Cultural Pedagogy Mathematics Learners Literature Review

The decline in student mathematics performance between lower elementary grades (1–2) and upper elementary grades (3–4) is a critical concern in educational research and policy. Although foundational numeracy skills are typically established in early grades, disparities in performance often widen as students encounter more complex mathematical concepts. This literature review synthesizes existing research on the relationship between teacher perspectives and student achievement in mathematics, with a focus on identifying factors that contribute to this decline.  This chapter discusses theoretical frameworks, findings, and methodological approaches to contextualize the research problem.

Research on mathematics instruction has drawn attention to various factors that influence teaching practices and student learning outcomes. The research reveals significant themes in mathematics education, which can be categorized under instructional factors and individual factors. These interconnected dimensions shed light on how teacher perspectives, beliefs, instructional strategies, and student attributes influence the teaching and learning of mathematics. More shall now be said on this, beginning with the theoretical perspective used herein.

This study is grounded in multiple theoretical perspectives that collectively provide a comprehensive understanding of the factors influencing mathematics performance in upper elementary grades. The theoretical framework integrates Social Cognitive Theory (Bandura, 1986, 1997), Sociocultural Theory (Vygotsky, 1978), and Attribution Theory (Weiner, 1985) to analyze how teacher perspectives, instructional strategies, and student learning experiences shape mathematical achievement.

Social Cognitive Theory is particularly relevant because it explains how teachers\\\\\\\' self-efficacy beliefs influence their instructional decisions and, in turn, impact student motivation and achievement. Given that teacher confidence affects pedagogical choices, this framework helps to explore how instructional quality may contribute to the observed decline in math performance. Similarly, Sociocultural Theory highlights the role of social interaction, scaffolding, and culturally responsive teaching in shaping student learning experiences. It provides a lens through which to examine how early-grade instructional support may not always transition effectively into later elementary years. Finally, Attribution Theory is helpful in understanding how teachers perceive student ability and how these perceptions influence their instructional decisions, potentially reinforcing achievement gaps. Through the integration of these theories, this study provides a fresh and fuller perspective on the factors influencing mathematics performance. This approach will allow for a more complete analysis of how teacher beliefs, instructional strategies, and student experiences interact, so that more effective interventions can be developed to improve math education in upper elementary classrooms.

Analysis of the problem of declining mathematics performance in upper elementary grades is grounded in the Social Cognitive Theory. This theory was originally developed by Albert Bandura in 1986 and was primarily used to study how individuals learn in social contexts. The Social Cognitive Theory indicates that learning occurs in a social context with a dynamic and reciprocal interaction of the person, environment, and behavior. According to this theory, students\\\\\\\' learning and academic performance can be influenced by their social interactions, personal factors, and environmental factors, such as their teachers\\\\\\\' instructional strategies and competence.

The map depicted in Figure 1 below presents a visual overview of how the selected literature fits within the broader categories of instructional factors and individual factors, both of which potentially contribute to the problem statement under consideration. The hierarchical structure signifies the flow of topics under each category, ultimately connecting them to the problem statement.

Bandura’s (1997) comprehensive work went on to describe in more detail the theory of self-efficacy and how teachers’ confidence in their ability to instruct effectively directly influences student engagement and achievement. This concept is important in understanding the dynamics of teaching and learning, as it exposes the significance of teacher self-perception in shaping educational outcomes. Studies by Klassen and Tze (2014) reveal that teachers with high self-efficacy in mathematics are more likely to employ student-centered pedagogies, fostering deeper conceptual understanding. These pedagogies often involve collaborative learning, problem-solving, and critical thinking, which are essential for developing students\\\\\\\' mathematical literacy.

Conversely, teachers who doubt their competence often resort to rote instruction, which correlates with declining performance in upper grades (Stipek, 1996). Rote instruction focuses on memorization and repetition, rather than comprehension and application, which can lead to a superficial understanding of mathematical concepts. This approach can result in students struggling to apply mathematical principles to real-world problems, ultimately affecting their academic achievement. For example, a longitudinal study found that Grade 3 students taught by low-efficacy teachers scored 12% lower on problem-solving assessments than peers in high-efficacy classrooms (Goos & Beswick, 2021). This disparity reveals the importance of teacher self-efficacy in promoting student success.

The implications of Bandura\\\\\\\'s theory apply in other ways, too, such as when it comes to the shaping of teacher professional development and school policies. Teachers with high self-efficacy are more likely to seek out opportunities for professional growth, such as attending workshops or conferences, to improve their instructional skills (Martin et al., 2008). In contrast, teachers with low self-efficacy may avoid these opportunities due to feelings of inadequacy or fear of being evaluated (Friedman, 2000). Schools can support teacher development by providing resources and training that foster a sense of self-efficacy among educators (Bray-Clark & Bates, 2003).

