Cultivating Math Mindsets: Teaching Practices That Enable Equitable Classroom Learning

As a result of schooling disruptions related to the COVID-19 pandemic, students in the United States experienced significant declines in their math learning outcomes. This steep decline in math achievement has renewed attention on how to improve math instruction. Reducing math anxiety, improving students’ general interest in math, and addressing persistent racial and socioeconomic achievement gaps are each important components of this work. Research indicates that improving math classroom learning conditions is a promising avenue for addressing each of these goals.

Rethinking how to design a classroom learning environment in ways that better enable math learning is a complex task. Recent syntheses of research from the fields of neuroscience, psychology, and other developmental and learning sciences (often referred to as the science of learning and development) emphasize the impact of the classroom learning environment on students’ cognition and learning. Research also indicates that data on students’ perceptions about their classroom learning environment as well as school and district practices can further enable teachers to improve the classroom learning environment.

In particular, there is evidence that students learn math best when they experience these classroom conditions:

• positive relationships with teachers and peers,
• a strong sense of classroom and mathematics belonging,
• support in adopting a growth mindset, and
• opportunities to engage with high-quality instruction.

These positive classroom conditions particularly matter for students from historically marginalized groups and for all students during the middle school years, which is a time when students’ general school motivation and math engagement can sharply decline. Taken together, the evidence suggests that teachers can provide all students greater opportunities to thrive as math learners by cultivating positive learning conditions in math classrooms.

This study documents how 10 math teachers in five California middle schools promoted positive conditions for math learning. It provides examples of how teachers fostered positive relationships in the classroom, developed students’ sense of classroom and mathematics belonging, encouraged growth mindsets, and delivered high-quality instruction. In addition, this report discusses the extent to which data on students’ perceptions about their classroom learning environment and school and district practices enabled these teachers to foster a positive math classroom learning environment. These teachers’ experiences yield insights and practices that can inform how other teachers, school and district leaders, and policymakers might improve classroom conditions for all students.

Cultivating Positive Classroom Conditions for Learning Math

Drawing on teachers’ perspectives from interviews and classroom observations, the report begins by documenting how teachers cultivated each of the four positive classroom conditions in their middle school math classroom.

Fostering Positive Relationships

Positive relationships are developmentally important for student learning, and they help establish the classroom as a safe environment for intellectual exploration and growth. In their math classrooms, teachers in this study prioritized the development of positive relationships with students and between students. Teachers acknowledged that some students entered middle school with negative attitudes toward math due to their previous classroom experiences. The teachers viewed the relationships they cultivated with students as essential for helping students develop a more positive attitude toward math and aimed to establish the classroom as a safe, kind environment for learning. They also emphasized the importance of positive peer relationships for learning and engagement and worked to channel their students’ sociality into learning-focused collaboration, in part because they viewed student peers as coeducators who could help translate academic content. Classroom routines and norms helped sustain positive teacher–student relationships and peer relationships by making the classroom a welcoming, predictable environment. Some common examples included welcoming students at the door, structuring daily group work, and creating a space of learning without fear of ridicule or shame.

Developing Students’ Sense of Classroom and Mathematics Belonging

When students feel a sense of social belonging in their school or classroom community, they tend to experience more positive social-emotional and academic outcomes. This study illustrates how teachers made every student feel like they belonged as part of the classroom and mathematics community. Teachers gained and demonstrated knowledge of each student as an individual, created activities for students to connect on a personal level with their peers, established behavioral expectations that allowed students to feel safe to be themselves, and designed opportunities so that every student could contribute to the classroom math community.

In addition to general social belonging in school, it is important for students to feel a sense of “mathematics belonging.” To cultivate their sense of mathematics belonging, teachers explicitly communicated to their students that each and every student could be successful at math, routinely recognized students’ abilities as mathematical thinkers in front of their peers, and looked for opportunities to highlight the learning and success of students who doubted their abilities to succeed mathematically.

Encouraging Growth Mindsets

Students’ beliefs about their ability to learn and succeed in math matter for their learning. Those who embrace a growth mindset tend to have better learning outcomes in math than those who think that ability and intelligence are static and innate.

