Show Your Work:
Research & Evidence
This work is grounded in decades of research on how students learn mathematics and how instruction can best support understanding. The sources below reflect key ideas that shape this approach to teaching, learning, and decision-making in mathematics classrooms.
Conceptual Understanding
Conceptual understanding is the foundation of meaningful math learning. When students understand the why behind a strategy, they are able to apply their thinking flexibly across different problems and contexts.
Rather than relying on memorization alone, effective instruction emphasizes connections between models, representations, and mathematical ideas. Students learn to explain their reasoning, recognize patterns, and make sense of problems—not just follow steps.
Over time, this approach leads to stronger retention, improved problem-solving skills, and greater confidence. Students aren’t just doing math, they’re understanding it.
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Student Discourse
Student discourse is a powerful driver of learning. When students are given opportunities to explain their thinking, justify their reasoning, and respond to others, they deepen their understanding of mathematical concepts.
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These conversations help students clarify their ideas and expose them to multiple strategies and perspectives. They also give teachers valuable insight into how students are thinking, allowing instruction to be more responsive and targeted.
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A classroom that prioritizes discourse is one where students are actively engaged, thinking critically, and learning from one another - not just listening for the “right answer.”
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Standards-Aligned Instruction
Standards provide a clear framework for what students should understand and be able to do at each grade level. However, effective instruction goes beyond simply “covering” standards - it focuses on the intent, depth, and application of each one.
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When lessons are aligned to the full rigor of the standards, students engage in meaningful learning experiences that build both procedural skill and conceptual understanding.
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This alignment ensures consistency across classrooms and grade levels, helping students develop knowledge that builds over time rather than existing in isolated pieces.
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Real Experiences. Real Impact.
"Our faculty has had the pleasure of working with Cheryl Fricchione, a master teacher and professional development trainer, as we transition to Illustrative Math after more than 20 years with our previous program. Cheryl has been instrumental in helping us embrace this significant shift, providing not only her expertise but also a customized approach that goes far beyond traditional publishing house support."
Coherence & Progression
Mathematics is intentionally structured to build from one concept to the next. Skills introduced in early grades form the foundation for more complex ideas in later years.
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When instruction highlights these connections, students begin to see math as a coherent system rather than a collection of unrelated topics. They understand how ideas evolve and how prior knowledge supports new learning.
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This sense of progression not only improves comprehension, but also reduces frustration. Students are better equipped to approach new challenges because they recognize the patterns and relationships that connect their learning.
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Productive Struggle
Productive struggle is an essential part of the learning process. When students are challenged appropriately, they develop perseverance, critical thinking skills, and a deeper understanding of mathematical concepts.
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Instead of immediately providing answers, effective instruction creates opportunities for students to grapple with problems, test ideas, and refine their thinking. Teachers play a key role in guiding this process, offering support without removing the challenge.
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This balance helps students build confidence and resilience, showing them that effort and persistence are key components of success in mathematics.
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Using Data & Student Thinking
Data is most powerful when it goes beyond right and wrong answers. By analyzing student work, educators can uncover patterns in thinking, identify misconceptions, and better understand where support is needed.
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This approach shifts the focus from simply measuring performance to improving instruction. Teachers can adjust their strategies in real time, targeting specific needs and building on student strengths.
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When used effectively, data becomes a tool for insight - not just evaluation - leading to more intentional and impactful teaching.
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