Surreal illustration of interconnected brain nodes representing math problems and cognitive interference.

Unlock Your Mind's Potential: How to Conquer Math Anxiety and Sharpen Your Mental Math Skills

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Nico Varela in Mind & Education October 2026 • 4 min read.

"New research reveals the key to disentangling problem size and interference in multiplication, paving the way for enhanced learning and cognitive performance."


Arithmetic is an essential skill for daily life and mental multiplication stands out as a common arithmetic task that most people use regularly. Mental math relies heavily on memory retrieval which explains why numerical cognition and memory retrieval share a connection. Understanding how our brains process multiplication facts is key to improving our cognitive functions.

The ease or difficulty we experience when retrieving multiplication facts is influenced by problem size (the magnitude of the numbers) and interference (how similar different multiplication problems are). These two factors often intertwine. Disentangling their unique effects can lead to strategies for better learning and reduced math anxiety.

Recent studies have sought to clarify the distinct roles of problem size and interference on our performance and neural responses. By understanding how each factor uniquely impacts our cognitive processes, we can unlock new ways to enhance mental math skills and alleviate math-related stress.

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Tracing Math Anxiety

Basic math skills matter in school and everyday life, yet many people feel apprehension or fear around numerical information—a response termed math anxiety. Research has begun probing its antecedents, onset, risk factors, and possible remediation. A 2019 IBE summary describes math anxiety as distinct from cognitive mathematical learning problems and says several personal and environmental factors interact in its origins. It also notes that societal stereotypes about math may help trigger the gender gap in math anxiety.

The Problem Size Effect: Why Bigger Problems Feel Harder

Surreal illustration of interconnected brain nodes representing math problems and cognitive interference.

The problem size effect (PSE) is a well-known phenomenon where we tend to perform worse (slower and more prone to errors) on larger problems compared to smaller ones. Several explanations for this effect have been proposed. One explanation attributes it to the frequency with which we encounter arithmetical problems in school. Smaller problems are taught more frequently and therefore stored more strongly in our memory, making them easier to retrieve.

Another perspective suggests that small problems have a lesser history of errors. That is because we create stronger associations with the correct answer and it makes it easier to retrieve. Larger problems can have a larger error history since it can be easier to make a mistake when calculating. If you make a mistake, you are more likely to retrieve an incorrect answer.

  • Frequency of Exposure: Problems encountered more often are easier to recall.
  • Error History: Smaller problems have fewer associated errors, leading to more accurate retrieval.
  • Interacting Neighbors: This principle suggests that neighboring problems either cooperate (lead to the same response) or compete (lead to a different response). Consistent neighbors facilitate retrieval, while inconsistent neighbors cause interference.
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Anxiety Does Not Always Impair Calculation

One study found comparable performance between groups with different math-anxiety levels on simple calculation tasks, suggesting elevated trait anxiety alone was not sufficient to significantly impair performance in that setting. The broader relationship between math anxiety and math performance remains unsettled: studies examining its direction have produced conflicting results, and longitudinal studies are scarce. A 2024 review identifies math avoidance as a key mediator that can perpetuate a cycle between math achievement and anxiety. These findings caution against treating anxiety as a uniform, direct cause of poor performance.

Interventions and Anxiety Forms

A meta-analysis of math-anxiety interventions comprised 50 studies and 75 effect sizes. A separate meta-analysis examined math anxiety (MA) and test anxiety (TA), forms of anxiety that have both been associated with aspects of mathematics. It distinguished between different types of mathematical tasks when evaluating their impact. The available descriptions do not provide comparable effect estimates, so they do not establish which anxiety form or intervention approach has the larger effect.

These principles collectively illustrate why larger problems often feel more challenging. Each factor plays a role in how efficiently our brains access and process mathematical information.

Unlocking Cognitive Potential

Disentangling the influences of problem size and interference offers a roadmap for improving mental math skills and reducing math anxiety. The research suggests that targeted strategies and tailored educational approaches can help individuals overcome these cognitive obstacles, leading to enhanced performance and confidence in mathematical tasks. This represents a significant step forward in understanding and optimizing human cognitive abilities.

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Anxiety and Mathematical Performance

A meta-analysis distinguishes math anxiety (MA) from test anxiety (TA) and evaluates their impact across different types of mathematical tasks. A 2022 article defines math anxiety as feelings of anxiety when confronted with mathematics and reports a moderate negative correlation with math achievement. It also notes possible negative implications for mental health and well-being. Together, these sources frame math anxiety as relevant to both mathematical outcomes and well-being, without establishing that it affects every task or person in the same way.

Early and Lasting Consequences

A 2026 brief reports that approximately 20% of the general population experiences math anxiety, including children as young as 5. It says the negative impact on children’s mathematical performance is well documented and that anxiety, if unaddressed, can last into adulthood. A separate 2026 source says math anxiety can disrupt immediate academic performance and have lasting implications for educational and career choices. These sources point to concerns extending beyond a single classroom or test, while the supplied summaries do not quantify those long-term effects.

