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Educational Psychology
An International Journal of Experimental Educational Psychology
ISSN: (Print) (Online) Journal homepage: www.tandfonline.com/journals/cedp20
Motivational profiles in mathematics among
Chinese secondary school students and their
relations with perceived parent/teacher goals and
academic achievement
Zheng Luo, Yixue Yang, Jiacan Sun, Wenjing Yuan, Siyuan Liu & Ling Wang
To cite this article: Zheng Luo, Yixue Yang, Jiacan Sun, Wenjing Yuan, Siyuan Liu & Ling
Wang (27 Jun 2024): Motivational profiles in mathematics among Chinese secondary school
students and their relations with perceived parent/teacher goals and academic achievement,
Educational Psychology, DOI: 10.1080/01443410.2024.2369232
To link to this article: https://doi.org/10.1080/01443410.2024.2369232
Published online: 27 Jun 2024.
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EDUCATIONAL PSYCHOLOGY
Motivational proles in mathematics among Chinese
secondary school students and their relations with
perceived parent/teacher goals and academic
achievement
Zheng Luoa , Yixue Yanga, Jiacan Sunb, Wenjing Yuanc, Siyuan Liua and
Ling Wanga
aBeijing Key Laboratory of Learning and Cognition, School of Psychology, Capital Normal University,
Beijing, China; bDepartment of Preschool Education, Shijiazhuang Preschool Teachers College, Hebei,
China; cExperimental School Aliated to HaiDian Teachers Training College, Beijing, China
ABSTRACT
This study identified maths motivation profiles in a sample of
878 Chinese secondary school students, and examined the
effects of perceived parent/teacher achievement goals on maths
motivation profiles and the effects of the latter on academic
outcomes. Latent profile analysis conducting on three achieve-
ment goals (mastery-approach, performance-approach, and
performance-avoidance) and four interest components (emotion,
value, knowledge, engagement) identified four profiles: medium,
high all, low, and high mastery-oriented and interest. Students who
perceived more parent/teacher mastery-approach and performance-
approach goals were more likely to belong to the high all pro-
files. Students with the high all and the high mastery-oriented
and interest profiles showed the highest use of deep and
surface learning strategies and maths achievement. The results
revealed distinct motivational profiles by integrating achieve-
ment goal theory and four-phase interest development theory,
and provided preliminary evidence to help parents and teachers
enhance students’ maths motivation.
Introduction
Mathematics is highly correlated with both future educational achievement and career
development of secondary school students (Singh etal., 2002). Many secondary school
students find mathematics difficult and disconnected from real life, which brings
serious challenges to their motivation in mathematics, such as the pursuit of negative
goal patterns (Pulfrey et al., 2011), diminished interest (Frenzel et al., 2010), etc.
All these lead to a significant decrease in maths performance (Chan et al., 2012;
Zhang & Wang, 2020).
© 2024 Informa UK Limited, trading as Taylor & Francis Group
CONTACT Zheng Luo luozheng@cnu.edu.cn; Ling Wang wangling@cnu.edu.cn Beijing Key Laboratory of
Learning and Cognition, School of Psychology, Capital Normal University, Bai Dui Zi, Haidian District, Beijing, PR China
https://doi.org/10.1080/01443410.2024.2369232
ARTICLE HISTORY
Received 25 July 2023
Accepted 12 June 2024
KEYWORDS
Person-centered;
achievement goal;
academic interest;
learning strategy;
academic achievement
2 Z. LUO ETAL.
Thus far, there has been a large body of literature on the study of maths motiva-
tion, with most studies based on a single motivation theory, such as achievement
goal theory (Schwinger et al., 2016) and interest theory (Roure & Lentillon-Kaestner,
2022). Studies have also suggested that maths motivation can be better explained
by combining different motivation theories (Conley, 2012; Hulleman et al., 2008;
Linnenbrink-Garcia et al., 2018). The person-centered approach allows us to explore
patterns of students by combining with variables from different theories, focusing
more directly on similarities and differences among individuals (Bergman & Trost,
2006). Therefore, by integrating achievement goal theory (Dweck, 1986) and four-phase
interest development theory (Hidi & Renninger, 2006), this study will investigate
mathematics motivation patterns of Chinese secondary school students through a
person-centered approach.
Theoretical background
Achievement goal theory
Achievement goal theory focuses on competence-relevant goals in achievement
settings (Elliot, 1999). Researchers initially defined two primary goal orientations:
mastery (characterised by developing competence) and performance (characterised
by demonstrating competence) goals (Ames, 1992). Both types of goal orientations
have been further differentiated into approach and avoidance components (Elliot
& McGregor, 2001). The trichotomous model (Elliot, 1999) including mastery-approach,
performance-approach, and performance-avoidance goals has the strongest empirical
support in the study of adolescent achievement goals and maths motivation in
school settings (Bardach et al., 2018). Mastery-approach goals focus on improving,
understanding and learning. Performance-approach goals focus on demonstrating
one’s abilities and surpassing peers, while performance-avoidance goals focus on
avoiding appearing incompetent and performing inferior to peers (Hulleman
et al., 2010).
Mastery-approach goals typically positively predicted the use of deep learning
strategies and academic performance (Liu, 2021), and positively or negatively related
to surface learning strategies (Chan et al., 2012; Liu, 2021). Performance-avoidance
goals positively predicted the use of surface strategies and and negatively predicted
academic performance (Chan et al., 2012). Performance-approach goals generally
contribute to academic success in mathematics learning (Chan etal., 2012; Liu, 2021).
