Summary: A recent study found that kids learn arithmetic the best through a structured technique that incorporates theoretical knowledge with briefed timed reflection and practice. The most effective training cycles through both strengthening quantity sense and using intellectual strategies rather than rote memorization or wealthy discussion.
According to researchers, automated recall and the ability to freely apply number relationships should be a key component of fluency. These mental science findings can influence earlier math instruction and improve educational and other long-term outcomes.
Important Information
- Mathematical fluency Redefined: It includes both quick recall and flexibly reasoning with numbers.
- The best training combines timed practice with representation and philosophical understanding, according to the Integrated Approach.
- Potential Impact: A high first level of math proficiency is expected to help students succeed in algebra, word problems, and even potential income.
APS Resource
What is the best way for kids to learn math: remembering number values and multiplication tables, or studying math concepts at a deeper, theoretical level?  ,  ,
The benefits of these two approaches have been debated for a while, but a new record in Psychological Science in the Public Interest shows that children learn best when they are taught to follow an evidence-based period: establishing facts in philosophical understanding, using short, timed practice to create those facts involuntary, and then returning to discussion and reflection to strengthen that knowledge.  ,
What Arithmetic Fluency Can Learn from the Science of Learning?, according to the report, includes insight from developmental mental technology that can help children develop their mathematical fluency, which is typically defined as a child’s ability to solve math problems quickly and accurately.
The researchers suggest expanding the definition of mathematical competency to include not only the automatic remember of details, such as 6 8 = 48, but also the use of number relationships to fix problems.  ,
Nicole McNeil ( University of Notre Dame ), Nancy Jordan ( University of Delaware ), Alexandria Viegut ( University of Wisconsin–Eau Claire ), and Daniel Ansari ( Western University ) are the authors of the paper.
The researchers, who are all authorities on children’s math learning, describe their observations on how mathematical competence develops, why it matters, and how teachers can support students in achieving it.  ,  ,
” We want to become clear: Teachers don’t have to choose between rich class discussions and timed discipline,” said lead author Nicole McNeil.
Students are given the fluency they need to succeed by a properly structured approach that involves brief, timed sessions that reinforce memories with deliberate reasoning and discussion activities that weave those memories into an integral knowledge network.
To identify the building blocks and effects of fluency, which starts with quantity sense and quantitative reasoning in preschool, the paper incorporates findings from cognitive experiments, horizontal studies, neuroimaging, and design-based research.
First math activities help children understand the meaning of figures, relations, and functions in much the same way that phonics support reading.
The authors recommend using opportunities to help children count and tag the total number of items in normal sets, such as blocks or grain bits, as parents and educators.  ,
The authors turn to fundamental theories of mental development to clarify how fluency develops, which view mathematical learning as an entangled shift between implicit and explicit understanding.
Children first acquire intuitive insights; they mix numbers without being able to express their reasoning ( implicit knowledge ).
Eventually, they make that knowledge obvious by articulating styles and approaches ( for example, “order doesn’t problem in addition,”” start with the bigger number,” etc. ) and arguing why they work.
Students can retrieve facts and strategies quickly, with little mental effort, after a deliberate, well-organized practice that then reprograms this explicit knowledge.  ,
According to the authors, instruction should encourage shifts between implicit and explicit knowledge by laying out the rationale behind earlier intuitions and providing sufficiently focused practice to enable those concepts to advance quickly and effectively for higher level problem solving.
They claim that first mathematical education should include the following:  ,
- First progress monitoring is used to identify gaps in a boy’s intellectual understanding of numbers.  ,
- obvious instruction  on thinking methods, such as using 10 as a point of reference for simple emotional calculations.  ,
- Babies recall well-organized searching practice, including mathematical combinations and their amounts or products.  ,
- Time-limited practice that encourages individuals to use quick recovery techniques rather than slower counting techniques. This should only be used after kids demonstrate higher precision with the information being used, though.
