the resurgence of future waves of COVID-19.

    If there are no confirmed cases in a region for a long time, then the risk of disease re-emergence might be mainly from imported cases or viruses. The major COVID-19 transmission pathway is from human to human through respiratory droplets [15,16]. In particular, asymptomatic individuals who do not have COVID-19 symptoms can still spread the virus. Transmission from asymptomatic individuals poses a significant public health challenge [17,18,19,20,21,22,23]. The cases imported from other high-risk places are another path of viral spread. To reduce the potential of imported cases, many countries have issued travel restrictions, for example, reducing the frequency of flights from abroad [24,25]. However, as the infection is still prevailing in many places, imported cases still represent a tremendous risk, which may lead to new local outbreaks [26,27,28,29]. Another possible path of SARS-CoV-2 transmission might be through the food supply chain, surfaces and environment. In China, the coronavirus was detected on frozen foods, including their packaging materials and storage environment in July 2020. There seemed to have two outbreaks related to the transmission via frozen food [30]. In view of this, interventions that reduce foodborne transmission of pathogens need to be considered [32].

    Non-pharmaceutical control measures implemented so far are mainly wearing mask, hand washing, social distancing, quarantine and city/region lockdown [31]. These interventions were gradually lifted in consideration of the trade-off between economic sustainability and public health. An agent-based model was developed to evaluate the possibility of a second-wave emergence under different extents and timing of intervention relaxation [32]. More work assessed the risk of secondary waves since the control measures like lockdowns were relaxed [33,34,35,36,37,38,39,40]. The study [41] compared the data of the epidemiological pattern of COVID-19 in 53 countries or regions where the pandemic experienced two waves, and analyzed the differences between the two outbreaks. Their results suggested that there was a shift of infection to younger age groups, which may make it more difficult to control the pandemic.

    In this work, we focus on the COVID-19 spread in serval places where the epidemic has been under control but new cases have been reported occasionally. To study the impact of imported cases on the dynamics of COVID-19 in China under different scenarios of prevention and control measures, Jia et al. developed an impulsive epidemic model to describe imported cases from abroad [42]. In their model, the time when the exposed cases were imported was fixed. However, the exposed cases who carry virus without symptoms are usually unknown. When an infected case is identified, the virus has probably been spreading for a period of time. In the beginning of a new wave of epidemic, the infection might be induced by a small number of infected cases. The disease transmission in this stage can be affected by many random factors. In addition, the data of new/accumulated cases were reported on every day. All of these motivate us to develop a stochastic discrete-time compartmental model that considers randomness, epidemic data, as well as the impact of input virus/cases and the initial entry time. By fitting the model to the two waves of outbreaks in two places in mainland China (Beijing and Xinjiang) and Hong Kong SAR, we evaluate the risk factors that can affect the second or future wave of COVID-19.

    We develop a stochastic discrete-time model based on the classic compartmental model. Individuals who have no clinical manifestations such as fever, cough, sore throat and other symptoms that can be self-perceived or clinically recognized, but test positive in serological or blood test are referred to as asymptomatic infection. This population includes two types of individuals. One is asymptomatic infection in the incubation period. They will later develop clinical symptoms or become a confirmed case by screening test or CT (Computed Tomography) examination. The other has no symptoms until the nucleic acid test turns negative. The total population is divided into five epidemiological classes, including susceptible (S), exposed (E), asymptomatically infected (A), symptomatically infected (I), and recovered (R). Due to quarantine, the susceptible and exposed states are further divided into Sq and Eq. With hospitalization, the infected class (both asymptomatic and symptomatic) can be further divided into HA and HI. Because the infection and disease progression can be affected by random factors, we assume that the flow between any two compartments is a stochastic process [43,44,45]. For example, D11(t) is the number of susceptible individuals who become newly infected and this process obeys a binomial distribution. The diagram of the model is shown in Figure 1 and the corresponding stochastic discrete-time model is given by the following system:

    St+1=StD11(t)D12(t)+D51(t),Et+1=Et+(1q)D11(t)D21(t),At+1=At+(1ρ)D21(t)D31(t)D32(t)D33(t),It+1=It+ρD21(t)D41(t)D42(t)D43(t)+D33(t),Sqt+1=Sqt+D12(t)D51(t),Eqt+1=Eqt+qD11(t)D61(t),HAt+1=HAt+D31(t)+(1ρ)D61(t)D71(t)D72(t),HIt+1=HIt+D41(t)+ρD61(t)+D71(t)D81(t)D82(t),Rt+1=Rt+D32(t)+D42(t)+D72(t)+D82(t), (2.1)
    Figure 1.  Flow diagram of the COVID-19 infection model.

    where Dij(t) obeys a binomial distribution Bin(n,p) with the parameters (n,p), and the specific form is as follows

    D11(t)Bin(St,P11(t)),  D12(t)Bin(St,P12(t)),  D21(t)Bin(Et,P21),D31(t)Bin(At,P31(t)),  D32(t)Bin(At,P32),  D33(t)Bin(At,P33),D41(t)Bin(It,P41),  D42(t)Bin(It,P42),  D43(t)Bin(It,P43),D51(t)Bin(Sqt,P51),  D61(t)Bin(Eqt,P61),  D71(t)Bin(HAt,P33),D72(t)Bin(HAt,P32),  D81(t)Bin(HIt,P43)  D82(t)Bin(HIt,P42).
    P11(t)=1exp[βc(t)(I+θA)N],  P12(t)=1exp[(1β)qc(t)(I+θA)N],P21=1exp(σ),  P31=1exp(δA),P32(t)=1exp(γA),  P33=1exp(k),P41=1exp(δI),  P42=1exp(γI),P51=1exp(λ),  P61=1exp(δq).

    Here exp[βc(t)(I+θA)Nh] is the probability of staying in the compartment S. The time period h is chosen to be one, so it is omitted in the expression. Thus, P11 is the probability of individuals leaving the susceptible compartment. The other P functions can be explained in a similar way. The meaning of each parameter in the model is summarized in Table 1.

