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The CASEL Framework in Action: How Eureka Math® Integrates Social, Emotional, and Academic Learning

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by Great Minds

September 27, 2019
The CASEL Framework in Action: How Eureka Math® Integrates Social, Emotional, and Academic Learning

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Posted in: Aha! Blog > Eureka Math Blog > Eureka Math > The CASEL Framework in Action: How Eureka Math® Integrates Social, Emotional, and Academic Learning

By Joe Roicki and Andi Misemer with contribution from Ricky Mikelman

How does Eureka Math® integrate social-emotional learning with mathematics instruction?


The learning of mathematics has been defined to include the development of five interrelated strands that together constitute mathematical proficiency (National Research Council 2001):

  1. Conceptual understanding
  2. Procedural fluency
  3. Strategic competence
  4. Adaptive reasoning
  5. Productive disposition
... [P]roductive disposition is “the tendency to see sense in mathematics, to perceive it as both useful and worthwhile, to believe that steady effort in learning mathematics pays off, and to see oneself as an effective learner and doer of mathematics” (p. 131). Student learning of mathematics “depends fundamentally on what happens inside the classroom as teachers and learners interact over the curriculum” (Ball and Forzani 2011, p. 17).

Excerpted from Principles to Actions: Ensuring Mathematical Success for All (NCTM 2014)

Learning is a social process.1 Students’ social and emotional well-being is intimately connected to their academic success. Social and emotional well-being requires that students feel a sense of belonging and significance in the classroom and school environments and have a measure of autonomy or control over their learning.2 Research has demonstrated that students succeed when these needs are met and struggle when they are not.3 Academic success requires developing key social-emotional skills, such as how to communicate effectively with others, how to organize and manage tasks, and how to recover from setbacks or failures.4 These skills allow students to develop the productive disposition that is critical for learning mathematics. Schools must accordingly foster students’ social-emotional development in seamless integration with academic learning.5 In addition, researchers argue that academic success for students relies on educators’ identifying the most effective teaching practices and working collaboratively to implement them well across all of a student’s instructional experiences.6

Academic curricula play a central role in supporting the development of social-emotional competencies. The National Council of Teachers of Mathematics (2014) defines curriculum as “the program used to help students meet the standards, including instructional materials, activities, tasks, [modules], lessons, and assessments” (p. 70) and adds that “it is a coherent sequencing of core mathematical ideas that are well articulated within and across grades and courses” (p. 72).7 In mathematics classrooms, the curriculum allows for teachers and students to interact in a variety of ways. Teachers contribute to the curriculum by first understanding the mathematics both horizontally and vertically—horizontally in that teachers need an in-depth understanding of the mathematics of a particular grade or course and vertically in that they need to understand how the grade or course they teach fits into the progression of mathematics learning. Teachers also contribute to the curriculum by making informed decisions about the teaching practices that will most benefit student learning of the content. An effective curriculum can support teachers in this work by (1) providing teachers with a detailed description of the mathematics taught in each module in a grade or course and how the mathematics of that grade or course fits in the broader progression of mathematics understanding; (2) sequencing the mathematics coherently so that it builds logically across lessons, topics, and modules; and (3) illustrating how lessons might look, sound, and feel in a classroom with effective teaching practices.

Students contribute to the curriculum when they engage in tasks, activities, and exercises that are intended to develop their mathematical understanding. They also contribute to the curriculum when they engage in discussions with diverse groups to explain their thinking and reasoning and to consider and critique the thinking and reasoning of others. Through these learning experiences, students master the mathematical practices and the social-emotional competencies. An effective curriculum can support students in this work by (1) regularly providing tasks that promote reasoning and problem solving to help them make sense of new mathematical ideas and allow them opportunities to learn through productive struggle, (2) explicitly calling out points in lessons where they might pause to reflect on and discuss the mathematical learning that is taking place, and (3) providing opportunities for ongoing assessment and feedback to help them monitor their own progress over time.

EM Effective Student Learning

This document describes Eureka Math’s integration of social-emotional learning in the following sections:

  • Overview: How Eureka Math Builds SEL—an overview of SEL integration
  • Elaboration: How Eureka Math Builds SEL—a detailed table outlining the integration of the Mathematics Teaching Practices, Standards for Mathematical Practice, and Social-Emotional Competencies within the curriculum with the dual goals of developing students’ mathematical and social-emotional skills
  • Lesson Example: How Eureka Math Builds SEL—a sample lesson, annotated to illustrate SEL integration
  • Family and Community Connections: How Eureka Math Builds SEL—a description of the parent and community resources available in the Eureka Math curriculum

Overview: How Eureka Math Builds SEL

Eureka Math, a PK–12 mathematics curriculum, fosters the development of the five social-emotional competencies identified by the Collaborative for Academic, Social, and Emotional Learning (CASEL) through the interaction of eight Effective Teaching Practices (NCTM 2014) and eight Standards for Mathematical Practice (NGA Center and CCSSO 2010)8. The lists below provide descriptions of these competencies, teaching practices, and mathematical practices.