Vygotsky’s (1978) sociocultural theory emphasizes the role of social interaction and scaffolding in learning. This theory posits that students learn best through collaborative activities with peers and instructors who provide guidance and support. According to Vygotsky (1978), scaffolding is an essential component of sociocultural theory. Scaffolding refers to the temporary support provided by more knowledgeable peers to help learners complete tasks that are beyond their current level of competence. As learners become more proficient, the scaffolding is gradually removed, allowing them to take on more responsibility for their own learning. Research has shown that effective scaffolding can have a positive impact on student learning outcomes (Doo et al., 2020). For example, Mercer (2013) found that teachers who used scaffolding techniques such as questioning, prompting, and feedback saw significant improvements in their students\\\\\\\' science scores.

In addition to scaffolding, culturally responsive teaching is also an important aspect of sociocultural theory (Chenowith, 2014). Culturally responsive teaching involves using instructional strategies that are tailored to the cultural backgrounds and experiences of diverse learners. This approach recognizes that culture plays an essential role in shaping learners\\\\\\\' perceptions of themselves and their place in the world. Evidence indicates that culturally responsive teaching can have a positive impact on student engagement and motivation (Ginsberg, 2015). A study by Howard and Terry (2011) found that African American high school students who received instruction from culturally responsive teachers reported higher levels of motivation and engagement than those who received instruction from non-culturally responsive teachers.

Wolfmeyer (2017) has shown that teachers who integrate collaborative problem-solving and culturally responsive strategies in Grades 1–2 build stronger mathematical foundations. These strategies involve incorporating real-world examples, using diverse texts and materials, and encouraging student discussion and feedback.

However, as curriculum demands shift in Grades 3–4 toward abstract concepts (e.g., fractions, multi-step equations), teachers may struggle to adapt scaffolding techniques, leading to disengagement (Boaler, 2019). The transition from concrete to abstract thinking requires significant cognitive adjustments from students. Teachers must be able to adjust their instructional approaches accordingly to ensure students receive adequate support during this critical phase. Overall, this misalignment between early and upper-grade pedagogy is a key theoretical gap explored in this review. The gap itself indicates a need for educators to develop better understanding of how students\\\\\\\' cognitive abilities evolve over time.

Some attention has been given by scholars to the problem of how to address the misalignment between early and upper-grade pedagogy, with evidence indicating that educators must develop more nuanced understandings of how students\\\\\\\' cognitive abilities evolve over time (Goldstein, 2007). This requires recognizing that learners progress through different stages of development at different rates (Jimenez et al., 2024). One approach is differentiated instruction which involves tailoring instructional methods materials to meet individual needs (Goyibova et al., 2025). Another approach involves Universal Design Learning, which provides multiple means for granting all learners with equal access to educative processes.

Weiner’s (1985) Attribution Theory provides a critical framework for understanding how teachers interpret student success or failure and how these interpretations shape their instructional decisions. According to this theory, teachers attribute student struggles to different causes, such as effort, ability, or external factors (e.g., home environment or socio-economic status). When teachers believe that students struggle due to lack of effort or external circumstances, they are more likely to provide additional instructional support or modify their teaching strategies. However, when teachers attribute difficulties to fixed ability, they may become less inclined to intervene, reinforcing existing inequalities and further limiting students\\\\\\\' opportunities for growth.

Studies by Wang and Hall (2018) found that teachers in lower grades often attribute math struggles to developmental readiness whereas upper-grade teach frequently blame fixed ability. These divergent perceptions may exacerbate achievement gap ,as internalize limiting beliefs (Zhang, 2022). If educators view certain groups as inherently less capable, they may inadvertently communicate lower expectations creating conditions where those expectations become reality. This phenomenon is particularly relevant in mathematics education, where students are often labeled as either \\\\\\\"math people\\\\\\\" or \\\\\\\"not math people\\\\\\\" based on their perceived natural ability. Wang and Hall (2018) indicate that lower-grade teachers tend to make assumptions about students, believing that they will simply improve with time and appropriate support. In contrast, upper elementary teachers more frequently attribute difficulties to innate ability, leading them to lower their expectations for struggling students. This shift in perception can exacerbate the achievement gap, as students internalize limiting beliefs about their own potential (Zhang, 2022).

Moreover, Pettigrew (1979) showed that attribution errors contribute to an environment of prejudice. The research findings suggest that schools that implement equitable teaching practices take proactive steps dismantling biases present educational system. When teachers unconsciously communicate low expectations, students may disengage from learning, reinforcing cycles of underachievement. Thus, there is the need for equity-focused teaching practices that challenge deficit-based thinking and actively dismantle biases in the educational system. Schools that adopt growth mindset approaches—emphasizing that intelligence and skills can be developed through effort and persistence—are better positioned to counteract these attribution biases and support all students in reaching their full potential (Pettigrew, 1979).

