Why Do So Many Students Find Word Problems Challenging?

“I don’t understand word problems.”

“I don’t know what to do.”

“Do I add, subtract, multiply or divide?”

I have heard these statements many times from students. On the surface, they may appear to describe the same difficulty: the student does not know how to solve word problems. Over the years, however, my experience in teaching and tutoring has shown me that the same statement can reflect very different difficulties.

I remember one student who would look at a word problem and, before even reading it, say, “I don’t understand.”

Another student reacted differently. If he saw fractions in a problem, he would immediately say, “I don’t know how to do it.” When the numbers looked more familiar, he would read the problem and then ask, “Do I need to add, subtract, multiply or divide?”

A third student experienced a different challenge. When reading quickly, she sometimes skipped words that she had not fully processed. By the time she reached the end, important information was missing from her understanding of the situation, and the problem no longer made sense to her.

All three students might have described themselves as having difficulty with word problems, yet the source of that difficulty was not necessarily the same. As a result, understanding what each student needed required looking beyond the statement, “I don’t understand word problems.”

In my own tutoring experience, approximately 95% of the students I have worked with who struggled significantly with word problems also showed gaps in prerequisite knowledge, learning skills, or both. This is an observation from my practice, not a published statistic, but it has strongly influenced the way I approach these difficulties. Rather than immediately showing a student how to solve the problem in front of them, I first try to understand what is preventing that student from solving it.

That question shifts the focus from whether the student can produce an answer to what happens between reading the problem and arriving at that answer.

A Word Problem Begins With a Situation

Although we tend to associate word problems with mathematics, students encounter problems presented through language across STEM subjects. A physics problem may describe the motion of an object and require the student to identify relevant quantities and physical principles. A chemistry problem may present quantities of reactants and ask about the amount of product that can be formed. A biology problem may involve experimental data, population change, rates, inheritance, or relationships between variables. In mathematics, the context may involve finances, geometry, proportional relationships, patterns, or rates of change.

The subject knowledge varies, but these problems share an important characteristic: students are given a situation and a question, but they are not necessarily told which knowledge to use, how to represent the situation, or which strategy will lead to a solution.

Consider the difference between being given

3x+5=20 and being asked to solve for \(x\), and being presented with a situation in which the same relationship is embedded in a paragraph. In the first case, the mathematical representation has already been constructed, allowing the student to concentrate on solving the equation. In the second, the student may first have to understand the situation, determine what needs to be found, recognize how the information is connected, and decide how those relationships can be represented mathematically.

This distinction is reflected in the OECD’s PISA mathematics framework, which describes contextual mathematical problem solving in terms of formulating a situation mathematically, employing mathematical knowledge and procedures, and interpreting and evaluating the result in relation to the original context. Importantly, the framework does not describe authentic problem solving as a rigid sequence. A solver may return to an earlier interpretation, reconsider an assumption, or change a representation as their understanding develops.

A word problem, therefore, is not simply a calculation surrounded by words. For the calculation to be meaningful, students first need to understand what the situation is describing.

Reading the Words Is Not Necessarily Understanding the Situation

Imagine that a student leaves home to go to school. Halfway there, they realize that they have forgotten a notebook, return home to get it, and then leave for school again.

There is no calculation to perform yet, but there is already information to understand and connect. To make sense of what happened, the reader needs to construct a coherent representation of the journey:

home → halfway to school → home → school

Once the situation is understood, the reader can recognize that the student travelled farther than on a normal trip and that the journey took additional time.

A student could read every sentence correctly without forming this complete picture. Reading the words and understanding the situation created by those words are related, but they are not the same thing.

Research on arithmetic word problems supports the importance of this mental representation. In a study involving adults, Catherine Thevenot found evidence that participants constructed a mental model of the situation described in arithmetic word problems rather than relying only on their literal wording.