In their classrooms, the teachers in this study adopted different strategies to encourage and reinforce growth mindsets. One strategy was to repeatedly communicate to their students the conviction that each and every student can grow their mathematical abilities. Teachers also described regularly reminding students that learning math is a process and that it is typical not to experience success right away. At the same time, nearly half of the teachers described emphasizing to their students that learning does not happen automatically—it requires them to take risks, try new approaches, and exert sustained effort. In addition to explicitly communicating ideas related to growth mindset, teachers implemented classroom practices that implicitly reinforced a growth mindset toward math learning, including through their approach to collaborative work, praise of students’ problem-solving processes, and use of mastery-oriented assessments.

Delivering High-Quality Instruction

High-quality math instruction is essential for creating a classroom environment in which students can fully engage in learning math. Teachers’ instructional approaches integrate research-based strategies to learn math content by incorporating students’ relationships, sense of belonging, and mindset. Together, students can fully engage with, make meaning of, and benefit from well-designed math learning experiences.

When asked to share which of their instructional practices they believed matter most for students’ math learning, teachers in our study often pointed to similar practices. These practices included designing direct instruction in short, manageable chunks; developing students’ conceptual understanding; activating students’ prior knowledge when introducing new concepts; providing ongoing feedback as students practice skills and solidify their knowledge; and supporting math language development through discussion of mathematical ideas and problem-solving strategies.

Using Data to Understand Student Perceptions About Learning Math

Research also suggests that monitoring how students perceive their classroom learning environment may be an important component to optimizing their experiences. The majority of teachers in this study indicated that their most important data sources for understanding students’ feelings about math and their classroom learning conditions were based on their own observations—by noticing and interpreting student behavior and engagement. Some teachers also mentioned how their direct conversations with students offer another important data source. All teachers supplemented this informal data with more formal, recorded student survey data. Access to timely, disaggregated data remained rare, limiting teachers’ ability to identify instructional inequities that may occur between different groups of students.

Teachers discussed using formal and informal data on their students’ perceptions of classroom conditions to shift lesson design, modify classroom norms and practices, and identify students for personalized intervention. Teachers also identified a number of challenges that inhibited their integration of data, most notably their already heavy workload. For formal survey data, teachers shared that the practice of reporting student responses at the school or grade level made it difficult to use these data to inform improvement for the specific students they taught.

School- and District-Level Conditions Supporting Math Teachers

School and district conditions influence teachers’ abilities to establish positive classroom learning conditions. At the district level, teachers highlighted that resources supporting their math teaching practices included professional development, instructional materials, and math coaches. Teachers viewed some district-level structures, such as pacing calendars and standardized assessments, as impediments to establishing positive classroom learning conditions when these structures pressured them to rush through material with little regard for student mastery. At the school level, teachers appreciated in-classroom support staff to help personalize instruction to individual student needs. Teachers also valued collaboration with colleagues and noted the impact when leaders set strong norms around collaboration time and developed structures to guide improvement-focused conversations between teachers.

Conclusions and Policy Considerations

This study shows how fostering positive relationships, developing students’ sense of belonging, and encouraging growth mindsets can occur simultaneously with and reinforce high-quality instruction. This study highlights how teacher training, collaborative opportunities, and support from school leadership and other instructional staff further enable teachers to cultivate positive classroom conditions for students to engage with and learn math. The findings also underscore the need for practical, teacher-driven data tools and professional supports to enhance teachers’ math teaching practices.

The findings from this report point to ways that state policymakers can support teachers in cultivating classroom conditions that are more conducive to math learning. They can:

• issue curriculum and instructional guidance for educators that articulates the importance of positive classroom conditions for students’ math learning,
• ensure that teacher education programs instruct future teachers about the importance of positive classroom conditions for students’ math learning so they can create these conditions in their own classrooms, and
• allocate funds at the state level for professional learning to support in-service math teachers.

District and school leaders seeking to support improvements in math learning have opportunities to:

• establish a shared vision for excellent math instruction that includes positive classroom conditions for math learning as an essential feature and
• support data-informed reflection on classroom learning conditions.

Cultivating Math Mindsets: Teaching Practices That Enable Equitable Classroom Learning by Heather Price and Julie Fitz is licensed under the 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 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.