Topics: Eureka Math Squared

Supporting Educators in Improving Practice Through Instructional Materials

Alyssa Buccella

by Alyssa Buccella

December 12, 2022
Supporting Educators in Improving Practice Through Instructional Materials

every child is capable of greatness.

Posted in: Aha! Blog > Eureka Math Blog > Eureka Math Squared > Supporting Educators in Improving Practice Through Instructional Materials

Can curriculum and instructional materials be developed to not only support students in building knowledge and skills, but also support educators in honing their practice? Educative curriculum materials help teachers acquire new content and pedagogical knowledge, typically through embedded notes, annotations, and models of practice. The presence of educative features in a curriculum has been shown to improve teachers’ instructional planning and curriculum implementation as well as student learning.

Defining Educative Curriculum Materials
In 1996, Ball and Cohen introduced the concept of educative curriculum materials in their seminal paper, which suggested that curriculum resources themselves had the potential to support not only students’ learning but teachers’ learning as well. This idea differentiated educative curriculum materials from those that mainly focus on instruction without developing teachers’ own content and pedagogical knowledge.

For example, teachers using highly educative mathematics curriculum materials are more likely to identify the big ideas in a curricular program while planning collaboratively and are more likely to maintain cognitive demand and elicit student thinking during a lesson (Stein and Kaufman 2010). Research also suggests that teachers who use educative curriculum materials show increases in pedagogical content knowledge and use a greater number of strategies to support student learning (Schuchardt et al. 2017).

In 2005, researchers Elizabeth A. Davis and Joseph S. Kracjik—who was also a Next Generation Science Standards writing team leader—offered five design principles to help guide the development of educative curriculum materials, stating that educative resources should do the following:

  • Support teachers’ learning of subject matter.
  • Help teachers anticipate what learners might say or do in response to activities.
  • Help teachers consider how to relate units throughout the year.
  • Make curriculum developers’ pedagogical judgments visible.
  • Promote a teacher’s capacity to make pedagogical adaptations for learners.

All Great Minds® curricula were intentionally and uniquely designed to contain educative elements because we believe in empowering teachers to not only deliver a high-quality curriculum, but also to effectively adapt it to meet the unique needs of the students in their classroom. Unlike a scripted curriculum where content is provided to educators with little to no guidance or rationale, our educative curricula help teachers improve their practice while enabling all students to achieve greatness.

Seven Educative Features Embedded in Eureka Math

The Eureka Math2 Teach book—the Teacher Edition for each module in the curriculum—is the core resource that teachers use to plan for and deliver instruction. Crafted by our team of teacher–writers, the Teach book includes seven educative features that support teachers own learning and help them achieve flexible, high-quality math instruction for all students.

 1. Module Overviews

The Teach book for a module begins with the Overview, a topic-by-topic summary that shows the development of learning throughout the module. It also provides connections to the work done before and after the module, helping teachers understand the module’s underlying structure, flow of the content, and coherence of the different parts of the curriculum.

Eureka Math - Before and After Module + Overview – 1

“As a teacher, I have learned so much more about how to teach math in this one year [using Eureka Math2]—it’s just unbelievable. I was always told ‘Here’s the formula. Use it, and don’t ask why. Just do it’… But now I’m understanding the why, and it’s helping me to be a better teacher because I understand what I’m teaching. Instead of saying ‘I know it works, but I can’t tell you why it works or where it came from,’ now I actually understand it.”  

—Teacher, Calcasieu Parish Public Schools, LA

2. The Why

Each module also includes a Why section that highlights and explains elements of the mathematics in the module to give teachers insight into decisions made during the writing of the module and the reasoning that concepts are taught in a particular way.

Eureka Math Squared - Book Sample Image - The Why

“I love the why. There was one time I was questioning why we didn’t teach something differently and then I read the why of it, and it helped me understand the reason behind the lesson. Most of the time I agree with the why, or it helps me understand why we set the lessons up the way we do.”  

— Tonya Hill, Grade 3 Teacher
Paragould School District, AR


3. Topic- and Lesson-Level Support

Within a module, small groups of related lessons are organized into topics. Each topic begins with a detailed Topic Overview that is a summary of the learning in that topic and typically includes information about how the content connects to previous or upcoming content. A Progression of Lessons chart shows a list of the lessons in the topic along with sample, student-friendly statements of each lesson’s major learning.