Overall, these theoretical frameworks show the need for addressing the intersectionality of educational experiences and how intertwined relationships are of teacher perceptions, student identities, and classroom dynamics.

Instructional factors that researchers have considered when researching this problem include teacher perspectives (Engledowl et al., 2021; Oppermann et al., 2019), beliefs (Kiliçaslan, 2023), instructional strategies (Yeh et al., 2019), approaches to curriculum (Bovill & Woolmer, 2019; Le Cornu, 2013), and teacher competency (Lee & Santagata, 2020; Mohamed et al., 2017). Each of these factors is important in understanding the overall depth of the problem and where the research is to date.

The role of teacher perspectives in shaping instructional practices and student outcomes is well-documented. For instance, Oppermann et al. (2019) examined preschool teachers\\\\\\\' self-efficacy beliefs and their impact on teaching practices and student motivation. The researchers used questionnaires to gather information from teachers; they found that those who held strong beliefs in their own teaching abilities applied more effective teaching strategies, which yielded higher levels of motivation among students. Their study revealed the important influence of teacher confidence and attitudes on classroom success and student engagement. Similarly, Engledowl et al. (2021) explored how elementary teachers\\\\\\\' use of curriculum materials relates to their expertise. Through surveys and classroom observations, the study found that effective utilization of curriculum resources positively correlated with teaching proficiency. This finding also showed the value of providing teachers with strong, well-structured materials to support their instructional capabilities.

The evidence indicates that teacher perspectives impact the overall learning environment (Arifin et al., 2024). When teachers possess a growth mindset and are confident in their abilities, they are more likely to create a supportive and inclusive classroom atmosphere. This, in turn, can foster a sense of belonging among students, leading to increased participation and engagement in academic activities. Furthermore, teacher perspectives can influence the way they approach lesson planning, assessment, and feedback, all of which are critical components of effective instruction (Arifin et al., 2024). Through a recognition of the importance of teacher perspectives, educational institutions can provide targeted support and professional development opportunities to help teachers refine their craft and improve student outcomes. Ultimately, acknowledging the role of teacher perspectives can be helpful in creating a positive and productive learning environment that benefits both teachers and students alike. Effective teachers are able to adapt their instructional strategies to meet the needs of their students and improve academic achievement and social-emotional growth (Arifin et al., 2024).

Another critical aspect of instructional factors is teacher beliefs about mathematics teaching and learning. Research indicates that teacher beliefs concerning optimal instructional strategies are important considerations in primary mathematics education (Kiliçaslan, 2023). Schoen and LaVenia (2019) examined three constructs of teacher beliefs and their influence on instruction. Using surveys and interviews, they identified that beliefs about the nature of mathematics, pedagogical approaches, and the learning process significantly impact how teachers design and implement lessons. These findings reveal the importance of supporting and nurturing positive and evidence-based beliefs among educators to improve mathematics instruction.

The way teachers perceive mathematics as a subject can greatly influence their instructional approaches. For instance, if a teacher views mathematics as a set of procedures to be memorized, they may focus on drilling formulas and equations into their students. On the other hand, if a teacher believes that mathematics is a problem-solving discipline that requires critical thinking and creativity, they are more likely to design lessons that encourage exploration, inquiry, and collaboration. Teacher beliefs about pedagogy also play a significant role in shaping their instructional practices. Teachers who believe in student-centered approaches tend to create learning environments that promote autonomy, self-directed learning, and peer-to-peer interaction (Schoen & LaVenia, 2019).

Moreover, teacher beliefs about the learning process can affect how they assess student understanding and progress. Teachers who believe that learning is a gradual process that requires effort, persistence, and feedback are more likely to use formative assessments to inform their instruction and adjust their teaching strategies accordingly (Schoen & LaVenia, 2019). In contrast, teachers who view learning as an innate ability may focus on summative assessments that primarily measure student achievement at the end of a lesson or unit (Schoen & LaVenia, 2019). Understanding the impact of teacher beliefs on instruction can give educational institutions better sense of how to pursue professional development opportunities that might help educators to reflect on their assumptions about teaching and learning (Kiliçaslan, 2023).

