1. Bibliographic Information

1.1. Title

A multifactorial model of intrinsic / environmental motivators, personal traits and their combined influences on math performance in elementary school

1.2. Authors

• Antonios Christodoulou ($^{1}$)

• Konstantinos Tsagkaridis ($^{2,3}$)

• Amarylhis- Chryssi Maleqiannaki ($^{3}$)

  ($^{1}$) Cyprus Ministry of Education, Sport and Youth, Nicosia, Cyprus ($^{2}$) European University Cyprus, Nicosia, Cyprus ($^{3}$) University of Cyprus, Nicosia, Cyprus

1.3. Journal/Conference

Published in a peer-reviewed journal, implied by the Received, Revised, Accepted, Published online timestamps and the © The Author(s) 2024 copyright. The specific journal name is not explicitly stated in the provided text but its content and structure are typical of academic journals in educational psychology or related fields. The publication date is May 21, 2024.

1.4. Publication Year

2024

1.5. Abstract

This study investigates the complex interplay of achievement goals, interest, self-efficacy, and environmental factors (parental and classroom influences) on elementary school students' mathematical performance. Building upon existing research that often focuses on one or two factors, this paper develops a holistic multifactorial path analysis model to explore direct and indirect influences. Data was collected from 762 5th and 6th-grade students across 22 public primary schools in Cyprus using established self-report scales (e.g., Achievement Goal Questionnaire (AGQ-R), Patterns of Adaptive Learning Scales (PALS)) and a custom-designed mathematics performance test. The results indicate a robust model effectively capturing these associations. A key finding is that self-efficacy and interest mediate the relationship between students’ mastery goals and mathematical performance. The research highlights the profound significance of mastery goals, self-efficacy, and interest in predicting mathematical achievement.

1.6. Original Source Link

/files/papers/6936dd174a3ffba76e41c68e/paper.pdf (This is a local file path, indicating the paper content was provided directly.) Publication Status: Officially published (based on the provided publication dates and author information).

2. Executive Summary

2.1. Background & Motivation

The paper addresses the multifaceted nature of student motivation and its impact on academic performance, particularly in mathematics during elementary school. Existing research often examines the influence of one or two motivational factors (e.g., achievement goals, self-efficacy, interest) on performance. However, students' achievement goals are not isolated but are themselves shaped by environmental factors like parental and teacher influences, and the broader socio-cultural context.

The core problem is that previous studies often lack a holistic view, failing to model the complex web of direct and indirect influences among intrinsic motivators (e.g., students' achievement goals), environmental motivators (e.g., perceived parental and classroom goals), and personal traits (e.g., self-efficacy and interest) on academic performance. This creates a gap in understanding how these factors combine and interact to affect student outcomes.

This problem is important because understanding these complex relationships can inform more effective educational interventions. If mastery goals, self-efficacy, and interest are crucial, and if environmental factors shape these, then interventions targeting parents, teachers, and student self-perception could significantly boost math performance. The paper's innovative idea is to expand the traditional framework of achievement goal theory by building a comprehensive multifactorial path analysis model that simultaneously considers all these influences.

2.2. Main Contributions / Findings

The paper makes several significant contributions:

• Holistic Multifactorial Model: It constructs a comprehensive path analysis model that integrates intrinsic motivators (student achievement goals), environmental motivators (perceived parental and classroom goals), and personal traits (self-efficacy and interest) to predict mathematics performance. This is presented as the first study to combine all these variables in a single comprehensive model.

• Identification of Direct and Indirect Effects: The model effectively disentangles the complex grid of associations, revealing both direct and indirect influences among the variables. This moves beyond simple correlations to explain mediating pathways.

• Mediation Role of Self-Efficacy and Interest: A primary finding is that self-efficacy and interest mediate the relationship between students' mastery goals and mathematical performance. This means mastery goals don't directly improve performance but do so by fostering higher self-efficacy and interest.

• Environmental Influence on Intrinsic Motivators: The study confirms that perceived parental and classroom goals significantly influence students' individual achievement goals. Classroom mastery goals had a stronger impact on individual mastery goals, while parental performance goals had a stronger influence on individual performance goals.

• Stronger Influence of Self-Efficacy: Among the mediating personal traits, self-efficacy was found to have a stronger influence on mathematical performance compared to interest.

• Practical Implications: The findings provide actionable insights for educators and policymakers, emphasizing the importance of fostering mastery goals (over performance goals), self-efficacy, and interest through supportive classroom and home environments to enhance mathematical performance in elementary school children.

  The study's findings directly address the gap in understanding the combined influences of these factors, providing a more nuanced and integrated view of student motivation and its impact on academic outcomes.

3. Prerequisite Knowledge & Related Work

3.1. Foundational Concepts

To understand this paper, a beginner should be familiar with several core concepts in educational psychology and research methodology:

• Motivation (in education): This refers to the internal and external factors that stimulate desire and energy in people to be continually interested in and committed to a role, subject, or to make an effort to achieve a goal. In an academic context, it explains why students choose to learn, how much effort they put in, and how long they persist. The paper distinguishes between intrinsic motivators (coming from within the individual, like personal goals) and environmental motivators (coming from the surroundings, like parental or teacher expectations).

• Achievement Goal Theory (AGT): A prominent socio-cognitive theory that explains how students' beliefs about the purpose of achievement influence their learning and behavior. It posits that students' behaviors are driven by the pursuit of specific goals. The paper discusses its evolution:

  • Dichotomous Model: Initially, AGT distinguished between two main types of goals:
    • Mastery Goals: Students with mastery goals focus on learning, understanding, skill development, knowledge acquisition, and self-improvement. They are driven by a desire to become competent.
    • Performance Goals: Students with performance goals focus on demonstrating their ability, recognizing their own competence, comparing themselves to others, and striving to excel or outperform others.
  • Valence Distinctions (Approach vs. Avoidance): Later models added a valence dimension to both mastery and performance goals:
    • Approach Goals: Focus on achieving success (e.g., mastery-approach: learning as much as possible; performance-approach: outperforming others). These are generally associated with positive outcomes.
    • Avoidance Goals: Focus on avoiding failure (e.g., mastery-avoidance: avoiding misunderstanding; performance-avoidance: avoiding performing worse than others). These are generally associated with negative outcomes and anxiety.
  • The paper notes that for elementary school students, distinguishing approach-avoidance for performance goals can be challenging with self-reporting, and mastery-avoidance goals are less common at this age.

