Why Is My Student Struggling With Maths?
Every educator has worked with a student who seems to understand a mathematical concept one day, only to appear completely lost when they encounter it again. Perhaps they continue to rely on finger counting, despite repeated practice. They may be able to follow a procedure when it is modelled for them but cannot explain why it works. Or they may successfully complete one type of question, then become stuck as soon as the numbers, language or presentation change.
When a student is struggling with maths, it is easy to focus on what we can see: the incorrect answer, the unfinished work, the forgotten procedure or the slow recall of number facts. We might respond with additional practice, another explanation or a simpler worksheet. Sometimes that is exactly what is needed. But when the same difficulties persist, it is worth looking more closely at what sits underneath them.
The most useful question is often not, “Why can’t this student do this?” but rather, “What does this student understand, and where does that understanding begin to break down?”
The Difficulty We See May Not Be Where the Difficulty Began
Mathematics is cumulative. New learning is constantly being built on concepts developed earlier, which means a gap in foundational understanding can remain hidden until the mathematics becomes complex enough to expose it.
Consider a student who is struggling with multiplication. The immediate response might be to provide more multiplication practice, but the underlying difficulty may sit much earlier. Does the student understand equal groups? Can they skip count reliably? Do they recognise the relationship between repeated addition and multiplication? Can they build an array and explain what it represents? If these concepts are not secure, asking the student to memorise multiplication facts may improve performance temporarily without addressing the mathematical understanding underneath.
The same pattern occurs across mathematics. A student struggling with written addition may have an insecure understanding of place value. Difficulty with fractions may reflect gaps in part-whole understanding or multiplicative thinking. A student who becomes lost in multi-step problems may understand the mathematics itself but have difficulty managing the language, working-memory demands or sequence of the task.
This is why effective maths intervention begins with identifying the source of the difficulty rather than simply responding to its most visible symptom.
There Is No Single Reason a Student Struggles With Maths
Students can experience difficulty with mathematics for many different reasons, and it is important not to assume that every student who struggles has the same underlying need.
For some students, persistent difficulties with number, quantity, mathematical facts and calculations may be associated with dyscalculia or Specific Learning Disorder in mathematics. For students with ADHD, attention, working memory and executive functioning may affect their ability to retain instructions, organise information, maintain their place in a calculation or manage multiple steps. Students with dyslexia may understand the mathematical concept but experience additional difficulty when mathematics involves significant reading, unfamiliar vocabulary or complex word problems.
Maths anxiety can also affect how a student approaches and performs mathematical tasks, particularly following repeated experiences of difficulty. For other students, there may be no identified learning difference at all. Their difficulty may result from gaps in foundational knowledge, interrupted learning or earlier mathematical concepts that were learned procedurally without being fully understood.
These factors are not mutually exclusive. A student may experience more than one barrier to mathematical learning, which is why observation, assessment and careful identification are so important.
Start With What the Student Actually Understands
When students are struggling with maths, there can be pressure to keep them working on age- or year-level content. However, the curriculum continuing to move forward does not necessarily mean the student's mathematical understanding has moved forward with it.
A student may, for example, learn the written procedure for addition with regrouping and successfully reproduce the steps. Yet if they do not understand that ten ones can be regrouped as one ten, the procedure remains disconnected from the mathematical concept underneath it. When the procedure is forgotten or the question is presented differently, there is little conceptual understanding for the student to draw upon.
This distinction between performing a procedure and understanding the mathematics is critical. A correct answer can tell us that a student successfully completed a task, but it does not always tell us what they understood. Likewise, an incorrect answer does not tell us exactly where their understanding broke down.
Before deciding what to teach next, we need to establish what the student already knows.
Using I-CRAVE Maths® to Build Mathematical Understanding
At Maths Australia, the I-CRAVE Maths® Methodology provides a framework for identifying and developing mathematical understanding through Identify, Concrete, Representation, Abstract, Verbal and Explicit teaching.
The process begins with Identify. Rather than assuming where intervention should begin based on a student's age or year level, we identify what the student understands, where the difficulty occurs and which prerequisite concepts may not yet be secure.
From there, mathematical concepts can be explored at the Concrete level, allowing students to build and manipulate the mathematics using appropriate materials. This understanding is then connected to Representation, where students see the same mathematical relationships expressed through diagrams, drawings and visual models, before moving towards the Abstract numbers, symbols and notation used in formal mathematics.