The significance of instructional strategies has also been a focal point of research. This is because instructional strategies play a crucial role in shaping elementary school students\\\\\\\' mathematics achievement (Yeh et al., 2019). Research has shown that interactive, student-centered approaches, such as problem-based learning and collaborative group work, or tools like Math Island, an online educational game, can significantly boost mathematical understanding and retention (Yeh et al., 2019). Likewise, the use of concrete manipulatives and visual representations, particularly in the early grades, has been found to improve students\\\\\\\' grasp of abstract mathematical concepts, in support of improved better overall performance in mathematics (Dahal et al., 2019). Dahal et al. (2019) investigated the role of questioning as an instructional tool in mathematics classrooms. Through observations of teacher-student interactions, the study found that effective questioning strategies increased student engagement and enhanced their understanding of mathematical concepts. Thus, Dahal et al. (2019) revealed the importance of equipping teachers with techniques that promote critical thinking and active participation among students.

The conceptualization of curriculum is another substantial factor in shaping the teaching and learning process. Bovill and Woolmer (2019) explored how curriculum design influences student-teacher co-creation. Through interviews and document analysis, they discovered that when teachers adopt flexible and inclusive curriculum models, students are more likely to collaborate effectively in the learning process. Their study helps to show the value of involving students in curriculum development to create a sense of ownership and engagement among learners.

The design of the curriculum can have a profound impact on the overall educational experience, as it dictates the content, structure, and delivery of instruction (Ainsworth, 2011). A well-crafted curriculum can give a clear framework for teachers to follow, and help students have a better opportunity to receive a comprehensive and cohesive education (Ainsworth, 2011). However, there are many ways to approach curricula design. For instance, a flexible curriculum can give a teacher room for adaptability and responsiveness in consideration of the needs of diverse learners. Rigid adherence to formal and static curricula will not let teachers to tailor their instruction to meet the unique requirements of their learners (Ainsworth, 2011). Thus, by prioritizing student-centered approaches to curriculum design, educators can create learning environments that are engaging, relevant, helpful, and effective. This flexible approach also acknowledges the importance of teacher autonomy, as educators are empowered to make informed decisions about instructional strategies and content (Ainsworth, 2011).

In addition, the way curriculum is implemented can significantly influence teacher-student relationships and classroom dynamics (Wubbels et al., 2014). When teachers are able to exercise creativity and flexibility in their teaching practices, they are more likely to establish positive relationships with their students, built on trust, respect, and mutual understanding (Le Cornu, 2013). This, in turn, can lead to increased student motivation, improved academic performance, and enhanced overall well-being. If they understand the importance of curriculum in shaping educational experiences, educators can work towards creating learning environments that are supportive, inclusive, and tailored to meet the diverse needs of all students (Le Cornu, 2013). Ultimately, a thoughtfully designed and implemented curriculum is valuable for providing high-quality education that prepares students for success in the real world. However, effective curriculum design requires ongoing evaluation and refinement so that it remains relevant and effective in meeting the evolving needs of students and society (Ainsworth, 2011).

Finally, teacher competency has emerged in recent research as a critical instructional factor (Mohamed et al., 2017). Teacher competency encompasses pedagogical skills, classroom management, and interpersonal relationships (Zhang & Tian, 2024). Teachers who possess a high level of competency are better equipped to create supportive learning environments, adapt instruction to meet diverse needs, and foster positive relationships with students (Lee & Santagata, 2020). Moreover, competent teachers are more likely to stay updated with best practices, incorporate technology effectively, and develop innovative approaches to teaching and learning (Mohamad et al., 2017).

Lee and Santagata (2020) conducted a longitudinal study to examine the relationship between novice teachers\\\\\\\' knowledge and the quality of math instruction. Using classroom observations and interviews, the study concluded that teachers with stronger content knowledge delivered higher-quality lessons, which positively impacted student learning outcomes. This research reinforces the necessity of targeted professional development programs to enhance teachers\\\\\\\' expertise and instructional practices. The researchers conclude that investing in teacher competency development can help educational institutions improve the overall quality of instruction, leading to enhanced student achievement and increased teacher satisfaction.

Furthermore, teacher competency is closely related to teacher retention and turnover rates (Guha et al., 2017). When teachers feel confident in their abilities and are well-supported by their schools, they are more likely to remain in the profession and continue to develop their skills. On the other hand, teachers who lack confidence or feel overwhelmed by their responsibilities may be more prone to burnout or leave the profession altogether (Guha et al., 2017). Therefore, it is essential for schools and educational leaders to prioritize teacher competency development through ongoing professional development opportunities, mentoring programs, and coaching support. In doing so, they can help take better care that teachers have the necessary skills and knowledge to provide high-quality instruction and support student success. Effective teacher competency development requires a commitment to supporting educators throughout their careers (Guha et al., 2017).

In addition to instructional factors, studies have highlighted the role of individual student characteristics in mathematics achievement. Student motivation was a recurring theme across multiple studies. For instance, El-Adl and Alkharusi (2020) investigated the interplay between self-regulated learning strategies, motivation, and math achievement. Using surveys, the researchers found that students who actively employed self-regulated learning techniques were more motivated and achieved higher academic success in mathematics. This underscores the importance of fostering self-regulation skills to enhance students\\\\\\\' learning experiences.

