Just as mathematical ability begins to form in early childhood, so, too,
does the knowledge gap separating low-income children from their more affluent
peers, who generally enter school with much greater math knowledge.
This gap is troubling given that early deficits in mathematical knowledge
can have profound implications for future learning. Researchers report, for
example, that children’s knowledge of mathematics in kindergarten predicts
their scores on achievement tests during the elementary grades and on into high
One the many areas of math that young children from low-income backgrounds
struggle with is number sense. Number sense is about understanding numerical
magnitudes–being able to choose numbers whose magnitudes are close to the
correct values. Recent studies suggest there are simple ways to promote early
development of number sense that could be widely used to help low-income
preschoolers improve their overall mathematical knowledge.
After looking at how children’s understanding of numerical magnitudes
develops, Carnegie Mellon University researcher Robert Siegler and colleagues
applied their analysis to design and test a brief, inexpensive activity that
resulted in improving a wide range of numerical skills and knowledge. This
report examines the problem of early math deficits among low-income children,
and discusses the activity they developed and its implications.
Children from low-income families are more likely to begin school with much
less math knowledge than children from middle-class and wealthier backgrounds.
This gap is seen across several fundamental math tasks, including counting from
one, counting up or down from numbers other than one, recognizing written
numerals, adding, subtracting and comparing the magnitudes of numbers.2, 3? Early deficits in mathematical
knowledge can have long-lasting consequences. In general, a child who starts
out behind stays behind. Achievement test scores provide evidence of the math
achievement gap between low-income students and their more affluent peers.
This gap, for example, was identified by the 2003 Mayor’s Commission on
Public Education as one of the challenges facing the Pittsburgh Public Schools.
Test scores showed that only 29% of low-income students in the city public
school were proficient in math during the 2001-2002 school year.4 Statewide, 52% of all students were proficient in math
that year. The commission’s report defined low-income students as those whose
family income fell below poverty levels, as well as those with family incomes
low enough to qualify for the federal free and reduced lunch program. About 60%
of the students enrolled in the Pittsburgh Public Schools in 2001-2002 fell
into these categories.
Similar gaps are seen throughout Pennsylvania. Despite general improvement
in statewide academic proficiency scores during the 2007-2008 school year,
students who attended school in disadvantaged communities continued to
struggle, accounting for 68% of those whose math and verbal scores fell "below
basic," which is the lowest category on the Pennsylvania System of School
Research suggests that the mathematical knowledge gap reflects a difference
in the learning support children receive from their parents and others. Studies
have found, for example, that middle-income parents engage in a wider range of
math activities with their children and do so more frequently than do parents
in low-income households.6, 7
Studies also point out the benefits of such practices in the home: Children
whose parents engage in more numerical activities generally possess greater
math knowledge.8 Such findings underscore the
value of designing activities to improve the understanding of numbers that can
be widely used among low-income preschoolers who are less likely to be exposed
to adequate early math support at home.
Number sense is one area of mathematical knowledge found to be particularly
weak among low-income children. Definitions of number sense cite broad and
varied types of knowledge, including skill at immediately identifying the
numerical value associated with small quantities, facility with basic counting,
and understanding how to compose and decompose whole numbers.9
Siegler and colleagues focused on a single, important process in defining
number sense as the ability to approximate numerical magnitudes.10 Such approximations can be
applied to numerical operations, such as answering the question: “About how
much is 12 x 55?” Another common application is approximating objects, events
or sets. For example, “How many people were at the football game?”
The researchers found estimation tasks using a number line to be an
advantageous way to investigate children’s number sense. Studies suggest that
math achievement correlates with children’s ability to correctly space numbers
on number lines.
Young children typically have difficulty doing that, but improve with age
and experience. For example, even pre- school-age children who can count
perfectly from 1 to 10 do not understand the rank order of the numbers’ magnitude.11 Even after they learn the rank order of numbers’ magnitude, they do not
immediately show the magnitudes as increasingly linear.
Such findings led researchers to look at what experiences tend to lead
children to represent the magnitudes of small, verbally stated or written
numerals as increasingly linearly.