The OECD framework similarly recognizes text comprehension as important to mathematical literacy and includes reading, decoding, and making sense of statements among the activities involved in formulating a situation mathematically.

This helps explain why simply telling a student to “read the question again” may not address the actual difficulty. The student may have read every sentence several times without forming a clear picture of what is actually happening in the problem. In such a case, another reading may help only if the student also knows what to look for and how to connect the information.

Making Sense of a Problem Is Something Students Develop

When a student struggles to process the information in a word problem, it is important not to assume immediately that the difficulty reflects an inherent limitation in the student’s ability to process information. Cognitive, language, or learning-related factors may contribute for some learners, but learning and experience also matter.

As students gain experience with problem solving, they learn to do more than read for individual facts. They begin to connect pieces of information, recognize how quantities are related, represent those relationships when necessary, and connect the situation with knowledge they have already developed. They also learn to notice when their interpretation does not make sense and to reconsider it.

These abilities may eventually appear natural in an experienced problem solver, but they do not necessarily develop because a strategy has been demonstrated once. There is an important progression between being shown something, understanding it, applying it with guidance, using it independently, and recognizing when the same reasoning can be transferred to an unfamiliar situation.

A student may, for example, successfully answer the questions a teacher or tutor asks while solving one problem but remain uncertain about where to begin when faced with the next problem independently. Similarly, a student may solve several familiar problems successfully and then struggle when the context changes, even though the underlying concept remains the same.

Research with younger students provides evidence that some aspects of word-problem reasoning can be explicitly taught. A review by Sarah Powell examined 12 studies of schema-based instruction involving Grade 2 and 3 students who were at risk for, or identified with, learning disabilities. The studies focused on addition and subtraction word problems and included instruction designed to help students recognize underlying problem structures and connect them with appropriate solution methods.

Because this research concerned a specific age group, student population, and range of problems, its findings should not be generalized to all word-problem learning. It does, however, provide evidence that students can benefit from explicit instruction in recognizing problem structure rather than being expected to develop this ability entirely on their own.

Knowledge Gaps May Remain Hidden Until Students Have to Decide What to Use

In my experience, prerequisite knowledge is one of the most important—and sometimes overlooked—factors in word-problem difficulty.

Imagine a worksheet titled Solving Linear Equations. Before the student has read the first question, the title has already provided an important clue about which area of mathematics is likely to be needed. The same thing happens when students complete a page of problems immediately after a lesson on the Pythagorean theorem, Newton’s laws, or stoichiometry. The surrounding lesson often tells them which knowledge to retrieve.

A contextual problem may remove that support. The student must now recognize independently that the situation involves proportional reasoning, that a relationship may be linear, that conservation of energy is relevant, or that a mole ratio is needed.

This requires more than remembering a formula or carrying out a procedure. Students need enough conceptual understanding to recognize when and why that knowledge applies.

A student cannot readily recognize that a situation involves proportional reasoning if their understanding of proportionality is not yet well developed. Similarly, constructing an appropriate linear model is difficult without a solid understanding of rate of change. A student with gaps in their understanding of fractions may become so focused on the fractions themselves that they struggle to reason about the larger situation.

This is what made the response of one of my students particularly revealing. As soon as he saw fractions, he said, “I don’t know how to do it,” even though he had not yet read the problem.

The fractions had become the problem before he knew what the problem was about.

The OECD framework recognizes the importance of mathematical content knowledge in contextual problem solving. Students draw on what they know to recognize mathematical structures and relationships, make connections with mathematical concepts and procedures, and formulate a representation that can be used to address the problem.

This helps explain why word problems can reveal knowledge gaps that routine exercises do not always expose. A student may successfully perform a procedure when the type of procedure has effectively been selected for them. A different level of understanding and independence is required when the student must recognize which knowledge is relevant without being told.

From Words to Mathematical Representation

Another difficulty appears when students try to move too quickly from words to computation.

“Do I add or subtract?”

“Is this multiplication?”

