Teacher Perspectives and Math Achievement in Elementary Grades

Introduction

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.

Theoretical Perspectives

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, allowing 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 Social Cognitive Theory. Originally developed by Albert Bandura in 1986, this theory was primarily used to study how individuals learn in social contexts. It indicates that learning occurs through 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.

Bandura's (1997) comprehensive work described in 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 reveals the significance of teacher self-perception in shaping educational outcomes. Studies by Klassen and Tze (2014) found 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 and result in students struggling to apply mathematical principles to real-world problems. 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), revealing the importance of teacher self-efficacy in promoting student success.

The implications of Bandura's theory extend 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, positing that students learn best through collaborative activities with peers and instructors who provide guidance and support. Scaffolding—the temporary support provided by more knowledgeable peers to help learners complete tasks beyond their current level of competence—is gradually removed as learners become more proficient, 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 an important aspect of sociocultural theory (Chenowith, 2014). Culturally responsive teaching involves using instructional strategies tailored to the cultural backgrounds and experiences of diverse learners, recognizing that culture plays an essential role in shaping learners' perceptions of themselves and their place in the world. Evidence indicates that this approach 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 taught by 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 through real-world examples, diverse materials, and 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 student disengagement (Boaler, 2019). The transition from concrete to abstract thinking requires significant cognitive adjustments from students, and teachers must be able to adjust their instructional approaches accordingly to ensure adequate support during this critical phase. This misalignment between early and upper-grade pedagogy is a key theoretical gap explored in this review, indicating a need for educators to develop a better understanding of how students' cognitive abilities evolve over time (Goldstein, 2007). Addressing 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 and materials to meet individual needs (Goyibova et al., 2025). Another is Universal Design for Learning, which provides multiple means of granting all learners equal access to educational 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 socioeconomic 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 teachers frequently blame fixed ability. These divergent perceptions may exacerbate the achievement gap, as students 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 perceived natural ability. Lower-grade teachers tend to assume students will improve with time and appropriate support, while 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. Schools that implement equitable teaching practices take proactive steps toward dismantling biases present in the educational system. When teachers unconsciously communicate low expectations, students may disengage from learning, reinforcing cycles of underachievement. Thus, there is a need for equity-focused teaching practices that challenge deficit-based thinking and actively dismantle systemic biases. 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 demonstrate the need to address the intersectionality of educational experiences and the intertwined relationships among teacher perceptions, student identities, and classroom dynamics.

Instructional Factors

Instructional factors that researchers have examined in relation to 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 for understanding the overall scope of the problem and the current state of the research.

The role of teacher perspectives in shaping instructional practices and student outcomes is well-documented. Oppermann et al. (2019) examined preschool teachers' self-efficacy beliefs and their impact on teaching practices and student motivation. Using questionnaires, the researchers found that teachers who held strong beliefs in their own teaching abilities applied more effective teaching strategies, yielding higher levels of motivation among students. Their study demonstrated 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, highlighting the value of providing teachers with strong, well-structured materials to support their instructional capabilities.

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, fostering a sense of belonging among students and leading to increased participation and engagement. Furthermore, teacher perspectives can influence lesson planning, assessment, and feedback—all critical components of effective instruction (Arifin et al., 2024). By recognizing 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. Effective teachers are able to adapt their instructional strategies to meet the needs of their students and improve both 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, 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. On the other hand, if a teacher believes that mathematics is a problem-solving discipline requiring 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 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 affect how they assess student understanding and progress. Teachers who believe that learning is a gradual process requiring 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 help educational institutions pursue professional development opportunities that encourage 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, given their 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, collaborative group work, and 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 and support 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 and, through observations of teacher-student interactions, found that effective questioning strategies increased student engagement and enhanced their understanding of mathematical concepts. These findings reveal the importance of equipping teachers with techniques that promote critical thinking and active student participation.

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 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 gives teachers a clear framework to follow and helps students receive a comprehensive and cohesive education (Ainsworth, 2011). However, there are many ways to approach curriculum design. A flexible curriculum, for instance, allows for adaptability and responsiveness to the needs of diverse learners, whereas rigid adherence to static curricula prevents teachers from tailoring instruction to meet unique learner requirements (Ainsworth, 2011). By prioritizing student-centered approaches to curriculum design, educators can create learning environments that are engaging, relevant, 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 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. Effective curriculum design requires ongoing evaluation and refinement to ensure it remains relevant and effective in meeting the evolving needs of students and society (Ainsworth, 2011).

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 current with best practices, incorporate technology effectively, and develop innovative approaches to teaching and learning (Mohamed 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, and suggests that investing in teacher competency development can 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. Effective teacher competency development requires a sustained commitment to supporting educators throughout their careers (Guha et al., 2017).

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