Positive Conditions for Mathematics Learning: An Overview of the Research

Math achievement for K–12 students in the United States has long lagged behind that of other nations and has been relatively stagnant for 8th graders on national assessments over the past 2 decades. The need to understand how teachers can better support math learning is particularly acute in the wake of pandemic-era learning disruptions, which impacted already low math performance more than other subject areas. According to multiple analyses, the negative effects of disrupted learning hit students hardest in districts and schools serving higher proportions of students from low-income families and historically marginalized racial and ethnic groups. Data from the 2024 National Assessment of Education Progress show that average student achievement has not yet fully rebounded.

The factors contributing to disparate outcomes in math achievement are complex. Systemic barriers abound, including students’ inequitable access to well-prepared math teachers, high-quality curriculum and instruction, and advanced coursework. Resolving systemic disparities in student access to quality math instruction will be essential to improving U.S. learning outcomes in math and will require the careful design and implementation of policies that address each of these conditions.

However, educators need not wait for the resolution of systemic issues to begin creating more equitable learning opportunities within their own classrooms. A significant and growing body of research suggests that what happens in the classroom greatly influences student achievement in math, particularly for those historically marginalized or excluded from math. Deepening our shared understanding of the classroom conditions that are most conducive to math learning will help pave the path toward math classrooms in which all students can thrive and achieve their potential.

Why Classroom Conditions Matter

Recent syntheses of research from the fields of neuroscience, psychology, and other developmental and learning sciences—commonly known as the science of learning and development—emphasize the impact of the classroom environment on student learning. This research finds that students learn best in environments in which they feel a sense of physical, emotional, and identity safety; hold positive relationships with adults and peers; and experience belonging, purpose, and affirmation. These positive conditions promote healthy development, supporting students’ cognitive growth and their physical, psychological, social, and emotional development. They can also help to counter the negative effects of stress and trauma, which impact the brain in ways that biologically impair learning.

In the classroom, teachers play a central role in establishing the daily learning conditions that students experience. Through interpersonal relationships, classroom management practices, and instructional strategies, teachers can attend to the social-emotional developmental needs of students. When students’ developmental needs for safety, positive relationships, belonging, and meaningful engagement are met, they are better positioned to engage with cognitively demanding learning experiences.

Attending to learning conditions in math classrooms is particularly important due to the prevalent fear and anxiety that students experience related to math. Math-related fear, often referred to as “math anxiety,” changes the way children’s brains respond to mathematical situations in ways that are counterproductive to learning. Unsurprisingly, researchers have linked the experience of math anxiety with numerous negative outcomes, such as reduced math achievement and a tendency to avoid college math courses and majors or career paths that require math. Creating math classroom environments that are more aligned with students’ developmental needs can help to resolve the common experience of math anxiety and thereby enable more positive and productive math learning experiences.

Overview of Brief

This brief synthesizes research findings from the fields of mathematics teaching and learning, educational psychology, and the learning sciences to identify key classroom conditions that matter for K–12 math learning. To organize discussion of the research literature, the brief is divided into four sections, each describing a different environmental condition that emerged as important for student learning. The literature provides evidence that students learn math best when they can do the following:

1. Experience positive relationships with their teachers

2. Feel a sense of belonging in their classroom community and the broader mathematics community

3. Adopt a growth mindset, meaning the belief that their mathematical ability can be cultivated through effort

4. Engage with high-quality instruction delivered by teachers who hold high expectations and offer strong supports for their success

The Importance of Positive Relationships

A large body of research has found that students who report positive relationships with their teachers tend to experience other positive academic outcomes, including elevated math achievement. Associations between teacher–student relationships and academic outcomes tend to be stronger for specific student groups—namely, students who identify as members of racial and ethnic minority groups or who came from lower-income families.