• Self-Efficacy: Introduced by Albert Bandura, self-efficacy refers to an individual's belief in their capacity to execute behaviors necessary to produce specific performance attainments. In an academic context, it's a student's belief in their ability to succeed in specific academic tasks or domains (e.g., "I believe I can solve difficult math problems"). High self-efficacy is often linked to greater effort, persistence, and resilience in the face of challenges.

• Interest: In educational psychology, interest denotes the enjoyment, engagement, and satisfaction a student experiences when interacting with specific topics or activities (e.g., "I find mathematics class interesting"). It can lead to deeper learning, greater persistence, and more positive emotions toward the subject.

• Environmental Factors: These are external influences that shape a student's motivation and learning. The paper specifically focuses on:

  • Perceived Parental Goals: Students' perceptions of what their parents emphasize regarding academic achievement (e.g., whether parents prioritize understanding and learning (parental mastery goals) or grades and outperforming others (parental performance goals)).
  • Perceived Classroom Goals: Students' perceptions of the goals and values emphasized by their teachers and the classroom environment (e.g., whether the teacher promotes deep understanding (classroom mastery goals) or competition and high grades (classroom performance goals)).

• Path Analysis: A statistical technique used to examine direct and indirect effects among a set of variables. It's a type of structural equation modeling (SEM) that allows researchers to test hypothesized causal relationships between variables. Instead of just looking at simple correlations, path analysis estimates the strength and significance of hypothesized causal paths from one variable to another, including mediation effects.

  • Direct Effect: The influence of one variable on another without any intermediate variables.
  • Indirect Effect: The influence of one variable on another through one or more mediating variables.
  • Mediation: Occurs when the relationship between an independent variable (X) and a dependent variable (Y) is explained by a third variable, the mediator (M). X influences M, and M then influences Y. For example, mastery goals (X) might influence math performance (Y) indirectly through self-efficacy (M).

3.2. Previous Works

The paper extensively references prior research to establish its theoretical foundation and highlight existing gaps. Key prior studies and their contributions include:

• Pintrich (2003): Underscored the general role of student motivation in academic success. This work highlights the broader significance of the topic.
• Elliot & Hulleman (2017), Kaplan & Maehr (2007), Liem et al. (2008): These studies collectively establish that intrinsic motivators (achievement goals) and personal traits (self-efficacy, interest) are crucial for performance, and that environmental motivators (parental/classroom perceptions) also play a role.
• Elliot (1999): A foundational work on Achievement Goal Theory (AGT), establishing goal pursuit as a driver of student behavior.
• Chazan et al. (2022), Hulleman et al. (2010), Urdan & Kaplan (2020): These provide reviews of the evolution of AGT from dichotomous to more complicated models, noting that simpler models might be preferable depending on the research question.
• Elliot et al. (2011), Huang (2011): Introduced valence distinctions (approach/avoidance goals) within AGT.
• Anderman & Patrick (2012), Sideridis & Mouratidis (2008): Highlighted the challenges of approach-avoidance distinctions, especially with self-reporting in younger participants, which influenced this study's decision to consolidate performance goals.
• Mouratidis et al. (2018), Pantziara & Philippou (2015): Emphasized the vitality of motivation in mathematics education and the importance of mastery goals for academic performance.
• Linnenbrink-Garcia et al. (2008): Noted that the relationship between mastery-approach goals and academic performance is substantial in elementary school students but diminishes in higher education, justifying the current study's focus on elementary school.
• Bandura (1997): Defined self-efficacy as beliefs in one's ability to succeed, a core personal trait in this study.
• Gonida & Cortina (2014), Jiang et al. (2014), Lee et al. (2014), Martin & Elliot (2016), Michaelides et al. (2019), Tosto et al. (2016), Yu & Martin (2014): These studies collectively demonstrate a positive correlation between mastery goals and both self-efficacy and interest, supporting the trait influence aspect of the model.
• Friedel et al. (2007, 2010): Explored bidirectional relationships between mastery goals and self-efficacy, influencing how achievement goals and motivators form a dynamic continuum.
• Midgley et al. (2000): Developed the Patterns of Adaptive Learning Scales (PALS), a key instrument used to measure perceived classroom and parental goals, and self-efficacy.
• Elliot & Murayama (2008): Developed the Achievement Goal Questionnaire (AGQ-R), used here for individual achievement goals.

Technological Evolution: The field of motivational psychology in education has evolved from focusing on individual factors in isolation to increasingly complex models that acknowledge the interplay of multiple variables. Early research often relied on simpler correlational studies. The development of Achievement Goal Theory itself progressed from dichotomous models to those with approach-avoidance distinctions. Methodologically, the shift towards path analysis and structural equation modeling (SEM) represents a technological evolution, allowing researchers to test more intricate mediational and causal models rather than just identifying associations. This paper fits into this timeline by employing advanced modeling techniques to synthesize various established motivational constructs into a single, comprehensive framework.

3.3. Differentiation Analysis

Compared to prior work, this paper's core innovations and differentiations are:

• Holistic Modeling: Most related work tends to focus on subsets of the variables investigated here (e.g., achievement goals and self-efficacy, or environmental factors and achievement goals). This study differentiates itself by building a single, comprehensive multifactorial path analysis model that simultaneously includes intrinsic motivators, environmental motivators, and personal traits to predict math performance. This allows for a more complete understanding of their combined and interactive effects.
• Focus on Elementary School Mathematics: While AGT and related concepts have been studied across various age groups, this paper specifically targets 5th and 6th-grade students and mathematics performance. The authors note that the nature and strength of goal-performance relationships can differ at various educational levels, making this specific focus valuable.
• Mediation Analysis Emphasis: The study places a strong emphasis on mediation analysis, explicitly hypothesizing and testing how personal traits (self-efficacy, interest) mediate the effects of achievement goals (both individual and environmental) on performance. This helps to resolve conflicting findings in previous literature regarding the direct impact of certain achievement goals. For instance, it investigates dual mediation paths where students' goals mediate first, followed by self-efficacy or interest.
• Empirical Validation of a Complex Model: The paper successfully validates a complex model with good fit indices, demonstrating the feasibility and utility of integrating numerous motivational and environmental factors into a coherent predictive structure for academic performance. This robust empirical validation of a broad model is a key differentiator.