Counting experience in early childhood is believed to contribute. However,
children often are able to count in a numerical range for a year or longer
before they are able to make linear representations of numerical magnitudes in
that range,12 which suggests other experiences are also involved.
One activity seen as ideally suited for producing such representations is
playing board games with linearly arranged, consecutively numbered, equal-
spaces, such as the popular commercial children’s game, Chutes and Ladders.
That game’s board has numbers up to 100, each having its own square of equal, which are arranged in a grid.
Such games offer children cues to the order and the magnitude of numbers:
The greater the number in a square, for example, the greater number of moves
the child makes with the token or the greater distance the child has moved the
token. The games also give children practice in counting and in identifying numerals.
Board Game A Simple Board Game
Researchers tested the notion that a numerical board game could improve
mathematical knowledge by randomly assigning 4- and 5-year-olds from Head Start
centers to one of two simple board games they designed.
Each game had 10 squares of equal horizontally arranged. One game,
however, had the numbers 1-10 listed consecutively from left to right, while
the other game had colored squares without numbers. Children spun a spinner and
moved their token the number of spaces shown on the spinner. They were also
asked to say the numbers or colors on the spaces they moved the token through.
Children took part in four sessions that lasted 15-20 minutes each and were
spread over a two-week period. The games themselves lasted only about 2-4
In addition, children were given a number line estimation task with numbers
1-10 before and after they played the game. For comparison, the same number
line estimation task was given to a group of middle-income children who did not
play either version of the board game.
The idea was to use the task to measure any change in the estimating
abilities of the Head Start children who played the board game and to see how
their performance compared with that of middle-income children who, studies
suggest, are exposed to more math-related activities at home. In fact, a survey
taken in a follow-up study showed that middle-income children reported twice as
much experience playing board games than children from low-income backgrounds.
The brief experience of playing the numbered board game resulted in
significant gains in how Head Start children performed on the number line
estimation task. Before children played the numbered board game, the
best-fitting linear function accounted for an average of only 15% of the
variance in individual children’s scores. After they had experience playing the
game, the best-fitting linear function accounted for an average of 61% of the
That improvement brought their performance on the estimation task up to
levels seen among the middle-income children who had not played the game, but
as a group tend to have much more experience with board games and other math
activities at home.
On the other hand, playing the board game that used color squares did not
affect the number line estimation performance of the Head Start children who
were assigned to it. The best-fitting linear function accounted for an average
of only 18% of the variance in their estimates on both the tests given before
playing the game and the tests given afterward.
In a later study, researchers looked at the range of mathematical knowledge
that 124 Head Start children gained by playing the numbered board game and
whether those gains could be expected to last.
To investigate the range of math knowledge, they com- pared the effects of
playing both the numbered board game and the color game on the children’s
understanding of the numbers 1-10 in tasks that included making estimates with
a number line, comparing magnitude, identifying numerals and counting. These
tasks were done immediately before and after children played the games.
Researchers followed up those tests by having the children perform the tasks
again nine weeks after they had completed their last game session.
Again, playing the numbered board game produced wide benefits for the Head
Start children who were assigned to do so. The accuracy of their number line
estimations increased from pre-test to post-test, and their performances on the
magnitude comparison, numeral identification and counting tasks also improved
after having had the experience of playing the game.
The group of children who played the board game with colored squares showed
no change in their performance on the tasks used to assess mathematical
In all cases, the Head Start children who were assigned to play the
numbered board game showed improvements that lasted over the nine-week follow-up
period, while the children who played the color board games failed to demonstrate
any gains, either immediate or delayed.
Such findings add to a growing body of evidence that suggests improving the
numerical understanding of low-income preschool-age children leads to broad,
rapid learning. In this case, the learning tool was a simple, inexpensive board
game that could be widely used to help close the mathematical knowledge gap
between low-income children and their more affluent peers.
Siegler, R.S. (2009). Improving the numerical understanding of children from
low-income families. Child Development
Perspectives, 3(2), 118-124.
This Special Report is
based on the publication cited above. It is not intended to be an original work
but a summary for the convenience of our readers. References noted in the text
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