Xia et al. (2022) extended this line of inquiry by examining motivation, engagement, and achievement among Chinese primary students. Using surveys and tests, they identified a strong relationship between students’ motivation levels, their engagement in classroom activities, and their academic performance in mathematics. These findings highlight the interconnectedness of emotional and behavioral factors in shaping student success.

Another critical individual factor is self-efficacy, which refers to students’ confidence in their ability to succeed in mathematics. Falco (2020) conducted an intervention study targeting middle school students to enhance their math self-efficacy. Using pre- and post-tests, the study found that the intervention significantly improved students’ confidence and performance in mathematics. This finding underscores the importance of developing targeted programs to address students’ psychological barriers to learning.

The needs of students also depend heavily on the quality of teaching they receive. Kelcey et al. (2019) examined the effects of teacher mathematical knowledge, instructional quality, and student outcomes. Through a combination of classroom observations, interviews, and achievement data analysis, the study found that teachers with higher mathematical knowledge were better equipped to deliver high-quality instruction, leading to improved student performance. This research highlights the necessity of investing in teacher training to meet the diverse needs of students and improve educational outcomes.

These findings collectively illustrate the complex interplay between instructional and individual factors in mathematics education. Teacher-related elements, such as perspectives, beliefs, and competencies, directly influence instructional quality and classroom dynamics. In turn, these instructional practices shape students’ motivation, engagement, and achievement.

For instance, teachers with strong self-efficacy beliefs are more likely to employ effective questioning strategies and create engaging lesson plans, as shown by Oppermann et al. (2019) and Dahal et al. (2019). These practices, in turn, enhance student motivation and understanding, as evidenced by the findings of El-Adl and Alkharusi (2020) and Xia et al. (2022). Similarly, the use of well-structured curriculum materials and inclusive curriculum design facilitates active student participation, as demonstrated by Engledowl et al. (2021) and Bovill and Woolmer (2019).

Moreover, the relationship between teacher competency and student outcomes highlights the importance of professional development for educators. Teachers with a deep understanding of mathematical concepts are better equipped to address students\\\\\\\' needs and foster their academic growth, as shown in studies by Lee and Santagata (2020) and Kelcey et al. (2019). This underscores the need for comprehensive teacher training programs that address both content knowledge and pedagogical skills.

The insights gained from these studies have significant implications for educational practice and policy. To improve mathematics instruction, it is essential to focus on enhancing teacher self-efficacy, beliefs, and competencies. Professional development programs should prioritize building teachers\\\\\\\' confidence, equipping them with effective instructional strategies, and fostering positive attitudes toward mathematics teaching and learning.

Additionally, curriculum design should emphasize flexibility and inclusivity, allowing for greater student involvement in the learning process. By fostering a sense of ownership and collaboration, educators can create more engaging and meaningful learning experiences for students.

On the student side, interventions aimed at improving motivation, self-efficacy, and self-regulated learning strategies are crucial. Schools should implement programs that address students\\\\\\\' psychological and emotional needs, helping them develop the skills and confidence necessary for academic success.

Finally, policymakers should recognize the interconnectedness of instructional and individual factors in mathematics education. Investments in teacher training, curriculum development, and student support services are essential to creating a holistic approach to improving math achievement.

Despite the wealth of research on instructional and student-related factors influencing mathematics achievement in upper elementary grades, significant gaps remain in the literature. Many studies have explored teacher perspectives, beliefs, instructional strategies, curriculum approaches, and teacher competency (Engledowl et al., 2021; Oppermann et al., 2019; Kiliçaslan, 2023; Bovill & Woolmer, 2019; Lee & Santagata, 2020), as well as student-related factors such as motivation, self-efficacy, and engagement (Falco, 2020; Xia et al., 2022). However, much of the existing research has focused on these variables in isolation, failing to examine the intricate relationships between them. Further research should not only extend and refine these investigations but also explore the interplay between instructional and student factors, with particular attention to how these relationships evolve over time.

Extending Past Research: Examining the Interaction Between Instructional and Student Factors

Most prior studies have examined instructional or student factors as separate contributors to mathematics achievement, but there is a need for research that explores how these dimensions interact. For instance, teacher perspectives and instructional strategies are known to influence student motivation and engagement, yet there is limited empirical evidence on the reciprocal effects—how student engagement levels, in turn, shape teacher instructional choices. Future research should investigate:

1. How does student engagement and motivation influence teachers\\\\\\\' instructional decisions over time?

2. Do teachers with high self-efficacy adjust their teaching strategies in response to student engagement levels more effectively than those with lower self-efficacy?