- In mathematics activities, discussion, reflection, and justification are used to aid students in understanding the underlying principles of mathematical and give them the opportunity to express their ideas.  ,  ,
The authors also discuss how crucial mathematics proficiency is to the future of children. According to research, students who are fluent in math are more prepared to understand how to fix word problems, reason with fractions, and learn algebra. Additionally, research explores the relationship between competency and later-life effects, such as income and educational attainment.  ,
The experts advocate for evidence-based instruction that mirrors what we currently know about how kids learn.
In teacher preparing programs, especially in early childhood education, they advocate more andnbsp, developmental cognitive science, so that teachers you evaluate academic strategies through the lens of learning technology.  ,
Developmental psychologist Melissa E. Libertus ( University of Pittsburgh ) said the review raises a few questions for future research in an accompanying commentary. These include the use of digital tools to facilitate personal arithmetic learning and the role of parents ‘ math anxiety in their children’s math skills.  ,
However, McNeil and her coauthors make a compelling argument, Libertus said, because competence education is crucial for helping students develop math skills in the workforce of tomorrow.  ,
About this report on research into understanding, math, and neurodevelopment.
Author: Hannah Brown
Source: APS
Contact: Hannah Brown – APS
Image: The image is credited to Neuroscience News
Start access to original study.
Libertus, M. E., and the household environment’s” The Importance of Early Mathematical Foundations, Sensitivity, and the Development of Arithmetic Fluency” by Libertus, M. E., and others. Psychology in the Public Attention
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What the Science of Learning Teach Us About Arithmetic Fluency, by McNeil, N. and others. Psychology in the Public Attention
Abstract
The importance of children’s development of mathematical fluency is explained in a comment on McNeil et al.
McNeil et cetera. The paper’s review of the literature on arithmetic fluency, published in ( 2025 ), and made a compelling case for the value of mathematics education in developing arithmetic fluency.
They emphasized that the development of mathematical fluency is essential for developing and deepening one’s understanding of mathematical principles beyond simply memorizing mathematical facts.
It seems simple to understand how memorization frees mental resources during scientific problem-solving, but it could also be done using other means, such as a calculator.
However, an underrated idea is that learning mathematical fluency enables children to learn patterns and principles in relationships between numbers that transcend the plain facts. McNeil and Associates It is convincingly suggested that mathematical proficiency can thus serve as the foundation for the formulation of technique and conceptual understanding of numbers ( for instance, 9 = 4 + 5 = 4 + 4 + 1 or 9 = 5 + 4 = 5 + 1 ).
An essential framework for understanding why maintaining mathematical fluency is crucial is to be able to clearly identify this bidirectional interaction between implicit and explicit knowledge.
Abstract
What Arithmetic Fluency Can Learn from the Science of Learning?
High-quality mathematics training promotes innovation and advancement across society as well as improving individual life results. But what precisely qualifies as receiving a high-quality algebra training?
By focusing on mathematical competence in this article, we contribute to this debate. Long and contentious discussions have raged over how best to educate math.
If we illustrate memorization strategies like timed drills and flashcards or advocate” thinking strategies” through play and real problem solving? To frequently, recommendations for a “balanced” tactic lack the breadth and specificity needed to properly manual educators or advance public understanding.
To provide repetition and thinking techniques certainly as opposing methods but as complementary forces, we use developmental cognitive science, particularly Sfard’s process–object paradox and Karmiloff-Smith’s implicit–explicit information range. Based on the science of learning, this framework enables us to make specific suggestions for improving arithmetic fluency.
We define arithmetic fluency, provide proof of its significance, describe the cognitive processes and structures that support it, and provide support for it with evidence-based strategies.
Our suggestions include monitoring early numeracy progress, setting up clear instruction to teach crucial strategies and concepts, implementing well-structured retrieval practice, introducing time-limited practice only after students demonstrate accuracy, and giving students enough time for discussion and cognitive reflection.
We provide educators and policymakers with the knowledge necessary to ensure that all children have the opportunities to achieve arithmetic fluency by blending theory, evidence, and practical advice.
