Curriculum Coherence and Connections Across K-12 Math Instruction
by Stephanie Gold
Coherence within and across instructional materials is essential to ensuring that students understand their learning as an interconnected web of ideas, rather than isolated skills practiced in silos. In all subject areas, students benefit when lessons and activities build connections between key concepts, helping them recognize overarching patterns, big ideas, and relationships across topics within the same grade level.
Here's an example: a well-structured curriculum ensures that students learn fractions not as an isolated skill, but as a clear extension of their understanding of whole numbers, division, and proportional reasoning. In fourth grade, when students learn how to add fractions with unlike denominators, the instruction should be explicitly connected to their prior experience with equivalent fractions and least common multiples.
Research highlights the importance of coherence
When students can link new learning to prior knowledge and see how different concepts work together, they develop a deeper understanding and improve their ability to transfer knowledge to new contexts (National Research Council, 2001). Coherent instruction supports cognitive development by reducing cognitive overload, allowing students to focus on critical thinking rather than constantly learning new, disconnected procedures (Archer & Hughes, 2011).
Exact Path helps students build connections between key concepts
Edmentum’s Exact Path Learning in Math is intentionally designed to foster these connections from kindergarten through 12th grade:
In elementary grades, instruction is designed to consistently reinforce early number sense, place value understanding, and operations fluency across topics. For example, when students work on addition and subtraction within 100, they also encounter opportunities to apply these operations when solving problems related to measurement, data interpretation, and even introductory geometry. This cross-domain reinforcement helps students recognize addition and subtraction as flexible tools that apply across mathematical contexts, rather than isolated procedures used only in number-focused lessons.
Moving into middle school, proportional reasoning is not taught as a standalone skill; it is embedded across units on ratios, percentages, and linear relationships, reinforcing a consistent multiplicative reasoning thread across the grade. This approach helps students see proportionality as a fundamental mathematical structure that applies to diverse problems, from scaling recipes to analyzing unit rates in science experiments.
This emphasis on coherence not only supports mastery of individual skills but also helps students develop the mathematical reasoning and problem-solving mindsets they need to confidently approach new and increasingly complex material. When students don’t just memorize slope formulas, but understand that slope represents a rate of change, they are applying and reinforcing connections they've seen before when calculating speed, comparing prices per unit, or analyzing data patterns.
When students experience instruction that consistently links concepts, applies familiar strategies to new situations, and highlights underlying patterns, they begin to internalize a flexible and adaptable approach to mathematics. Whether they are transitioning from whole numbers to fractions, from arithmetic to algebra, or from numerical expressions to modeling real-world situations, students benefit when they can draw upon a well-connected network of prior knowledge and strategies, rather than treating each new topic as unrelated.
References:
Archer, A. L., & Hughes, C. A. (2011). Explicit instruction: Effective and efficient teaching. Guilford Press.
National Research Council. (2001). How people learn: Brain, mind, experience, and school (Expanded ed.). National Academy Press.
About the author
Stephanie Gold brings over two decades of experience in educational leadership, curriculum development, and digital learning to her role as a Learning Designer at Edmentum. With a deep-seated passion for transforming education through technology, Stephanie has held pivotal roles in STEM education, course design, and school leadership, notably influencing digital curriculum development across various educational settings.
With a Master of Arts in Science Education from New York University and now pursuing a Master's program in Learning Design and Technology, Stephanie is adept at integrating pedagogical expertise with technological acumen to craft educational experiences that resonate with both students and educators. Her journey through the educational landscape includes leadership positions in Independent Schools, Online Schools, and the development of Professional Learning Platforms.