However, performance-approach goals positively related to the use of both deep and
surface strategies (Chan etal., 2012; Wolters etal., 1996). One possible reason is that
surface strategies can also be adaptive, compatible with deep strategies, and
supportive of learning (e.g. Pintrich & De Groot, 1990).
Four-phase interest development model
Interest refers to a person’s preferred engagement with a specific object (Hidi, 1990).
The four-phase interest development model (Hidi & Renninger, 2006) addresses how
individual or long-term interests develop from situational or short-term interests
through four phases. The first two phases, triggered situational interest and maintained
EDUCATIONAL PSYCHOLOGY 3
situational interest, belong to situational interest. The last two phases, emerging
individual interest and well-developed individual interest, pertain to individual interest.
Earlier studies conceptualised interest as a single component, or as two components
including emotion and value (e.g., Eccles & Wigfield, 2002). Hidi and Renninger (2006)
characterised interest by ‘positive feelings, on-going information search, and increasing
coordination of individuals’ knowledge of and value for content’ (Renninger et al.,
2024). Therefore, interest includes four components: emotion, value, knowledge and
engagement. This four-component model has been validated among Chinese sen-
condary school students (Luo etal., 2019), offering a more comprehensive and specific
evaluation of students’ academic interest compared to single- and two-factor models.
Previous research on maths motivation has consistently found that interest positively
predicted the use of deep learning strategies (Zhu & Mok, 2018) and academic achieve-
ment in mathematics (Zhang & Wang, 2020).
Integrative theoretical approach
Based on expectancy-value theory (Wigfield et al., 2015), achievement goals and
interest are both subjective task values, representing the ‘Do I want to do this task
and why?’ component of achievement motivation. Achievement goals assess the
aim or focus of students’ engagement, while interest focuses on students’ preferred
engagement with a specific object, capturing students’ emotional response and the
perception of the personal significance of the domain (Wigfield et al., 2015).
Researchers have demonstrated that interest and mastery goals are reciprocally
related over time (Harackiewicz etal., 2008; Hulleman etal., 2008), as well as mas-
tery goals are a mediating factor for the continued development of interest
(Harackiewicz et al., 2008). These findings, along with the current calls to explain
the synergies between motivational variables (e.g. Hidi & Renninger, 2019), highlight
the significance of applying an integrative theoretical approach to identify motiva-
tional profiles consisting of interest and achievement goals. As previously noted,
both achievement goals and interest are related to different patterns of learning
strategies and academic achievement. However, it is less clear how they cohere
and function synergistically for different students, which requires a person-centered
approach.
Integrative motivation proles in mathematics
Research on mathematics motivation often uses a variable-centered approach,
which fails to explain heterogeneous patterns of multiple variable interactions. In
contrast, as a person-centered analysis technique, latent profile analysis (LPA) can
identify potential profiles or subgroups of students with similar characteristics by
analysing possible combinations of multiple motivation variables (Bergman & Trost,
2006). This would reveal homogeneity within latent subgroups and heterogeneity
across them.
In previous person-centered studies, motivation profiles in mathematics have been
mostly identified from a single theoretical perspective, such as achievement goal
theory. These studies have consistently identified profiles as high multiple, moderate
4 Z. LUO ETAL.
multiple, high mastery-oriented and motivated (e.g., Schwinger etal., 2016). Notably,
only one person-centered study, according to the four-phase interest development
model, identified four individual interest profiles from ‘Very low individual interest
and triggering situational interest’ to ‘Well-developed individual interest and actualized
situational interest’ among secondary students enrolled in swimming lessons (Roure
& Lentillon-Kaestner, 2022).
Some studies have explored maths motivation using an integrative theoretical
perspective. By combining achievement goals with expectancy-value theory, Conley
(2012) observed seven patterns, whereas Linnenbrink-Garcia et al. (2018) observed
four profiles. These studies all recognised a ‘low’ profile and a ‘high all’ profile.
Linnenbrink-Garcia et al. (2018) also revealed a profile with strong mastery goal
endorsement and high task value (labelled ‘intrinsic and confident’). By combining
motivational and affective factors, Xiao and Sun (2020) identified five profiles varying
in maths anxiety and motivation levels. As far as we know, however, there is no study
in mathematics that combines achievement goal theory with the four-phase interest
development model to explore integrative motivation profiles.
Motivational proles in mathematics with learning strategies and academic
achievement
It has long been debated between the mastery goal perspective (Ames, 1992) and
the multiple goal perspective (Barron & Harackiewicz, 2001) about the question of
which goal or combination of goals is most adaptive. A person-centered approach
may offer a more comprehensive understanding to answer this question. Wormington
and Linnenbrink-Garcia (2016) found that students with mastery high (mastery goal
pursuit) and approach high (multiple goal pursuit) profiles demonstrated similar
achievement levels. In terms of academic interest profiles, Roure and Lentillon-Kaestner
(2022) found that students with well-developed individual interest and actualised
situational interest profile reported the highest scores in ability belief in swimming
learning.
For integrative motivation profiles in mathematics, research found that students
with high all and intrinsic and confident profiles, as well as those with profiles char-
acterised by low maths anxiety and medium or high motivation exhibited the highest
maths achievement (Conley, 2012; Linnenbrink-Garcia et al., 2018; Xiao & Sun, 2020).
As far as we know, however, there has been no study based on an integrative moti-
vation profile examining the differences in learning strategy in mathematics.