“A mathematics curriculum is enhanced when it is intentional about developing social and emotional learning (SEL) core competencies” (CASEL 2017).9 When curriculum and instruction explicitly promote all five core competencies, academic achievement is significantly increased, attitudes and behaviors improve, and emotional distress is reduced (Durlak et al., 2011).10

Social-Emotional Competencies

  1. Self-awareness. The ability to accurately recognize one’s own emotions, thoughts, and values and how they influence behavior; the ability to accurately assess one’s strength and limitations, with a well-grounded sense of confidence, optimism, and a “growth mindset.”
  2. Self-management. The ability to successfully regulate one’s emotions, thoughts, and behaviors in different situations—effectively managing stress, controlling impulses, and motivating oneself; the ability to set and work toward personal and academic goals.
  3. Social awareness. The ability to take the perspective of and empathize with others, including those from diverse backgrounds and cultures; the ability to understand social and ethical norms for behavior and to recognize family, school, and community resources and support.
  4. Relationship skills. The ability to establish and maintain healthy and rewarding relationships with diverse individuals and groups; the ability to communicate clearly, listen well, cooperate with others, resist inappropriate social pressure, negotiate conflict constructively, and seek and offer help when needed.
  5. Responsible decision-making. The ability to make constructive choices about personal behavior and social interactions based on ethical standards, safety concerns, and social norms; the realistic evaluation of consequences of various actions, and consideration of the well-being of oneself and others.

Source—Core Social-Emotional Competencies (

The eight mathematics teaching practices provide a framework for enhancing mathematics teaching and learning, and they are closely linked to the core SEL competencies. Teachers using these critical practices will help their students acquire a deeper understanding of mathematics.

Effective Teaching Practices

  1. Establish mathematics goals to focus learning. Effective teaching of mathematics establishes clear goals for the mathematics that students are learning, situates goals within learning progressions, and uses the goals to guide instructional decisions.
  2. Implement tasks that promote reasoning and problem solving. Effective teaching of mathematics engages students in solving and discussing tasks that promote mathematical reasoning and problem solving and allow multiple entry points and varied solution strategies.
  3. Use and connect mathematical representations. Effective teaching of mathematics engages students in making connections among mathematical representations to deepen understanding of mathematics concepts and procedures as tools for problem solving.
  4. Facilitate meaningful mathematical discourse. Effective teaching of mathematics facilitates discourse among students to build shared understanding of mathematical ideas by analyzing and comparing student approaches and arguments.
  5. Pose purposeful questions. Effective teaching of mathematics uses purposeful questions to assess and advance students’ reasoning and sense making about important mathematical ideas and relationships.
  6. Build procedural fluency from conceptual understanding. Effective teaching of mathematics builds fluency with procedures on a foundation of conceptual understanding so that students, over time, become skillful in using procedures flexibly as they solve contextual and mathematical problems.
  7. Support productive struggle in learning mathematics. Effective teaching of mathematics consistently provides students, individually and collectively, with opportunities and supports to engage in productive struggle as they grapple with mathematical ideas and relationships.
  8. Elicit and use evidence of student thinking. Effective teaching of mathematics uses evidence of student thinking to assess progress toward mathematical understanding and to adjust instruction continually in ways that support and extend learning.

Source—Eight Effective Mathematics Teaching Practices (NCTM 2014, p. 10)

The eight Standards for Mathematical Practice (MP) describe ways in which students engage in and interact with the content they learn in elementary, middle, and high school. As their maturity and expertise in mathematics grows, so too should their proficiency with these practices.

Standards for Mathematical Practice

  1. Make sense of problems and persevere in solving them.
  2. Reason abstractly and quantitatively.
  3. Construct viable arguments and critique the reasoning of others.
  4. Model with mathematics.
  5. Use appropriate tools strategically.
  6. Attend to precision.
  7. Look for and make use of structure.
  8. Look for and express regularity in repeated reasoning.

Source—Standards for Mathematical Practice (NGA Center and CCSSO 2010)

The five social-emotional competencies, the eight effective mathematics teaching practices, and the eight mathematical practices have much in common, especially in the areas of goal-setting, discourse, and productive struggle. When teachers establish goals that are part of learning progressions and communicate the what, how, and why of those goals (Teaching Practice 1), students develop the ability to monitor their own progress toward the intended learning outcomes as well as the ability to set personal, related goals (Self-management); they are also more likely to be motivated to make sense of problems and persevere in solving them (MP.1). When teachers facilitate discourse among students to build shared understanding of mathematical ideas (Teaching Practice 4), students develop the ability to consider others’ perspectives and understand social norms as well as the ability to communicate, listen well, and to seek and offer help when needed (Social awareness, Relationship skills, MP.3). Finally, when teachers provide students with opportunities to engage in productive struggle and support their work (Teaching Practice 7), students learn to recognize and process their emotions and thoughts while building confidence, optimism, a growth mindset (Self-awareness), and their competence with reasoning about, modeling, and using patterns (MP.2, MP.4, MP.8).