3. What role does curriculum flexibility play in allowing teachers to adapt instruction based on student motivation and engagement?

By using longitudinal studies and classroom-based interventions, researchers could capture the dynamic nature of these interactions, providing deeper insight into how instructional strategies evolve in response to student behaviors and learning needs. This approach would extend past studies that have primarily relied on cross-sectional survey data (e.g., Yeh et al., 2019; Xia et al., 2022).

Differing from Past Studies: Investigating Grade-Level Transitions and Pedagogical Misalignment

Another key area for future research is the transition from early elementary mathematics (Grades 1–2) to upper elementary mathematics (Grades 3–4). Prior research has suggested that the shift from concrete, hands-on instruction in early grades to abstract mathematical concepts in later grades may contribute to declining performance (Boaler, 2019). However, limited studies have systematically examined the pedagogical misalignment between these grade levels and its effects on student achievement.

Future research should explore how instructional strategies differ between lower and upper elementary classrooms and how these variations impact student learning. In early elementary grades, teachers often rely on hands-on, concrete learning experiences, using manipulatives, real-world examples, and interactive activities to develop foundational numeracy skills. As students progress to upper elementary levels, instruction shifts toward more abstract mathematical concepts, often with a greater emphasis on procedural fluency and independent problem-solving. This transition can create a disconnect for students who struggle to bridge the gap between concrete and abstract reasoning, potentially contributing to declining engagement and performance. When viewing how these instructional shifts occur across different grade levels, researchers can identify best practices for making the transition more seamless and effective.

Another important question to investigate is the extent to which the shift from concrete to abstract instructional approaches contributes to disengagement and declining mathematics performance. Research suggests that many students experience difficulty adapting to more abstract mathematical concepts, particularly if they have not yet developed strong conceptual foundations in earlier grades. The challenge may be further compounded when teachers adopt instructional methods that do not align with students\\\\\\\' cognitive development stages. Understanding how and why disengagement occurs during this transition is essential for developing interventions that support students in maintaining motivation and confidence as they encounter increasingly complex material.

To address these challenges, future studies should examine what types of interventions can bridge the pedagogical gap between early and upper elementary mathematics instruction. Strategies such as increased scaffolding, the use of visual supports, and targeted curriculum adjustments may help ease the transition by providing students with structured support as they develop abstract reasoning skills. Comparative classroom observations and teacher interviews across different grade levels can offer valuable insights into instructional disconnects, while experimental studies testing the effectiveness of transition-oriented interventions could provide practical solutions for improving mathematics achievement. When identifying and implementing evidence-based strategies, researchers and educators can work toward a more cohesive instructional framework that supports student success throughout their elementary mathematics education.

Many existing studies on teacher perspectives, self-efficacy, and instructional strategies have been conducted primarily in Western educational contexts (e.g., Schoen & LaVenia, 2019; Stipek, 1996). However, educational practices, teacher training models, and student engagement norms vary significantly across different cultural and socio-economic settings. This variability suggests that findings from one region may not be universally applicable, highlighting the need to replicate these studies in diverse contexts. It is important to understand how teacher beliefs and instructional methods translate across different educational systems in order to better develop globally relevant strategies to improve mathematics achievement.

Future research should explore how teacher perspectives on mathematics instruction differ across cultures and educational systems. Variations in teaching philosophies, classroom structures, and assessment methods may influence how teachers perceive their role in facilitating student learning. Investigating these differences can provide insight into which instructional strategies are universally effective and which need to be adapted to specific cultural or socio-economic contexts. Additionally, research should assess whether teacher self-efficacy and instructional strategies have similar impacts on student motivation in non-Western settings. Previous studies have established strong correlations between teacher confidence and student achievement in Western schools, but it is unclear whether these relationships hold in educational systems that may place different emphases on teacher authority, student independence, or rote learning.

Another important area for investigation is the part that culturally responsive teaching can play in addressing disparities in mathematics achievement. Students from diverse backgrounds bring unique experiences and ways of thinking to the classroom, and instructional approaches that integrate cultural knowledge and real-world applications may enhance engagement and comprehension. Research should examine how culturally responsive teaching practices influence student motivation and performance, particularly in underrepresented or marginalized student populations.

Replicating Oppermann et al.’s (2019) work on teacher self-efficacy or Wang and Hall’s (2018) study on teacher attributions in different cultural settings would provide valuable insights into whether existing theories apply universally. Additionally, further research could explore whether growth mindset interventions—which have been shown to positively affect student motivation—have the same impact in under-resourced school districts compared to more affluent settings. If disparities exist, understanding the contextual factors that influence these interventions could help refine and tailor strategies to support students in diverse learning environments. It will help to extend research to other cultural settings to obtain a more comprehensive understanding of the factors influencing mathematics education and promote the development of inclusive, effective teaching practices worldwide.