A subset of studies has examined how positive teacher–student relationships bolster student math learning and achievement. In general, studies find that positive relationships with teachers increase student self-efficacy, or their belief in their ability to accomplish specific math goals, with higher levels of self-efficacy linked to greater math achievement. A study of middle school students found that, in addition to increased self-efficacy, students who felt more emotionally supported by their teachers reported a greater sense of belonging and academic enjoyment and that these factors were associated with greater self-reported levels of academic effort. Other evidence suggests that when teachers’ actions communicate support of all students, student achievement increases with students’ level of engagement and as they develop a sense of “mathematics identity.” Mathematics identity refers to a student’s belief that they can successfully engage and perform in the math classroom and be socially recognized as someone who is mathematically capable.

Further evidence suggests that emotionally supportive teachers create environments in which all students, including those with doubts about their ability to succeed in math, feel safe to participate fully in the learning process. For instance, one study found that students who have low self-efficacy toward math typically report being less engaged in their math classes. However, when taught by emotionally supportive teachers, low-efficacy students reported similar rates of engagement as their more self-efficacious peers. The findings from this study suggest that emotional support from teachers can help to reengage students who initially come to class with lower confidence in their mathematical abilities, potentially by minimizing the feeling of inhibition that may otherwise keep them from participating fully in classroom activities and interacting comfortably with peers. Put differently, in emotionally supportive environments, students can feel safe to take academic risks in their learning and fully engage with classroom learning opportunities.

The Importance of Belonging

For students, the feeling that they are “personally accepted, respected, [and] included by others in the school social environment” helps to establish the classroom as a psychologically safe space for social and cognitive inquiry, experimentation, and growth. Developmentally, this is very important, particularly during adolescence. Numerous studies provide evidence that students who feel a sense of belonging in their school or classroom community tend to experience more positive social-emotional and academic outcomes, including greater engagement, educational motivation and attitude, self-concept, self-efficacy, and academic achievement. One researcher hypothesized that students who feel a sense of social belonging no longer need to exert effort “avoiding the negative appraisals of others or approaching material from a solely competitive framework” and thus can better focus on their learning.

A developing research base suggests that, in addition to social belonging, it is also important for students to feel a sense of “mathematics belonging,” or a sense that they are socially accepted as an able “doer” of math. Mathematics belonging matters, at least in part, to counter the prevalent gender- and race-based stereotypes about innate math abilities that many students internalize. A recent study of middle school students showed that their competency expectations and sense of mathematics belonging—operationalized as their math-related feelings of acceptance, level of comfort, enjoyment of participation, and trust that their teachers will help them learn—predicted their algebra learning, even when taking into account their prior algebra knowledge and self-concept. A follow-up study found that sense of belonging was the only significant predictor of student learning as measured on a pre/post-test of algebra skills, even when considering students’ socioeconomic status, perceptions of the importance of math, incremental view of math ability, and interest in math. Notably, this study also found that Black, Hispanic, and Indigenous students reported lower levels of belonging than their Asian and White peers, even though there were no differences in their prior algebra knowledge. Together, these findings suggest that practices that help students identify themselves as “part of the mathematics community” may help to promote student learning, particularly for students who are members of groups historically stereotyped as mathematically incapable.

The Importance of a Growth Mindset

Students’ beliefs about their ability to learn and succeed in math matter for their learning. Researchers and practitioners alike commonly discuss students’ beliefs about their ability to learn and succeed through the lens of mindset theory. This theory posits that students either ascribe to a “fixed” mindset, whereby they view ability and intelligence as static and innate, or a “growth” mindset, whereby they view ability and intelligence as malleable and able to be developed over time. The growth mindset perspective aligns with contemporary scientific understandings of how the brain works.

A growth mindset is positively associated with student math learning outcomes. In one large-scale study following students in 4th through 7th grades for a full academic year, researchers found statistically significant relationships between students’ growth mindset orientation and their math growth in the following school year. The researchers who ran the study estimated the effect of a strong growth mindset (relative to a fixed mindset) to be the equivalent of 23–31 additional days of learning. A follow-up study longitudinally followed students and found that positive changes in students’ self-reported growth mindset–oriented beliefs quickened their rate of growth on standardized math and English language arts achievement.