4. Methodology

4.1. Principles

The core principle of this study is to move beyond examining isolated factors affecting academic performance and instead build a holistic, multifactorial model that captures the complex interplay of intrinsic motivators, environmental motivators, and personal traits on mathematics performance in elementary school students. The theoretical basis is rooted in Achievement Goal Theory (AGT), which posits that students' goal pursuits drive their behavior, complemented by theories on self-efficacy and interest. The intuition is that learning is not just about a student's personal drive, but also deeply influenced by how their environment (parents, teachers) shapes their goals and how these goals, in turn, affect their self-belief and engagement with the subject, ultimately impacting their performance. By using path analysis, the researchers aim to identify both direct and indirect (mediated) relationships within this complex system.

4.2. Core Methodology In-depth (Layer by Layer)

The methodology involved data collection through self-report scales and a custom math test, followed by statistical analyses including factor analysis, correlations, and path analysis.

4.2.1. Participants

• Recruitment: A cluster sampling method was used. From roughly 40 elementary schools in the greater Pafos province in Cyprus, 25 suitable schools were identified (excluding the smallest ones). Letters were sent to principals, and 22 granted consent.
• Selection: All 5th and 6th-grade students and their teachers from these 22 schools were invited to participate, conditional on parental consent. Approximately 50.5% of parents and all teachers provided affirmative responses. Verbal consent was also obtained from children.
• Sample Size: The final sample comprised 762 students.
• Demographics:
  • Age: 49.1% 5th graders (approximately 10–11 years old), 50.9% 6th graders (approximately 11–12 years old).
  • Gender: 48% boys, 51.2% girls, 0.8% missing.
  • Location: 50.8% from the city of Paphos, 34.1% from Pafos' suburbs, 15.1% from rural areas.
  • Additional Data: Basic demographic information (age, gender, academic grade), student/parent country of birth, duration of residence in Cyprus (for immigrants), household languages, parental occupational status, and educational level were also collected.

4.2.2. Materials (Measures)

The study used a student questionnaire and a mathematics test.

4.2.2.1. Student Questionnaire

A self-report questionnaire consisting of 46 statements from various normed scales, translated into Greek and back-translated, then adjusted for elementary school comprehension. A pilot study with 22 children ensured clarity. Responses were on a five-point Likert scale (from $1 = \text{"Strongly Disagree"}$ to $5 = \text{"Strongly Agree"}$). Factor analysis was used to verify scale validity. After averaging relevant statement scores, each factor ranged from 1 to 5.

The questionnaire was divided into three sections, presented in the same order: a) Students' achievement goals, self-efficacy, and interest in mathematics. b) Perceived classroom goals. c) Perceived parental goals. Statements within each section were randomly ordered.

• Individual Achievement Goals of Students:

  • Measured using the Achievement Goal Questionnaire (AGQ-R) (Elliot & Murayama, 2008).
  • The AGQ-R typically measures four goal types: mastery-approach, mastery-avoidance, performance-approach, and performance-avoidance.
  • For this study, mastery-avoidance goals statements were not used as they are less common at this age.
  • The questionnaire included nine statements, three for each of the remaining three goal types.
  • Mastery Goals (9 statements): Example: "My goal is to learn everything I am taught in mathematics."
  • Performance-Approach Goals (9 statements): Example: "My goal is to do well in mathematics compared to other students."
  • Performance-Avoidance Goals (9 statements): Example: "I try not to perform worse than others in mathematics."
  • In the original AGQ-R study on university students, reliability (Cronbach's alpha) was reported as $\alpha = 0.84$ for mastery-approach goals, $\alpha = 0.92$ for performance-approach goals, and $\alpha = 0.94$ for performance-avoidance goals.
  • Operational Definition: Each goal type was defined as the average of participants' scores on the relevant statements.

• Perceived Classroom Achievement Goals:

  • Measured using the Patterns of Adaptive Learning Scales (PALS) (Midgley et al., 2000), originally developed and validated on elementary school students.
  • Classroom Mastery Goals: Six statements. Example: "In our class, it is important to try hard in mathematics." (Original $\alpha = 0.76$)
  • Classroom Performance-Approach Goals: Six statements. Example: "In our class, the main goal is to get good grades in mathematics." (Original $\alpha = 0.70$)
  • Classroom Performance-Avoidance Goals: Five statements. Example: "In our class, it is very important to show others that you are not doing poorly in math assignments." (Original $\alpha = 0.83$)
  • Operational Definition: Mean scores for each type of classroom goal, ranging from 1 to 5.

• Perceived Parents' Achievement Goals:

  • Measured using the corresponding section of PALS (Midgley et al., 2000).
  • Parental Mastery Goals: Six statements. Example: "My parents want me to spend time thinking about the math I am learning." (Original $\alpha = 0.71$)
  • Parental Performance Goals: Six statements. Example: "My parents want me to show others that I am good at math assignments." (Original $\alpha = 0.71$)
  • Operational Definition: Mean scores for each category, ranging from 1 to 5.

• Self-Efficacy:

  • Measured using five statements from PALS (Midgley et al., 2000).
  • Example: "I am confident that I can find a way to solve even the most difficult math problems." (Original $\alpha = 0.78$)
  • Operational Definition: Mean of participants' responses to these five statements, ranging from 1 to 5.

• Interest:

  • Measured using seven statements developed by Elliot and Church (1997).
  • Example: "I think mathematics class is interesting." (Original $\alpha = 0.92$)
  • Operational Definition: Mean of responses to all statements, ranging from 1 to 5.

4.2.2.2. Mathematics Test

• Need: Due to the absence of systematic numerical grading in Cypriot elementary schools, a valid assessment tool was created.
• Development: Created by the first author (an experienced elementary math teacher) for each grade (5th/6th).
• Content: Each test included 14 math problems covering all five areas of the centrally defined curriculum for each grade, up to December (data collection Jan-Mar). Problems were similar in format to examples in curriculum and textbooks.
• Pilot Study: Conducted with three teachers and 22 students (15 5th, 7 6th graders) to identify and rectify comprehension challenges and content issues.
• Grading: All tests were graded by the researcher on a scale of 0 to 100.
• Teacher Evaluation: Teachers were also asked to grade each student in mathematics on a scale of 0 to 100 to provide a supplementary evaluation for face validity comparison.

4.2.3. Experimental Design

The study collected self-report data on:

1. Environmental Motivators: Perceived classroom and parental (mastery and performance) achievement goals.
2. Intrinsic Motivators: Individual (mastery and performance) achievement goals.
3. Personal Traits: Self-efficacy and interest in mathematics.
4. Dependent Variable: Math performance scores.

