Positive Conditions for Mathematics Learning: An Overview of the Research

United States math achievement 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 mathematics 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. However, even prior to the pandemic, United States math performance outcomes have long featured significant racial and socioeconomic achievement gaps.

The factors contributing to disparate outcomes in math achievement are complex. Systemic barriers abound. In particular, these include students’ inequitable access to well-prepared math teachers, high-quality curriculum and instruction, and advanced coursework. Resolving systemic disparities in students’ opportunities to learn math 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 historically marginalized student groups. Deepening 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 emphasize the impact of the classroom environment on student learning. Commonly referred to as the science of learning and development (SoLD), this body of research finds that students learn best in environments where 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 both cognitive growth and 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.

Attending to learning conditions in math classrooms is particularly important due to the prevalent fear and anxiety that students experience related to 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.

Report Overview

This report synthesizes research findings from the fields of mathematics teaching and learning, educational psychology, and the learning sciences to identify key classroom learning conditions that matter for K–12 math learning. To organize discussion of the research literature, the report is divided into four sections, each describing a different classroom 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

Each section of the report reviews the research findings of greatest relevance for teachers and articulates research-supported practices that can foster positive math learning experiences.

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. Different studies found that positive teacher–student relationships increased student self-efficacy, intrinsic motivation for learning math, classroom engagement, and sense of mathematics identity—with each of these qualities linked to heightened math achievement. Other studies provide evidence that emotionally supportive teachers create environments in which all students, including those students with doubts about their ability to succeed in math, feel safe to participate fully in the learning process.

The literature also points toward several relationship-based approaches that can support improvements in students’ experiences within their math classrooms. For instance, teachers can:

• cultivate caring classroom relationships by providing sincere encouragement, creating space for students to share their personal identities and experiences, incorporating one-on-one teacher–student interactions, and explicitly communicating expectations;

• collect data on students’ perceptions of teacher–student relationships to monitor the quality of their classroom interactions; and

• couple classroom care and support with high expectations and quality instruction.

The Importance of Belonging

For students, the feeling that they are “personally accepted, respected, 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. 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 mathematical ability that many students internalize.

Teachers’ practices can influence students’ sense of social and mathematics belonging. For instance, teachers can:

• position students as mathematically competent during classroom interactions;

• support the development of positive and collaborative peer relationships; and

• examine their own beliefs about mathematical ability and cultivate more inclusive practices that communicate value for students as members of the classroom mathematics community.

The Importance of a Growth Mindset

Students’ beliefs about their abilities 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. 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. Growth mindset aligns with contemporary scientific understandings of how the brain works and positively associates with student math learning outcomes.

Fortunately, research shows that interventions designed to teach students a growth mindset positively impact their math outcomes, with particularly notable effects for economically disadvantaged and academically high-risk students. For instance, teachers can:

• learn more about what it means to have a growth mindset so that they can further establish a classroom context that encourages students’ own growth mindsets;

• provide students with explicit instruction about the malleable nature of human intelligence and ability;

• adopt teaching practices that reinforce a growth mindset orientation and equip students with strategies that help them learn and grow in response to failure; and

• collect data on students’ perceptions of their teacher’s growth mindset orientation.

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 for students to achieve to their potential and thrive as mathematical thinkers, learners, and doers.

Teachers, supported by well-designed curricular materials, can promote students’ mathematical growth and development through high-quality instruction. For instance, teachers can:

• emphasize conceptual understanding rather than algorithmic problem-solving;

• give students opportunities to grapple with mathematically challenging content that is within reach but that also allows them to creatively flex their skills and knowledge;

• create opportunities for well-structured collaborative learning;

• offer instructional tasks that allow for multiple means of solving, which better mirror real-world math problems and are more interesting and stimulating for students;

• provide culturally relevant and empowering learning experiences that leverage students’ assets to support, extend, and solidify their math learning; and

• include timely evidence-based interventions, when needed, to address student knowledge gaps and areas where they need additional skills development.

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 four 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 Conditions for Math Learning: An Overview of the Research 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 LPI 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. We are grateful to them for their generous support. The ideas voiced here are those of the authors and not those of our funders.