Unlocking Number Sense: The Eardley Approach to Math Instruction

For many students, mathematics is a source of intense anxiety. When instruction relies solely on rote memorization and abstract formulas, students who learn differently are often left behind, leading to a frustrating cycle of confusion and lost confidence.

At Eardley Education, we believe that every student has the capacity to master mathematics. The secret does not lie in relentlessly drilling flashcards or endlessly repeating worksheets; it lies in changing the way we teach the language of numbers. By utilizing highly specialized, evidence-based methodologies, we help students build deep, lasting conceptual understanding.

Whether your child is struggling with foundational number sense, navigating a learning difference like dyscalculia, or simply needs a more engaging way to learn, our tailored approach bridges the gap between confusion and comprehension. Here is a look inside the core methodologies that drive our mathematics instruction.

Moving Beyond Memorization: The Importance of Conceptual Math

Traditional math education often jumps straight to the "Abstract" phase—expecting students to manipulate numbers and symbols (x, y, +, −, ÷) on a page without first understanding what those symbols actually represent in the real world.

At Eardley Education, we prioritize number sense and concept imagery. We want our students to understand why an equation works, not just how to solve it to pass a test. To achieve this, our educators are trained in specialized instructional frameworks designed to reach every type of learner.

The CRA Approach: Building a Concrete Foundation

One of the foundational pillars of our math intervention is the Concrete-Representational-Abstract (CRA) Approach. This highly effective, research-backed instructional strategy ensures students genuinely understand mathematical concepts before they are asked to solve complex equations on paper.

The CRA framework moves through three distinct stages of learning:

1. Concrete (The "Doing" Stage)

We begin by bringing math into the physical world. During this stage, students use physical, multi-sensory manipulatives—such as base-ten blocks, fraction tiles, counting bears, or geometric solids—to solve problems. By physically moving objects to add, subtract, multiply, or divide, the student builds a tactile understanding of quantities and operations.

2. Representational (The "Seeing" Stage)

Once a student demonstrates mastery with physical objects, we transition to the Representational stage. Here, the physical manipulatives are replaced with visual representations. Students learn to draw tallies, dots, circles, or use number lines to represent the math problem. This critical bridge helps students move away from needing physical objects while still relying on visual proof of the concept.

3. Abstract (The "Symbolic" Stage)

Only after a student has mastered the first two stages do we introduce the Abstract stage. This is the traditional math most people recognize: using numbers and mathematical symbols (2+2=4). Because the student has already built a concrete and visual foundation, the abstract symbols finally hold real meaning.

By utilizing the CRA approach, we ensure that foundational gaps are closed, drastically reducing the frustration students feel when faced with abstract math on their exams.

Visualizing Math: Lindamood-Bell® On Cloud Nine®

For many students—particularly those with dyscalculia or significant math anxiety—numbers feel like an entirely foreign language. To support these learners, we incorporate the principles of Lindamood-Bell’s On Cloud Nine® Math program.

The core philosophy of On Cloud Nine is that mathematical success requires concept imagery—the ability to visualize numbers and mathematical processes in the mind's eye.

How On Cloud Nine Works in Our Sessions

When a student struggles to hold a number in their head or fails to grasp the difference between "10" and "100," rote counting will not solve the issue. Our instructors use On Cloud Nine strategies to help students develop:

Numeral Imagery: We train students to visualize numbers and sequences, bringing the mental number line to life

Concept Imagery: We connect language to math, helping students visualize word problems so they can "see" what the problem is asking them to do before they ever pick up a pencil

The Math/Language Connection: We integrate verbal processing, asking students to describe their visual imagery and explain their problem-solving steps aloud. This cements the concept in their long-term memory

By stimulating the brain to process math visually and verbally, we help students develop the robust number sense required to tackle higher-level mathematics.

A Customized, Multi-Sensory Approach

No two students process information exactly the same way. That is why we do not rely on a "one-size-fits-all" curriculum. Our math instruction is completely highly individualized.

When a student joins us, we assess their unique learning profile to determine which methodologies will be most effective. We frequently blend the CRA approach and On Cloud Nine strategies with executive functioning support—teaching students how to organize their work, check their answers, and manage their time during math tests.

Our comprehensive math support includes:

• One-on-one, customized lesson plans

• Pacing dictated by the student’s mastery, not a rigid calendar

• Integration of games and multi-sensory tools to keep learning engaging

• A nurturing, low-pressure environment that explicitly addresses and mitigates math anxiety

Experience the Eardley Difference

Mathematics does not have to be a roadblock to your child’s academic success. With the right methodologies, a supportive environment, and educators who understand the science of learning, every student can experience the "lightbulb moment" where math finally makes sense.

At Eardley Education, we are dedicated to transforming how your child sees numbers, empowering them with the tools they need for lifelong confidence in the classroom and beyond.

Ready to transform your child's relationship with math?
Learn more about our Mathematics Instruction today to learn more about
how we can transform the way your student learns!