Perceived parent/teacher achievement goals on students’ motivation in
mathematics
According to achievement goal, environmental cues (e.g. family and classroom goal
structures or perceived parent and teacher achievement goals) affect students’
achievement goals, interests, and academic outcomes (Friedel et al., 2007; Park etal.,
2018). Perceived parent and teacher mastery-approach goals refer to students’ per-
ception of parents’ and teachers’ goal-related messages that emphasise students’ skill
acquisition and self-improvement, whereas perceived parent and teacher
EDUCATIONAL PSYCHOLOGY 5
performance-approach goals refer to students’ perception of those messages that
highly value displays of ability or interpersonal comparisons at school (Gonida
et al., 2009).
Achievement goal theory assumes that students adopt goals matching their envi-
ronment. Each personal achievement goal should be best predicted by its respective
contextual counterpart (Bardach et al., 2020). Some studies have also examined the
cross-relationship between each teacher/parent achievement goal and personal
achievement goals. In general, research has shown that perceived parent/teacher
mastery-approach goals positively correlate with students’ mastery-approach and
performance-approach goals (Bardach et al., 2020; Gonida etal., 2009), while teacher
mastery-approach goals have a small positive effect on students’ performance-avoidance
goals (Bardach et al., 2020). Parent/teacher performance-approach goals positively
correlate with students’ performance-approach and performance-avoidance goals
(Friedel etal., 2007; Gonida et al., 2009) and positively or negatively related to mastery-
approach goals (Friedel et al., 2007). Meanwhile, parent/teacher mastery-approach
goals enhance students’ academic interest (Gonida et al., 2009; Park et al., 2018),
while parent/teacher performance-approach goals undermine it (Urdan &
Midgley, 2003).
The present study
Previous studies utilising a variable-centered approach have shown that students’
achievement goals and interest are associated with their perceived parent/teacher
goals and academic outcomes. Additionally, achievement goals mediate the relation
between perceived parent/teacher goals and coping strategies in mathematics learning
(Friedel etal., 2007). Nevertheless, these studies did not investigate how achievement
goals and interest are combined among individuals, and how such patterns relate to
their perceived parent/teacher goals and academic outcomes. A person-centered
approach is well-suited for addressing these questions, which could contribute to a
further theoretical understanding of whether perceived parent/teacher goals can act
as predictors (covariates) of the motivation profile, and whether learning strategies
and mathematics achievement are distal outcomes.
The purposes of this study were threefold: (1) to identify integrative mathematics
motivation profiles of secondary school students based on possible combinations of
three types of achievement goals (mastery-approach, performance-approach,
performance-avoidance) and four components of interest (emotion, value, knowledge,
and engagement); (2) to examine how students’ motivational profile membership was
predicted by their perceived parent and teacher achievement goals; (3) to investigate
the association between students’ motivational profiles with learning strategies and
academic achievement.
Our research model is depicted in Figure 1. We also included gender and grade
as demographic covariates in the model (not shown in the model), as previous research
has indicated that girls (e.g. Frenzel et al., 2010; Peterson & Kaplan, 2016) and students
in higher grades (Balta et al., 2023; Gonida et al., 2007) have reported lower
performance-approach and -avoidance goals, as well as reduced interest in mathe-
matics learning.
6 Z. LUO ETAL.
Due to the nature of latent profile analysis and the lack of previous research on
specific profiles combining achievement goals and interest components, we adopted
an exploratory approach. Nevertheless, based on previous similar research studies
(Conley, 2012; Linnenbrink-Garcia et al., 2018; Xiao & Sun, 2020), we formulated the
following hypotheses:
Hypothesis 1: There were four to seven motivation profiles, including high all, medium and
low profiles, as well as a profile characterised by high mastery-approach goals and interest
components and low performance goals.
Hypothesis 2: Perceived parent and teacher mastery-approach goals would predict the pro-
les with higher mastery-approach goals and interest components.
Hypothesis 3: Students in proles with higher mastery-approach goals and higher interest
components, with or without accompanying performance goals, would be more motivated
to use deep learning strategies and achieve higher academic achievement, especially
compared to students in low proles.
Figure 1. Hypothesised structural model, including the measurements of the proles, covariates,
and distal outcomes.
EDUCATIONAL PSYCHOLOGY 7
Methods
Participants and procedure
Eight hundred seventy-eight secondary school students (30.6% in suburban areas;
54.8% girls) were recruited by cluster sampling from 20 classes in 12 public secondary
schools in Beijing, China. Of all the participants, 203 were in 7th grade, 164 were in
8th grade, 162 were in 9th grade, 113 were in 10th grade, 117 were in 11th grade
and 119 were in 12th grade. Their ages ranged from 10 to 18 years old (M = 14.70 years,
SD = 1.68 years). The only child rate was 70%. Paternal and maternal education levels
were 11.9% and 8.7% for graduate and above, 46.8% and 47.5% for university, 25.2%
and 26.5% for senior high school, and 16.1% and 17.2% for junior high school and
below, respectively.
The questionnaire was distributed in the classroom and was collected on the spot.
The entire process took approximately 25 min. Before the survey, the students were
informed of the study purpose and about confidentiality. They volunteered to partic-
ipate in this study and provided informed consent. Informed assent from the partic-
ipants’ parents/legal guardians and consent from the school principals were obtained
before the study was conducted. Ethical approval for the study was obtained from
the Ethics Research Committee (ERC) of the School of Psychology, Capital Normal
University.
