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Decoding the Math in Your Mind: How Problem Size and Interference Shape Your Arithmetic Skills

Lena Kashyap in Mind & Education August 2025 • 4 min read.

"New research delves into the intricate neural processes behind mental math, revealing the surprising ways our brains tackle multiplication."

Arithmetic, a cornerstone of our daily lives, often seems like a straightforward skill. However, the mental processes involved, particularly in tasks like multiplication, are surprisingly complex. Recent research, published in the Journal of Cognitive Neuroscience, delves into the fascinating interplay of two key factors: problem size (how big the numbers are) and interference (how similar problems compete for your attention).

This study, spearheaded by Kerensa Tiberghien and colleagues, moves beyond simply observing these effects. It utilizes cutting-edge brain imaging techniques and advanced statistical methods to untangle how problem size and interference uniquely shape our performance and neural activity during multiplication. The results offer a deeper understanding of the cognitive mechanisms driving our mathematical prowess.

This exploration is more than an academic exercise. It provides a window into how our brains learn, process information, and overcome challenges. Understanding these intricacies can potentially inform educational strategies, helping us optimize learning and improve our mathematical abilities across the lifespan.

The Brain's Math Lab: Unraveling Problem Size and Interference

Illustration of a brain with math symbols and equations.

The study's findings highlight the significant impact of both problem size and interference on our ability to quickly and accurately recall multiplication facts. Researchers found that both factors independently influenced the speed and accuracy with which adults solved multiplication problems.

The research utilized a combination of behavioral tests (measuring reaction times and accuracy) and fMRI brain scans to pinpoint the neural underpinnings of these effects. The fMRI scans allowed researchers to observe which brain regions were most active during multiplication and how those regions responded to variations in problem size and interference.

Problem Size: Refers to the magnitude of the numbers being multiplied. Larger numbers generally lead to slower and less accurate performance.
Interference: Represents the degree of overlap between the current multiplication problem and previously learned facts. Similar problems can 'interfere' with each other, making retrieval more difficult.

The brain scans revealed that problem size and interference activated overlapping regions in the brain, particularly in areas associated with attention, working memory, and number processing. However, the analysis also showed that problem size often had a more substantial and consistent influence, suggesting that it plays a particularly crucial role in the efficiency of mental math.

Implications and Future Directions

This research underscores the intricate interplay of factors that shape our mathematical abilities. The findings suggest that while both problem size and interference are important, the magnitude of the numbers themselves may be the most dominant factor in the efficiency of mental math. Future research could explore how these insights translate into improved learning strategies and interventions for individuals struggling with mathematical concepts. Further studies could also examine how these effects change over the lifespan, from childhood through adulthood.

About this Article -

This article was crafted using a human-AI hybrid and collaborative approach. AI assisted our team with initial drafting, research insights, identifying key questions, and image generation. Our human editors guided topic selection, defined the angle, structured the content, ensured factual accuracy and relevance, refined the tone, and conducted thorough editing to deliver helpful, high-quality information.See our About page for more information.

This article is based on research published under:

DOI-LINK: 10.1162/jocn_a_01359, Alternate LINK

Title: Disentangling Neural Sources Of Problem Size And Interference Effects In Multiplication

Subject: Cognitive Neuroscience

Journal: Journal of Cognitive Neuroscience

Publisher: MIT Press - Journals

Authors: Kerensa Tiberghien, Muhammet I. Sahan, Bert De Smedt, Wim Fias, Ian M. Lyons

Published: 2019-03-01

Everything You Need To Know

What is the primary focus of the research on mental math discussed?

The research primarily focuses on the cognitive processes involved in mental math, particularly multiplication. It investigates the impact of problem size and interference on the speed, accuracy, and neural activity associated with solving multiplication problems. This includes utilizing fMRI brain scans to observe brain region activity during these processes, and behavioral tests to measure reaction times and accuracy when solving multiplication problems.

How does problem size affect mental math performance, according to the study?

According to the research, problem size, which refers to the magnitude of the numbers being multiplied, has a significant impact on mental math performance. Larger numbers generally lead to slower and less accurate performance when solving multiplication problems. This suggests that the brain requires more cognitive resources to process and retrieve multiplication facts involving larger numbers.

What is interference in the context of mental math, and how does it influence problem-solving?

Interference in mental math represents the degree of overlap between the current multiplication problem and previously learned facts. Similar problems can interfere with each other, making the retrieval of the correct answer more difficult. For example, if you are trying to solve 7 x 8, previously learned facts that are similar, such as 7 x 7 or 8 x 8, can create interference, slowing down the problem-solving process and potentially leading to errors.

What brain regions are involved in mental math, and how were they studied?

The research utilized fMRI brain scans to observe which brain regions were most active during multiplication and how those regions responded to variations in problem size and interference. The brain scans revealed that problem size and interference activated overlapping regions in the brain, particularly in areas associated with attention, working memory, and number processing. This allowed the researchers to pinpoint the neural underpinnings of these effects and gain deeper insights into how our brains perform math.

How can understanding problem size and interference influence educational strategies?

Understanding the impact of problem size and interference can potentially inform educational strategies by helping to optimize learning and improve mathematical abilities. Recognizing that problem size significantly influences the efficiency of mental math suggests that instructional approaches might focus on building a strong foundation with smaller numbers before introducing larger ones. Furthermore, strategies to minimize interference, such as spaced repetition or differentiating between similar multiplication facts, could be beneficial for students struggling with multiplication. Future research could further explore these insights to develop more effective learning methods and interventions.