The Verbal component is equally important. Mathematical language needs to be explicitly developed, and students benefit from opportunities to explain what they are doing and why. Throughout the process, instruction remains Explicit: important mathematical relationships are clearly modelled and taught rather than left for students to discover independently.
The purpose is not to make mathematics more complicated by adding additional stages. It is to make the mathematical thinking visible so that educators can see what the student understands and students can build connections between the concept, its representation and the abstract notation.
What Does This Look Like in Practice?
Imagine a student who cannot reliably solve a multiplication question such as 3 x 4. Rather than beginning with another page of multiplication facts, an educator can investigate the concepts underneath the calculation.
Can the student build three equal groups of four objects? Can they describe what they have built? Can they rearrange the same quantity into an array? Can they represent that array visually and connect it to repeated addition? Can they then connect those representations to the abstract expression 3 x 4 = 12?
If the student can complete some of these steps but not others, the educator has gained useful information about where instruction needs to focus. Instead of simply knowing that the student “cannot do multiplication”, we begin to understand which part of multiplication is not yet secure.
This same approach can be applied to place value, addition, subtraction, division, fractions and more advanced mathematical concepts. When a student becomes stuck, we can look beneath the current task and investigate the prerequisite understanding that supports it.
Why Explicit, Structured Teaching Matters
This approach is consistent with established principles from cognitive science and explicit instruction. Working memory is limited, and learning becomes more difficult when students are required to manage too much new information simultaneously. A maths task may require a student to interpret mathematical vocabulary, recall number facts, remember a procedure, keep track of multiple steps and record their working, all while trying to understand a new concept.
Clear, explicit instruction helps manage these demands. New concepts can be broken into manageable components, connected to prior knowledge, modelled carefully and practised with guidance before students are expected to work independently. Concrete materials and visual representations can also make important mathematical relationships visible, reducing the need for students to hold every element of a problem mentally while they are still developing understanding.
Within a Response to Intervention (RTI) or multi-tiered model of support, this becomes particularly important. Increasing the intensity of intervention should not simply mean giving a student more work. It should mean becoming increasingly precise about what the student needs to learn, how that concept will be taught and how progress will be monitored.
More Practice Is Not Always Better Intervention
Practice is essential when a student understands a concept and needs to develop accuracy, fluency or automaticity. However, if the underlying concept has not been understood, repeating the same type of question may simply give the student more opportunities to practise something that does not yet make sense.
Before increasing the quantity of practice, it is useful to investigate the quality of the student's understanding. Can they demonstrate the concept using concrete materials? Can they represent it visually? Can they explain what is happening using mathematical language? Can they connect the representation to the symbols? Can they apply the same idea when the question looks slightly different?
These observations give educators far more information than simply recording how many questions were answered correctly. They help distinguish between a student who needs further practice and a student who needs the concept to be retaught in a different, more explicit way.
Greater Clarity for Teachers, Better Access for Students
When we identify where mathematical understanding has broken down, intervention becomes more focused. Teachers are no longer selecting activities based on trial and error or continually wondering whether the student simply needs more practice. There is a clearer starting point and a clearer purpose for the teaching that follows.
This can also change the student's experience of mathematics. Instead of being presented with increasingly abstract procedures that feel disconnected, students have opportunities to see mathematical relationships, build them, discuss them and connect them to formal notation. For students who have spent years believing that maths is something they simply cannot do, developing genuine understanding can be particularly important.
Returning to an earlier concept is not about lowering expectations. It is about ensuring the foundations required for future learning are secure.
Maths Should Make Sense
When a student is struggling with maths, our goal should extend beyond helping them complete today's task. We need to understand what is preventing the mathematics from making sense.
Sometimes that means revisiting an earlier concept. Sometimes it means reducing unnecessary language or working-memory demands. Sometimes it means moving away from abstract notation temporarily and making the concept concrete and visible. And sometimes it means explicitly teaching something we had assumed the student already understood.
Effective maths intervention is not about doing more for the sake of doing more. It is about knowing what to teach, where to begin and how to make the mathematics clear.
Because ultimately, mathematics should not be a collection of rules for students to remember. It should be something they can understand.
Further Professional Learning
Maths Australia provides online educator training courses in multi-sensory mathematics and the I-CRAVE Maths® Methodology, with a practical focus on building mathematical understanding and supporting students who are struggling with maths or have gaps in foundational learning.
Educators interested in developing their knowledge and practice can explore the available online training courses at mathsaustralia.com.au/training/