Measures
Student achievement goal orientations
Fourteen items from the Patterns of Adaptive Learning Survey (PALS; Midgley et al.,
2000) were used to assess students’ mastery-approach, performance-approach, and
performance-avoidance goals in learning mathematics. Example items include ‘One
of my goals in math class is to learn as much as I can’ (mastery-approach), ‘It’s import-
ant to me that I look smart compared to others in math class’ (performance-approach)
and ‘It’s important to me that I don’t look stupid in math class’ (performance-avoidance).
Each item was rated on a 5-point Likert scale, ranging from 1 (‘Not at all true’) to 5
(‘Very true’). The PALS has been validated among Chinese secondary school students
(Shi etal., 2001). In this study, the confirmatory factor analysis (CFA) showed that the
three-factor model had a satisfactory model fit [
χ
2
(70) = 417.89, p < 0.001, CFI = 0.95,
TLI = 0.94, RMSEA = 0.075, SRMR = 0.060]. The average variance extracted (AVE) values
were 0.67, 0.67, and 0.67, and composite reliabilities were 0.91, 0.91, and 0.89 for
mastery-approach, performance-approach, and performance-avoidance goals,
respectively.
Perceived parent and teacher goal orientations
Students’ perceptions about their parent and mathematics teachers’ achievement goals
were assessed using nineteen items from the PALS (Midgley et al., 2000). The measure
assessed perceived parent mastery-approach (e.g. ‘My parents want my math work
to be challenging for me’), parent performance-approach (e.g. ‘My parents don’t like
it when I make mistakes in math class work’), teacher mastery-approach (e.g. ‘My
8 Z. LUO ETAL.
mathematics teacher really wants us to enjoy learning new things’) and teacher
performance-approach (e.g. ‘My math teacher points out those students who get
good grades as an example to all of us’). Each item was rated on a 5-point Likert
scale from 1 (‘Not at all true’) to 5 (‘Very true’). The perception of teachers’ goals
subscale has been validated among Chinese secondary school students (Zhao et al.,
2020). In this study, the CFA showed satisfactory model fit for the perception of parent
goals subscale with
χ
2
(33) = 185.53, p < 0.001, CFI = 0.96, TLI = 0.93, RMSEA = 0.075,
SRMR = 0.047, for perception of teachers’ goals subscale with
χ
2
(17) = 99.05, p < 0.001,
CFI = 0.96, TLI = 0.94, RMSEA = 0.074, SRMR = 0.044. The AVE values were 0.60, 0.49,
0.55, and 0.59, and composite reliabilities were 0.90, 0.83, 0.84, and 0.81 for perceived
parent mastery-approach, parent performance-approach, teacher mastery-approach,
and teacher performance-approach, respectively.
Academic interest
The Academic Interest Scale for Adolescents (AISA; Luo et al., 2019), validated among
Chinese secondary school students, was used to assess students’ academic interest
in maths learning. The 29-item measure consists of four components: emotion
(e.g. ‘Studying mathematics makes me feel happy’), value (e.g. ‘The knowledge of
mathematics is important’), knowledge (e.g. ‘I know all kinds of knowledge about
mathematics’) and engagement (e.g. ‘I want to learn things that are not included in
math textbooks’). Each item was rated on a 5-point Likert scale, ranging from 1 (‘Not
at all true’) to 5 (‘Very true’). In this study, the CFA showed that the four-factor model
had a satisfactory model fit with
χ
2
(484) = 2569.91, p < 0.001, CFI = 0.90, TLI = 0.90,
RMSEA = 0.070, SRMR = 0.044. The AVE values were 0.71, 0.64, 0.53 and 0.60, and
composite reliabilities were 0.95, 0.93, 0.89 and 0.92 for emotion, value, knowledge,
and engagement, respectively.
Learning strategies
Students’ learning strategies were assessed using the Cognitive and Metacognitive
Strategy Subscale from the Motivated Strategies for Learning Questionnaire (MSLQ;
Pintrich, 1991). The 13-item measure consists of surface learning strategies (e.g. ‘When
I read content in math class, I read it over and over to help me remember it’) and
deep learning strategies (e.g. ‘I outline chapters to help me learn math’). Each item
was rated on a 5-point Likert scale, ranging from 1 (‘Not at all true’) to 5 (‘Very true’).
The MSLQ has been validated among Chinese secondary school students (Rao & Sachs,
1999). In this study, the CF showed that the two-factor model had a satisfactory fit
[
χ
2
(31)=157.88, p < 0.001, CFI = 0.96, TLI = 0.95, RMSEA = 0.068, SRMR = 0.031].
The AVE values were 0.71 and 0.56, and composite reliabilities were 0.83 and 0.86
for surface learning strategies and deep learning strategies, respectively.
Academic achievement
Self-reported mathematics scores ranging from 0 to 120 were collected using the
question ‘‘What were your midterm mathematics exam scores in this semester?’’. The
scores were first standardised within each class and then represented by 1-6 for z
scores below −2, −2 to −1, −1 to 0, 0 to 1, 1 to 2, and above 2.
EDUCATIONAL PSYCHOLOGY 9
Statistical analysis
The statistical analysis was performed using SPSS 24.0 and Mplus 8.0. Full information
maximum likelihood (FIML) method was used to address missing data. The results of
Harman’s single factor test found no significant common method bias in the current study.