4.2.3.1. Data Analysis Plan

1. Initial Descriptive Analyses: For all data, including student demographics.
2. Factor Analysis: Performed on participants' responses for each normed questionnaire to verify validity and confirm the expected structure.
3. Internal Validity of Math Test: t-test comparisons and Pearson correlation analyses between student test scores and teacher grades.
4. Path Model Application and Improvement:
   • An initial full mediation model (Fig. 1/3.jpg) was first attempted.
   • If the fit was poor, a model including all possible direct and indirect effects was considered.
   • Residual errors of individual mastery goals and performance goals, as well as self-efficacy and interest (variables at the same level), were correlated based on modification indices.
   • Bootstrapping with 2000 samples was performed for bias correction.
   • Progressive simplification was applied by removing paths between non-significant variables to achieve the final model (Fig. 3/1.jpg).

4.2.4. Procedure

1. Approvals: Initial approval from the Center for Educational Research and Evaluation (C.E.R.E.), Directorate of Primary Education, Ministry of Education and Culture, and National Bioethics Committee of Cyprus.
2. Consent: Letters sent to school principals for consent. Teachers received study details. Consent letters distributed to students, and parents provided signed consent.
3. Data Collection Period: Second trimester (January-March) of the 2017-18 academic year.
4. Personnel: The researcher and 18 trained associate research coordinators (mainly teachers) oversaw consent form collection and data collection. Training included written instructions.
5. Anonymity: Students were assured of anonymity before questionnaire completion.
6. Timeline: 40 minutes for the questionnaire, 60 minutes for the math test (within a two-week window).
7. Correlation of Data: Class registration numbers were recorded on both questionnaires and tests to link responses.
8. Teacher Input: Teachers evaluated overall performance of each student in mathematics on a 0-100 scale.
9. Data Entry: All data (student/teacher responses, math test scores, teacher ratings) were recorded and entered into separate SPSS datafiles.

4.2.5. Model Fitting Process (Path Analysis)

The modeling process involved several steps:

1. Initial Hypothesized Model: The researchers started with an initial full mediation model (represented conceptually in Fig. 1 of the paper, but the actual model tested as a first step is shown in fig 2.jpg in the provided images), based on existing theory. This model assumed a hierarchical flow of influence.

   • This initial model's fit to the data was evaluated using several fit indices.
   • The paper reported: $\chi^{2}(24, 762) = 908.53, p < 0.001$, CFI $= 0.53$, RFI $= 0.11$, NFI $= 0.53$, PCLOSE $< 0.001$, RMSEA $= 0.22$, and CMIN/DF $= 37.86$. These values indicate a poor fit (e.g., CFI, RFI, NFI ideally $> 0.90$, RMSEA ideally $< 0.06$).

2. Exploration of All Possible Effects: Next, the researchers attempted to fit a model including all possible direct and indirect effects between the variables. This is a common approach to identify potential paths not captured by the initial theory-driven model.

3. Model Improvement with Modification Indices: The model was further improved by correlating residual errors of variables at the same level of analysis (e.g., individual mastery goals and performance goals, and self-efficacy and interest). Modification indices in path analysis software suggest potential improvements to model fit by adding paths (or correlations between errors) that are not currently included but would significantly improve fit. This step acknowledges that some variables might share unexplained variance.

4. Bootstrapping: Bootstrapping with 2000 samples was performed. This technique is used to estimate the sampling distribution of a statistic (like path coefficients or indirect effects) by resampling with replacement from the observed data. It helps in bias correction and provides more robust confidence intervals for parameter estimates, especially in mediation analysis (MacKinnon et al., 2004; Preacher & Hayes, 2004).

5. Progressive Simplification: Since the model with all possible effects likely had a poor fit or was overly complex, a progressive simplification approach was adopted. This involves iteratively removing non-significant paths (i.e., paths where the p-value was above a chosen significance level, typically $p > 0.05$). This process aims to create a more parsimonious model that still fits the data well, focusing only on the most influential relationships.

6. Final Model Evaluation: The resulting model (Fig. 3/1.jpg) was then evaluated for its fit.

   • The paper reported: $\chi^{2}(8, 762) = 30.77, p < 0.001$, CFI $= 0.99$, RFI $= 0.93$, NFI $= 0.99$, PCLOSE $= 0.19$, RMSEA $= 0.06$, and CMIN/DF $= 3.85$. These indices indicate an excellent fit for the final model, suggesting it effectively captures the underlying relationships in the data.

     An example of the initial model structure, which showed poor fit, is conceptually similar to this:

     Fig. 1 from the original paper, an initial model for the potential effects of intrinsic and environmental motivators, as well as personal traits, on math performance.

The actual initial full mediation model that demonstrated poor fit is shown in fig 2.jpg.

Fig. 2 from the original paper, showing the initial full mediation model of multifactorial influences on students' mathematical performance. Standardized $\beta$ values are presented, with statistically significant effects ($p < 0.05$) in bold.

The final, robust model, after simplification, is shown in fig 3.jpg.

Fig. 3 from the original paper, displaying the final model of direct and indirect multifactorial influences on students' mathematical performance. Standardized $\beta$ values are presented, with statistically significant effects ($p < 0.05$) in bold. Continuous arrows represent positive influences; dashed arrows represent negative influences. Additional indirect effects are mentioned in the main text to avoid an overly complicated graphical representation.

5. Experimental Setup

5.1. Datasets

The dataset for this study was collected directly by the researchers from 762 5th and 6th-grade students across 22 public primary schools in Cyprus. This is not a pre-existing public dataset but primary data collected specifically for this research.

• Source: Students and teachers from public primary schools in the greater Pafos province, Cyprus.
• Scale: 762 students.
• Characteristics:
  • Age: Approximately 10-12 years old (5th and 6th graders).
  • Gender: Balanced (48% boys, 51.2% girls).
  • Location: Represented urban, suburban, and rural areas of Pafos.
  • Immigrant Background: The paper mentions "the substantial percentage of students with immigration background" as a potential factor influencing findings, suggesting the dataset includes a diverse student population in terms of origin.
• Domain: Educational psychology, specifically focusing on mathematics performance and related motivational/environmental factors.
• Data Samples (Conceptual Examples):
  • Self-report statement (Interest): "I think mathematics class is interesting." (Rated on a 5-point Likert scale).
  • Self-report statement (Self-efficacy): "I am confident that I can find a way to solve even the most difficult math problems." (Rated on a 5-point Likert scale).
  • Math Test Problem: (Conceptual, not explicitly provided in the text, but mentioned as covering curriculum areas.) An example could be: "Solve for x: $2x + 5 = 15$." (For 6th grade) or "If you have 3 apples and buy 2 more, how many apples do you have?" (For 5th grade, simplified example).
• Why these datasets were chosen: The researchers specifically aimed to study elementary school students in Cyprus to build a comprehensive model relevant to that context, address the lack of systematic grading, and ensure representativeness within the chosen region. The use of self-report scales is standard for measuring psychological constructs like goals, self-efficacy, and interest, while the custom math test provided an objective measure of performance adapted to the local curriculum. This combination effectively validates the method's performance by linking self-reported psychological states to tangible academic outcomes.

