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Research article

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


  • Received: 17 January 2025 Revised: 18 May 2025 Accepted: 27 May 2025 Published: 16 June 2025
  • 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 Z-subalgebra of an ambient field F=Q(u1,,un) generated by certain combinatorially defined generators (i.e., cluster variables), which are grouped into overlapping clusters. Many relations between cluster algebras and other branches of mathematics have been discovered, for example, Poisson geometry, discrete dynamical systems, higher Teichmüller spaces, representation theory of quivers and finite-dimensional algebras.

    We first recall the definition of cluster automorphisms, which were introduced by Assem, Schiffler and Shamchenko in [1].

    Definition 1.1 ([1]). Let A=A(x,B) be a cluster algebra, and f:AA be an automorphism of Z-algebras. f is called a cluster automorphism of A if there exists another seed (z,B) of A such that

    (1)f(x)=z;

    (2) f(μx(x))=μf(x)(z) for any xx.

    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 f is a Z-algebra homomorphism.

    Conjecture 1. [5,Conjecture 1] Let A be a cluster algebra, and f:AA be a Z-algebra homomorphism. Then f is cluster automorphism if and only if there exist two clusters x and z such that f(x)=z.

    The following is our main result, which affirms the Conjecture 1.

    Theorem 3.6 Let A be a cluster algebra, and f:AA be a Z-algebra homomorphism. Then f is a cluster automorphism if and only if there exist two clusters x and z such that f(x)=z.

    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 n, we will always denote by [1,n] the set {1,2,,n}.

    Recall that B is said to be skew-symmetrizable if there exists an positive diagonal integer matrix D such that BD is skew-symmetric.

    Fix an ambient field F=Q(u1,u2,,un). A labeled seed is a pair (x,B), where x is an n-tuple of free generators of F, and B is an n×n skew-symmetrizable integer matrix. For k[1,n], we can define another pair (x,B)=μk(x,B), where

    (1) x=(x1,,xn) is given by

    xk=ni=1x[bik]+i+ni=1x[bik]+ixk

    and xi=xi for ik;

    (2) B=μk(B)=(bij)n×n is given by

    bij={bij,if i=k or j=k;bij+sgn(bik)[bikbkj]+,otherwise.

    where [x]+=max{x,0}. The new pair (x,B)=μk(x,B) is called the mutation of (x,B) at k. We also denote B=μk(B).

    It can be seen that (x,B) is also a labeled seed and μk is an involution.

    Let (x,B) be a labeled seed. x is called a labeled cluster, elements in x are called cluster variables, and B is called an exchange matrix. The unlabeled seeds are obtained by identifying labeled seeds that differ from each other by simultaneous permutations of the components in x, and of the rows and columns of B. We will refer to unlabeled seeds and unlabeled clusters simply as seeds and clusters respectively, when there is no risk of confusion.

    Lemma 2.1 ([2]). Let B be an n×n skew-symmetrizable matrix. Then μk(B)=(Jk+Ek)B(Jk+Fk), where

    (1) Jk denotes the diagonal n×n matrix whose diagonal entries are all 1s, except for 1 in the k-th position;

    (2) Ek is the n×n matrix whose only nonzero entries are eik=[bik]+;

    (3) Fk is the n×n matrix whose only nonzero entries are fkj=[bkj]+.

    Definition 2.2 ([9,11]). (1) Two labeled seeds (x,B) and (x,B) are said to be mutation equivalent if (x,B) can be obtained from (x,B) by a sequence of mutations;

    (2) Let Tn be an n-regular tree and valencies emitting from each vertex are labelled by 1,2,,n. A cluster pattern is an n-regular tree Tn such that for each vertex tTn, there is a labeled seed Σt=(xt,Bt) and for each edge labelled by k, two labeled seeds in the endpoints are obtained from each other by seed mutation at k. We always write

    xt=(x1;t,x2;t,,xn;t),Bt=(btij).

    The cluster algebra A=A(xt0,Bt0) associated with the initial seed (xt0,Bt0) is a Z-subalgebra of F generated by cluster variables appeared in Tn(xt0,Bt0), where Tn(xt0,Bt0) is the cluster pattern with (xt0,Bt0) lying in the vertex t0Tn.

    Theorem 2.3 (Laurent phenomenon and positivity [11,15,12]). Let A=A(xt0,Bt0) be a cluster algebra. Then each cluster variable xi,t is contained in

    Z0[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 0B be a skew-symmetrizable integer matrix. If B is obtained from B by a sequence of mutations and B=aB for some aZ, then a=±1 and B=±B.

    Proof.. Since B is obtained from B by a sequence of mutations, there exist integer matrices E and F such that B=EBF, by Lemma 2.1. If B=aB, then we get B=aE(B)F. Also, we can have

    B=aE(B)F=a2E2(B)F2==asEs(B)Fs,

    where s0. By B0, we know a0. Thus 1asB=Es(B)Fs holds for any s0.

    Assume by contradiction that a±1, then when s is large enough, 1asB will not be an integer matrix. But Es(B)Fs is always an integer matrix. This is a contradiction. So we must have a=±1 and thus B=±B.

    A square matrix A is decomposable if there exists a permutation matrix P such that PAPT is a block-diagonal matrix, and indecomposable otherwise.

    Lemma 3.2. Let 0B be an indecomposable skew-symmetrizable matrix. If B is obtained from B by a sequence of mutations and B=BA for some integer diagonal matrix A=diag(a1,,an), then A=±In and B=±B.