The analysis followed the three-step method for identifying integrative motivational
profiles and examining the covariates and distal outcomes of latent profile membership
(Asparouhov & Muthén, 2014). First, LPA was conducted to identify latent profiles
according to three achievement goal orientations and four academic interest compo-
nents. Lower comparative values of AIC, BIC and adjusted BIC (ABIC) indicate an
improved model fit (Bergman et al., 2003). Entropy is used to assess the classification
accuracy, Entropy ≥ 0.80 indicates that the classification accuracy is greater than 90%,
which is an acceptable range (Lubke & Muthén, 2007). The Vuong-Lo-Mendall-Rubin
test (VLMR) and the Lo-Mendell-Rubin Likelihood Ratio Test (LMRLRT) are used to
compare the difference in fit between the k-1 and k-category models. If the p-value is
significant, then the k-category model outperforms the k-1-category model (Lo
et al., 2001).
In the second step, each student was assigned the most likely class membership
based on the posterior probabilities obtained in the first step. In the third step, the
R3STEP procedure (Asparouhov & Muthén, 2014) was conducted to test whether
covariates (perceived parent and teacher achievement goals) affect the membership
of integrative motivational profiles. The Bolck-Croon-Hagenaars (BCH; Bolck et al.,
2004) method was employed to investigate the associations of integrative motivational
profiles with the distal outcomes (learning strategies and academic achievement).
Results
Descriptive statistics
Means, standard deviations, and correlations for all the motivation variables are pre-
sented in Table 1. Significant positive correlations existed between students’ three
achievement goals (ps < 0.01) and between the four interest components (ps < 0.001).
Both student’s mastery-approach and performance-approach goals were significantly
and positively associated with all four interest components (ps < 0.001). Students’
performance-avoidance goals were significantly and positively associated with knowl-
edge (ps < 0.05) and engagement (ps < 0.01).
Motivation proles
Based on multiple fit indices, the four- and five-class solutions were all reasonable
considerations. The five-class model had lower AIC, BIC and ABIC values than the
four-class model, but the identified profile was similar to other profiles in structure,
which would result in limited benefit. For the rule of parsimony, we deemed the
four-class patterns model to be optimal, which had lower AIC, BIC, and ABIC values
than the three-class model and had significant p values for LMR LR and VLMR. The
entropy value of the four-class model was 0.87 (Table 2).
10 Z. LUO ETAL.
Raw score values for the four-class model are reported in Table 3, with standardised
scores available in Figure 2. Univariate ANOVAs and Bonferroni post hoc tests revealed
typological differences between the different profiles, except for the difference in the
four interest components between profiles two and four. Profile one showed medium
levels across achievement goals and interest components, and was labelled medium.
Profile two had the highest levels in performance-approach, performance-avoidance,
four interest components, and higher levels of mastery-approach; thus, we defined it
as high all. Profile three, which was labelled low, exhibited the lowest levels in
mastery-approach, four interest components, and lower levels of performance-approach
and performance-avoidance. Profile four was defined as high mastery-oriented and
interest given the highest levels in mastery-approach, four interest components, and
the lowest levels of performance-approach and performance-avoidance. The
Classification probabilities of most likely profile assignment (see Table 4) indicated a
clear classification of the four-class patterns model.
Table 1. Descriptive statistics and correlation matrix of motivation variables.
Variable 1 2 3 4 5 6 7
1. Student mastery-approach –
2. Student performance-approach 0.17*** –
3. Student performance-avoidance 0.10** 0.77*** –
4. Emotion 0.44*** 0.21*** 0.03 –
5. Value 0.57*** 0.16*** 0.04 0.77*** –
6. Knowledge 0.39*** 0.27*** 0.07* 0.81*** 0.69*** –
7. Engagement 0.51*** 0.21*** 0.07** 0.83*** 0.81*** 0.79*** –
M4.23 3.07 3.10 4.00 4.25 3.77 4.00
SD 0.71 0.97 1.02 0.81 0.70 0.79 0.72
*p < 0.05. **p < 0.01. ***p < 0.001.
Table 2. Model t indices for one to seven class solutions of integrative motivational prole.
Model AIC BIC ABIC Entropy LMR LR (p)VLMR (p)
2-class 12476.40 12581.51 12511.64 0.89 <0.001 <0.001
3-class 11640.46 11783.79 11688.52 0.89 <0.001 <0.001
4-class 11316.95 11498.50 11377.82 0.87 <0.001 <0.001
5-class 10978.41 11198.18 11052.10 0.88 0.03 0.03
6-class 10829.44 11087.44 10915.95 0.85 0.77 0.77
Note. Indices of the best-tting model are in boldface. AIC: akaike information criterion; BIC: Bayesian information
criterion; ABIC: adjusted Baysian information criterion; LMR LR: Lo-Mendell-Rubin likelihood ratio test; VLMR:
Vuong-Lo-Mendall-Rubin test.
Table 3. Achievement goals, academic interesting components for four integrative motivational
proles.
Medium High all Low
High mastery-oriented
and interest F
Eect size
(ηp2)
Student mastery-approach 4.11c4.54b3.51d4.73a144.06*** 0.33
Student performance-approach 3.10b3.95a2.54c2.24d195.00*** 0.40
Student performance-avoidance 3.23b3.91a2.79c1.96d209.31*** 0.42
Emotion 3.79b4.65a2.81c4.68a723.17*** 0.71
Value 4.13b4.75a3.19c4.81a628.90*** 0.68
Knowledge 3.51b4.44a2.76c4.35a503.13*** 0.63
Engagement 3.78b4.60a2.94c4.60a804.25*** 0.73
Note. Values with dierent subscripts in same row represent signicantly dierent values based on Bonferroni post
hoc tests for achievement goals and academic interesting components. ηp2: partial eta squared; values of ηp2 of
0.01, 0.06, 0.14 indicate small, medium, large eect, respectively.