5.2. Evaluation Metrics

The study used several statistical metrics to evaluate questionnaire reliability, test validity, and model fit.

5.2.1. Cronbach's Alpha ($\alpha$)

• Conceptual Definition: Cronbach's Alpha is a measure of internal consistency, or how closely related a set of items are as a group. It is considered a measure of scale reliability. A high $\alpha$ value (typically > 0.70) indicates that the items within a scale are measuring the same underlying construct.
• Mathematical Formula: $ \alpha = \frac{N^2 \bar{c}}{V + N(N-1)\bar{c}} \quad \text{or, more commonly, for standardized items:} \quad \alpha = \frac{N \cdot \bar{r}}{1 + (N-1)\bar{r}} $ Where the more common formula for non-standardized items is: $ \alpha = \frac{k}{k-1} \left(1 - \frac{\sum_{i=1}^{k} \sigma_{Y_i}^2}{\sigma_X^2}\right) $
• Symbol Explanation:
  • $k$: The number of items in the scale.
  • $\sigma_{Y_i}^2$: The variance of item $i$.
  • $\sigma_X^2$: The variance of the total score of the scale (sum of all item scores).
  • $N$: The number of items (in the simplified formula).
  • $\bar{r}$: The average inter-item correlation (in the simplified formula for standardized items).
  • $\bar{c}$: The average inter-item covariance (in the first formula).
  • $V$: The sum of all item variances (in the first formula).

5.2.2. Pearson Correlation Coefficient ($r$)

• Conceptual Definition: The Pearson correlation coefficient measures the linear relationship between two quantitative variables. It indicates the strength and direction of a linear association. The value ranges from -1 to +1, where +1 indicates a perfect positive linear relationship, -1 indicates a perfect negative linear relationship, and 0 indicates no linear relationship.
• Mathematical Formula: $ r = \frac{N \sum xy - (\sum x)(\sum y)}{\sqrt{[N \sum x^2 - (\sum x)^2][N \sum y^2 - (\sum y)^2]}} $
• Symbol Explanation:
  • $N$: The number of paired observations.
  • $\sum xy$: The sum of the products of the paired scores.
  • $\sum x$: The sum of the $x$ scores.
  • $\sum y$: The sum of the $y$ scores.
  • $\sum x^2$: The sum of the squared $x$ scores.
  • $\sum y^2$: The sum of the squared $y$ scores.

5.2.3. t-test ($t$)

• Conceptual Definition: A t-test is a statistical hypothesis test used to determine if there is a significant difference between the means of two groups. The paper uses it to compare the mean of the teacher's grades with the mean of the custom math test scores.
• Mathematical Formula (for dependent samples, as used for comparing two measures from the same students): $ t = \frac{\bar{D}}{\frac{s_D}{\sqrt{N}}} $
• Symbol Explanation:
  • $\bar{D}$: The mean of the differences between the paired scores (e.g., math test score - teacher grade for each student).
  • $s_D$: The standard deviation of these differences.
  • $N$: The number of paired observations (students).

5.2.4. Chi-squared ($\chi^2$)

• Conceptual Definition: In structural equation modeling and path analysis, the chi-squared test evaluates the discrepancy between the observed covariance matrix (from the data) and the covariance matrix implied by the proposed model. A non-significant $\chi^2$ value (i.e., high $p$-value, usually $p > 0.05$) indicates a good fit, meaning the model accurately reproduces the observed relationships. However, $\chi^2$ is very sensitive to sample size, often becoming significant even for good models with large samples.
• Mathematical Formula: The formula is complex and depends on the specific estimation method (e.g., Maximum Likelihood). Conceptually: $ \chi^2 = (N-1) [ \mathrm{log}|\Sigma(\theta)| + \mathrm{tr}(S\Sigma(\theta)^{-1}) - \mathrm{log}|S| - p ] $
• Symbol Explanation:
  • $N$: The sample size.
  • $S$: The observed covariance matrix.
  • $\Sigma(\theta)$: The implied covariance matrix from the model, which is a function of the model parameters $\theta$.
  • $p$: The number of observed variables.
  • $\mathrm{log}|\cdot|$: The natural logarithm of the determinant of a matrix.
  • $\mathrm{tr}(\cdot)$: The trace of a matrix.

5.2.5. Comparative Fit Index (CFI)

• Conceptual Definition: The CFI assesses the relative improvement in fit of the target model compared to a baseline model (often a null model where all observed variables are uncorrelated). Values range from 0 to 1, with values closer to 1 (typically $\geq 0.90$ or $\geq 0.95$) indicating a very good fit.
• Mathematical Formula: $ \mathrm{CFI} = 1 - \frac{\mathrm{max}(0, \chi^2_M - df_M)}{\mathrm{max}(0, \chi^2_B - df_B)} $
• Symbol Explanation:
  • $\chi^2_M$: Chi-squared value for the proposed model.
  • $df_M$: Degrees of freedom for the proposed model.
  • $\chi^2_B$: Chi-squared value for the baseline (null) model.
  • $df_B$: Degrees of freedom for the baseline model.
  • $\mathrm{max}(0, x)$: Returns the maximum of 0 and $x$.

5.2.6. Relative Fit Index (RFI) / Normed Fit Index (NFI)

• Conceptual Definition: Both RFI and NFI are incremental fit indices that compare the proposed model to a baseline model. NFI (also known as Bentler-Bonett Normed Fit Index) measures the proportion by which the model reduces the $\chi^2$ value compared to the null model. RFI (also known as Bollen's Relative Fit Index) is a modification of NFI that takes into account the number of degrees of freedom. Values closer to 1 (typically $\geq 0.90$) suggest a good fit.
• Mathematical Formula (NFI): $ \mathrm{NFI} = \frac{\chi^2_B - \chi^2_M}{\chi^2_B} $
• Symbol Explanation:
  • $\chi^2_B$: Chi-squared value for the baseline model.
  • $\chi^2_M$: Chi-squared value for the proposed model.

