Number sense and mathematical aptitude - 08/12/11 08:14 PM
http://www.futurity.org/science-technology/kids-with-number-sense-excel-in-math/
Kids with �number sense� excel in math
JOHNS HOPKINS (US) � Add it up: Evidence shows math ability is as much an inborn talent as artistry or athleticism.
A new study concludes the strength of a child�s primitive �number sense� is strongly predictive of the level of the math skills he or she learns.
�Number sense� is a skill that allowed hunter-gatherers to ascertain�without counting or calculation�where they could find the most nuts, plants, or game. It allows modern humans, at a glance, to estimate the number of open seats in a movie theater or the number of people in a crowded meeting.
The link between number sense�also known as �approximate number system,� or ANS�and ability to master formal mathematics already has been established in adolescents. The new study is the first to examine the role of �number sense� in children too young to already have had substantial formal mathematics instruction, says lead study author Melissa Libertus, a post-doctoral fellow in the psychological and brain sciences department at Johns Hopkins University.
�The relationship between �number sense� and math ability is important and intriguing because we believe that �number sense� is universal, whereas math ability has been thought to be highly dependent on culture and language and take many years to learn,� Libertus says. �Thus, a link between the two is surprising and raises many important questions and issues, including one of the most important ones, which is whether we can train a child�s number sense with an eye to improving his future math ability.�
For its study, published online in a recent issue of Developmental Science, the team tested 200 4-year-old (on average) children on several tasks measuring number sense, mathematical ability and verbal ability. The children were rewarded for their participation with small trinkets, such as stickers and pencils.
To assess their number sense, researchers asked the children to view flashing groups of blue and yellow dots on a computer screen and estimate which color was more numerous. Counting wasn�t an option, both because the dots were flashed so quickly and because most of the children were not yet skilled counters. Some comparisons were easy (like five yellow versus 10 blue dots). Others were much harder (like five yellow versus six blue dots). A test similar to the one administered to the children is available at Panmath.
The children also were given a standardized test of early mathematics ability that measures numbering skills (verbally counting items on a page), number-comparison (determining which of two spoken number words is greater or lesser), numeral literacy (reading Arabic numbers), mastery of number facts (such as addition or multiplication), calculation skills (solving written addition and subtraction problems), and number concepts (such as answering how many sets of 10 are in 100.) This standardized test is often given to children between the ages of 3 and 8 years.
Lastly, parents and guardians of the children were asked to indicate each word on a list that their children had been heard to say. Libertus says this verbal test was administered because language and math abilities are to some extent linked through general intelligence, and the researchers wanted to make sure that the differences in math ability that they found were not just due to some children performing better on all kinds of tasks or to some children feeling more comfortable being tested than others.
Libertus and colleagues Lisa Feigenson and Justin Halberda found the precision of children�s estimations correlated with their math skill. That is, the children who could make the finest-grained estimations in the dot comparison task (for example, judging correctly that eight yellow dots were more than seven blue dots) also knew the most about Arabic numerals and arithmetic.
According to the researchers, this means that inborn numerical estimation abilities are linked to achievement (or lack thereof) in mathematics.
�Previous studies testing older children left open the possibility that differences in instructional experience is what caused the difference in their number sense; in other words, that some children tested in middle or high school looked like they had better number sense simply because they had had better math instruction,� Libertus said. �Unlike those studies, this one shows that the link between �number sense� and math ability is already present before the beginning of formal math instruction.�
<end of excerpt>
Here is the NYT article.
http://www.nytimes.com/2011/08/16/science/16obmath.html
In Future Math Whizzes, Signs of �Number Sense�
By SINDYA N. BHANOO
New York Times
August 11, 2011
Children as young as 3 have a �number sense� that may be correlated with mathematical aptitude, according to a new study.
Melissa Libertus, a psychologist at Johns Hopkins University, and colleagues looked at something called �number sense,� an intuition � not involving counting � about the concepts of more and less. It exists in all people, Dr. Libertus said, including infants and indigenous peoples who have had no formal education.
The researchers measured this intuition in preschoolers by displaying flashing groups of blue and yellow dots on a computer screen. The children had to estimate which group of dots was larger in number. Since the display was fleeting, they had to use their number sense rather than count the dots.
Children with a better number sense were also better at simple math problems the researchers posed. The children were asked to count the number of images on a page out loud, read Arabic numbers and make other simple calculations.
Previous studies have shown that there is a connection between number sense and mathematical ability in adolescents. But this is the first study to explore the connection in children with little formal education.