    Proof. If there exists i0 such that ai0=0, then the i0-th column vector of B is zero, by B=BA. This contradicts that B is indecomposable and B0. So each ai0 is nonzero for i0=1,,n.

    Let D=diag(d1,,dn) be a skew-symmetrizer of B. By B=BA and AD=DA, we know that

    BD=BAD=(BD)A.

    By the definition of mutation, we know that D is also a skew-symmetrizer of μk(B), k=1,,n. Since B is obtained from B by a sequence of mutations, we get that D is a skew-symmetrizer of B. Namely, we have that both BD and BD=(BD)A are skew-symmetric. Since 0B is indecomposable, we must have a1==an. So A=aIn for some aZ, and B=aB. Then by Lemma 3.1, we can get A=±In and B=±B.

    Lemma 3.3. Let B=diag(B1,,Bs), where each Bi is a nonzero indecomposable skew-symmetrizable matrix of size ni×ni. If B is obtained from B by a sequence of mutations and B=BA for some integer diagonal matrix A=diag(a1,,an), then aj=±1 for j=1,,n.

    Proof. By the definition of mutation, we know that B has the form of B=diag(B1,,Bs), where each Bi is obtained from Bi by a sequence of mutations. We can write A as a block-diagonal matrix A=diag(A1,,As), where Ai is a ni×ni integer diagonal matrix. By B=BA, we know that Bi=BiAi. Then by Lemma 3.2, we have Ai=±Ini and Bi=±Bi for i=1,,s. In particular, we get aj=±1 for j=1,,n.

    Lemma 3.4. Let A=A(x,B) be a cluster algebra, and f:AA be a Z-homomorphism of A. If there exists another seed (z,B) of A such that such that f(x)=z, then f(μx(x))=μf(x)(z) for any xx.

    Proof. After permutating the rows and columns of B, it can be written as a block-diagonal matrix as follows.

    B=diag(B1,B2,,Bs),

    where B1 is an n1×n1 zero matrix and Bj is nonzero indecomposable skew-symmetrizable matrix of size nj×nj for j=2,,s.

    Without loss of generality, we assume that f(xi)=zi for 1in.

    Let xk and zk be the new obtained variables in μk(x,B) and μk(z,B). So we have

    xkxk=ni=1x[bik]+i+ni=1x[bik]+i,andzkzk=ni=1z[bik]+i+ni=1z[bik]+i.

    Thus

    f(xk)=f(ni=1x[bik]+i+ni=1x[bik]+ixk)=ni=1z[bik]+i+ni=1z[bik]+izk=ni=1z[bik]+i+ni=1z[bik]+ini=1z[bik]+i+ni=1z[bik]+izk.

    Note that the above expression is the expansion of f(xk) with respect to the cluster μk(z). By

    f(xk)f(A)=AZ[z±11,,(zk)±1,,z±1n],

    we can get

    ni=1z[bik]+i+ni=1z[bik]+ini=1z[bik]+i+ni=1z[bik]+iZ[z±11,,z±1k1,z±1k+1,,z±1n].

    Since both ni=1z[bik]+i+ni=1z[bik]+i and ni=1z[bik]+i+ni=1z[bik]+i is not divided by any zi, we actually have

    ni=1z[bik]+i+ni=1z[bik]+ini=1z[bik]+i+ni=1z[bik]+iZ[z1,,zk1,zk+1,,zn].

    So for each k, there exists an integer akZ such that (b1k,b2k,,bnk)T=ak(b1k,b2k,,bnk)T. Namely, we have B=BA, where A=diag(a1,,an). Note that B has the form of

    B=diag(B1,B2,,Bs),

    where B1 is an n1×n1 zero matrix and Bj is a nonzero indecomposable skew- symmetrizable matrix of size nj×nj for j=2,,s. Applying Lemma 3.3 to the skew-symmetrizable matrix diag(B2,,Bs), we can get aj=±1 for n1+1,,n. Since the first n1 column vectors of both B and B are zero vectors, we can just take a1==an1=1. So for each k, we have ak=±1 and

    (b1k,b2k,,bnk)T=ak(b1k,b2k,,bnk)T=±(b1k,b2k,,bnk)T.

    Hence,

    ni=1z[bik]+i+ni=1z[bik]+ini=1z[bik]+i+ni=1z[bik]+i=1.

    Thus we get

    f(xk)=ni=1z[bik]+i+ni=1z[bik]+ini=1z[bik]+i+ni=1z[bik]+izk=zk.

    So f(μx(x))=μf(x)(z) for any xx.

    Lemma 3.5. Let A=A(x,B)F be a cluster algebra, and f be an automorphism of the ambient field F. If there exists another seed (z,B) of A such that f(x)=z and f(μx(x))=μf(x)(z) for any xx. Then

    (i) f is an automorphism of A;

    (ii) f is a cluster automorphism of A.

    Proof. (ⅰ) Since f is an automorphism of the ambient field F, we know that f is injective.

    Since f commutes with mutations, we know that f restricts to a surjection on X, where X is the set of cluster variables of A. Because A is generated by X, we get that f restricts to an epimorphism of A.

    Hence, f is an automorphism of A.

    (ⅱ) follows from (ⅰ) and the definition of cluster automorphisms.

    Theorem 3.6. Let A be a cluster algebra, and f:AA be a Z-algebra homomorphism. Then f is a cluster automorphism if and only if there exist two clusters x and z such that f(x)=z.

    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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  • 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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