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.
Cluster algebras were invented by Fomin and Zelevinsky in a series of papers [9,2,10,11]. A cluster algebra is a
We first recall the definition of cluster automorphisms, which were introduced by Assem, Schiffler and Shamchenko in [1].
Definition 1.1 ([1]). Let
Cluster automorphisms and their related groups were studied by many authors, and one can refer to [6,7,8,14,13,4,5,16] for details.
The following very insightful conjecture on cluster automorphisms is by Chang and Schiffler, which suggests that we can weaken the conditions in Definition 1.1. In particular, it suggests that the second condition in Definition 1.1 can be obtained from the first one and the assumption that
Conjecture 1. [5,Conjecture 1] Let
The following is our main result, which affirms the Conjecture 1.
Theorem 3.6 Let
In this section, we recall basic concepts and important properties of cluster algebras. In this paper, we focus on cluster algebras without coefficients (that is, with trivial coefficients). For a positive integer
Recall that
Fix an ambient field
x′k=n∏i=1x[bik]+i+n∏i=1x[−bik]+ixk |
and
b′ij={−bij,if i=k or j=k;bij+sgn(bik)[bikbkj]+,otherwise. |
where
It can be seen that
Let
Lemma 2.1 ([2]). Let
(1)
(2)
(3)
Definition 2.2 ([9,11]).
xt=(x1;t,x2;t,…,xn;t),Bt=(btij). |
The cluster algebra
Theorem 2.3 (Laurent phenomenon and positivity [11,15,12]). Let
Z≥0[x±11;t0,x±12;t0,…,x±1n;t0]. |
In this section, we will give our main result, which affirms the Conjecture 1.
Lemma 3.1. Let
Proof.. Since
B′=aE(B′)F=a2E2(B′)F2=⋯=asEs(B′)Fs, |
where
Assume by contradiction that
A square matrix
Lemma 3.2. Let
Proof. If there exists
Let
BD=B′AD=(B′D)A. |
By the definition of mutation, we know that
Lemma 3.3. Let
Proof. By the definition of mutation, we know that
Lemma 3.4. Let
Proof. After permutating the rows and columns of
B=diag(B1,B2,⋯,Bs), |
where
Without loss of generality, we assume that
Let
xkx′k=n∏i=1x[bik]+i+n∏i=1x[−bik]+i,andzkz′k=n∏i=1z[b′ik]+i+n∏i=1z[−b′ik]+i. |
Thus
f(x′k)=f(n∏i=1x[bik]+i+n∏i=1x[−bik]+ixk)=n∏i=1z[bik]+i+n∏i=1z[−bik]+izk=n∏i=1z[bik]+i+n∏i=1z[−bik]+in∏i=1z[b′ik]+i+n∏i=1z[−b′ik]+iz′k. |
Note that the above expression is the expansion of
f(x′k)∈f(A)=A⊂Z[z±11,…,(z′k)±1,…,z±1n], |
we can get
n∏i=1z[bik]+i+n∏i=1z[−bik]+in∏i=1z[b′ik]+i+n∏i=1z[−b′ik]+i∈Z[z±11,⋯,z±1k−1,z±1k+1,⋯,z±1n]. |
Since both
n∏i=1z[bik]+i+n∏i=1z[−bik]+in∏i=1z[b′ik]+i+n∏i=1z[−b′ik]+i∈Z[z1,⋯,zk−1,zk+1,⋯,zn]. |
So for each
B=diag(B1,B2,⋯,Bs), |
where
(b1k,b2k,…,bnk)T=ak(b′1k,b′2k,…,b′nk)T=±(b′1k,b′2k,…,b′nk)T. |
Hence,
n∏i=1z[bik]+i+n∏i=1z[−bik]+in∏i=1z[b′ik]+i+n∏i=1z[−b′ik]+i=1. |
Thus we get
f(x′k)=n∏i=1z[bik]+i+n∏i=1z[−bik]+in∏i=1z[b′ik]+i+n∏i=1z[−b′ik]+iz′k=z′k. |
So
Lemma 3.5. Let
(i)
(ii)
Proof. (ⅰ) Since
Since
Hence,
(ⅱ) follows from (ⅰ) and the definition of cluster automorphisms.
Theorem 3.6. Let
Proof. "Only if part": It follows from the definition of cluster automorphism.
"If part": It follows from Lemma 3.4 and Lemma 3.5.
This project is supported by the National Natural Science Foundation of China (No.11671350 and No.11571173) and the Zhejiang Provincial Natural Science Foundation of China (No.LY19A010023).
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