<end of excerpt>
The paper abstract is at http://onlinelibrary.wiley.com/doi/10.1111/j.1467-7687.2011.01080.x/abstract . The Panamath site to measure "Approximate Number System (ANS) aptitude" is at http://www.panamath.org/testyourself.php .
Kids with �number sense� excel in math
JOHNS HOPKINS (US) � Add it up: Evidence shows math ability is as much an inborn talent as artistry or athleticism.
A new study concludes the strength of a child�s primitive �number sense� is strongly predictive of the level of the math skills he or she learns.
�Number sense� is a skill that allowed hunter-gatherers to ascertain�without counting or calculation�where they could find the most nuts, plants, or game. It allows modern humans, at a glance, to estimate the number of open seats in a movie theater or the number of people in a crowded meeting.
The link between number sense�also known as �approximate number system,� or ANS�and ability to master formal mathematics already has been established in adolescents. The new study is the first to examine the role of �number sense� in children too young to already have had substantial formal mathematics instruction, says lead study author Melissa Libertus, a post-doctoral fellow in the psychological and brain sciences department at Johns Hopkins University.
�The relationship between �number sense� and math ability is important and intriguing because we believe that �number sense� is universal, whereas math ability has been thought to be highly dependent on culture and language and take many years to learn,� Libertus says. �Thus, a link between the two is surprising and raises many important questions and issues, including one of the most important ones, which is whether we can train a child�s number sense with an eye to improving his future math ability.�
For its study, published online in a recent issue of Developmental Science, the team tested 200 4-year-old (on average) children on several tasks measuring number sense, mathematical ability and verbal ability. The children were rewarded for their participation with small trinkets, such as stickers and pencils.
To assess their number sense, researchers asked the children to view flashing groups of blue and yellow dots on a computer screen and estimate which color was more numerous. Counting wasn�t an option, both because the dots were flashed so quickly and because most of the children were not yet skilled counters. Some comparisons were easy (like five yellow versus 10 blue dots). Others were much harder (like five yellow versus six blue dots). A test similar to the one administered to the children is available at Panmath.
The children also were given a standardized test of early mathematics ability that measures numbering skills (verbally counting items on a page), number-comparison (determining which of two spoken number words is greater or lesser), numeral literacy (reading Arabic numbers), mastery of number facts (such as addition or multiplication), calculation skills (solving written addition and subtraction problems), and number concepts (such as answering how many sets of 10 are in 100.) This standardized test is often given to children between the ages of 3 and 8 years.
Lastly, parents and guardians of the children were asked to indicate each word on a list that their children had been heard to say. Libertus says this verbal test was administered because language and math abilities are to some extent linked through general intelligence, and the researchers wanted to make sure that the differences in math ability that they found were not just due to some children performing better on all kinds of tasks or to some children feeling more comfortable being tested than others.
Libertus and colleagues Lisa Feigenson and Justin Halberda found the precision of children�s estimations correlated with their math skill. That is, the children who could make the finest-grained estimations in the dot comparison task (for example, judging correctly that eight yellow dots were more than seven blue dots) also knew the most about Arabic numerals and arithmetic.
According to the researchers, this means that inborn numerical estimation abilities are linked to achievement (or lack thereof) in mathematics.
�Previous studies testing older children left open the possibility that differences in instructional experience is what caused the difference in their number sense; in other words, that some children tested in middle or high school looked like they had better number sense simply because they had had better math instruction,� Libertus said. �Unlike those studies, this one shows that the link between �number sense� and math ability is already present before the beginning of formal math instruction.�
<end of excerpt>
Here is the NYT article.
http:/
In Future Math Whizzes, Signs of �Number Sense�
By SINDYA N. BHANOO
New York Times
August 11, 2011
Children as young as 3 have a �number sense� that may be correlated with mathematical aptitude, according to a new study.
Melissa Libertus, a psychologist at Johns Hopkins University, and colleagues looked at something called �number sense,� an intuition � not involving counting � about the concepts of more and less. It exists in all people, Dr. Libertus said, including infants and indigenous peoples who have had no formal education.
The researchers measured this intuition in preschoolers by displaying flashing groups of blue and yellow dots on a computer screen. The children had to estimate which group of dots was larger in number. Since the display was fleeting, they had to use their number sense rather than count the dots.
Children with a better number sense were also better at simple math problems the researchers posed. The children were asked to count the number of images on a page out loud, read Arabic numbers and make other simple calculations.
Previous studies have shown that there is a connection between number sense and mathematical ability in adolescents. But this is the first study to explore the connection in children with little formal education.
<end of excerpt>
The paper abstract is at http:/