    Table 1.  Parameter estimates for the COVID-19 epidemics in Beijing, Xinjiang and Hong Kong SAR.
    Parameters Definition Values Source
    Beijing Xinjiang Hong Kong SAR
    c(t) c0 Contact rate at the initial time 17.0142 14.0025 11.9175 Estimated
    cb Minimum contact rate under the most strict control strategies 1.0869 2.0468 3.0460 Estimated
    r1 Exponential decreasing rate of contact rate in the first period 0.2196 0.2049 0.0703 Estimated
    r2 Exponential increasing rate of contact rate in the second period 0.0506 0.0200 0.0324 Estimated
    r3 Exponential decreasing rate of contact rate in the third period 0.2241 0.3096 0.1445 Estimated
    β Probability of transmission per contact 0.2801 0.2722 0.1504 Estimated
    q(t) q0 Quarantined rate at the initial time 0.2820 Estimated
    qm Maximum quarantined rate with control strategies 0.7083 Estimated
    r4 Exponential increasing rate of quarantined rate in the first period 0.2027 Estimated
    r5 Exponential decreasing rate of quarantined rate in the second period 0.1010 Estimated
    r6 Exponential increasing rate of quarantined rate in the third period 0.2028 Estimated
    q Quarantined rate 0.2935 0.4866 Estimated
    ρ Ratio of symptomatic infection 0.5142 0.5520 0.5529 Estimated
    σ Transition rate of exposed individuals to the infected class 1/5 1/5 1/5 [47]
    λ Rate at which the quarantined uninfected contacts were released into the wider community 1/14 1/14 1/14 [47]
    δI Constant transition rate of symptomatic infected 0.3474 0.2008 0.0999 Estimated
    δA Constant transition rate of asymptomatic infected 0.2860 0.2006 0.3027 Estimated
    δq Constant transition rate of quarantined exposed 0.3599 0.2816 0.2571 Estimated
    θ Correction factor for transmission probability of asymptomatic infectious 0.5919 0.5031 0.5041 Estimated
    k Conversion rate from asymptomatic infected to symptomatic infected 0.6124 0.6221 0.5026 Estimated
    γI Recovery rate of infected individuals 0.0701 0.1632 0.0799 Estimated
    γA Recovery rate of asymptotic infected individuals 0.0906 0.1629 0.2393 Estimated
    τ The time of importation of the first case in the second wave 17 16 Estimated
    pE(T2τ) The number of exposed cases entered at the time T2τ in the second wave 6 7.02 Estimated
    α Disease-induced death rate 0 0 0 Assumed
    – means the parameter is not included in that place.

     | Show Table
    DownLoad: CSV

    Due to limited pharmaceutical interventions, wearing mask and social distancing play a critical role in the control of the COVID-19 pandemic. As the epidemic is gradually controlled, people's vigilance will decrease. Strict intervention measures may have to be lifted because of economic consideration. We use a time-varying function for the contact rate to describe this change. When the pandemic began and spread rapidly, control measures such as city lockdown, wearing masks and social activity reduction greatly reduced the contact between people. We denote the time of strict control implementation by T0. When the number of infected cases gradually decrease after the peak, the control measures are relaxed and people's lives gradually return to normal. We denote this time by T1. When new cases are reported again, people's vigilance increases, and prevention and control measures are implemented again. We denote this time by T2. The following time-varying function for the contact rate c(t) is used to describe the change of human behavior and effect of control measures during the epidemic.

    c(t)={c0,t<T0,(c0cb)er1(tT0)+cb,T0t<T1,(cb1c0)er2(tT1)+c0,T1t<T2,(c01cb)er3(tT2)+cb,tT2. (2.2)

    Here cb1=(c0cb)er1(T1T0)+cb and c01=(cbc0)er2(T2T1)+c0.

    We define the quarantine rate q(t) in a similar way. The quarantine rate increases as the epidemic gets worse and decreases as it improves. Thus, we assume that the quarantine rate is a time-dependent piecewise function, given by

    q(t)={q0,t<T0,(q0qm)er4(tT0)+qm,T0t<T1,(qm1q0)er5(tT1)+q0,T1t<T2,(q01qm)er6(tT2)+qm,tT2, (2.3)

    where qm1=(q0qm)er4(T1T0)+qm and q01=(qmq0)er5(T2T1)+q0. The functions c(t) and q(t) are shown in Figure 2(a–b), Figure 3(e–f) and Figure 4(a–b) for three different places.

    Figure 2.  The fitting of model (2.1) to the data of COVID-19 in Beijing from January 26 to July 31 in 2020. (a-c): the change of contact rate c(t), quarantine rate q(t), and the total population N(t), respectively. The daily confirmed cases are shown in (d), daily asymptomatic cases are shown in (e), recovered cases are shown in (f). Stochastic fit was performed 50 times with light blue lines. The data and the fitting are represented by black points and the deep blue lines, respectively.
    Figure 3.  The fitting of model (2.1) to the data of COVID-19 in Xinjiang from January 23 to August 18, 2020. The daily confirmed cases are shown in (a), daily asymptomatic new cases are shown in (b), daily asymptomatic cases are shown in (c), cumulative confirmed cases are shown in (d). Stochastic fit was performed 50 times with light blue lines. The data and the fitting are represented by black points and deep blue lines, respectively. (e-g): the change of contact rate c(t), quarantine rate q(t), and the total population N(t), respectively.
    Figure 4.  The fitting of model (2.1) to the data of COVID-19 in Hong Kong SAR from February 23 to July 31, 2020. (a-c): the change of contact rate c(t), quarantine rate q(t), and the total population N(t), respectively. The daily confirmed cases are shown in (d), recovered cases are shown in (e). Stochastic fit was performed 50 times with light blue lines. The data and the fitting are represented by black points and deep blue lines, respectively.

    We collected the data of Beijing and Xinjiang from the local health commissions in mainland China, and the data of Hong Kong SAR from the Centre for Health Protection. It includes the time series data of confirmed COVID-19 cases, recovered cases, and asymptomatic coronavirus carriers. On December 26, 2019, a respiratory and critical care physician in Wuhan reported the pneumonia of unknown cause for the first time. The epidemic then spread rapidly in mainland China, and the number of newly confirmed cases reached the peak on February 4, 2020. As of March 18, the number of newly confirmed cases in mainland China became 0 and the number of confirmed cases fell below 20,000. After that, the reported cases in mainland China were mainly imported cases. A few months later, infected cases began to rise again in some places. On June 11, 2020, a confirmed case was reported in Beijing, without history of traveling outside Beijing and without close contact with suspected infection in the past two weeks. This ended a 56-day streak of no local infection in Beijing. On July 15, 2020, i.e., 149 days since the previous confirmed cases, one confirmed case and three asymptomatic cases were found in Xinjiang. In Hong Kong SAR, there were sporadic confirmed cases after April 20. On July 5, a second-wave outbreak emerged. This paper will focus on the data from these three places to study the risk of the emergence of a future wave of COVID-19. The switching time T0, T1 and T2 in the piecewise function are determined by the responding time in each place.