To guide future research, it is helpful to identify key variables that influence mathematics achievement and develop testable research questions.

Instructional factors play a crucial role in shaping student achievement in mathematics. One important aspect is teacher perspectives, which include self-efficacy and how teachers attribute student difficulties in learning mathematics. Teachers\\\\\\\' confidence in their own instructional abilities and their perceptions of why students struggle can significantly influence their teaching approaches. Additionally, beliefs about mathematics, such as whether mathematical ability is fixed or malleable, affect the way teachers structure their lessons and support student learning. Instructional strategies are another key factor, as different methods—such as inquiry-based learning, direct instruction, and scaffolding—vary in effectiveness depending on students\\\\\\\' needs and classroom contexts. Furthermore, curriculum approaches, whether rigid or flexible, impact student engagement and achievement. Integrating real-world applications into the curriculum can make mathematics more relevant and accessible to students. Finally, teacher competency, which includes subject-matter knowledge and classroom management skills, is essential in delivering high-quality instruction.

Several research questions emerge when examining instructional factors in mathematics education. One critical question is how teachers’ beliefs about mathematics ability influence their instructional choices and student engagement. Understanding this relationship could inform teacher training programs and classroom interventions. Another important question is identifying which instructional strategies are most effective for maintaining student motivation in upper elementary mathematics. Since motivation plays a key role in learning outcomes, determining which teaching methods best sustain student interest and persistence in mathematical problem-solving is essential. Additionally, investigating how curriculum flexibility affects student achievement and engagement could provide insights into whether more adaptable instructional models lead to better learning outcomes.

In addition to instructional factors, student-related factors also contribute significantly to mathematics performance. Motivation is a central component, encompassing both intrinsic and extrinsic motivation as well as goal orientation. Students who are intrinsically motivated often demonstrate higher levels of persistence and curiosity, whereas extrinsically motivated students may rely more on external rewards to succeed. Another essential factor is self-efficacy, which refers to students\\\\\\\' confidence in their ability to solve mathematical problems. A strong sense of self-efficacy has been linked to greater perseverance and academic achievement. Engagement, including participation in classroom discussions and persistence with challenging problems, is also a key determinant of student success.

To further explore the impact of student factors on mathematics achievement, future research should address several important questions. One area of inquiry is the role of self-efficacy in mediating the relationship between teacher instructional strategies and student achievement. Examining how students’ confidence in their abilities interacts with various teaching methods could help refine instructional approaches to better support learning. Another critical question is how student engagement in early grades predicts later success in mathematics. Longitudinal studies tracking students from early to upper elementary grades could shed light on the long-term effects of engagement on academic outcomes. Finally, understanding whether student motivation affects mathematics achievement differently based on socio-economic background could provide valuable insights into equity in education, highlighting potential disparities and informing targeted interventions to support all learners.

To address the gaps identified above, future studies should employ mixed-methods approaches that combine quantitative measures (e.g., standardized test scores, survey data on self-efficacy and motivation) with qualitative insights (e.g., teacher and student interviews, classroom observations). Additionally, researchers should consider:

1. Longitudinal Designs – Tracking students and teachers over multiple years to examine how instructional factors and student engagement evolve.

2. Experimental and Quasi-Experimental Studies – Testing targeted interventions (e.g., teacher self-efficacy training, scaffolded instructional strategies) to determine their effectiveness in improving math achievement.

3. Cross-Cultural Comparisons – Investigating whether instructional and motivational factors operate differently across educational systems.

Building on existing research, future studies should extend current knowledge by exploring the interaction between instructional and student factors, examining transitions between early and upper elementary grades, and replicating findings across different cultural contexts. Additionally, new research should aim to refine the critical variables affecting mathematics achievement, incorporating longitudinal and experimental methodologies to develop actionable solutions. By addressing these research gaps, scholars and educators can work towards more effective teaching practices and policy recommendations that foster long-term improvements in mathematics education.

Research on instructional and student-related factors influencing mathematics achievement has contributed valuable insights, but several methodological shortcomings limit the generalizability and applicability of findings. Future studies must address these limitations while also incorporating strengths from previous research to improve study design, reliability, and impact.

One major shortcoming in prior research is the overreliance on cross-sectional studies, which capture data at a single point in time rather than tracking changes over an extended period. Many studies examining teacher perspectives, instructional strategies, and student motivation have relied on surveys or self-reported data collected at one time (Engledowl et al., 2021; Oppermann et al., 2019). While these studies provide useful snapshots of the relationships between instructional factors and student outcomes, they fail to capture how these relationships evolve over time. Without longitudinal data, it is difficult to determine causal relationships between teacher beliefs, instructional strategies, and student engagement. Future research should prioritize longitudinal designs that follow teachers and students over multiple years to assess how instructional practices and student learning trajectories develop.