***p < 0.001.
EDUCATIONAL PSYCHOLOGY 11
Parent/teacher goals as predictors of motivational proles membership
The R3STEP revealed that, after controlling for gender and grade, parent and teacher
goals acted as covariates and predicted the ensuing class memberships (Table 5).
Specifically, Students who perceived higher parent mastery-approach goals were more
likely to belong to the high all and high mastery-oriented and interest profiles, rather
than to the medium or low profiles. Students who perceived higher parent
performance-approach goals were more likely to be assigned to the high all profile
than to the high mastery-oriented and interest, medium or low profiles, to the medium
and low profiles than to the high mastery-oriented and interest profile, and to the
medium profile than to the low profile. Students who perceived the higher teacher
mastery-approach goals were more likely to belong to the high all, high mastery-oriented
and interest and medium profiles than to the low profile, and to the high
mastery-oriented and interest profile than to the medium profiles. Students who
perceived higher level teacher’s performance-approach goals were more likely to
belong to the high all, medium and low profiles than to the high mastery-oriented
and interest profile. Being female and being in a higher grade increased the likelihood
Figure 2. The four integrative motivational proles and relative size of the proles.
Table 4. Classication probabilities of most likely prole membership (row) by latent prole
(column).
Prole 1234
1 Medium 0.932 0.028 0.022 0.019
2 High all 0.026 0.908 0.000 0.066
3 Low 0.046 0.000 0.954 0.000
4 High mastery-oriented and interest 0.034 0.074 0.000 0.893
Note. Bolded values indicate average posterior probabilities (AvePP).
12 Z. LUO ETAL.
of belonging to the low profile than the high mastery-oriented and interest profile
or medium profile. In general, parent and teacher mastery-approach goals increase
the likelihood of belonging to the profiles with high mastery-oriented and interest
components, with or without high performance goals, compared to the low profile.
Meanwhile, parent and teacher performance-approach goals increase the likelihood
of belonging to the high all profile in comparison to the high mastery-oriented and
interest profile or low profile.
Associations between motivational proles and learning strategies and
academic achievement
The BCH indicated that, after controlling for gender and grade, the association between
latent profile membership and learning-related distal outcomes was statistically
Table 5. Covariates predicting integrative motivational profile membership.
High all as comparison class
B(SE)OR(SE)95%CI
High mastery-oriented
and interest
Gender 0.12(0.25) 1.12(0.28) [0.70, 1.82]
Grade −0.13(0.07) 0.88(0.06) [0.76, 1.01]
Parent mastery-approach 0.33(0.31) 1.39(0.42) [0.76, 2.52]
Parent performance-approach −1.45(0.20)*** 0.23(0.05) [0.16, 0.34]
Teacher mastery-approach 0.48(0.31) 1.62(0.49) [0.89, 2.94]
Teacher performance-approach −0.61(0.17)*** 0.55(0.09) [0.40, 0.76]
Medium Gender 0.31(0.19) 1.37(0.26) [0.94, 1,99]
Grade −0.04(0.06) 0.96(0.05) [0.86, 1.07]
Parent mastery-approach −0.71(0.21)** 0.49(0.10) [0.33, 0.74]
Parent performance-approach −0.55(0.21)*** 0.58(0.09) [0.43, 0.78]
Teacher mastery-approach −0.13(0.21) 0.88(0.19) [0.58, 1.33]
Teacher performance-approach −0.25(0.14) 0.78(0.11) [0.60, 1.03]
Low Gender 0.94(0.28)*** 2.56(0.63) [1.58, 4.15]
Grade 0.05(0.07) 1.05(0.07) [0.92, 1.20]
Parent mastery-approach −0.80(0.26)** 0.45(0.12) [0.27, 0.74]
Parent performance-approach −0.92(0.21)*** 0.40(0.08) [0.27, 0.60]
Teacher mastery-approach −1.15(0.26)*** 0.32(0.08) [0.19, 0.53]
Teacher performance-approach 0.01(0.19) 1.01(0.19) [0.69, 1.47]
High mastery-oriented and interest as comparison class
Medium Gender 0.20(0.23) 1.22(0.28) [0.78, 1.90]
Grade 0.09(0.07) 1.09(0.07) [0.96, 1.25]
Parent mastery-approach −1.04(0.27)*** 0.35(0.10) [0.21, 0.60]
Parent performance-approach 0.90(0.16)*** 2.47(0.39) [1.82, 3.35]
Teacher mastery-approach −0.61(0.28)* 0.55(0.15) [0.31, 0.95]
Teacher performance-approach 0.36(0.15)* 1.43(0.21) [1.08, 1.91]
Low Gender 0.82(0.27)** 2.28(0.62) [1.34, 3.88]
Grade 0.18(0.08)* 1.20(0.09) [1.03, 1.40]
Parent mastery-approach −1.13(0.30)*** 0.32(0.10) [0.18, 0.59]
Parent performance-approach 0.54(0.20)** 1.71(0.34) [1.17, 2.51]
Teacher mastery-approach −1.63(0.32)*** 0.20(0.06) [0.10, 0.37]
Teacher performance-approach 0.61(0.20)** 1.84(0.37) [1.25, 2.72]
Medium as comparison class
Low Gender 0.63(0.22)** 1.87(0.40) [1.23, 2.85]
Grade 0.10(0.06) 1.10(0.06) [0.98, 1.23]
Parent mastery-approach −0.09(0.21) 0.92(0.19) [0.61, 1.38]
Parent performance-approach −0.37(0.18)* 0.69(0.12) [0.49, 0.98]
Teacher mastery-approach −1.03(0.22)*** 0.36(0.08) [0.23, 0.55]
Teacher performance-approach 0.25(0.17) 1.28(0.22) [0.92, 1.80]
Note. Gender (1 = Male; 2 = Female).