    If there are no cases for a long period of time, e.g., several months, after a wave of COVID-19 outbreak, then the new infection is likely to be caused by imported cases or exposure to the virus. The virus that caused a second wave can be summarized by the following three sources: (1) imported cases from abroad. Despite strict regulations on international travel and border inspections, there are still some reported cases imported from abroad. There is no guarantee that 100% of the infected or exposed cases entering the country will be isolated. The incubation period of the infection is not well known and may not be the same for all infected people. With fixed-duration quarantine implemented, the infected individual may become a confirmed case after the quarantine is over. This may be a risk for a second wave in mainland China. (2) Asymptomatic cases. These people carry the virus but cannot be identified if they do not have the nucleic acid test. However, they can infect other people. Therefore, asymptomatic carriers represent another risk for the occurrence of the second wave. (3) Virus from the environment. Some studies have shown that low temperature can greatly promote the persistence of coronaviruses. Frozen foods are potential carriers. Transmission occurs via touching contaminated objects that mediate the infection through mouth, nose, or eyes. This seems to be another risk of transmission that have been ignored.

    The potential causes summarized above can be described by new exposed individuals added to our model at a certain time. The time point when the new confirmed case was reported is T2 but when the exposed individual was introduced remains unknown. Here we assume that the number of input exposed individuals is pE(T2τ) where τ represents the time lag from the entry of the exposed individual to the later confirmation of infection. Thus, T2τ is the time point when the exposed individuals entered. The equation of E(t) in model (2.1) can be replaced by the following equation

    Et+1=Et+(1q)D11(t)D21(t)+pE(T2τ).

    It is noted that the reported case and the imported case may not be the same person.

    The increase in the susceptible population due to lifted interventions may also contribute to the second wave. The first wave of COVID-19 emerged in Wuhan in early January of 2020. The time happened to be about ten days before the Lunar New Year. This made most people stay at home and take the longest vacation, which greatly reduced the probability of contact. In addition, public transportation was terminated and schools and restaurants were all closed. This series of strict measures reduced the number of susceptible people to a very small level. In our model, we assume that the number of susceptible people in the first wave of outbreak is S01. After the first wave, social activities gradually returned to normal and the size of susceptible population increases to S02 when the second wave emerges. The time of the susceptible population change, denoted by T3, depends on the region. For Beijing and Xinjiang, we let it be the same as T1. For Hong Kong SAR, it is the time when the local restriction policy is released. Thus, the number of susceptible is given by the following piecewise function

    S0={S01,t<T3,S02,tT3. (2.4)

    We use the discrete stochastic model (2.1) with the input parameter pE(T2τ) to fit the data of the two waves of outbreaks in Beijing and Xinjiang using the least square method. The data fitted include the number of reported confirmed cases, asymptomatic cases and recovered cases. For the epidemic in Hong Kong SAR, there were still sporadic reports of confirmed cases after the first wave. The reason for the second wave in Hong Kong SAR is likely the increase in the number of susceptible population due to lifted restriction of interventions. We use the model (2.1) without the input parameter pE(T2τ) to fit the data in Hong Kong SAR. Parameter values obtained from the fitting are listed in Tables 1 and 2. The population size of susceptible in the three places is less than the entire population of those places. Here the susceptible population refers to those who may contact with the infected cases. The stochastic simulations provide good fits to the data in these three palaces, see Figure 2(d–f), Figure 3(d–f) and Figure 4(d–f). The corresponding contact rate c(t), quarantine rate q(t) and the susceptible population change S0(t) are shown in Figure 2(a–c), Figure 3(e–g) and Figure 4(a–c), respectively.

    Table 2.  Initial values for the COVID-19 epidemics in Beijing, Xinjiang and Hong Kong SAR.
    Initial values Definition Values Source
    Beijing Xinjiang Hong Kong SAR
    S01 The value of susceptible population in the first wave 5.0014×103 9.4767×103 7.3327×103 Estimated
    S02 The value of the susceptible in the second wave 6.0119×103 4.9377×104 2×104 Estimated
    E(0) The initial value of exposed population 8.0747 8.0209 6.0401 Estimated
    I(0) The initial value of infected symptomatic population 4.0902 3.0368 6.0316 Estimated
    A(0) The initial value of infected asymptomatic population 5.0848 4.0312 2.0328 Estimated
    Sq(0) The initial value of quarantined susceptible population 49.7473 49.9653 45.7412 Estimated
    Eq(0) The initial value of quarantined exposed population 20.0155 5.0235 13.1394 Estimated
    HI(0) The initial value of confirmed and hospitalized symptomatic population 1 3 5 Data
    1 3 5 Data
    HA(0) The initial value of confirmed and hospitalized asymptomatic population 0 1 0 Data
    0 1 0 Data
    R(0) The initial value of recovered population 0 0 0 Data

     | Show Table
    DownLoad: CSV

    The emergence of the second wave is influenced by the number of input exposed individuals and how long the infection has been spreading before the report of confirmed cases. We conduct numerical simulations to study the risk of having a second wave. The occurrence of a second wave is evaluated by the maximum number of confirmed cases in 500 stochastic simulations. We denote the average number by MH and choose a threshold value 30. If the MH value exceeds 30, it will be regarded as a second wave. The result shows that not all the scenarios result in a second wave. From 500 stochastic simulations, we calculate the probability of the occurrence of a second wave, which is denoted by Prop.

    In Figures 5 and 6, we explore the effect of varying the input parameter on the risk of second wave in Beijing and Xinjiang, respectively. The range of the parameter pE is set to [0,30] at time T2τ, and the time delay parameter τ is within the range [0,20]. From Figure 5(a), we find that both the number of input exposed individuals and the time between initial entry and subsequent confirmation affect the severity of the second wave. The average maximum value of the second wave peak can reach 1600 cases in Beijing. Increasing the number of input exposed individuals can expand the scale of the disease spread. A larger time delay τ implies that the disease had spread for a longer time without any interventions before its detection. This poses a substantial challenge for the subsequent control of the disease.

    Figure 5.  Maximum cases and the probability of occurrence of the second wave with different imported cases and time to detection in Beijing. (a, c): the results when imported cases are 1 to 30 from top to bottom. The time delay before detection is 1 to 20 from left to right. (b): The red point means that the maximum cases MH excess the threshold 30 and the blue point means MH is below the threshold.
    Figure 6.  Maximum cases and the probability of occurrence of the second wave with different imported cases and time to detection in Xinjiang. The other is the same as that in Figure 5.

