How to Close Math Learning Gaps and Build Foundational Skills Through Conceptual Understanding and Procedural Fluency

When students struggle in math, it's often because a critical foundation is missing: conceptual understanding (knowing why math works) or procedural fluency (knowing how to apply it accurately and efficiently)—or both. Without these building blocks, gaps widen, and success in future courses like Algebra 1 becomes harder to achieve.

Edmentum’s Exact Path is designed to identify and close these learning gaps—not just by reteaching procedures, but by helping students deeply understand core ideas while building the understanding and skills needed to solve problems confidently. This balanced approach helps struggling learners become confident, proficient math students. 

What Are Conceptual Understanding and Procedural Fluency? 

• Conceptual Understanding refers to grasping the relationships, structures, and underlying logic of mathematical ideas. It's what allows students to see why strategies work and apply them flexibly.
• Procedural Fluency is the ability to accurately and efficiently perform calculations and solve problems using appropriate methods. 

Students who lack one or both often get stuck: they might memorize steps without meaning (and forget them later) or understand ideas loosely but struggle to actually work through math problems. Exact Path targets both areas, giving students what they need to truly move forward. 

How Does Exact Path Close Math Learning Gaps? 

Exact Path begins by identifying students’ specific needs with a valid, adaptive diagnostic assessment. Once those needs are known, students are provided with individualized learning paths designed to meet them exactly where they are, building understanding and fluency in tandem. Here’s how: 

Strengthening Conceptual Understanding 

• Concrete and Visual Models: Students engage with number lines, fraction strips, area models, and geometric figures to ground abstract concepts in tangible ways.
• Real-World Scenarios: Lessons connect math to everyday situations, helping students see why the math matters.
• Guided Reasoning: Students are prompted with questions that require them to reason through processes, not just complete steps.

Building Procedural Fluency in Mathematics

Through this structure, Exact Path ensures that students don’t just learn more math—they learn it better:

• Scaffolded Practice: New math concepts are introduced with step-by-step strategies and examples, helping students build accuracy and confidence as they practice.
• Gradual Removal of Supports: Over time, scaffolds fade, encouraging students to work independently and flexibly.
• Immediate Feedback and Hints: When mistakes happen, students aren’t left guessing—they’re guided back to understanding and success.
• Mastery Focus: Students practice skills to reach true proficiency, not just completion.

Why It’s Essential to Close Gaps Before Students Reach Algebra 1 

Mathematics is cumulative. Gaps in early skills—like fractions, place value, or solving simple equations—snowball into bigger struggles in later grades, especially in courses like Algebra 1, where students must solve multi-step problems and model abstract relationships. 

By simultaneously rebuilding understanding and strengthening procedural skills, Exact Path helps students: 

• Bridge critical gaps and catch up to grade level
• Develop the ability to reason through complex problems
• Gain confidence by mastering foundational concepts they previously missed
• Build a stable platform for success in Algebra 1 and beyond 

Exact Path in Action: Closing Math Learning Gaps, One Concept at a Time 

Each Exact Path module begins with concept exploration. For example, in a lesson on volume, students might: 

• Visualize a 3D Model: Explore a fish tank filled with unit cubes to understand how volume works.
• Develop a Strategy: Recognize how to calculate volume based on layers and base area.
• Solve Problems: Apply the volume formula through scaffolded practice with immediate feedback.
• Reflect and Reason: Explain why the strategy works and revisit any misconceptions. 

This process ensures that learning isn’t superficial. Students build understanding, master skills, and gain the confidence to tackle new challenges independently. 

By explicitly targeting both conceptual understanding and procedural fluency, Exact Path provides the structured, supportive, and personalized pathway students need to close math learning gaps, build true mathematical proficiency, and prepare for future success in Algebra 1 and beyond.