This case study describes the journey of a young student who struggled with the most basic numerical concepts. Through structured instruction that addressed both cognitive processes and the academic foundations of mathematics, she progressed to scoring in the 98th percentile on a standardized mathematics test.
Introduction
Emma* was seven years old and entering 3rd grade when she started the Edublox Math Program. She had a math learning disability and had previously completed an intensive cognitive training program lasting six months. Despite the significant time and financial investment, there had been little improvement in her ability to work with numbers.
When I first met Emma, it became clear that her difficulties lay in the most basic foundations of mathematics.
Counting
Counting is the foundational skill upon which all other mathematical learning depends. Teaching children to count and skip count prepares them for success in mathematics.
Emma was able to count from 1 to 100 without difficulty. However, she could not count backward. This indicated that she did not yet understand subtraction, since backward counting is the most basic prerequisite for subtracting.
Mental math
Mental math refers to performing calculations “in one’s head” without the use of pencil and paper or a calculator. These skills help learners develop number sense and understand how numbers relate to one another.
Emma could add one to any number between 10 and 99. However, she could not add two to a number. When I explained that adding two simply means counting forward two numbers, she quickly understood the idea. This indicated that the difficulty was not a lack of ability, but rather a missing foundational numerical concept.
Procedural mathematics
Procedural memory is used to remember step-by-step methods for solving mathematical problems, such as column addition or long division.
Because Emma could not yet add two to a number, I did not ask her to complete written procedures such as column addition during the initial assessment. Introducing procedures before foundational number concepts are secure can create confusion and unnecessary math anxiety.
Place value
Understanding place value is essential for developing number sense — the ability to understand and connect numbers.
Initially, Emma showed little understanding of place value and did not recognize that a digit’s position determines its value. During the assessment, I introduced the concepts of ones, tens, and hundreds. She understood them very quickly, indicating that the difficulty was not a lack of ability but rather a lack of foundational instruction.
Prior intervention
Before beginning the Edublox Math Program, Emma had completed an intensive cognitive training program lasting six months and requiring a substantial financial investment from the family. Despite the time and effort involved, the training produced little measurable improvement in her mathematical ability.
This experience highlights an important principle in education: cognitive training alone does not automatically transfer to academic skills such as mathematics. Strengthening abilities such as memory, processing speed, and attention is invaluable, but these improvements do not, by themselves, teach a child how numbers work.
At the same time, the opposite is also true. Academic practice alone is insufficient when the underlying cognitive processes required for learning are weak.
Effective intervention, therefore, requires both components: strengthening the cognitive processes that support learning and systematically teaching the academic structure of mathematics.
In some cases, cognitive development may begin first. However, the most effective approach is often to develop cognitive and academic skills simultaneously, allowing improvements in one domain to support progress in the other.
Equally important is how the academic material is taught. Mathematics instruction must follow a carefully layered progression in which foundational concepts are mastered before more complex procedures are introduced.
Intervention
Emma completed 80 lessons of 30 minutes each, typically three sessions per week with Edublox. On the remaining days, her grandmother worked with her, repeating the exercises and concepts covered during the lessons. This consistent reinforcement played an important role in stabilizing the newly learned skills.
The program systematically developed both the underlying processes involved in learning and the academic structure of mathematics, beginning with counting systems, number relationships, place value, and foundational arithmetic procedures.
What Emma learned during the program
Over the course of the program, Emma developed the foundational mathematical concepts that had previously been missing.
Once forward counting was secure, she learned to count backward in ones, establishing the basis for subtraction. She also developed strong skip-counting skills, learning to skip count from 2 through 12, as well as 15, and was able to both multiply and divide using these numbers.
Emma made particularly strong progress in mental math and mastered the doubles facts up to 27.
Procedural mathematics was introduced in a carefully structured sequence. Instruction included addition, subtraction, multiplication (up to three-digit by three-digit), and long division. After these skills were secure, instruction progressed to fractions, including addition and subtraction of fractions, multiplication and division of fractions, finding factors, and simplifying fractions.
Emma also developed a strong understanding of place value and value, working with numbers up to the hundred millions, including both reading and writing large numbers correctly.
Eventually, Emma was confidently performing mathematical tasks that had been impossible for her at the start.
Outcome
After 80 lessons, Emma was tested using a standardized achievement test (CAT). The initial assessment took place in mid-July 2025, and the CAT test was administered eight months later, on March 13. At the time of testing, she was in the last quarter of 4th grade.
Her results were as follows:
| Test Area | Raw Score | Grade Equivalent | Percentile | Stanine |
|---|---|---|---|---|
| Mathematics Computation | 70/72 | 4.7 | 98 | 9 |
| Mathematics Concepts & Problems | 40/45 | 4.9 | 90 | 8 |
| Mathematics Composite | 110/117 | 4.8 | 98 | 9 |
These results place Emma well above the average range, particularly in computation, where she scored in the 98th percentile.
What Emma’s story shows
Emma’s story illustrates an important principle in learning. Severe math difficulties are rarely solved by practicing cognitive skills or academic skills alone. Meaningful progress occurs when both the underlying cognitive processes and the academic structure of mathematics are addressed together, and when instruction follows a carefully layered progression that secures foundational concepts before moving to more advanced procedures.
With the right approach, even students who struggle with the most basic numerical concepts can develop strong mathematical skills and confidence.
Edublox offers cognitive training and live online tutoring to students with math learning disabilities and other learning challenges. We support families in the United States, Canada, Australia, and beyond. Book a free consultation to discuss your child’s learning needs.
From Struggling with Basic Math to the 98th Percentile: A Case Study was authored by Sue du Plessis (B.A. Hons Psychology; B.D.), an educational specialist with 30+ years of experience in the field of learning disabilities.
* Emma is a pseudonym.
