Summary: Children’s intuitive number sense supports approximate calculations, including true division. These findings point to ways educators might build on that intuition when teaching formal math.
Source: Frontiers
Many people assume multiplication and division are skills acquired only through schooling. Yet decades of research indicate that children possess an intuitive capacity for arithmetic well before formal instruction begins.
A recent paper in Frontiers in Human Neuroscience shows that this intuitive capacity—the approximate number system—extends to true division. The study suggests that young children can perform approximate division operations and that this ability could inform classroom strategies for teaching mathematical concepts.
The study is grounded in the concept of the approximate number system (ANS), a robust body of research demonstrating that humans and some nonhuman primates can estimate and compare large quantities without relying on language, numerals, or counting. For example, a child can tell that 20 dots is more than four dots even when the four dots are arranged to occupy more space on a page. As people grow older, their precision in discriminating nearer quantities—such as 20 versus 17—improves.
Bridging the achievement gap
Beyond understanding how children perceive numbers naturally, researchers want to know whether that intuition can be used to support formal math learning. That question is especially important for children from low-income backgrounds, who made up a large portion of the school-age participants in this study and who often face greater risk of falling behind in mathematics.
“The ANS is universal, and finding ways to harness it might be one of several promising routes to closing the achievement gap,” said Dr. Elizabeth M. Brannon, director of the Developing Minds Lab at the University of Pennsylvania and a co-author of the study.
Brannon and her colleagues tested six- to nine-year-old children alongside college students in experiments that measured performance on symbolic and non-symbolic forms of approximate division. The researchers aimed not only to verify whether young children can perform approximate division before formal instruction, but also to explore whether this non-symbolic number sense connects to later, symbol-based math learning.
“Previous findings have been mixed, so this question is controversial,” Brannon said. “Our results are encouraging: they show that children can flexibly divide quantities and even symbolic values before formal instruction in division.”
A new dividing line
In one of the experiments, participants watched either groups of dots (non-symbolic) or Arabic numerals (symbolic) appear at the top of a screen and “fall” onto a flower with a certain number of petals (the divisor). The task was to compare the imagined quotient—the dividend divided among the petals—with a visible target quantity shown on a single petal on the right side of the screen. Participants judged which side represented the larger amount.
Both children and adults performed well above chance. Children selected the correct response between 73% and 77% of the time, depending on task conditions and feedback; adults were correct nearly 90% of the time. Notably, even children who could not solve or verbally explain basic written division problems still succeeded at the symbolic version of the experimental task.
Brain imaging studies complement these behavioral results: the ANS relies on brain regions that remain important for formal mathematics later in life. “We were surprised that children who could not answer simple verbal division problems—such as ‘what is four divided by two?’—still performed quite well on the symbolic flower task,” Brannon noted. “This indicates that an intuitive division ability exists before formal instruction and that it engages neural systems involved in number processing.”
About this math and neuroscience research news
Author: Press Office
Source: Frontiers
Contact: Press Office – Frontiers
Image: The image is in the public domain
Original Research: Open access. “Young Children Intuitively Divide before they Recognize the Division Symbol” by Elizabeth M. Brannon et al., Frontiers in Human Neuroscience
Abstract
Young Children Intuitively Divide before they Recognize the Division Symbol
Children bring an intuitive arithmetic toolkit into the classroom long before formal instruction begins. Prior work shows children can use number sense to add, subtract, compare ratios, and scale sets of objects by simple factors (for example, doubling or quartering a set). Whether children can carry out a true division operation prior to formal teaching has been less clear.
This study tested 6- to 9-year-old children and college students on symbolic (Arabic numerals) and non-symbolic (dot arrays) approximate division tasks. Dividends ranged from 32 to 185 and divisors from 2 to 8. Participants were asked to imagine the quotient and compare it to a visible target quantity.
Children (Experiment 1: N = 89; Experiment 2: N = 42) and adults (Experiment 3: N = 87) succeeded at the approximate division tasks across both formats. Importantly, success held even for children who could not yet recognize the division symbol or solve simple written division problems, indicating that intuitive division precedes formal instruction.
For both children and adults, performance on non-symbolic division mediated the relationship between ANS acuity and symbolic math ability. This suggests that the capacity to compute non-symbolically may be one mechanism linking ANS precision to later symbolic mathematics.
Overall, these findings highlight the numerical competencies children possess before formal math teaching and point to potential educational approaches that build on intuitive number sense to support mathematics learning.