How anxiety findings compare across groups

A meta-analysis reported moderate average effects for interventions aimed at reducing math anxiety and improving math performance, but these are separate outcomes rather than a single combined measure.[1]

In young Chinese students, math anxiety had a negative association with math performance (r = −0.318); in young USA children, the reported association was also negative (r = −0.23).[2]

A longitudinal study of US adolescents found correlations between performance in one year and anxiety in the following year, while a separate analysis found a significant relationship only among students whose performance did not improve over time.[3] [4]

What the reported figures measure

  • g = -0.467 effect sizeAverage effect size for reducing math anxiety: g = -0.467.[1]
  • approximately 55% variance explainedThe overall model combining math anxiety, working memory, age, and biological sex explained approximately 55% of the variance in math achievement.[5]

What the evidence suggests about anxiety and calculation

The combined model links anxiety and working memory with achievement, but it does not show that anxiety alone causes a particular result; the reported relationship may run in either direction or develop iteratively.[5] [6]

Anxiety could affect performance by diverting attention with intrusive thoughts or by hindering the development of effective study techniques, while another account describes effects on information processing and retrieval.[3] [7]

What remains unclear about anxiety and working memory

  • Does working memory, especially difficulty inhibiting irrelevant information, help explain how anxiety relates to mathematics performance? The reported work could not disentangle the direction of these relationships.[8]
  • Would a more fine-grained numerical cognition task reveal an association that the task used did not clearly show?[5]
  • Can the observed links establish developmental or causal pathways, given that one source describes a concurrent correlational study with adults?[9]
  • How might limited attentional resources affect complex operations, and how does that account fit with the evidence on retrieval and working memory?[5] [6]

What learning practices are described

Which arithmetic learning practices do the sources recommend?

The recommendations include monitoring early numeracy, explicitly teaching strategies and concepts, using structured retrieval practice, delaying timed practice until accuracy is established, and allowing time for discussion and cognitive reflection.[10]

Sources

  1. A Meta-Analysis of Math Anxiety Interventions| Journal of Numerical Cognition (jnc.psychopen.eu)
  2. The Relationship Between Math Anxiety and Math Performance: A Meta-Analytic Investigation (pmc.ncbi.nlm.nih.gov)
  3. The Chicken or the Egg? The Direction of the Relationship Between Mathematics Anxiety and Mathematics Performance (pmc.ncbi.nlm.nih.gov)
  4. Assessment of math anxiety as a potential tool to identify students at risk of poor acquisition of new math skills: longitudinal study of grade 9 Italian students (pmc.ncbi.nlm.nih.gov)
  5. The Neurocognitive Architecture of Individual Differences in Math Anxiety in Typical Children (pmc.ncbi.nlm.nih.gov)
  6. Math Anxiety and Working Memory Updating: Difficulties in Retrieving Numerical Information From Working Memory (www.frontiersin.org)
  7. Strategies for remediating the impact of math anxiety on high school math performance (pmc.ncbi.nlm.nih.gov)
  8. Mathematics Anxiety, Working Memory, and Mathematics Performance in Secondary-School Children (www.frontiersin.org)
  9. Basic Symbolic Number Skills, but Not Formal Mathematics Performance, Longitudinally Predict Mathematics Anxiety in the First Years of Primary School (pmc.ncbi.nlm.nih.gov)
  10. What the Science of Learning Teaches Us About Arithmetic Fluency. (journals.sagepub.com)

About this Article -

Written with AI assistance from published research, and reviewed by the Mystum team. See our About page for more information.

Everything You Need To Know

1

What is the 'problem size effect' in mental math?

The problem size effect refers to the phenomenon where individuals typically perform worse on larger arithmetic problems compared to smaller ones. This means people are generally slower and make more errors when dealing with problems involving bigger numbers. Factors contributing to this include the frequency of exposure to smaller problems during learning, the lesser error history associated with them, and the way neighboring problems interact in our memory.

2

What does 'interference' mean in the context of mental multiplication?

Interference in mental math refers to the cognitive challenge that arises from the similarity between different arithmetic problems. When problems are too alike, especially in terms of their numbers, our brains may struggle to differentiate and retrieve the correct answers, leading to confusion and errors. The concept of interacting neighbors, where similar problems either cooperate or compete in memory, is closely related to interference.

3

How do problem size and interference affect my ability to do mental math?

The interplay between problem size and interference impacts our mental math abilities. Problem size dictates the magnitude of numbers we're working with, while interference deals with the similarity between different problems. Larger problem sizes often lead to decreased accuracy, while interference can cause confusion. Research aims to disentangle these effects so that tailored learning strategies can overcome these obstacles.

4

What is meant by the term 'error history' and why is it important?

Error history refers to the record of mistakes we've made while learning and practicing arithmetic problems. Smaller problems typically have a lesser error history compared to larger ones. When we have fewer incorrect associations with a problem, it becomes easier to retrieve the correct answer. This is why consistent practice with smaller problems can lead to more accurate and quicker recall.

5

What is 'frequency of exposure' and how does it relate to mental math skills?

Frequency of exposure refers to how often we encounter certain arithmetic problems, especially during our early education. Problems we see more frequently are more strongly stored in our memory, making them easier to recall. This is why smaller problems tend to be easier, as they are often taught and practiced more than larger ones. Consistent reinforcement strengthens memory traces and improves retrieval speed.

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