*p < 0.05. **p < 0.01. ***p < 0.001.
EDUCATIONAL PSYCHOLOGY 13
significant (Table 6). Students from the high all and the high mastery-oriented and
interest profiles had the highest academic achievement and most often used surface
and deep learning strategies. The next highest levels of academic achievement and
moderate use of surface and deep learning strategies were observed for the medium
profile. The low profile had the lowest academic achievement and was not adept at
using surface or deep learning strategies.
Discussion
The present study was the first to adopt a person-centered approach based on
achievement goal theory and four-phase interest development theory to explore
integrative mathematics motivation among Chinese secondary school students. Our
findings provided empirical support for the existence of four distinct profiles, which
are consistent with previous research (Linnenbrink-Garcia et al., 2018; Roure &
Lentillon-Kaestner, 2022).
Some prominent features exist among all four identified profiles, characterised by
simultaneously high, medium, or low levels of certain motivation variables or com-
ponents. For example, mastery-approach goals and interest components,
performance-approach and performance-avoidance goals, and four interest compo-
nents generally work together. In addition, our study revealed the medium, low and
high all profiles, which reflect relative level differences in maths motivation among
Chinese secondary school students, which is largely in line with prior research on
student motivation in maths learning in Western samples (Conley, 2012;
Linnenbrink-Garcia et al., 2018; Schwinger et al., 2016). Overall, these patterns of
results suggest that students’ maths motivation, drawing from achievement goal
theory and four-phase interest development theory, is to some extent a coherent
latent construct.
Our study identified a unique profile (i.e. high mastery-oriented and interest),
which is similar to the ‘primarily mastery-oriented’ profile described by Schwinger
etal. (2016) and the ‘intrinsic and confident’ profile described by Linnenbrink-Garcia
et al. (2018). Students in this profile tend to focus on developing intrapersonal
competence without reference to others and perceive that mathematics is enjoyable
and valuable, with high levels of stored knowledge, engaging more with maths
activities. This pattern indicates a certain differentiation in students’ maths motiva-
tion drawing from achievement goal theory and four-phase interest develop-
ment theory.
Table 6. Learning strategies and academic achievement for four integrative motivational
proles.
Medium High all Low
High mastery-oriented
and interest
χ
2
Surface learning strategy 3.76b4.36a3.39c4.34a239.19***
Deep learning strategy 3.67b4.23a3.26c4.22a615.57***
Academic achievement 3.53b3.75a3.23c3.88a79.91***
Note. Values with dierent subscripts in the same row represent signicantly dierent values based on
χ
2
tests for
learning strategies, and academic achievement.
***p < 0.001.
14 Z. LUO ETAL.
Our study demonstrated that parent and teacher achievement goals perceived by
students were meaningfully associated with profile membership. The results showed
that parent and teacher achievement goals had very similar predictions for the four
profiles. Specifically, students who perceived more parent/teacher mastery-approach
goals were more likely to belong to the high all and high mastery-oriented and
interest profiles and less likely to belong to the low profile. Students who perceive
more parent/teacher performance-approach goals were more likely to belong to the
high all profile and less likely to belong to the high mastery-oriented and interest
profile or low profile. The above findings closely parallel previous studies that exam-
ined the predictive value of perceived teacher and parental goals (Bardach et al.,
2020; Friedel et al., 2007) through a variable-centered approach, and teacher goals
through a person-centered approach (Stavropoulou etal., 2023).
To date, a large body of research documents that each achievement goal is posi-
tively related to its contextual matching goal (Bardach etal., 2020; Park et al., 2018).
This explains why high levels of teacher/parent mastery-approach goals and low levels
of teacher/parent performance-approach goals can predict high membership proba-
bilities of the high mastery-oriented and interest profile. Meanwhile, some research
demonstrated the cross-relationship between each achievement goal with its contex-
tual goals (e.g. Friedel et al., 2007; Gonida et al., 2009). Therefore, high levels of
parent/teacher mastery-approach goals and parent/teacher performance-approach
goals can predict high membership probabilities of the high all profile and low
membership probabilities of the low profile in this study.
Our findings suggested that students in the high mastery-oriented and interest
and high all profiles reported the most use of deep and surface learning strategies,
followed by those in the medium and low profiles. These findings are consistent
with previous variable-centered research showing that mastery-approach goals and
interest were positively associated with the use of deep and surface learning strat-
egies (Chan et al., 2012; Liu, 2021). One possible reason is that mastery-approach
goals lead students to a higher sense of self-efficacy and a willingness to accept
challenges, while interest motivates students intrinsically. Both will subsequently
facilitate the adoption of more learning strategies (Park etal., 2018). There are several
reasons why deep and surface learning strategies co-occurrence. First, the surface
strategy measured in this study only emphasised rehearsal efforts, which are com-
patible with deep strategies and effective learning (e.g. Pintrich & De Groot, 1990).