Among other social-emotional measures—including student self-efficacy, social awareness, and self-management—growth mindset had the strongest effect on student achievement growth in math. The role of growth mindsets may play a more important role for some students than others. Analyses of international data from the Programme for International Student Assessment (PISA) find that the benefits of having a growth mindset were greater for female, immigrant, and socioeconomically disadvantaged students.

Fortunately, research shows that interventions designed to teach students a growth mindset positively impact their math outcomes, with studies finding increases in general classroom motivation; math grades, particularly among lower-achieving students; achievement on math standardized tests, particularly for female students; and enrollment in advanced math courses following participation in growth mindset interventions. While the strength of the relationship between growth mindset interventions and academic achievement continues to be debated, meta-analyses find evidence that economically disadvantaged and academically high-risk students tend to benefit from these interventions, even if the effects on the overall student population are weaker. One recent study also found that the impact of growth mindset interventions on students’ math grades is greater when their teacher also has a growth mindset.

The Importance of High-Quality Instruction

Classroom learning conditions that allow students to feel emotionally safe, supported, and able to succeed establish the necessary preconditions for deep engagement in academic learning opportunities. However, these developmentally enabling classroom conditions must be coupled with high-quality math instruction in order for students to achieve their potential and thrive as mathematical thinkers, learners, and doers.

Teacher instructional practices matter for student learning, with multiple studies finding that teacher instructional practices have a stronger relationship with student math achievement than other factors, such as the quality of their relationships with students. High-quality math instruction requires students to move beyond the memorization and reproduction of algorithmic problem-solving methods. Instead, it involves “ambitious learning goals that are grounded in the expectation that all students will develop high-level thinking, reasoning, and problem-solving skills.”

This means that, in addition to procedural fluency, math instruction should support all learners in developing deep conceptual understanding that enables them to draw connections between different areas of math, model their mathematical thinking, strategically select methods that suit different contexts, and reason adaptively to solve challenging and authentic problems. It should also give students opportunities to grapple with mathematically challenging content, allow for well-structured collaboration, support the flexibility of students’ mathematical thinking and problem-solving, leverage students’ culture and experience as assets for learning, and include timely evidence-based intervention when needed. These practices bring students’ classroom activities more in line with the actual practices of working mathematicians and communicate the expectation that all students can engage with math at a high level. Indeed, students show greater growth in math achievement when they view their teacher as academically challenging, with an especially strong relationship between challenge and academic growth in classrooms with more African American students.

Conclusion

Both developmentally and cognitively, students benefit from learning math in classrooms that provide them with supportive relationships, a strong sense of belonging within the classroom and broader mathematics community, and a firm conviction in their capacity to grow their mathematical abilities through experience and practice. In such classrooms, students are better situated to benefit from high-quality math instruction. When experienced together, these positive classroom conditions set the foundation to promote math learning experiences that are characterized not by fear, but instead by the excitement of discovering mathematical relationships and grappling with challenging and meaningful problems in the context of a supportive classroom community. Positive learning conditions show promise for helping all students achieve their full potential in math. Notably, student groups that have been historically marginalized in math education—namely, female students, students of color, and students experiencing poverty—may stand to benefit most from a transition toward more developmentally nurturing classroom environments. Continued investigation into how positive K–12 classroom conditions impact student math learning and how teachers can cultivate these productive environmental conditions will be an important part of developing math teaching practices that help more students find success in and beyond their math classrooms.

Positive Conditions for Math Learning: An Overview of the Research (brief) by Julie Fitz and Heather Price is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

This research was supported by the Gates Foundation. Core operating support for the Learning Policy Institute is provided by the Carnegie Corporation of New York, Heising-Simons Foundation, William and Flora Hewlett Foundation, Raikes Foundation, Sandler Foundation, Skyline Foundation, and MacKenzie Scott. The ideas voiced here are those of the author and not those of our funders.