    We provide the parameter region of a second wave occurrence in Figure 5(b). The deep blue points represent the parameter range of the occurrence of a second wave, while the deep red points represent the parameter range of no second wave. The simulation shows that a second outbreak would not take place when less than three exposed cases were imported. If the infection induced by the imported cases can be quickly identified, then the chance of having a second wave decreases. Figure 5(c) further shows the probability of the occurrence of the second wave under the same parameter range in Figure 5(a). Large values of pE and τ will make a second wave inevitable. We have the similar conclusion from the simulation for Xinjiang (see Figure 6). The scale of the second wave is larger than Beijing with the same parameter range because the average maximum value of possible second wave peak can reach 5000 cases in the worst scenario.

    Figure 9(a) shows the average result of 500 stochastic simulations of the model (2.1) with six different susceptible populations in Hong Kong SAR. As the susceptible population increases, the average maximum value of the second wave peak also increases. Interestingly, the probability of the occurrence of the second wave remains almost the same for different susceptible populations (see Figure 9(b)). Numerical results on the effect of varying the susceptible population size in Beijing and Xinjiang are shown in Figures 7 and 8, respectively. Based on the simulations in these two places, we have a conclusion similar to Hong Kong SAR. This analysis suggests that the susceptible population size plays a minor role in leading to the second wave when the other parameters are fixed.

    Figure 7.  (a) Simulation of confirmed cases under six scenarios in Beijing when the susceptible population is chosen to be 0.5S01, 0.8S01, S01, S02, 1.2S02 and 1.5S02. (b) The probability of occurrence of a second wave under the six scenarios.
    Figure 8.  Simulation of confirmed cases under five scenarios in Xinjiang when the susceptible population is chosen to be 0.5S01, S01, middle value of S01 and S02, S02, 1.5S02. (b) The probability of occurrence of a second wave under the five scenarios.
    Figure 9.  Simulation of confirmed cases under five scenarios in Hong Kong SAR when the susceptible population is chosen to be 0.5S01, S01, middle value of S01 and S02, S02, 1.5S02. (b) The probability of occurrence of a second wave under the five scenarios.

    COVID-19, a highly contagious disease first reported in December 2019, has been spreading globally for more than one year. Some countries/regions have mitigated the outbreak by various measures but are still at risk of recurrence. In this paper, we constructed a stochastic discrete-time compartmental epidemic model to analyze the risk of the occurrence of a second or future wave of outbreak. Compared with a deterministic system, a stochastic model is able to include the random factors in the spread of an infectious disease, particularly when the number of initial infected individuals is small. This is the case when a new wave of outbreak occurs. This discrete model can more intuitively describe the flow between any two compartments. The transition between two compartments is not deterministic and assumed to obey binomial distributions in our model. The change between two compartments in one time step corresponds to the daily data. Thus, using the discrete stochastic model facilitates full use of the data from multiple sources, thereby improving the reliability of the parameter estimation results.

    To describe the change in the intensity of control measures in response to the COVID-19 pandemic, we adopt time-varying contact rate and quarantine rate in the model. There are a few possible factors that may lead to a second wave, including import exposed cases, asymptomatic cases, and the presence of viruses in the environment such as the frozen food chain. The common characteristic of these factors is that the transmission is silent and difficult to be identified. We find that the time between the exposed case entry and the confirmation of subsequent infection plays a critical role in the occurrence of the second wave.

    The cause of the second-wave outbreak in Beijing and Xinjiang is mainly the imported cases and an increase in the susceptible population due to relaxed interventions. The model provided a good fit to the data of the second wave in Beijing in June 2020. Based on the fitting, the value of input exposed cases is estimated to be 6 and the time from exposed individual entry to the detection of infection is 17 days. The size of susceptible population increases from 5.001×103 in the first wave to 6.012×103 in the second wave. For Xinjiang where the second wave of the epidemic occurred in July 2020, the value of input exposed cases is estimated to be 7 and the time from entry to detection is 16 days. The change in the number of susceptible people is greater than in Beijing.

    Hong Kong SAR also experienced a second wave in July 2020. Unlike Beijing and Xinjiang, there were occasional reports of infected cases all the time in Hong Kong SAR after the first wave and the main cause of the second wave is likely to be the increase in the number of susceptible people. Our modeling result suggests that in a region where the infection is not cleared (e.g., in Hong Kong SAR) susceptible people will increase as the control measures are lifted and this may lead to a second wave. If there is no case for a long time (e.g., in Beijing and Xinjiang), it is necessary to screen imported cases and viruses (e.g., via the food chain), which may be the major cause of the second wave.

    On the basis of the fitting to the data in Beijing and Xinjiang, we further evaluated the possibility of having a future outbreak and its severity. Because there were no confirmed cases for a long time after the first wave in Beijing and Xinjiang, the contact rate returned to the normal level, as shown in Figures 2 and 3. If there are imported exposed cases, the time to detect the infection is shown to be critical in leading to the second wave. The simulation shown in Figure 5 and Figure 6 indicates that the second wave is determined by the number of imported exposed individuals and the time needed to detect them. The results suggest that if the imported exposed cases are less than three, then the number of confirmed cases will be below the threshold 30 we set, which would not be considered as a second wave. If the values of imported exposed individuals and the time lag in detection are larger (e.g., in the red region in Figures 5 and 6), a second wave will emerge. The more imported exposed cases and the longer for the infection to be detected, the more likely a second wave will occur. Once a confirmed case is found, it is imperative to track the trajectory of that case and the contacted persons. The information obtained from this study can be used to evaluate the possibility (i.e., the possibility of infected cases above a threshold level) and scale of a future wave of outbreak.

    By investigating the effect of the susceptible population on the second wave in Beijing, Xinjiang and Hong Kong SAR, we found that the larger the susceptible population size, the more infections if the second wave occurs. However, the susceptible population size itself does not affect the probability of the occurrence of a second wave. This result suggests that imported cases might be an important factor leading to the occurrence of a second wave in a place where the epidemic has been well controlled. Once a case is found, reducing the number of susceptible people will help control the disease spread in the second wave.

    Our study cannot predict when a second or future wave of COVID-19 would take place. When a new wave occurs, the model can be used to predict the scale or severity of the outbreak. This is based on the fitting of the model to existing data. If the data are not sufficient for fitting, then the power of the model prediction would be limited. Lastly, the model does not include the influence of vaccination on the disease spread. How the vaccine rollout influences the emergence of future waves remains to be further investigated.

