Place value (the value indicated by where a digit is in a multi-digit number, e.g.: units, tens, hundreds) is one of the keystone concepts in children’s math education. An understanding of place value is necessary for carrying out operations like addition and subtraction with numbers that exceed a single digit. For decades, educators have based their math curricula on the idea that place value is too difficult for most preschoolers to understand.
The researchers administered a battery of tests to kids from ages three to seven involving numerals, pictorial representations of numbers, and greater / smaller quantities. The results were filtered by age range and subjected to statistical analyses. The study yielded some surprising results.
The study, led by Kelly Mix from Michigan State University, indicates children as young as three are capable of understanding both the meaning and the value of multi-digit numbers (even ones as high as three and four digits long).
Long considered to be too abstract for young children, exposure to symbolic numbers has traditionally been set aside in favor of concrete representations of digits (three apples instead of the numeral 3, for instance). But the study indicates something quite new to educational research — kids are far better than previously thought at figuring out numbers.
What are researchers saying about place value and preschool math?
The authors of this study suspect children learn numbers in much the same way they learn language, a process called statistical learning. Statistical learning basically means that while a child is being exposed to a steady stream of input (let’s say a bunch of sentences in English), they are able to scan the stream for statistical patterns. The earliest stages of language acquisition draw on statistical learning. For example, children quickly learn to distinguish individual words and consonant combinations.
The authors of the Michigan study think kids learn about numbers the same way. Throughout earliest childhood, children are as awash in numbers as they are in words. They see numbers on elevators, on television, on their parents’ calendars, and on packaging. They overhear phone numbers, addresses, and on and on. Their exposure to numbers happens in much the same way as their exposure to language — that is to say by way of a steady, random stream of inputs. The new research seems to indicate kids are capable of gradually making sense of the input on their own.
One of the misconceptions about kids’ early abilities to process numbers stems from the mistakes they make with respect to place value. Young kids who have never received formal instruction in place value are bound to make mistakes. One of the common ones cited in the Michigan study features an invented notation — like “113” being written as “10013.” It’s wrong, for sure. But the error isn’t as wrong as people might think. It’s based on some previously existing knowledge about place value. The authors of the Michigan study compare this kind of mistake to the mistakes a novice English speaker will make — like saying “goed” instead of “went.” “Goed” might be wrong, but it stems from rules that are correct some of the time. And this kind of mistake indicates a more advanced knowledge of English than meets the eye.
The authors of the Michigan study think the same is true for numbers. They say people are too preoccupied with correctness and see mistakes as proof that place value is too difficult for young learners. In fact, kids are able to “bootstrap” their way into the place value system, purely from their random exposure to numbers. Put simply, kids know more about math than adults think they do.
What does this mean for early math learning?
Researchers and policymakers are starting to understand that young children are ready for more instruction, earlier on. This will likely involve a major overhaul of curricula, since most are based on the idea, supported by decades of research, that preschool-aged children can’t grasp the concept of multi-digit numbers and place value.
With mathematics such a crucial skill for employment, all eyes are going to be on math curricula. Maryland is already looking to take this new research into account, proposing that every preschooler should be able to count to 20, sort numbers in order of sequence, and carry out basic operations like addition and subtraction. And the new research indicates this should be possible.
Early childhood educators and primary teachers — particularly those who teach Kindergarten — have a great deal of anecdotal knowledge. They’ve seen first-hand what works and what doesn’t, what children are capable of, and where their limitations lie. The thing is, most have been educated to believe understanding of multi-digit numerals and operations is beyond the cognitive abilities of preschoolers.
As an educator or parent, how do you believe the education system should respond to this new research? Do you think there are more pressing areas of early math education that need to be addressed? Feel free to let us know.
Funny how times change. Not even a decade ago, smartphones and mobile devices were seen as contraband in the classroom. By the time 2013 rolled around, 85% of educational institutions in the U.S. and U.K. allowed mobile devices in the classroom, according to research by Bradford Networks.
Today, schools aren’t only allowing mobile devices in the classroom, but increasingly educators are turning to smartphones, tablets, and Chromebooks as both a cost-effective learning tool and a vehicle for student engagement.
In fact, according to a recent survey of 2,500 K-12 teachers conducted by Front Row Education, 75% of teachers report using technology daily with their students, and more than 50% of teachers say they now have a 1:1 student-to-device ratio, up nearly 10% from last year.
Within this trend, two primary themes emerge: BYOD, and the iPads versus Chromebook debate.
How Does a Growth Mindset Affect Learning?
Mindset Works, a leader in growth mindset training for educators and students, writes: “Dr. Dweck found that people’s theories about their own intelligence had a significant impact on their motivation, effort, and approach to challenges. Those who believe their abilities are malleable are more likely to embrace challenges and persist despite failure … for example, 7th graders who were taught that intelligence is malleable and shown how the brain grows with effort showed a clear increase in math grades.”
This leads to the second part of the equation: educators. Students have to be taught that their brains are indeed malleable and that their intelligence can improve.
“The feedback that teachers give their students can either encourage a child to choose a challenge and increase achievement or look for an easy way out. For example, studies on different kinds of praise have shown that telling children they are smart encourages a fixed mindset, whereas praising hard work and effort cultivates a growth mindset,” explains Mindset Works.
Written By: Zorbit's Math Adventure
Zorbit’s Math Adventure is a game-based learning program for K-3 math, created by a team of experienced teachers, educators, & game designers. The curriculum-based math activities engage young learners in rich, immersive environments that are cognitively & developmentally appropriate for their age. Aligned to all curricula within North America, Zorbit also delivers teachers a suite of tools & resources to help close learning gaps & differentiate instruction.