Another limitation in past studies is insufficient experimental or quasi-experimental research to test interventions. Many studies establish correlations between variables, such as teacher self-efficacy and student motivation, but do not implement interventions to determine whether modifying one factor leads to improvements in another (Schoen & LaVenia, 2019). A stronger emphasis on experimental designs—such as randomized controlled trials (RCTs) or quasi-experimental studies—would allow researchers to test specific instructional strategies, professional development programs, or student engagement techniques in controlled settings. These methodologies would provide causal evidence for what works in improving math instruction and learning outcomes.

Additionally, many studies have relied on self-reported data from teachers and students, which can introduce biases. Teachers may overestimate the effectiveness of their instructional strategies or self-efficacy, while students might report engagement levels based on social desirability rather than actual experience. While self-reports provide valuable perspectives, they should be complemented with objective measures such as classroom observations, student performance data, and teacher instructional logs. Mixed-methods research that integrates both qualitative and quantitative approaches would improve reliability by triangulating data sources.

A further shortcoming is the lack of diverse and representative samples in many studies. Much of the existing research has been conducted in Western educational contexts, limiting the generalizability of findings to other cultural settings (Stipek, 1996; Wang & Hall, 2018). Educational systems vary significantly in terms of curriculum structure, teacher training models, and student expectations, which means findings from one region may not apply universally. Future studies should aim for greater cultural and socio-economic diversity in participant samples, ensuring that research findings are applicable across different educational settings.

Lastly, previous research has often overlooked the interplay between instructional and student-related factors, treating them as independent influences on mathematics achievement. Studies may focus solely on teacher beliefs or instructional strategies without considering how these interact with student engagement, motivation, and self-efficacy. Future research should use integrated models that examine these relationships holistically, recognizing that student outcomes are shaped by a complex combination of teacher practices, curriculum structures, and individual student characteristics.

While there are shortcomings to address, several strengths from previous research should be replicated to ensure robust study design and meaningful findings. One of the most valuable aspects of prior studies is the emphasis on teacher self-efficacy and instructional strategies as critical factors in student achievement (Oppermann et al., 2019; Kiliçaslan, 2023). Research has consistently demonstrated that teachers’ confidence in their instructional abilities influences their teaching methods, which in turn affects student motivation and engagement. Future studies should continue to explore interventions aimed at improving teacher self-efficacy, particularly those focused on fostering student-centered teaching approaches.

Another strength in previous research is the use of classroom observations to examine instructional practices in real-world settings. Observational studies allow researchers to assess how teachers interact with students, implement instructional strategies, and adapt to classroom challenges (Yeh et al., 2019). Replicating this approach in future research would provide a more accurate representation of teacher behavior compared to self-reported survey data alone.

Additionally, some studies have successfully incorporated student perspectives into their analyses. Understanding student experiences—such as how they perceive their teachers\\\\\\\' instructional strategies or their own self-efficacy in mathematics—adds depth to research findings (Xia et al., 2022). Future research should continue to integrate student voices through focus groups, interviews, and student self-assessments, ensuring that studies capture both teacher and learner perspectives.

Another methodological strength that should be replicated is the use of mixed-methods research designs, which combine quantitative data (e.g., standardized test scores, survey responses) with qualitative insights (e.g., interviews, case studies, classroom observations). Mixed-methods studies provide a richer, more comprehensive understanding of instructional and student-related factors, allowing researchers to explore not just whether an intervention is effective but also why and how it works.

Finally, studies that have explored culturally responsive teaching and equity in mathematics education should be expanded. Research has shown that integrating students’ cultural backgrounds and real-world applications into math instruction can enhance motivation and engagement (Howard & Terry, 2011). Future studies should build on this work by testing specific culturally responsive strategies in diverse educational settings and evaluating their impact on student learning outcomes.

To improve future research on mathematics instruction and student achievement, it is essential to address key shortcomings while replicating effective research strategies. Future studies should move beyond cross-sectional research and self-reported data by incorporating longitudinal designs, experimental studies, and objective measures such as classroom observations. Additionally, expanding research to include diverse cultural and socio-economic contexts will enhance the generalizability of findings. At the same time, strengths from previous research—such as a focus on teacher self-efficacy, classroom observations, student perspectives, and mixed-methods approaches—should be maintained and refined. By addressing these methodological concerns, future research can provide more actionable insights into how instructional and student-related factors interact to shape mathematics achievement, ultimately leading to more effective teaching strategies and improved student outcomes.