Math Framework

The 2023 California Mathematics Framework (CMF) offers us a transformative roadmap that shifts the focus from a "one-size-fits-all" approach toward a more inclusive, investigative, and deeply engaging experience for every student. As instructional leaders, our role is to move beyond the "what" of standards and focus on the "how" of meaningful learning. The CMF encourages us to transition away from seeing math as a series of sterile, isolated rules and toward a classroom environment where math is an active, joyful exploration.

We broke down sections of the CMF into sections to help sites transition smoothly and seamlessly.

Math Moments

A Shared Vision for the New Year

This transition requires a culture of trust and a shared understanding that all students are "capable learners who can learn and do anything," a sentiment echoed by many educational leaders across the state. In our role as superintendents and site leaders, the most impactful work we can do this month is to communicate this vision to our staff and families: that math is not just about getting the right answer quickly, but about developing the thinking skills necessary to navigate a complex world. We are not just teaching arithmetic; we are building mathematical identities.

Action Step for Leaders: Review Chapter 1 of the framework as well as the CA Math Framework Summary to ground your leadership team in the core values of the new guidelines. Share a specific success story of student investigation during your next staff meeting to highlight the shift toward deeper learning.

Resource: 2023 CA Math Framework - Chapter 1: Introduction

Cultivating Growth through Professional Development

The CMF emphasizes that effective professional development is not a "one-and-done" event but a "structured professional learning process that results in changes in teacher practices." For our math instruction to evolve, our teachers need the space and time to engage in active inquiry themselves. This means moving away from passive workshops and toward collaborative, data-driven "cycles of improvement."

As leaders, we can facilitate this by ensuring that professional learning is embedded into the school day. When we provide teachers with the opportunity to analyze student work together and experiment with new instructional strategies, we are modeling the very growth mindset we want for our students. According to Chapter 10 of the CMF, the most successful professional learning is focused on authentic instructional problems of practice. This month, we encourage you to look at your professional development calendar through the lens of longevity and depth. Are we providing our educators with a "one-time fix," or are we building a community of practice that evolves alongside our students?

Action Step for Leaders: Join a grade-level collaboration meeting this month and participate in the "cycle of inquiry." Review the Leveraging Systemic Assets-Systemic Moves document. Using the Potential Questions and/or /Systemic Moves, look for how teachers are using student work to decide their next instructional moves.

Resource: 2023 CA Math Framework - Chapter 10: Instructional Materials and Professional Learning

Embracing Every Student’s Potential (Dimension 1)

This principle asks us to radically shift our perspective from what students cannot do to the "funds of knowledge" they bring with them on Day 1. Every student walks into our classrooms with a unique cultural background, a primary language, and a personal history of problem-solving. These are not obstacles to overcome; they are intellectual resources to be leveraged.

Instructional leaders can champion this shift by encouraging teachers to see a student’s diverse strategy or linguistic background as a strength. In an asset-based classroom, we don't just "remediate" deficits; we "accelerate" learning by connecting new concepts to the student’s lived experience. As leaders, when we walk through classrooms, we should look for evidence that student voices are the starting point of the lesson. When a student explains a problem in a non-traditional way, is that celebrated? When we see our students as "capable doers of mathematics," we begin to close the opportunity gap in a way that data points alone never can.

Action Step for Leaders: During your next walkthrough, use an "asset-based lens." Rather than looking for what is missing in a student’s response, look for the unique strategy they are attempting and how the teacher validates that thinking.

Resource: 2023 CA Math Framework - Chapter 2: Instruction and Mathematics

Sparking Curiosity through Investigation (Dimension 2)

The CMF highlights that students learn best when they are driven by curiosity and the desire to solve meaningful problems. This moves instruction away from the "I do, we do, you do" model toward a "Think, Pair, Share, and Investigate" model. The goal is to make math multidimensional—incorporating visuals, movement, objects, and collaborative reasoning.

This is where the Universal Design for Learning (UDL) guidelines become essential. As principals and superintendents, we can support this by ensuring teachers have the resources they need to create these "multidimensional" experiences. Are there enough manipulatives? Is there space for students to move and collaborate? In an investigative classroom, the teacher acts as a facilitator of discovery rather than a gatekeeper of information. By allowing students to ask their own questions and test their own conjectures, we help them develop a positive, active relationship with mathematics that will serve them long after they leave our halls.