“Which formula do I use?”

These questions are understandable because students know that a calculation will often form part of the solution. The difficulty is that they are moving toward computation before fully understanding the situation.

I often tell students that mathematics is a language because a situation can be expressed mathematically through quantities, relationships, symbols, diagrams, graphs, or equations. Translating a word problem into mathematical language is therefore not about matching individual words with operations. It is about understanding the relationships described in the situation and finding an appropriate way to represent them mathematically.

Before choosing an operation or formula, the student needs to understand what is happening, what needs to be determined, and how the information in the problem is connected. Only then does the question of how to represent those relationships mathematically become meaningful.

Depending on the problem, that representation may take the form of an equation, diagram, table, graph, function, proportion, vector diagram, or another model. The OECD includes this movement from contextual information to mathematical structure and representation within the process of formulating a problem mathematically.

This becomes increasingly important as students move into more advanced mathematics and science. In mathematical modelling, a student may need to identify variables and establish their relationship before an equation or function exists. In physics, the student needs to understand the motion or interaction described before deciding which physical principle or mathematical relationship is appropriate. In chemistry, knowing how to perform a calculation is of limited use if the student has not first understood the chemical relationship represented by the situation.

Computation is therefore only one part of the work. The mathematical procedure needs to follow from an appropriate understanding and representation of the problem.

Learning Skills Influence the Entire Process

Even when the necessary knowledge and problem-solving strategies are present, students still have to manage their own thinking while working through the problem. This is where learning skills become particularly important.

A student may need to slow down rather than rush toward a calculation, reread a sentence when its meaning is unclear, organize information, notice when an interpretation does not make sense, and reconsider an approach that is not working. They may also need to continue working when the correct approach is not immediately obvious rather than assuming that not knowing what to do immediately means that they cannot solve the problem.

This brings me back to the student who would look at a problem and immediately say, “I don’t understand.” Because she had not yet read and engaged with the problem, I could not determine whether she was struggling with the mathematical concepts, with making sense of the situation described in the problem, or with another aspect of the task. Her response therefore became a starting point for understanding the difficulty rather than evidence of what the difficulty actually was.

The same caution applies to the student who stopped as soon as he saw fractions. His reaction showed that the fractions were creating a barrier, but it did not explain the source of that barrier. A gap in fraction knowledge might have contributed, but other factors could also have been involved. The behaviour gave me something to investigate rather than a conclusion to draw.

This distinction matters in tutoring because demonstrating the solution immediately can sometimes conceal the underlying difficulty. The student may leave knowing how one particular problem was solved without having developed a better way to approach the next one. At times, the more important work is helping the student learn how to remain engaged with a problem, examine what they understand, and decide what to try when the solution is not immediately apparent.

Why Can a Student Do the Calculation but Struggle With the Word Problem?

This is a question that can be puzzling for both students and parents. A student may know how to solve an equation, multiply fractions, or apply a formula when the task is presented directly, yet struggle when the same mathematical knowledge is embedded in a contextual problem.

Research on working memory provides another perspective on why contextual problems can differ from isolated calculations. A 2023 meta-analysis synthesized 130 studies involving 43,938 participants and 1,355 effect sizes and found a moderate association between working memory and mathematical problem solving. The association was stronger for contextualized, or what the researchers called “dressed-up,” word problems than for intra-mathematical problems.

This does not mean that a student who struggles with word problems necessarily has a working-memory deficit. The research describes an association across many studies and cannot be used to diagnose the reason an individual student is struggling.

It does, however, help illustrate how much information and reasoning may need to be coordinated during contextual problem solving. A student may need to connect information from different parts of the text while keeping the question in mind. At the same time, they may be retrieving prior knowledge, examining how quantities are related, developing a representation, and deciding which strategy to use before or while carrying out the necessary mathematical procedures.

