Brain with multiplication symbols representing problem size and interference

Unlocking the Secrets of Multiplication: How Problem Size and Interference Affect Your Brain

Elliot Brynn in Mind & Education August 2025 • 4 min read.

"New research reveals how your brain tackles multiplication, separating the impact of problem size and mental interference for clearer insights into cognitive processes."

Arithmetic, a fundamental skill we use daily, relies heavily on memory, especially when it comes to multiplication. Think about it: quickly recalling that 7 x 8 = 56 is much faster than counting it out. But what makes some multiplication facts easier to remember than others? Researchers have long been intrigued by two main factors: problem size and interference.

Problem size refers to the magnitude of the numbers being multiplied. For instance, most people find 2 x 3 easier than 8 x 9. Interference, on the other hand, involves the competition between similar math facts stored in our memory. Imagine trying to recall 6 x 7 when you also know 6 x 8; the similar facts can interfere with accurate retrieval.

A recent study published in the Journal of Cognitive Neuroscience sought to disentangle these two intertwined influences, examining how problem size and interference uniquely affect both performance and brain activity during multiplication. By using sophisticated brain imaging techniques, the researchers aimed to uncover the distinct neural pathways involved in these processes, providing new insights into how our brains perform arithmetic.

Why is Multiplication so Reliant on Memory?

Brain with multiplication symbols representing problem size and interference

From splitting the bill at a restaurant to calculating grocery costs, arithmetic is woven into the fabric of daily life. Its automaticity stems from the fact that multiplication and basic math are heavily rooted in memory. Over years of schooling and everyday application, we've trained our brains to recall these facts directly, rather than recalculating them each time. Direct retrieval speeds up processing and frees up cognitive resources for more complex tasks.

The problem size effect (PSE) has fascinated researchers for decades. It's the phenomenon where larger problems (like 8 x 7) typically result in slower and more error-prone responses compared to smaller problems (like 2 x 3). Several explanations have been proposed:

Frequency of Exposure: Larger problems are encountered less often, leading to weaker memory traces.
Error History: Larger problems are more prone to errors during the initial learning phases, creating stronger associations with incorrect answers.
Network Interference: Verguts and Fias's (2005) model suggests that neighboring problems in our memory network compete with each other. When problems lead to the same answer (e.g., 4 x 6 = 24 and 4 x 7 = 28), they cooperate, facilitating retrieval. However, when they lead to different answers (e.g., 4 x 4 = 16 and 4 x 5 = 20), they compete, causing interference.

In addition to problem size, interference also plays a significant role. The multiplication interference effect suggests that similar math facts stored in memory compete during retrieval, causing delays and errors. But how can we determine unique contributions of each in explaining the cognitive and neural bases of mental multiplication.

Untangling Cognitive Complexity

By carefully disentangling the influences of problem size and interference, this study sheds new light on the complex cognitive processes underlying multiplication. While both factors play a role, problem size appears to be the dominant driver of both behavior and brain activity in adults. The findings highlight the importance of considering both overlapping and unique contributions of each factor in understanding how we learn and remember math facts.

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Everything You Need To Know

Why do larger multiplication problems, like 8 x 9, seem harder than smaller ones, such as 2 x 3?

The difficulty in solving multiplication problems is influenced by 'problem size'. Larger problems, like 8 x 9, are typically more challenging because of several factors. Firstly, we encounter these problems less frequently, leading to weaker memory traces. Secondly, there's a higher chance of making errors during initial learning, solidifying incorrect associations. Furthermore, 'Network Interference', as proposed by Verguts and Fias's (2005) model, comes into play. Similar problems compete with each other in our memory network, which can cause interference, and slow down the retrieval process. This combination of factors makes larger multiplication problems harder to recall quickly and accurately.

What is the role of 'interference' in mental multiplication, and how does it affect our ability to solve problems?

The 'interference' effect in multiplication refers to the competition between similar math facts stored in our memory. When we try to recall a specific multiplication fact, similar facts can 'interfere' with the retrieval process, leading to delays and errors. For instance, if you're trying to remember 6 x 7, the related facts like 6 x 6 or 6 x 8 can cause interference, making it harder to access the correct answer immediately. This interference is more pronounced when the neighboring problems in our memory network lead to different answers, which is the core idea behind Verguts and Fias's (2005) model of network interference. The study examines how problem size and interference uniquely affect both performance and brain activity during multiplication.

How does our brain's reliance on memory affect our ability to perform multiplication quickly?

Multiplication's automaticity stems from its deep roots in memory. We've trained our brains to directly recall these facts rather than recalculating them each time, thanks to years of practice. This direct retrieval greatly speeds up processing and frees up cognitive resources for more complex tasks. The ability to quickly recall that 7 x 8 = 56, rather than calculating it from scratch, highlights this reliance on memory and its impact on cognitive efficiency. The study aimed to uncover the distinct neural pathways involved in these processes, providing new insights into how our brains perform arithmetic.

What are the key factors, as highlighted by research, that influence the difficulty we experience with multiplication problems?

The primary factors that impact the difficulty of multiplication problems are 'problem size' and 'interference'. 'Problem size' refers to the magnitude of the numbers being multiplied; larger numbers generally make problems more challenging. 'Interference' involves the competition between similar math facts stored in our memory. Both factors significantly affect our performance and brain activity during multiplication. The research sought to disentangle these intertwined influences to understand their unique contributions to cognitive processes. The problem size appears to be the dominant driver of both behavior and brain activity in adults.

How can understanding 'problem size' and 'interference' help us improve our multiplication skills or strategies?

Understanding the impact of 'problem size' and 'interference' can inform more effective learning strategies for multiplication. Recognizing that larger problems are often harder due to weaker memory traces and error history, we can focus on more frequent practice of these facts to strengthen memory. Being aware of the 'interference' effect, we can use spaced repetition and varied practice to differentiate between similar math facts and reduce the competition between them. For example, when learning multiples of 6, actively contrasting 6 x 7 with 6 x 6 and 6 x 8 can help reinforce the correct answer and minimize confusion. This awareness also helps us appreciate the importance of consistent practice and the development of a robust memory network for multiplication facts.