Action Step for Leaders: Check in with your department heads or grade-level leads. Ask: "What is one investigative task your team has tried recently that sparked the most student debate?" Focus on the process of the investigation rather than just the final answer.

Resource: 2023 CA Math Framework - Chapter 2: Teaching for Equity and Engagement

Bringing the Framework to Life (Video Resource of Grade Span Vignettes)

UDL 3.0 Guidelines

Building Identity and Belonging (Dimension 3)

Dimension 3: Cultural and Personal Relevance is about ensuring that every student feels they belong in the math classroom. The CMF suggests that teaching toward social justice and cultural relevance isn't just a separate unit; it's a daily practice of centering instruction on the student.

Simple, high-impact changes—such as using student names in word problems or incorporating local community data into lessons—can make a world of difference. When students see their own lives reflected in the numbers they study, their engagement skyrockets. As leaders, we must ask: "Do our students see themselves as successful doers of mathematics?" This month, let’s celebrate the diverse ways our students have grown. Our goal is to ensure that when students leave for the summer, they carry with them the confidence that math is a tool they can use to understand and improve their own worlds.

Action Step for Leaders: Audit the visual environment of your school. Do the posters and displays reflect a diverse range of mathematicians? Encourage teachers to share a "Personal Math Story" from a student during your end-of-year celebrations.

Resource: 2023 CA Math Framework - Chapter 2: Teaching for Equity and Engagement

The Big Ideas and the Coherent Math Story

The 2023 California Mathematics Framework (CMF) urges us to move away from treating the Common Core State Standards (CCSS) as a fragmented "checklist" of isolated skills. Instead, we are encouraged to organize instruction around Big Ideas. These Big Ideas are intentional groupings of standards that allow students to see the "why" behind the math. By focusing on these clusters, we move from a mile-wide, inch-deep curriculum to a narrative where math builds logically and beautifully from one grade to the next.

To lead this shift, it is helpful to understand the framework’s architecture: the Drivers of Investigation (the "Why") provide the purpose for learning; the Content Connections (the "What") organize the math topics; and the Standards for Mathematical Practice (the "How") describe the habits of mind students develop. When these three elements intersect within a "Big Idea," students aren't just doing math—they are making sense of their world. As leaders, our goal this June is to ensure our curriculum and pacing guides reflect this interconnected vision, moving beyond rote procedures toward deep, conceptual storytelling.

Action Step for Leaders: Audit your district’s math pacing guides for the upcoming year. Are they organized by individual, isolated standards, or are they grouped into Big Ideas that reflect the Content Connections of the CMF?
CMF Reference: Chapter 1: Mathematics for All,
Gradespan Chapters:
Appendix A: Big Ideas

Launching with Open Tasks

One of the most powerful levers a leader has to increase student agency is promoting the use of Open Tasks. Unlike traditional "closed" problems that have one right answer and one narrow path to get there, open-ended tasks invite students to bring their own unique perspectives to the table. These tasks are "low floor, high ceiling," meaning every student can find a way into the problem, while the potential for deep mathematical exploration is limitless.

By centering instruction on open tasks, we immediately activate the Drivers of Investigation (the "Why"). We shift the focus from "finishing the page" to "making sense of a situation." This approach allows teachers to observe how students naturally apply the Standards for Mathematical Practice (the "How"), such as persevering in problem-solving and constructing viable arguments. As you welcome teachers back, encourage them to choose tasks that spark curiosity and allow for multiple strategies. When we open up the tasks, we open up the possibility for every student to see themselves as a "math person."

Action Step for Leaders: Look for "Rich Tasks" or Mathematical Language Routines. Note whether students are working in silos on worksheets or collaborating on problems that allow for multiple pathways and solutions.

Reference: 2023 CA Math Framework Chapter 2: Teaching for Equity and Engagement (Section on Open Tasks).

Fostering a Culture of Questions and Conjectures

A high-quality math classroom is a "thinking classroom" where the intellectual authority is shared between the teacher and the students. The goal is to foster an environment where students feel safe to take risks, ask "Why does this work?", and make mathematical conjectures. When a student makes a conjecture—a reasoned guess based on evidence—they are engaging in the very heart of the Standards for Mathematical Practice (the "How").