5.2.7. PClose (P-value for Close Fit)

• Conceptual Definition: PClose is the p-value for the test of close fit for RMSEA. It tests the null hypothesis that the RMSEA is $\leq 0.05$ (or some other specified value indicating close fit). A high PClose (typically $p > 0.05$) indicates that the model has a close fit to the data, meaning the hypothesis of close fit cannot be rejected.
• Mathematical Formula: No direct formula, it's a p-value derived from the RMSEA statistic.

5.2.8. Root Mean Square Error of Approximation (RMSEA)

• Conceptual Definition: RMSEA is an absolute fit index that estimates the discrepancy per degree of freedom. It measures how well the model approximates the population covariance matrix. Values less than or equal to 0.06 are generally considered to indicate a good fit, while values up to 0.08 indicate an acceptable fit.
• Mathematical Formula: $ \mathrm{RMSEA} = \sqrt{\frac{\mathrm{max}(0, \chi^2 - df)}{(N-1)df}} $
• Symbol Explanation:
  • $\chi^2$: Chi-squared value for the proposed model.
  • df: Degrees of freedom for the proposed model.
  • $N$: Sample size.
  • $\mathrm{max}(0, x)$: Returns the maximum of 0 and $x$.

5.2.9. CMIN/DF ($\chi^2/df$)

• Conceptual Definition: The chi-squared to degrees of freedom ratio is a common measure for assessing model fit, particularly useful with large sample sizes where $\chi^2$ often becomes statistically significant. A ratio of less than 2 or 3 (or sometimes 5) is generally considered to indicate a good fit.
• Mathematical Formula: $ \mathrm{CMIN/DF} = \frac{\chi^2}{df} $
• Symbol Explanation:
  • $\chi^2$: Chi-squared value for the proposed model.
  • df: Degrees of freedom for the proposed model.

5.3. Baselines

The paper does not compare its final model against external baseline models from other studies. Instead, its baseline for evaluation of model fit is the null model (a model assuming no relationships between variables, used in CFI, NFI, RFI calculations). More importantly, the paper internally compares its final, simplified model to an initial full mediation model that was hypothesized based on existing literature.

• Initial Full Mediation Model (Fig. 2/2.jpg): This served as the starting point, representing a more traditional, direct mediation approach. It was found to have poor fit indices.

• Model with All Possible Direct/Indirect Effects: An intermediate "baseline" that was too complex but allowed identification of crucial paths.

• Final Simplified Model (Fig. 3/1.jpg): This is the model proposed by the authors, achieved through progressive simplification (removal of non-significant paths) from the more complex models. It is the successful outcome of their iterative modeling process, demonstrating excellent fit.

  The comparison is therefore internal to the study's modeling process, showing that a theoretically driven, but simplified, path model effectively captures the data better than a simplistic or overly complex initial model.

6. Results & Analysis

6.1. Core Results Analysis

The study's results are presented in several stages: questionnaire reliability, math test validity, and finally, the comprehensive path analysis mediation model.

6.1.1. Questionnaire Reliability

After filtering out statements with low inter-item correlations ($r < 0.02$), the reliability of the scores for all variables was assessed using Cronbach's alpha.

The following are the results from Table 1 of the original paper:

• Interpretation: Most Cronbach's alpha values were acceptable or good (above 0.70). Some subscales, such as Mastery Goals ($\alpha = 0.63$) and Classroom Mastery Goals ($\alpha = 0.60$), and Parental Performance Goals ($\alpha = 0.67$), fell slightly below the commonly accepted threshold of $\alpha > 0.70$, but were still considered adequate (above 0.60). The authors note that similar lower alphas for AGQ-R subscales have been reported in other studies and adaptations, possibly due to language or cultural differences.
• High Mean Scores: Notably, Mastery Goals ($M=4.61$) and Classroom Mastery Goals ($M=4.51$) showed very high mean scores on the 1-5 scale, indicating a strong orientation towards mastery among students and a perception of teachers emphasizing mastery. Interest ($M=4.37$) and Self-efficacy ($M=4.24$) were also high. In contrast, Classroom Performance Goals ($M=3.10$) and Parental Performance Goals ($M=3.50$) had lower means.

6.1.2. Correlations Among Variables

The following are the results from Table 2 of the original paper:

** *p< 0.001 p< 0.05

• Interpretation: Most measures showed small to medium, statistically significant correlations.
  • Mastery Goals had strong positive correlations with Interest ($r = 0.53, p < 0.001$) and Self-efficacy ($r = 0.46, p < 0.001$).
  • Self-efficacy was also strongly correlated with Interest ($r = 0.53, p < 0.001$).
  • Classroom Mastery Goals and Parental Mastery Goals showed moderate to strong positive correlations with individual mastery goals, self-efficacy, and interest.
  • Classroom Performance Goals and Parental Performance Goals were strongly correlated with individual performance goals.
  • Interestingly, Math Test Score had significant positive correlations with Mastery Goals, Interest, Self-efficacy, Classroom Mastery Goals, and Parental Mastery Goals.
  • Crucially, Math Test Score showed negative correlations with Classroom Performance Goals ($r = -0.16, p < 0.001$) and Parental Performance Goals ($r = -0.19, p < 0.001$). This suggests that a perceived emphasis on outperforming others by the classroom or parents is negatively associated with actual math performance. Individual Performance Goals had a non-significant correlation with Math Test Score ($r = 0.03$).

6.1.3. Math Test Validity

• Comparison of Grades: The mean grade given by teachers ($M_1 = 78.55, SD_1 = 16.72$) was significantly higher than the mean grade of the researcher-created test ($M_2 = 62.39, SD_2 = 19.82$). This difference was highly significant ($\Delta_t(684) = -32.30, \Delta_p < 0.001$). Similar significant differences were found for both 5th and 6th graders.
• Correlation: Despite the mean difference, the scores from the math tests were significantly and strongly correlated with the teachers' subjective grades ($r = 0.78$). This strong positive correlation ($r = 0.81$ for 5th graders, $r = 0.76$ for 6th graders) demonstrates convergent validity, meaning both measures largely assessed the same underlying construct of mathematical competence. The math test scores were used in the mediation model as a more objective measure.

6.1.4. Mediation Model (Path Analysis)

The initial full mediation model (Fig. 2/2.jpg) showed poor fit: $\chi^{2}(24, 762) = 908.53, p < 0.001$, CFI $= 0.53$, RFI $= 0.11$, NFI $= 0.53$, PCLOSE $< 0.001$, RMSEA $= 0.22$, and CMIN/DF $= 37.86$. This indicated the need for refinement.