Prior knowledge can affect these demands as well. If working with fractions still requires substantial conscious effort, for example, reasoning about the larger situation may become more difficult. Similarly, a student who is still trying to reconstruct the meaning of rate of change while interpreting a graph and deciding what the problem requires is managing a different task from a student for whom those concepts are already well established.

The research does not justify reducing every difficulty to working memory or “cognitive overload.” It does, however, reinforce an important distinction: knowing how to perform a computation in isolation does not necessarily mean that a student can readily coordinate all the reasoning required to recognize when and how to use it in context.

What Neuroscience Adds—and What It Does Not

Neuroscience provides another perspective on the complexity of word-problem solving, although its contribution needs to be interpreted carefully.

Earlier neuroimaging research with proficient adults found differences in brain activation and connectivity when participants solved arithmetic word problems compared with closely matched non-arithmetic narratives. The findings support the broader idea that arithmetic word-problem solving involves more than text comprehension alone and includes processes associated with mathematical model building and calculation.

More recent research has examined arithmetic word-problem solving directly in children. A 2025 study by Ng, Chen, and Chang investigated Grade 3 and Grade 4 students using arithmetic word problems and comparable non-arithmetic narrative problems. Children’s performance on the arithmetic word problems was associated with both reading comprehension and arithmetic fluency, whereas performance on the non-arithmetic problems was associated with reading comprehension but not arithmetic fluency.

These findings illustrate how both language comprehension and mathematical fluency are related to children’s performance on arithmetic word problems. They do not establish that either factor, by itself, explains why an individual student struggles. The researchers also found developmental differences between children and adults in the neural systems recruited during arithmetic word-problem solving, reinforcing the need for caution when applying findings from proficient adults directly to children.

Neuroscience can therefore help researchers investigate what happens during problem solving, but it cannot, on its own, explain why an individual student is struggling with a particular problem. From an educational perspective, I need to follow the student’s reasoning from the beginning. First, can the student make sense of the situation and explain what is happening? Next, can they determine what the problem is asking and understand how the information given is connected? I can then examine whether they have the prerequisite knowledge needed to recognize the mathematical or scientific concepts involved. From there, I can observe whether they can represent the situation appropriately, select and apply a suitable strategy, carry out the necessary computation, and finally interpret the result in relation to the original situation.

Following the student’s reasoning in this way helps me identify where the process begins to break down and what kind of support may be needed. These are not rigid steps; during authentic problem solving, students may move back and forth between them as their understanding develops or as they reconsider an earlier decision.

Why Progress Can Take Time

Identifying where a student’s reasoning begins to break down is only the beginning. Addressing the underlying difficulty may require time, particularly when the goal extends beyond correcting a discrete gap in knowledge.

If a student has forgotten how to solve a particular type of equation, targeted review and practice may produce visible improvement relatively quickly. Developing a more independent approach to unfamiliar problems may require considerably more time because the student is not simply learning another calculation. They may be developing new ways of interpreting information, connecting ideas, selecting strategies, monitoring their understanding, and continuing to reason when the solution is not immediately apparent.

Consider a student who habitually extracts the numbers from a problem and immediately searches for an operation. Initially, I may deliberately ask the student not to calculate anything.

What is happening in the situation?

Can you explain it in your own words?

Could you represent it with a diagram?

Which quantities are related?

What changes?

What remains constant?

What previous knowledge might be useful here?

Why?

At first, the student may rely heavily on these prompts to guide their thinking. With repeated practice and gradually reduced support, however, the goal is for the student to begin asking these questions independently.

That progression matters because being able to solve a problem with guidance is not yet the same as being able to solve it independently. Even independent success with a familiar type of problem does not necessarily mean that the student will immediately recognize how to transfer the same reasoning to a problem whose context or presentation looks different.

In tutoring and coaching, I often see development before I see consistency. A student may begin to read more carefully but still need support selecting a strategy. Later, the same student may construct an appropriate representation but hesitate to proceed without confirmation. Eventually, the student may solve the problem independently while still needing to develop the habit of evaluating whether the result is reasonable.