    In summary, we established a stochastic modeling framework that incorporates control measures at different stages of the epidemic and potential causes for the second wave emerged in Beijing, Xinjiang, and Hong Kong SAR. Because infected people without symptoms are contagious and the virus attached to goods is difficult to be detected, comprehensive measures are still imperative to curb the COVID-19 pandemic. It is necessary to screen the imported cases in flights and to detect the virus that may be transported by various routes. If a confirmed case is found, the contact of the case should be thoroughly tracked and the close contacts should be quarantined. Finally, it is important to continue protective measures such as wearing masks and avoiding large-scale gathering to reduce the number of susceptible people. This will make the future wave of outbreak less severe if it takes place.

    This work was finished when the first author visited the University of Florida in 2020. This research was partially supported by the National Natural Science Foundation of China (grant numbers: 12031010(ST), 11631012(ST)) and by the Fundamental Research Funds for the Central Universities (grant numbers: 2018CBLZ001(SH), GK201901008(ST)). L. Rong is supported by the National Science Foundation (grant number: DMS-1950254).

    No conflict of interest.



    [1] World Economic Forum, Global Gender Gap Report 2023. Accessed: Sep. 28, 2024. Available from: https://www3.weforum.org/docs/WEF_GGGR_2023.pdf
    [2] UNESCO, 2024 GEM Gender Report, 2024. Accessed: Jul. 15, 2024. Available from: https://www.unesco.org/gem-report/en/2024genderreport
    [3] Napp, C. and Breda, T., The stereotype that girls lack talent: A worldwide investigation. Sci Adv, 2022, 8(10): eabm3689. https://doi.org/10.1126/sciadv.abm3689 doi: 10.1126/sciadv.abm3689
    [4] Breda, T., Jouini, E., Napp, C. and Thebault, G., Gender stereotypes can explain the gender-equality paradox. Proceedings of the National Academy of Sciences, 2020,117(49): 31063–31069. https://doi.org/10.1073/pnas.2008704117 doi: 10.1073/pnas.2008704117
    [5] Boivin, N., Täuber, S. and Mahmoudi, M., Overcoming gender bias in STEM. Trends Immunol, 2024, 45(7): 483–485. https://doi.org/10.1016/j.it.2024.05.004 doi: 10.1016/j.it.2024.05.004
    [6] Wrigley-Asante, C., Ackah, C. G. and Frimpong, L. K., Gender differences in academic performance of students studying Science Technology Engineering and Mathematics (STEM) subjects at the University of Ghana. SN Social Sciences, 2023, 3(1): 12. https://doi.org/10.1007/s43545-023-00608-8 doi: 10.1007/s43545-023-00608-8
    [7] Stefani, A., Parental and peer influence on STEM career persistence: From higher education to first job. Adv Life Course Res, 2024, 62: 100642. https://doi.org/10.1016/j.alcr.2024.100642 doi: 10.1016/j.alcr.2024.100642
    [8] Starr, C. R., "I'm Not a Science Nerd!" STEM stereotypes, identity, and motivation among undergraduate women. Psychol Women Q, 2018, 42(4): 489–503. https://doi.org/10.1177/0361684318793848 doi: 10.1177/0361684318793848
    [9] Chi, S., Wang, Z. and Qian, L., Scientists in the Textbook. Sci Educ (Dordr), 2024, 33(4): 937–962. https://doi.org/10.1007/s11191-022-00414-3 doi: 10.1007/s11191-022-00414-3
    [10] Lindner, J. and Makarova, E., Challenging gender stereotypes: Young women's views on female role models in secondary school science textbooks. International Journal of Educational Research Open, 2024, 7: 100376. https://doi.org/10.1016/j.ijedro.2024.100376 doi: 10.1016/j.ijedro.2024.100376
    [11] Qiu, R., Traditional gender roles and patriarchal values: Critical personal narratives of a woman from the Chaoshan region in China. New Directions for Adult and Continuing Education, 2023, 2023(180): 51–63. https://doi.org/10.1002/ace.20511 doi: 10.1002/ace.20511
    [12] Xie, G. and Liu, X., Gender in mathematics: how gender role perception influences mathematical capability in junior high school. The Journal of Chinese Sociology, 2023, 10(1): 10. https://doi.org/10.1186/s40711-023-00188-3 doi: 10.1186/s40711-023-00188-3
    [13] Luo, Y. and Chen, X., The Impact of Math-Gender Stereotypes on Students' Academic Performance: Evidence from China. J Intell, 2024, 12(8): 75. https://doi.org/10.3390/jintelligence12080075 doi: 10.3390/jintelligence12080075
    [14] Murphy, S., MacDonald, S., Wang, C. A. and Danaia, L., Towards an Understanding of STEM Engagement: a Review of the Literature on Motivation and Academic Emotions. Canadian Journal of Science, Mathematics and Technology Education, 2019, 19(3): 304–320. https://doi.org/10.1007/s42330-019-00054-w doi: 10.1007/s42330-019-00054-w
    [15] Master, A. H. and Meltzoff, A. N., Cultural Stereotypes and Sense of Belonging Contribute to Gender Gaps in STEM. Grantee Submission, 2020, 12(1): 152‒198.
    [16] Justicia-Galiano, M. J., Martín-Puga, M. E., Linares, R. and Pelegrina, S., Gender stereotypes about math anxiety: Ability and emotional components. Learn Individ Differ, 2023,105: 102316. https://doi.org/10.1016/j.lindif.2023.102316 doi: 10.1016/j.lindif.2023.102316
    [17] Starr, C. R. and Simpkins, S. D., High school students' math and science gender stereotypes: relations with their STEM outcomes and socializers' stereotypes. Social Psychology of Education, 2021, 24(1): 273–298. https://doi.org/10.1007/s11218-021-09611-4 doi: 10.1007/s11218-021-09611-4
    [18] Starr, C. R., Gao, Y., Rubach, C., Lee, G., Safavian, N., Dicke, A. L., et al., "Who's Better at Math, Boys or Girls?": Changes in Adolescents' Math Gender Stereotypes and Their Motivational Beliefs from Early to Late Adolescence. Educ Sci (Basel), 2023, 13(9): 866. https://doi.org/10.3390/educsci13090866 doi: 10.3390/educsci13090866
    [19] Taraszow, T., Gentrup, S. and Heppt, B., Egalitarian gender role attitudes give girls the edge: Exploring the role of students' gender role attitudes in reading and math. Social Psychology of Education, 2024, 27(6): 3425–3452. https://doi.org/10.1007/s11218-024-09913-3 doi: 10.1007/s11218-024-09913-3