The final simplified model (Fig. 3/1.jpg), achieved through progressive simplification by removing non-significant paths and correlating residual errors, demonstrated excellent fit indices: $\chi^{2}(8, 762) = 30.77, p < 0.001$, CFI $= 0.99$, RFI $= 0.93$, NFI $= 0.99$, PCLOSE $= 0.19$, RMSEA $= 0.06$, and CMIN/DF $= 3.85$.

6.1.4.1. Key Findings from the Final Model (Fig. 3/1.jpg)

A. Extrinsic Motivator Influences (Row 1 to Row 2: Environmental to Intrinsic Goals):

• Classroom Mastery Goals had a strong positive direct effect on Individual Mastery Goals ($\beta = \mathbf{0.36}, p < 0.001$).
• Parental Mastery Goals had a moderate positive direct effect on Individual Mastery Goals ($\beta = \mathbf{0.20}, p < 0.001$).
• Parental Performance Goals had a strong positive direct effect on Individual Performance Goals ($\beta = \mathbf{0.31}, p < 0.001$).
• Classroom Performance Goals had a moderate positive direct effect on Individual Performance Goals ($\beta = \mathbf{0.18}, p < 0.001$).
• Notably, Parental Mastery Goals ($\beta = \mathbf{0.11}, p = 0.003$) and Classroom Mastery Goals ($\beta = \mathbf{0.15}, p < 0.001$) also had weaker but significant positive direct effects on Individual Performance Goals. This suggests that an emphasis on mastery can also, to some extent, foster performance-oriented goals.

B. Influences on Personal Traits (Row 2 & 1 to Row 3: Intrinsic/Environmental to Self-Efficacy/Interest):

• On Self-Efficacy:

  • Individual Mastery Goals had the strongest positive direct effect ($\beta = \mathbf{0.30}, p < 0.001$).
  • Parental Mastery Goals ($\beta = \mathbf{0.15}, p < 0.001$) and Classroom Mastery Goals ($\beta = \mathbf{0.15}, p < 0.001$) had moderate positive direct effects.
  • Individual Performance Goals had a weaker positive direct effect ($\beta = \mathbf{0.09}, p = 0.01$).
  • Indirect Effects (via Individual Mastery Goals): Classroom Mastery Goals ($\beta = \mathbf{0.11}, p = 0.001$) and Parental Mastery Goals ($\beta = \mathbf{0.06}, p = 0.001$) influenced self-efficacy indirectly through individual mastery goals.
  • Indirect Effects (via Individual Performance Goals): Classroom Mastery Goals ($\beta = \mathbf{0.01}, p = 0.004$), Parental Mastery Goals ($\beta = \mathbf{0.001}, p = 0.01$), Classroom Performance Goals ($\beta = \mathbf{0.02}, p = 0.005$), and Parental Performance Goals ($\beta = \mathbf{0.03}, p = 0.006$) all had indirect effects on self-efficacy through individual performance goals (though these effects were very small).
  • Summary for Self-Efficacy: Mastery goals (individual, classroom, parental) consistently had strong direct and indirect positive effects on self-efficacy.

• On Interest:

  • Individual Mastery Goals had a very strong positive direct effect ($\beta = \mathbf{0.45}, p < 0.001$).
  • Classroom Mastery Goals ($\beta = \mathbf{0.12}, p = 0.001$) and Parental Mastery Goals ($\beta = \mathbf{0.07}, p = 0.041$) had weaker positive direct effects.
  • Indirect Effects (via Individual Mastery Goals): Classroom Mastery Goals ($\beta = \mathbf{0.16}, p = 0.001$) and Parental Mastery Goals ($\beta = \mathbf{0.09}, p = 0.001$) influenced interest indirectly through individual mastery goals.
  • Summary for Interest: Similar to self-efficacy, mastery goals (individual, classroom, parental) significantly boosted interest. No significant direct or indirect influence on interest was observed from individual or classroom performance goals.

C. Influences on Mathematics Performance (Row 3 & 1 to Row 4: Personal Traits/Environmental to Performance):

• Direct Effects on Performance:

  • Self-efficacy had the strongest positive direct effect ($\beta = \mathbf{0.22}, p < 0.001$).
  • Interest had a positive direct effect ($\beta = \mathbf{0.11}, p = 0.01$).
  • Perceived Parental Performance Goals had a negative direct effect ($\beta = -\mathbf{0.18}, p < 0.001$).
  • Perceived Classroom Performance Goals had a negative direct effect ($\beta = -\mathbf{0.09}, p = 0.038$).
  • Crucially, there were NO significant direct effects on performance from individual (mastery or performance) achievement goals.

• Indirect Effects on Performance (Mediation):

  • Via Self-Efficacy:
    • Mastery Goals to Performance mediated by Self-efficacy ($\beta = \mathbf{0.07}, p = 0.001$).
    • Perceived Classroom Mastery Goals to Performance mediated by Self-efficacy ($\beta = \mathbf{0.03}, p = 0.001$).
    • Perceived Parental Mastery Goals to Performance mediated by Self-efficacy ($\beta = \mathbf{0.03}, p = 0.001$).
  • Via Interest:
    • Mastery Goals to Performance mediated by Interest ($\beta = \mathbf{0.05}, p = 0.003$).
    • Students' Perceived Classroom Mastery Goals to Performance mediated by Interest ($\beta = \mathbf{0.01}, p = 0.004$).
    • Students' Perceived Parental Mastery Goals to Performance mediated by Interest ($\beta = \mathbf{0.001}, p = 0.05$).
  • Dual Mediation Effects:
    • Mastery goals and Self-efficacy mediated the effects of Classroom Mastery Goals ($\beta = \mathbf{0.02}, p = 0.001$) and Parental Mastery Goals ($\beta = \mathbf{0.01}, p = 0.001$) on Performance.
    • Mastery goals and Interest similarly mediated the effects of Classroom Mastery Goals ($\beta = \mathbf{0.02}, p = 0.003$) and Parental Mastery Goals ($\beta = \mathbf{0.01}, p = 0.05$) on Performance.
    • Performance goals and Self-efficacy also mediated effects from Classroom Mastery Goals ($\beta = \mathbf{0.003}, p = 0.001$), Parental Mastery Goals ($\beta = \mathbf{0.002}, p = 0.009$), Classroom Performance Goals ($\beta = \mathbf{0.003}, p = 0.003$), and Parental Performance Goals ($\beta = \mathbf{0.01}, p = 0.004$) on Performance. These effects were very small.
    • The dual mediation of performance goals and interest did not yield significant indirect effects.
  • Summary for Performance: Self-efficacy and interest were the primary direct positive predictors of math performance. Crucially, mastery goals (individual, classroom, and parental) influenced performance indirectly through self-efficacy and interest. Conversely, perceived performance goals (classroom and parental) had a direct negative effect on math performance. Self-efficacy generally played a stronger mediating role than interest.