These intermediate changes matter. Progress should not be judged only by the number of correct answers because greater independence may first appear in the way the student approaches the problem: pausing before calculating, explaining the situation, choosing a representation, justifying a strategy, or reconsidering an approach that does not make sense.

More Practice Is Not Always the First Answer

Practice is essential to learning, but More Practice and Targeted Practice are not the same thing.

If a student does not understand proportional reasoning, assigning twenty additional proportional word problems without first addressing the conceptual gap may simply reproduce the same difficulty. If a student routinely extracts the numbers and guesses an operation, additional problems may provide more opportunities to rehearse the same ineffective approach. Similarly, if a student does not know how to represent relationships within a situation, telling them to “keep practising word problems” does not, by itself, teach that missing skill.

The support therefore needs to correspond to the difficulty. For one student, this may mean rebuilding prerequisite knowledge; for another, it may require explicit modelling of how to understand and represent a situation. Another student may need support monitoring their understanding or persisting when the strategy is not immediately apparent, while a student who can already do these things with guidance may primarily need carefully structured opportunities to practise them with progressively less support.

The word problem may be where the difficulty becomes visible, while the source of that difficulty may lie in prerequisite knowledge, problem-solving strategies, learning skills, or a combination of these.

Getting an Answer Is Not the End of the Problem

There is another part of problem solving that is easily overlooked: returning to the original situation after the mathematical work has been completed.

Students sometimes treat a numerical result as the end of the task, yet the result still needs to be interpreted. Does it make sense in the original situation? Are the units appropriate? Is the magnitude reasonable? Does the answer actually address what was asked?

A calculation can be performed correctly even when the model on which it is based is inappropriate. In that case, accurate computation does not produce an appropriate solution.

The OECD framework treats this return to context as an important component of mathematical problem solving. Interpreting and evaluating mathematical outcomes includes considering whether a result makes sense in context, explaining what the result means, and recognizing limitations in the model or assumptions used.

This is more than checking arithmetic. It requires students to think critically about what their answer means and whether the mathematical work they completed actually answers the original question.

So, Why Do Students Find Word Problems So Challenging?

There is no single explanation because successful word-problem solving brings several areas of learning together. Students need to make sense of the situation, connect it with relevant knowledge, determine how to represent and approach it mathematically, carry out the necessary procedures, and return to the original situation to decide whether their answer makes sense. How independently they can manage this reasoning is also influenced by the learning skills they have developed.

These aspects of problem solving interact. A gap in prerequisite knowledge can make an important relationship difficult to recognize, while an incomplete understanding of the situation can lead to an inappropriate mathematical representation. A suitable representation combined with a computational error can still produce an incorrect answer, just as an accurately performed calculation based on an inappropriate model can produce a result that does not make sense.

This is why, when a student tells me, “I’m not good at word problems,” the statement itself does not tell me enough. I need to understand what happens when that student actually encounters one and identify where their reasoning begins to break down.

Sometimes the work involves rebuilding prerequisite knowledge. Sometimes students need explicit support learning how to understand and represent a situation. At other times, learning skills and problem-solving habits need further development. Often, several of these areas need attention together, which is one reason meaningful and consistent progress may take time.

The purpose of tutoring, in my view, is not to make difficult thinking disappear by doing it for the student. Guidance may be substantial at first, particularly when knowledge or learning skills are still developing, but the goal is gradually to reduce that support as the student becomes more capable of managing the reasoning independently.

Ultimately, the questions I once needed to ask should become questions the student asks independently.

For me, that is one of the most meaningful signs of progress. The change is not simply that the student can solve more word problems, but that when faced with an unfamiliar situation, the immediate response gradually shifts from “I don’t know how to do this” toward a much more productive question:

“What do I know, and how can I use it to figure this out?”