The Eureka Math curriculum was built from the ground up, incorporating the progressions of mathematical understanding described in the Progressions Documents for the Common Core State Standards (Arizona Board of Regents 2007) and the Common Core State Standards. By starting from scratch, the writers and consulting mathematicians had a unique opportunity to tell the story of mathematics cohesively from Prekindergarten through Grade 12, presenting mathematics as one body of knowledge rather than a collection of isolated activities.

At each grade level, the curriculum is organized into modules, topics, and lessons that progress logically and build on one another. Over the course of their studies, students master a variety of representations and thinking strategies that will guide their mathematical learning. The curriculum introduces and consistently uses specific structures and routines, which fosters students’ connections to one another and to their learning and allows them to feel safe enough to take the academic risks needed to be successful in the classroom. Each lesson arranges for students to interact with the teacher, the content, and one another in a variety of ways, including interactive fluency activities, collaborative problem solving, and daily reflection and debrief.

Beyond the integration of academic and social-emotional skills at individual grade levels, the curriculum is vertically aligned to foster social-emotional development over time. As the curriculum’s mathematics becomes more complex, so too does the complexity of social-emotional expectations across the PK–12 grade span. Initially, young students may be asked to respond chorally or turn and talk with a partner. As students progress, their choral responses become written responses in whiteboard exchanges and their turn-and-talk interactions become small group discussions or whole class discourse. Over time, students come to view themselves as authors of ideas whose contributions are valuable in the construction of shared mathematical understanding in the classroom.

Research has demonstrated the powerful and lasting effects of integrating academic, social, and emotional learning.11 Indeed, such integration is key to the success of Eureka Math. Students thrive because they have the pedagogical, social, and emotional support needed for rigorous academic learning. Moreover, with a strong foundation of social, emotional, and academic competence, students are prepared to succeed in all walks of life, not just in school.

Access the elaboration and rest of the CASEL framework in action in Eureka Math by submitting the form to download the free detailed analyses and infographic.

  1. Vygotsky, L. S. (1962). Thought and Language. Cambridge, MA: MIT Press.

  2. Maslow, A. H. (1970). Motivation and Personality. New York: Harper & Row.

  3. Adolphs, R. “Cognitive Neuroscience of Human Social Behaviour.” Nature Reviews Neuroscience. Vol. 4, No. 3, p. 165.

  4. Payton, J., R. P. Weissberg, J. A. Durlak, A. B. Dymnicki, R. D. Taylor, K. B. Schellinger and M. Pachan. (2008). “The Positive Impact of Social and Emotional Learning for

    Kindergarten to Eighth-Grade Students: Findings from Three Scientific Reviews.” Chicago, IL: Collaborative for Academic, Social, and Emotional Learning.

  5. Jones, S. M., and J. Kahn. (2017). “The Evidence Base for How We Learn: Supporting Students’ Social, Emotional and Academic Development,” National Commission on Social,

    Emotional, and Academic Development, The Aspen Institute.

  6. Ball, D. L, and F. M. Forzani. (2011). “Building a Common Core for Learning to Teach and Connecting Professional Learning to Practice.” American Educator 35, no. 2:17–21.

  7. National Council of Teachers of Mathematics (NCTM). (2014). Principles to Actions: Ensuring Mathematical Success for All. Reston, VA: NCTM, 70, 72.

  8. National Governors Association Center for Best Practices and Council of Chief State School Officers. (2010). Common Core State Standards for Mathematical

    Practice. NGA Center and CCSSO, Washington, DC.

  9. Collaborative for Academic, Social, and Emotional Learning. (2017). “Examples of Social and Emotional Learning in Elementary Mathematics Instruction.”

  10. Durlak, J. A., Weissberg, R. P., Dymnicki, A. B., Taylor, R. D. and Schellinger, K. B. (2011). “The impact of enhancing students’ social and emotional learning: A meta-analysis of school-based universal interventions.” Child Development, 82(1): 405–32.

  11. Durlak et al.; Jones et al.; Dusenbury, L., Weissberg, R.P., and Meyers, D.C. “Skills for Life: How Principals Can Promote Social and Emotional Learning in Schools.” Principal. (2016); Patrick, H., J. C. Turner, D. K. Meyer, and C. Midgley. “How Teachers Establish Psychological Environments During the First Days of School: Associations with Avoidance in Mathematics.” Teachers College Record 105: 1521–58; Deming, D. J. “The Growing Importance of Social Skills in the Labor Market.” The Quarterly Journal of Economics. Vol. 132, No. 4, pp. 1593-1640, 2015; Dodge, K. A., Bierman, K. L, Cole, J. D., Greenberg, M. T., Lochman, J. E., McMahon, R. J., and Pinderhughes, E. E. “Impact of Early Intervention on Psychopathology, Crime, and Well-Being at Age 25. American Journal of Psychiatry. Vol. 172, No. 1, pp. 59-70 (2014); Watson, M., and V. Battistich. “Building and Sustaining Caring Communities.” In Handbook of Classroom Management: Research, Practice, and Contemporary Issues,” ed. C. M. Evertson and C. S. Weinstein, New York: Routledge, pp. 253-80, 2006.

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Topics: Eureka Math