Curriculum, Students, and Teachers: Choosing Integrity Over Fidelity

In conversations about instructional materials, the terms fidelity and integrity are often used interchangeably. They shouldn’t be. The distinction reflects fundamentally different orientations to teaching, learning, and the role of curriculum in classrooms.

Teaching with fidelity centers the curriculum as the primary object of attention. It asks: Are we doing the lesson as written? In practice, fidelity often becomes synonymous with compliance. The teacher’s role is to deliver materials as designed, regardless of the particular students in front of them. This orientation toward delivery also ignores their professional expertise. This approach assumes that consistency in implementation will produce consistent outcomes. But classrooms are inherently variable, and students bring unique experiences that cannot be standardized.  A one-size-fits-all enactment inevitably disregards differences in prior knowledge, identity, language, and ways of making sense of mathematics. 

Teaching with integrity, by contrast, centers the purpose and design principles of the curriculum. It asks: What is this lesson designed to do? What are the key mathematical ideas and experiences students should have? High-quality instructional materials are engineered for all students and no particular students at the same time. They reflect a vision of learning that positions students as capable sense-makers, while also requiring teachers to adapt based on their understanding of what the students they actually teach need. Because materials cannot anticipate every context, they rely on teachers to make principled decisions that connect the curriculum’s intent to students’ lived realities.

This is where the instructional core matters—the dynamic relationship among teacher, student, and content. Teaching with integrity means actively managing that relationship: preserving the integrity of the mathematics while strengthening students’ access and engagement. Teaching with fidelity, particularly when reduced to compliance, can flatten the instructional core, minimizing interactions between teachers and students.

Consider a fifth-grade lesson designed to help students make and interpret line plots displaying fractions in eighths. In the original task, students use egg weights to construct a line plot and answer questions about the data. Our colleague, Karina Calderon, taught this lesson with integrity by adapting the context while preserving the mathematical goal. Instead of egg weights, students recorded how many hours they slept the previous night and rounded their responses to the nearest ⅛ hour. They then represented the data on a line plot and interpreted the distribution.  

Karina extended the task to deepen engagement and ownership. Students generated their own questions about the data set, positioning them as authors of inquiry rather than responders to provided questions. She selected one question for all students to solve, based on her goals for students’ learning, and invited students to choose an additional question to explore. Grounding the work in students’ own data made it meaningful and worthy of their investment.

The mathematical goals, representing fractional data, interpreting line plots, and reasoning about distributions remained intact. But the pathway into that work was more accessible and responsive. Karina’s decisions strengthened the instructional core: the content stayed rigorous, her moves were intentional, and students were actively making sense of mathematics.

Why does this matter? Because the goal of high-quality instructional materials is not merely coverage, it is supporting critical thinking and deep learning of important mathematical ideas. When we shift from “high-quality instructional materials” to “high-quality mathematical instruction,” we commit to enact curriculum in ways that align with how students learn: actively, socially, and through sense-making. Teacher decision-making is centered. Teaching with integrity ensures that the curriculum’s vision, designed for all students, yet requiring responsiveness to each, is realized in diverse classrooms. Teaching with fidelity, when reduced to compliance, risks valuing coverage and superficial learning.  The ideas in this post are influenced by the following scholars and practitioners:  Elham Kazemi, Bill McCallum, Kristin Umland; Elham Kazemi, Karina Calderon, and Kristin Gray authors of the forthcoming paper “Adapting Tasks: Honoring Students’ Sensemaking and Intellectual Capabilities.”