    [20] Eccles, J., Expectancies, values and academic behaviors. In: J. T. Spence (Ed.), Achievement and achievement motives: Psychological and sociological approaches, 1983, 75‒146. San Francisco, CA: Free man.
    [21] Kang, J., Keinonen, T. and Salonen, A., Role of Interest and Self-Concept in Predicting Science Aspirations: Gender Study. Res Sci Educ, 2021, 51(S1): 513–535. https://doi.org/10.1007/s11165-019-09905-w doi: 10.1007/s11165-019-09905-w
    [22] McGuire, L., Mulvey, K. L., Goff, E., Irvin, M. J., Winterbottom, M., Fields, G. E., et al., STEM gender stereotypes from early childhood through adolescence at informal science centers. J Appl Dev Psychol, 2020, 67: 101109. https://doi.org/10.1016/j.appdev.2020.101109 doi: 10.1016/j.appdev.2020.101109
    [23] Bem, S. L., Gender schema theory: A cognitive account of sex typing. Psychol Rev, 1981, 88(4): 354–364. https://doi.org/10.1037/0033-295X.88.4.354 doi: 10.1037/0033-295X.88.4.354
    [24] Wolter, I., Braun, E. and Hannover, B., Reading is for girls!? The negative impact of preschool teachers' traditional gender role attitudes on boys' reading related motivation and skills. Front Psychol, 2015, 6: 1267. https://doi.org/10.3389/fpsyg.2015.01267 doi: 10.3389/fpsyg.2015.01267
    [25] Ward, L. M. and Grower, P., Media and the Development of Gender Role Stereotypes. Annu Rev Dev Psychol, 2020, 2(1): 177–199. https://doi.org/10.1146/annurev-devpsych-051120-010630 doi: 10.1146/annurev-devpsych-051120-010630
    [26] Wolfram, H. J. and Gratton, L., Gender Role Self-Concept, Categorical Gender, and Transactional-Transformational Leadership. J Leadersh Organ Stud, 2014, 21(4): 338–353. https://doi.org/10.1177/1548051813498421 doi: 10.1177/1548051813498421
    [27] Ostuni, A., Sacco, G., Sacco, P. and Zizza, A., Italian Society and Gender Role Stereotypes. How Stereotypical Beliefs Concerning Males and Females are Still Present in Italian People at the Beginning of the Third Millennium. European Scientific Journal, ESJ, 2022, 18(16): 10-19044. https://doi.org/10.19044/esj.2022.v18n16p1 doi: 10.19044/esj.2022.v18n16p1
    [28] Tabassum, N. and Nayak, B. S., Gender Stereotypes and Their Impact on Women's Career Progressions from a Managerial Perspective. IIM Kozhikode Society & Management Review, 2021, 10(2): 192–208. https://doi.org/10.1177/2277975220975513 doi: 10.1177/2277975220975513
    [29] UNESCO, Smashing gender stereotypes and bias in and through education. Accessed: Oct. 25, 2024. Available from: https://www.unesco.org/en/articles/smashing-gender-stereotypes-and-bias-and-through-education
    [30] Thoman, S. E., Stephens, A. K. and Robnett, R. D., "Squeezing the Life Out of Each Day: Emerging Adult Women's Work-Family Expectations in STEM. Emerging Adulthood, 2022, 10(1): 76–89. https://doi.org/10.1177/2167696821990910 doi: 10.1177/2167696821990910
    [31] Nurbatsin, A. S. and Kurmasheva, M. T., Gender Wage Inequality and Occupational Segregation in Kazakhstan. Eurasian Journal of Gender Studies, 2024, 1(2): 40‒53. https://doi.org/10.47703/ejgs.v1i2.12 doi: 10.47703/ejgs.v1i2.12
    [32] Gajda, A., Bójko, A. and Stoecker, E., The vicious circle of stereotypes: Teachers' awareness of and responses to students' gender-stereotypical behavior. PLoS One, 2022, 17(6): e0269007. https://doi.org/10.1371/journal.pone.0269007 doi: 10.1371/journal.pone.0269007
    [33] Charles, M. and Bradley, K., Indulging Our Gendered Selves? Sex Segregation by Field of Study in 44 Countries. American Journal of Sociology, 2009,114(4): 924–976. https://doi.org/10.1086/595942 doi: 10.1086/595942
    [34] Trusson, D. and Rowley, E., Qualitative study exploring barriers and facilitators to progression for female medical clinical academics: interviews with female associate professors and professors. BMJ Open, 2022, 12(3): e056364. https://doi.org/10.1136/bmjopen-2021-056364 doi: 10.1136/bmjopen-2021-056364
    [35] Hasanah, U., Key Definitions of STEM Education: Literature Review. Interdisciplinary Journal of Environmental and Science Education, 2020, 16(3): e2217. https://doi.org/10.29333/ijese/8336 doi: 10.29333/ijese/8336
    [36] Hyde, J. S., Lindberg, S. M., Linn, M. C., Ellis, A. B. and Williams, C. C., Gender Similarities Characterize Math Performance. Science, 2008,321(5888): 494–495. https://doi.org/10.1126/science.1160364 doi: 10.1126/science.1160364
    [37] Apkarian, N., Henderson, C., Stains, M., Raker, J., Johnson, E. and Dancy, M., What really impacts the use of active learning in undergraduate STEM education? Results from a national survey of chemistry, mathematics, and physics instructors. PLoS One, 2021, 16(2): e0247544. https://doi.org/10.1371/journal.pone.0247544 doi: 10.1371/journal.pone.0247544
    [38] Tong, T., Pi, F., Zheng, S., Zhong, Y., Lin, X. and Wei, Y., Exploring the Effect of Mathematics Skills on Student Performance in Physics Problem-Solving: A Structural Equation Modeling Analysis. Res Sci Educ, 2024, 1‒21. https://doi.org/10.1007/s11165-024-10201-5 doi: 10.1007/s11165-024-10201-5
    [39] Bandura, A., Self-efficacy: Toward a unifying theory of behavioral change. Psychol Rev, 1977, 84(2): 191–215. https://doi.org/10.1037/0033-295X.84.2.191 doi: 10.1037/0033-295X.84.2.191
    [40] Barrett, A. A., Smith, C. T., Hafen, C. H., Severe, E. and Bailey, E. G., The impact of gender roles and previous exposure on major choice, perceived competence, and belonging: a qualitative study of students in computer science and bioinformatics classes. Computer Science Education, 2024, 34(1): 114–136. https://doi.org/10.1080/08993408.2022.2160144 doi: 10.1080/08993408.2022.2160144
    [41] Silberstang, J., Learning Gender: The Effects of Gender-Role Stereotypes on Women's Lifelong Learning and Career Advancement Opportunities. In M. London (ed.), The Oxford Handbook of Lifelong Learning, Oxford Library of Psychology, Oxford Academic, 2011. https://doi.org/10.1093/oxfordhb/9780195390483.013.0122