Finally, each lesson begins with a two-page Lesson Overview to help teachers prepare to teach that lesson, which includes the following:

EM2_Topic-Lesson-Level_Supports_Progression of Lessons Sample

  • The Lesson at a Glance, which provides a snapshot of the lesson’s learning outcomes, tools, representations, and terminology.
  • Key Questions to help focus teachers’ instruction and classroom discourse.
  • The Exit Ticket, which is a formative assessment given at the end of the lesson.
  • Achievement Descriptors (AD) that are standards-aligned and detail what students should know and be able to do based on instruction. Each AD also has its own set of proficiency indicators that are more detailed and help teachers evaluate what they see in the classroom and in students’ written work

Eureka Math is an educative curriculum that teaches teachers how to do math…Last year we were going so fast. This year we were into customization and prep. We used to hear, ‘Math is not my subject.’ We’re not hearing that anymore. Instead, they’re taking the lessons and making them their own.”

—Julia Alvarez, Director of Mathematics
IDEA Public Schools

4. Margin Notes

There are several types of instructional guidance that appear in the margins throughout the Eureka Math2 Teach book. These notes provide information about facilitation, differentiation, and coherence. For example:

EM2_Margin Notes_Fluency_Teacher Note Samples

  • Teacher notes communicate information that helps with implementing the lesson. Teacher notes may enhance mathematical understanding, explain pedagogical choices, give background information, or help teachers identify common misconceptions.
  • Differentiation suggestions provide targeted ways to help meet the needs of specific learners based on teachers’ observations or other assessments. There are two types of suggestions: support and challenge. Teachers can use these to support students in the moment or to advance learning for students who are ready for more of a challenge.
  • Language support provides ideas to help students with receiving (reading and listening) and producing (speaking and writing) English in mathematical contexts. Suggestions may include ways to promote student-to-student discourse, define new and familiar content-specific terminology or academic language, or clarify multiple-meaning words.
  • Universal Design for Learning (UDL) suggestions offer strategies and scaffolds that address learner variance. These suggestions promote flexibility with engagement, representation, and action and expression— the three UDL principles described by CAST. These strategies and scaffolds are additional suggestions to complement the curriculum’s overall alignment with UDL Guidelines. 

5. Lesson-Level Sample Solutions

Eureka Math Squared_Book Sample

Sample Solutions are examples of answers to problems students will engage with during a lesson. Although specific solution paths are provided, teachers are also encouraged to accept accurate responses, reasonable explanations, and equivalent answers for student work even if they differ from the sample.


6. Visual Design

Throughout the Teach book, color coding and other types of text formatting are used to highlight facilitation recommendations and possible statements, questions, and student responses. These are always suggestions and are not intended to be a script. For example: 

EM2_Visual Design - Color Coded Text

  • Dark blue text shows suggested language for questions and statements that are essential to the lesson, and light blue text shows sample student responses.
  • Text that resembles handwriting indicates what a teacher might write on the board. Different colors signal what a teacher would add to the board at different times during the discussion.
  • Bulleted lists provide suggested advancing and assessing questions to guide learning as needed.
  • Text in purple throughout the Teach book also shows possible student responses.

7. Supplementary Resources

Near the end of the Teach book, teachers can find additional resources for assessment, lesson planning, and further study. These resources include a master copy of the Module Assessment, content standards and Achievement Descriptors addressed in the module, new and familiar terminology used in the module, resource lists, and more.

“I’ve learned a lot through using the curriculum and studying it. Eureka Math is very focused on presenting the mathematics very clearly. I think a lot of teachers don’t have a strong understanding of how kids learn math, of how an algorithm works, or what you’re doing when you’re regrouping with addition and subtraction. The new math standards expect students to have a stronger conceptual understanding of math, and I think it’s important that teachers have that too.”

—Jordan Meyer, Math Intervention Teacher
DC Public Schools


One of the great strengths of Eureka Math2 is its educative nature and its usefulness as point-of-use professional development with these embedded supports. Of course, Eureka Math2 professional learning is available in many forms, including professional development sessions, coaching, implementation services, and a variety of digital resources. Providing teachers with ongoing, curriculum-based professional learning is key to unlocking the potential of high-quality instructional materials.

Ball, Deborah Loewenberg, and David K. Cohen. 1996. “Reform by the Book: What Is—or Might Be—the Role of Curriculum Materials in Teacher Learning and Instructional Reform?” Educational Researcher 25, no. 9 (December): 6–14.

Davis, Elizabeth A., and Joseph S. Kracjik. 2005. “Designing Educative Curriculum Materials to Promote Teacher Learning.” Educational Researcher 34 (April): 3–14.

Schuchardt, Anita M., Miray Tekkumru‐Kisa, Christian D. Schunn, Mary Kay Stein, and Birdy Reynolds. 2017. “How Much Professional Development Is Needed with Educative Curriculum Materials? It Depends Upon the Intended Student Learning Outcomes.” Science Education 101, no. 6 (July): 1015–1033.

Stein, Mary Kay, and Julia H. Kaufman. 2010. “Selecting and Supporting the Use of Mathematics Curricula at Scale.” American Educational Research Journal 47, no. 3 (September): 663–693.

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Topics: Eureka Math Squared