Imagine jazz legend Miles Davis at the start of his career. Like most musicians, Davis meticulously mastered scales, notes, and rhythms in isolation. Yet, his genius truly emerged when he began to weave these discrete elements together, improvising and creating groundbreaking compositions. Davis recognized that — music and mathematics— are fundamentally about connections, patterns, and creative thinking, not isolated drills or fragmented skills.

Recent data from the National Assessment of Educational Progress (NAEP) underscores a similar truth in mathematics education. U.S. students’ math achievement has stagnated for over a decade, significantly trailing behind peers from countries like Singapore, Finland, and Japan. These countries consistently excel by emphasizing deep conceptual understanding, interconnected reasoning, and transferable skills rather than isolated procedural benchmarks. Recognizing this urgent need, California recently revised its Mathematics Framework, shifting its focus from isolated standards toward interconnected “big ideas.”

Historically, priority standards have pinpointed specific benchmarks within isolated domains. While beneficial for immediate accountability, this approach often restricts students’ abilities to flexibly and effectively apply mathematical concepts in diverse contexts.

New Structure to Guide Instruction: Drivers of Investigation, Mathematical Practices, and Content Connections

California’s innovative Mathematics Framework explicitly centers on “big ideas”—foundational concepts that span multiple mathematical domains, fostering interconnected learning and building enduring, transferable skills essential for lifelong success. This approach highlights conceptual depth, coherence, equitable access, and robust mathematical practices.

Jo Boaler played a significant role in shaping California’s 2023 Mathematics Framework. As a Stanford University professor specializing in math education, she is one of the primary authors of the framework, which the California State Board of Education adopted in July 2023.

Boaler’s educational philosophy emphasizes equity, student engagement, and inquiry-based learning. These principles are evident in the framework’s recommendations, such as encouraging collaborative problem-solving, integrating real-world applications, and offering data science as an alternative to traditional Algebra II courses. Her influence is further underscored by the frequent citations of her research and her organization, YouCubed, within the framework.

To support educators in implementing this visionary approach, California introduces an organizational framework highlighting the interplay among:

  • Drivers of Investigation (DIs): Sense-making, predicting, and having an impact, providing the essential “why” behind activities.
  • Standards for Mathematical Practice (SMPs): Eight critical practices defining “how” mathematics should be explored.
  • Content Connections (CCs): Ensuring coherence and continuity across grades, providing the “what” in mathematical instruction.

Figure 1.3 in California’s new framework illustrates how these components interrelate, empowering teachers to design instruction that fosters robust, inquiry-driven mathematical learning.

Five Reasons Why California Made This Shift

 

1. From Discrete Standards to Integrated Big Ideas

  • Priority Standards: Isolated, domain-specific targets.
  • CA Mathematics Framework: Promotes interconnectedness and coherence across domains.

Elementary Example: Grade 3 students connect area with multiplication and addition, understanding area as a measurable attribute linked to arithmetic operations.

Middle School Example: Grade 7 students solve multistep ratio and percent problems, applying proportional reasoning to real-world scenarios like calculating taxes and discounts.

High School Example: Integrated Math 1 students analyze and sketch graphs, interpreting functions in real-world contexts.

 

2. Emphasis on Transferable, Long-Term Learning

  • Priority Standards: Often narrowly focused on short-term assessment needs.
  • CA Mathematics Framework: Encourages deep, lasting conceptual learning, applicable across diverse situations.

Elementary Example: Grade 2 students explore place value deeply to solve real-world problems involving money and measurement.

Middle School Example: Grade 8 students apply linear equations to practical situations, like calculating phone plan costs based on usage.

High School Example: Integrated Math 3 students use probability concepts to analyze real-world scenarios like insurance risk and gaming probabilities.

 

3. Strengthening Conceptual Connections and Coherence

  • Priority Standards: Fragment mathematics into discrete topics.
  • CA Mathematics Framework: Advocates unified learning through comprehensive, interconnected concepts.

Elementary Example: Grade 5 students interpret numerical expressions, connecting algebraic thinking with arithmetic operations.

Middle School Example: Grade 6 students examine ratios and unit rates in practical contexts, like speed and density.

High School Example: Integrated Math 2 students derive algebraic equations directly from geometric definitions, such as equations of circles.

 

4. Promoting Equity and Access

  • Priority Standards: Potentially restrictive, limiting diverse learners.
  • CA Mathematics Framework: Explicitly fosters inclusive, culturally responsive, and equitable mathematical experiences.

Elementary Example: Grade 4 students connect mathematics with cultural backgrounds through patterns in traditional art.

Middle School Example: Grade 7 students analyze data on social issues, promoting discussions on equity and resources.

High School Example: Integrated Math 3 students investigate real-world issues like income inequality through statistical analysis.

 

5. Enhancing Rich Mathematical Practices

  • Priority Standards: Insufficiently address mathematical reasoning.
  • CA Mathematics Framework: Integrates rigorous mathematical practices emphasizing reasoning, problem-solving, and effective communication.

Elementary Example: Grade 1 students articulate reasoning using drawings and equations.

Middle School Example: Grade 8 students justify the Pythagorean Theorem through models and algebraic reasoning.

High School Example: Integrated Math 1 students engage in modeling tasks, analyzing scenarios like traffic congestion to develop practical solutions.

 

Looking Forward: A Model for National Change

California’s Mathematics Framework serves as a blueprint for nationwide educational transformation, offering:

  • Scalable Innovation: Aligns with global best practices emphasizing conceptual understanding and transferable skills.
  • National Need for Improvement: Addresses persistent national stagnation in mathematics achievement.
  • Equity and Inclusivity: Aligns explicitly with national efforts to close achievement gaps through culturally responsive and equitable practices.
  • Global Alignment: Echoes successful practices from top-performing educational systems globally, positioning states to boost their international competitiveness.

California’s commitment to interconnected big ideas, real-world application, and culturally responsive instruction represents a significant step forward in reshaping math education into an inclusive, engaging, and effective experience for every learner.

To further support educators in making this transformative shift, The Core Collaborative invites you to join our Competency-Based Learning Cadre. Engage with passionate educators committed to redefining mathematics instruction through competency-based principles, learner agency, and collaborative inquiry.

Join the Competency-Based Learning Cadre today and become part of the movement to elevate educational outcomes for all students.

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