    [42] Tandrayen-Ragoobur, V. and Gokulsing, D., Gender gap in STEM education and career choices: what matters?. Journal of Applied Research in Higher Education, 2022, 14(3): 1021–1040. https://doi.org/10.1108/JARHE-09-2019-0235 doi: 10.1108/JARHE-09-2019-0235
    [43] González-Pérez, S., Mateos de Cabo, R. and Sáinz, M., Girls in STEM: Is It a Female Role-Model Thing?. Front Psychol, 2020, 11: 564148. https://doi.org/10.3389/fpsyg.2020.02204 doi: 10.3389/fpsyg.2020.02204
    [44] Priyashantha, K. G., De Alwis, A. C. and Welmilla, I., Gender stereotypes change outcomes: a systematic literature review. Journal of Humanities and Applied Social Sciences, 2023, 5(5): 450–466. https://doi.org/10.1108/JHASS-07-2021-0131 doi: 10.1108/JHASS-07-2021-0131
    [45] Khattab, N., Students' aspirations, expectations and school achievement: what really matters?. Br Educ Res J, 2015, 41(5): 731–748. https://doi.org/10.1002/berj.3171 doi: 10.1002/berj.3171
    [46] Ding, Z., Liu, R. D., Ding, Y., Yang, Y. and Liu, J., Parent–child educational aspiration congruence and adolescents' internalizing problems: The moderating effect of SES. J Affect Disord, 2024,354: 89–97. https://doi.org/10.1016/j.jad.2024.03.052 doi: 10.1016/j.jad.2024.03.052
    [47] Yeung, J. W. K., The Dynamic Relationships between Educational Expectations and Science Learning Performance among Students in Secondary School and Their Later Completion of a STEM Degree. Behavioral Sciences, 2024, 14(6): 506. https://doi.org/10.3390/bs14060506 doi: 10.3390/bs14060506
    [48] J. Eccles, J., Who Am I and What Am I Going to Do With My Life? Personal and Collective Identities as Motivators of Action. Educ Psychol, 2009, 44(2): 78–89. https://doi.org/10.1080/00461520902832368 doi: 10.1080/00461520902832368
    [49] Khattab, N., Madeeha, M., Samara, M., Modood, T. and Barham, A., Do educational aspirations and expectations matter in improving school achievement?. Social Psychology of Education, 2022, 25(1): 33–53. https://doi.org/10.1007/s11218-021-09670-7 doi: 10.1007/s11218-021-09670-7
    [50] Ottavia, B. and Jody, M., Gender stereotypes in education: Policies and practices to address gender stereotyping across OECD education systems. OECD Education Working Papers, 2022, No. 271, OECD Publishing, Paris. https://doi.org/10.1787/a46ae056-en
    [51] Kevin, N. K., Chidiogo, U. A. and Chioma, A. U., GENDER EQUITY IN EDUCATION: ADDRESSING CHALLENGES AND PROMOTING OPPORTUNITIES FOR SOCIAL EMPOWERMENT. International Journal of Applied Research in Social Sciences, 2024, 6(4): 631–641. https://doi.org/10.51594/ijarss.v6i4.1034 doi: 10.51594/ijarss.v6i4.1034
    [52] Selimbegović, L., Karabegović, M., Blažev, M. and Burušić, J., The independent contributions of gender stereotypes and gender identification in predicting primary school pupils' expectancies of success in STEM fields. Psychol Sch, 2019, 56(10): 1614–1632. https://doi.org/10.1002/pits.22296 doi: 10.1002/pits.22296
    [53] Fiedler, I., Buchholz, S. and Schaeper, H., Does Gender Composition in a Field of Study Matter? Gender Disparities in College Students' Academic Self-Concepts. Res High Educ, 2024, 1‒23. https://doi.org/10.1007/s11162-024-09794-7 doi: 10.1007/s11162-024-09794-7
    [54] Bussey, K., Gender Identity Development, Handbook of Identity Theory and Research, New York, NY: Springer New York, 2011. https://doi.org/10.1007/978-1-4419-7988-9_25
    [55] Lapytskaia Aidy, C., Steele, J. R., Williams, A., Lipman, C., Wong, O. and Mastragostino, E., Examining adolescent daughters' and their parents' academic‐gender stereotypes: Predicting academic attitudes, ability, and STEM intentions. J Adolesc, 2021, 93(1): 90–104. https://doi.org/10.1016/j.adolescence.2021.09.010 doi: 10.1016/j.adolescence.2021.09.010
    [56] Chan, R. C. H., A social cognitive perspective on gender disparities in self-efficacy, interest, and aspirations in science, technology, engineering, and mathematics (STEM): the influence of cultural and gender norms. Int J STEM Educ, 2022, 9(1): 37. https://doi.org/10.1186/s40594-022-00352-0 doi: 10.1186/s40594-022-00352-0
    [57] Shrout, P. E., Commentary: Mediation Analysis, Causal Process, and Cross-Sectional Data. Multivariate Behav Res, 2011, 46(5): 852–860. https://doi.org/10.1080/00273171.2011.606718 doi: 10.1080/00273171.2011.606718
    [58] Otani, M., Relationships between parental involvement and adolescents' academic achievement and aspiration. Int J Educ Res, 2019, 94: 168–182. https://doi.org/10.1016/j.ijer.2019.01.005 doi: 10.1016/j.ijer.2019.01.005
    [59] National Bureau of Statistics of China, The Method of Dividing the Eastern, Central, Western, and Northeastern Regions, Beijing, 2011.
    [60] Ministry of Education of the People's Republic of China, The Ministry of Education issued the General High School Guidelines for the Evaluation of School Quality. Accessed: Sep. 13, 2024. Available from: http://www.moe.gov.cn/srcsite/A06/s3732/202201/t20220107_593059.html
    [61] Education Department of Guizhou Provincial Government, Basic overview of the development of education in 2023. Accessed: Dec. 03, 2024. Available from: https://jyt.guizhou.gov.cn/zfxxgk/fdzdgknr/tjxx/202411/t20241129_86149612.html
    [62] Education Department of Shaanxi Provincial Government, 2023 Shaanxi Provincial Educational Development Statistical Bulletin. Accessed: Nov. 23, 2024. Available from: http://jyt.shaanxi.gov.cn/news/tongjinianjian/202411/01/24594.html
    [63] Cochran, W. G., Sampling Techniques, 3rd ed., John Wiley & Sons, New York, 1977.
    [64] Thompson, S. K., Sampling, 3rd ed., John Wiley & Sons, Hoboken, 2012. https://doi.org/10.1002/9781118162934
    [65] Galambos, N. L., Petersen, A. C., Richards, M. and Gitelson, I. B., The Attitudes Toward Women Scale for Adolescents (AWSA): A study of reliability and validity. Sex Roles, 1985, 13(5): 343–356. https://doi.org/10.1007/BF00288090 doi: 10.1007/BF00288090