Second, the Chinese mathematics curriculum emphasises ‘Two Basics’: basic knowl-
edge, such as definitions and formulas, and basic skills, such as calculations (Zhang
et al., 2005). Therefore, both surface (memorisation, repeatedly practicing) and deep
(connecting information) strategies are crucial for maths learning. Thirdly, influenced
by Confucian culture, Asians, especially Chinese, often adopt a unique learning
approach of memorisation with understanding (Leung, 2001), in which both deep
and surface learning strategies are simultaneously used to achieve better achievement.
Consistent with prior research (Wormington & Linnenbrink-Gatcia, 2016), our study
found that the high all and high mastery-oriented and interest profiles showed the
best academic achievement. Both profiles have high mastery-approach goals and
interest. Mastery-approach goals foster challenge, engagement, enthusiasm (Santoro,
2022). The combination of mastery-approach goals and interest, an intrinsic motivation
EDUCATIONAL PSYCHOLOGY 15
factor (Hidi, 1990), can significantly enhance learning and performance. Remarkably,
these two profiles described the highest and lowest levels of performance goals,
respectively. This suggests that there are no additional benefits or losses in endorsing
or not endorsing performance goals as long as students endorse high levels of mas-
tery goals and interests (Wormington & Linnenbrink-Garcia, 2016).
Limitations
This study has several limitations. Firstly, our study design was cross-sectional. Further
longitudinal research is needed to examine the causal relationships between the
variables. Second, we used self-report measures of goals, interest and learning strat-
egies. Future studies could extend research methods (e.g. classroom observation,
student log files, teacher ratings and friend ratings) to reproduce the results. Third,
the convergent validity of perceived parental performance-approach goals was some-
what low (AVE was 0.49), and the inter-correlations among the interest components
(0.69–0.83) were relatively high. However, these limitations were compensated by the
acceptable model fit and the adequate composite reliability (Fornell & Larcker, 1981).
Future studies are still needed to replicate our findings with improved scales. Fourth,
although we have considered important environmental influences from school and
family, it might not fully encompass all the context factors (e.g. peer support; Song
et al., 2015) that affect motivation and achievement in mathematics. Further explo-
ration of broader environmental factors is needed. Last, this study focused on Chinese
secondary students, limiting generalisation to students in Western contexts, or the
primary school levels. Future research should test our findings across different cultures
and school levels.
Implications
Our findings have several theoretical implications. First, by integrating two important
achievement motivation constructs, namely achievement goals and interest, through
a person-centered approach, this study improves the understanding of how they
relate to one another between different profiles. That is, interest positively relates to
mastery-approach and performance goals among students with the medium, low and
high all profiles, but among students with the high mastery-oriented and interest
profile, it positively related to mastery-approach goals and negatively to achieve-
ment goals.
Second, this study provides a possible person-centered solution to the debate
between the mastery goal perspective and the multiple goal perspective. Different
perspectives reflect in specific profiles of students. Findings from this study indicate
that the high all and the high mastery-oriented and interest profiles are all adaptive
for learning strategies and achievement. These findings suggest that the effects of
pursing performance and mastery-approach goals concurrently are comparable to
those of pursing mastery goal pursuit alone. Third, the present study supports the
influence of parent and teacher goals on the motivation profiles on a contextual level,
which extends our understanding of how achievement motivation can be shaped,
which could not be manifested in the variable-centered approach literature.
16 Z. LUO ETAL.
Our findings are also of great significance for the improvement of educational
practice by proposing differentiated models of mathematical education. Secondary
students with different mathematical motivation profiles might have different levels
of academic achievement, indicating that parents and teachers should provide them
with different support. Secondary students in the high all profile and high
mastery-oriented and interest profile have a high level of motivation in mathematics,
which helps them attain great maths achievement. For these students, parents and
teachers can only provide general education without additional interventions. For
students with medium and low profiles, teachers and parents should provide addi-
tional support to help them improve their motivation in mathematics, for example,
by developing higher levels of parent and teacher mastery-approach and
performance-approach goals and using digital formative assessment tools (DFATS) on
teaching and learning processes (Faber etal., 2017). Our findings provide a theoretical
basis for parents and teachers to build a family and classroom environment to pro-
mote adaptive motivation profiles for optimal learning, and to design different inter-
ventions to improve secondary students’ motivation in mathematics.
Conclusions
The current study found that mathematics motivation among Chinese secondary
school students could be classified into four profiles: medium, high all, low and high
mastery-oriented and interest. Perceived parent/teacher mastery-approach and
performance-approach goals were meaningfully associated with profile membership.
For example, students who perceived higher parent/teacher mastery-approach goals
and performance-approach goals were more likely to belong to the high all profile.
Students in the four profiles also differed in their mathematics learning strategies
and achievement. Specifically, students with the high mastery-oriented and interest
and the high all profiles showed the highest use of deep and surface learning strat-
egies, as well as mathematics achievement.
Ethical approval
Ethical approval for the study was obtained from the Ethics Research Committee (ERC)
of the School of Psychology, Capital Normal University.
Disclosure statement
The authors report there are no competing interests to declare.
Funding
This work was supported by a grant from the Beijing Social Science Fund Project [23JYA006].
ORCID
Zheng Luo http://orcid.org/0000-0003-1497-9208
EDUCATIONAL PSYCHOLOGY 17
Data availability statement
The data that support the ndings of this study are available from the corresponding author
upon reasonable request.
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