6.2. Data Presentation (Tables)

The study provides detailed descriptive statistics and correlation matrices.

The following are the results from Table 1 of the original paper:

The following are the results from Table 2 of the original paper:

** *p< 0.001 p< 0.05

6.3. Ablation Studies / Parameter Analysis

The paper describes a process akin to ablation studies or model simplification by iteratively refining the path analysis model.

• Initial Model (Fig. 2/2.jpg): The researchers first tested an initial full mediation model based on theoretical assumptions. This model represented a baseline of their hypothesis.
  • Result: It showed poor fit to the data, indicating that the initial theoretical structure was insufficient or incorrect in its direct causal assumptions.
• Progressive Simplification: Instead of adding components, the "ablation" here involved removing paths that were found to be non-significant in a more complex model that included all possible direct and indirect effects. This iterative removal of non-contributing paths led to a more parsimonious and accurate model.
  • Process: The model was refined based on modification indices and statistical significance of paths. Bootstrapping was used to ensure robustness of estimates.
• Final Model (Fig. 3/1.jpg): The resulting simplified model, with fewer paths than the initial complex version, demonstrated excellent fit to the data. This indicates that the identified significant paths are indeed the crucial ones explaining the observed relationships.
• Conclusion: This iterative process of testing an initial model, exploring all potential paths, and then simplifying by removing non-significant ones acts as an effective way to verify the components (paths) of the model and identify the most robust explanatory structure. It confirms that the complex interactions are best understood through mediation rather than solely direct effects, particularly for individual achievement goals on performance.

7. Conclusion & Reflections

7.1. Conclusion Summary

This research successfully developed and validated a holistic multifactorial path analysis model to understand the complex influences on mathematics performance in 5th and 6th-grade students in Cyprus. The model integrates environmental motivators (perceived parental and classroom goals), intrinsic motivators (individual mastery and performance goals), and personal traits (self-efficacy and interest). A key finding is that individual mastery goals do not directly predict mathematics performance but exert their positive influence indirectly through self-efficacy and interest. Self-efficacy and interest emerged as significant direct predictors of performance, with self-efficacy having a stronger mediating role. Conversely, perceived parental and classroom performance goals had a direct negative impact on mathematics performance. The study underscores the profound importance of fostering mastery goals and cultivating high self-efficacy and interest in students for improved academic outcomes.

7.2. Limitations & Future Work

The authors acknowledge several limitations:

• Methodology (Path Analysis): Path analysis assumes specific causal directions. The bidirectional nature of relationships among motivational variables (e.g., goals influencing self-efficacy, and self-efficacy influencing goals) might be more complex than a unidirectional path model implies. The chosen model represents the researchers' best theoretical and empirical fit, but alternative models could exist.

• Sampling: While the sample was representative of the Pafos district, it was limited to one of the five major districts of Cyprus.

• Cultural Specificity: The findings might be influenced by the specific cultural context of Cyprus, especially given the mentioned "substantial percentage of students with immigration background" and potential differences in the relevance of mastery goals compared to Anglosaxonic countries.

  Suggested future research directions include:

• Replication in Other Contexts: Replicating the study in other countries and cultural contexts to test the external validity and cultural invariance of the proposed model.

• Extension to Other Subjects: Applying the model to other academic topics besides mathematics to explore its generalizability.

• Older Age Groups: Studying older students (e.g., junior high school) to examine potential similarities and differences in goal-performance relationships across developmental stages, as the influence of performance goals may become more pronounced in higher grades where pressure is greater.

• Impact of Policy Changes: Investigating the model's predictive value if grading systems in elementary schools change (e.g., incorporation of numerical grading from early grades in Cyprus), which could alter students' achievement goal orientations.

7.3. Personal Insights & Critique

This paper provides a highly valuable contribution by offering a comprehensive, integrated view of motivational factors in elementary school mathematics. The use of path analysis to disentangle direct and indirect effects is a significant strength, moving beyond simple correlations to explain how different factors influence performance. The finding that mastery goals operate indirectly through self-efficacy and interest is particularly insightful and helps to reconcile some conflicting results in the AGT literature regarding the direct impact of mastery goals.

Transferability: The core methodology of building a multifactorial path model is highly transferable. This framework could be applied to:

• Other academic domains: Exploring factors influencing performance in language arts, science, or social studies.
• Different educational levels: Adapting the model for middle school, high school, or even university students, with adjustments for age-appropriate instruments and potentially more pronounced performance goal influences.
• Non-academic contexts: Investigating motivation and performance in areas like sports, artistic endeavors, or vocational training.

Potential Issues/Areas for Improvement:

• Self-Report Data: A common limitation for many studies in social sciences, self-report data can be subject to social desirability bias or limited self-awareness, especially in elementary school children. While the authors took steps to ensure comprehension, children's understanding of abstract motivational constructs can still vary.

• Causal Assumptions: While path analysis allows for testing hypothesized causal relationships, it does not prove causality. The model is a snapshot, and longitudinal studies would provide stronger evidence for the causal flow over time, particularly for the dynamic interplay between goals, self-efficacy, and interest. The acknowledged bidirectionality of some associations is a pertinent point.

• Operationalization of Performance Goals: The decision to consolidate performance-approach and performance-avoidance goals into a single performance goals factor, while justified by challenges with self-reporting in young children, might obscure some nuanced effects. Previous literature often distinguishes these, as their outcomes can differ. Future studies with more refined measures or different age groups might re-evaluate this distinction.

• Teacher Influence Measurement: Classroom goals were measured by student perception, not directly from teachers. While student perception is important, directly assessing teachers' stated goals and practices could provide another layer of validation or reveal discrepancies between teacher intent and student perception.

  Overall, the paper offers a robust and well-articulated model that reinforces the importance of creating learning environments that foster mastery, build self-efficacy, and ignite interest, rather than solely focusing on competitive performance. This provides clear, actionable guidance for educational stakeholders.