    [66] Yang, F., Zheng, J., Li, W., Liu, S., Ya, X. and Gu, L., Does Gender Matter? The Mediating Role of Gender Attitudes on the Associations Between Grandparenting Styles and Adolescent Depression Among Skipped-Generation Families in Rural China. Youth Soc, 2025, 57(2): 279–303. https://doi.org/10.1177/0044118X241312355 doi: 10.1177/0044118X241312355
    [67] Brislin, R. W., Back-Translation for Cross-Cultural Research. J Cross Cult Psychol, 1970, 1(3): 185–216. https://doi.org/10.1177/135910457000100301 doi: 10.1177/135910457000100301
    [68] Cronbach, L. J. and Furby, L., How we should measure 'change': Or should we?. Psychol Bull, 1970, 74(1): 68–80. https://doi.org/10.1037/h0029382 doi: 10.1037/h0029382
    [69] Fornell, C. and Larcker, D. F., Structural Equation Models with Unobservable Variables and Measurement Error: Algebra and Statistics. Journal of Marketing Research, 1981, 18(3): 382. https://doi.org/10.2307/3150980 doi: 10.2307/3150980
    [70] Kline, R. B., Principles and Practice of Structural Equation Modeling, Guilford Press, New York, 2011.
    [71] Podsakoff, P. M., MacKenzie, S. B., Lee, J. Y. and Podsakoff, N. P., Common method biases in behavioral research: A critical review of the literature and recommended remedies. Journal of Applied Psychology, 2003, 88(5): 879–903. https://doi.org/10.1037/0021-9010.88.5.879 doi: 10.1037/0021-9010.88.5.879
    [72] Cohen, J., Cohen, P., West, S. G. and Aiken, L. S., Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences, Routledge, 2013. https://doi.org/10.4324/9780203774441
    [73] Baron, R. M. and Kenny, D. A., The moderator–mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. J Pers Soc Psychol, 1986, 51(6): 1173–1182. https://doi.org/10.1037/0022-3514.51.6.1173 doi: 10.1037/0022-3514.51.6.1173
    [74] Hayes, A. F., Introduction to Mediation, Moderation, and Conditional Process Analysis: A Regression-Based Approach, vol. 3, Guilford Press, New York, 2022.
    [75] Robitzsch, A., Why Ordinal Variables Can (Almost) Always Be Treated as Continuous Variables: Clarifying Assumptions of Robust Continuous and Ordinal Factor Analysis Estimation Methods. Front Educ, 2020, 5: 589965. https://doi.org/10.3389/feduc.2020.589965
    [76] Eccles, J., Gendered educational and occupational choices: Applying the Eccles et al. model of achievement-related choices. Int J Behav Dev, 2011, 35(3): 195–201. https://doi.org/10.1177/0165025411398185
    [77] Wang, M. T. and Degol, J. L., Gender Gap in Science, Technology, Engineering, and Mathematics (STEM): Current Knowledge, Implications for Practice, Policy, and Future Directions. Educ Psychol Rev, 2017, 29(1): 119–140. https://doi.org/10.1007/s10648-015-9355-x doi: 10.1007/s10648-015-9355-x
    [78] Plante, I., O'Keefe, P. A. and Théorêt, M., The relation between achievement goal and expectancy-value theories in predicting achievement-related outcomes: A test of four theoretical conceptions. Motiv Emot, 2013, 37(1): 65–78. https://doi.org/10.1007/s11031-012-9282-9 doi: 10.1007/s11031-012-9282-9
    [79] Chung, G., Kainz, K., Eisensmith, S. R. and Lanier, P., Effects of Youth Educational Aspirations on Academic Outcomes and Racial Differences: A Propensity Score Matching Approach. J Child Fam Stud, 2023, 32(1): 17–30. https://doi.org/10.1007/s10826-022-02227-y doi: 10.1007/s10826-022-02227-y
    [80] Roy-Chowdhury, V., Household factors and girls' aspirations for male-dominated STEM degrees and careers, 2021. Accessed: Oct. 21, 2024. Available from: https://www.bi.team/publications/household-factors-and-girls-aspirations-for-male-dominated-stem-degrees-and-careers/
    [81] Harms, M. B. and Garrett-Ruffin, S. D., Disrupting links between poverty, chronic stress, and educational inequality. NPJ Sci Learn, 2023, 8(1): 50. https://doi.org/10.1038/s41539-023-00199-2 doi: 10.1038/s41539-023-00199-2
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  • Author's biography Ping Chen received the M.Sc. degree in curriculum and instruction from Chongqing Normal University (CYU), China, in 2018. She is currently pursuing the Ph.D. degree in curriculum and instruction with Universiti Putra Malaysia (UPM), Malaysia. She specializes in teaching and learning, pedagogy and education, learning curriculum development, and educational psychology. Her research interests include STEM education, educational technology, and decision-making in education; Aminuddin B. Hassan is a professor of philosophy of education with Universiti Putra Malaysia (UPM), Malaysia. He is specialized in the philosophical underpinnings of education; he contributes significantly to the understanding of education's profound impact on society. His research interests include teaching and consultancy work, in the areas of philosophy of education, higher education, thinking skills, and logic; Firdaus M. Hamzah is a professor of environmental Statistics with the National Defence University of Malaysia (UPNM), Malaysia. He is specializes in applied statistics, data science, environmental science, and civil engineering. His research interests include data science, machine learning, wavelet analysis, temporal and spatial modeling, education, and management. He has published numerous high-quality articles in these areas; Sallar S. Murad received the M.Sc. degree in computer science from Universiti Putra Malaysia (UPM), Malaysia, in 2018. He is currently pursuing the Ph.D. degree in information and communication technology with Universiti Tenaga Nasional, Malaysia. He has published a few articles in reputable journals. He also publishes books on Amazon Kindle. His main research interests include the Internet of Things (IoT), cloud computing, visible light communication (VLC), hybrid optical wireless and RF communications, LiFi, and wireless technologies. He is a reviewer in many journals; Heng Wu received the Ph.D. degree in musicology from the Universiti Putra Malaysia (UPM) in 2024. Her research interests include folk music, traditional music, and music education. She is currently working in the fields of music education and education management
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