Fostering this culture requires a shift in how we view mistakes. In a classroom rooted in the 2023 CMF, a mistake isn't a dead end; it's a data point that leads to a new question. As leaders, we can support this by looking for "Discourse Routines" during our observations. Are students justifying their thinking? Are they politely critiquing the reasoning of others? By prioritizing questioning over "answer-getting," we ensure that the math remains a vibrant, investigative process. This month, let's empower our teachers to step back and let student voices—and student questions—lead the way.

Action Step for Leaders: Facilitate a "Learning Walk" with your site leads. Specifically listen for student-to-student discourse. Count how many times a teacher asks "How do you know?" versus "What is the answer?" and use that data to spark a conversation about mathematical reasoning.

Reference: 2023 CA Math Framework Chapter 4: Exploring, Discovering, and Reasoning With and About Mathematics.

Cultivating Number Sense

The 2023 California Math Framework Number Sense Chapter identifies number sense as the bedrock of mathematical fluency. It is not merely the ability to calculate quickly, but the capacity to think flexibly about numbers and their relationships. When our students develop a "feel" for numbers, they gain the confidence to decompose complex problems and approach mathematics with a sense-making mindset rather than a performance-based one.

For you as leaders, prioritizing number sense is an essential step toward instructional equity. By fostering classrooms where multiple strategies are celebrated, we dismantle the "math person" myth and invite all students—especially those traditionally underserved—to see themselves as capable mathematicians. This month, we focus on transitioning from "procedural speed" to "conceptual depth," ensuring that every student has the mental toolkit necessary to navigate high-level mathematics in the years to come.

Action Step for Leaders: Conduct a series of "Ten-Minute Math Walks" focused on Number Talks. Look for evidence of students explaining how they reached an answer using different mental strategies rather than just providing the correct result.

Resource: 2023 CA Math Framework Chapter 3: Number Sense and RMC Asynchronous Modules

Strengthening the Standards for Mathematical Practice (1, 3, & 7)

The Standards for Mathematical Practice (SMPs) are the habits of mind that define true mathematical literacy. This month, we highlight SMP 1 (Make sense of problems and persevere in solving them), SMP 3 (Construct viable arguments and critique the reasoning of others), and SMP 7 (Look for and make use of structure). These practices empower students to engage in productive struggle, allowing them to view challenges as opportunities for growth rather than roadblocks.

When students are encouraged to critique reasoning and find patterns in structure, the classroom becomes a laboratory for discourse. As leaders, our goal is to support teachers in creating "low-floor, high-ceiling" tasks where SMPs can flourish. By valuing the process of argumentation and structural thinking over the simple attainment of a final answer, we cultivate a culture of rigorous inquiry that prepares students for the complexities of the 21st-century workforce.

Leader Action Step: During PLC meetings, facilitate a "Task Audit." Ask grade-level teams to review an upcoming lesson and identify specific opportunities where students—not the teacher—are doing the heavy lifting of constructing arguments and finding structural patterns.

Resource: 2023 CA Math Framework Chapter 2: Teaching for Equity and Engagement

Modernizing with Data Science

The Framework’s Data Science Chapter underscores that data literacy is now a fundamental civil right in a data-driven global economy. This shift moves mathematics into the real world, asking students to pose statistical questions, collect evidence, and analyze variability. By engaging with data, students learn to navigate the influx of information they encounter daily, turning them into informed citizens who can make sense of their community and the world.

Integrating data science is an invitation to cross-curricular innovation. It allows students to see math as a tool for social and scientific investigation, grounding abstract concepts in tangible reality. As leaders, our role is to champion this modernization, ensuring that our math programs reflect the skills students actually need for the modern era. By prioritizing data literacy, we provide our learners with a lens through which they can critically analyze, interpret, and change the world around them.

Leader Action Step: Encourage a "Data-Rich Environment" by asking teachers to display student-generated data visualizations (graphs, infographics, or charts) in common areas. This celebrates math as a public, investigative tool rather than a private, textbook-bound exercise.
Resource: 2023 CA Math Framework Chapter 5: Data Science

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