James C. Kennedy Institute for Educational Success Position Paper #2
Douglas H. Clements and
Julie Sarama
January 16, 2015
Equity and Mathematics Education
A kindergartner stepped up to research assistant grinning and showing her "Happy Birthday" crown. The assistant asked how old she was. The girl stared without responding. "Can you show me on your <ingers?" The girl slowly shook her head "no." As we saw in our first Kennedy Institute position paper
(“Education and Equity”), students in some groups, such as those
from low-income communities, demonstrate significantly lower
levels of achievement. This is especially true of achievement in the domain of
mathematics (1-5). In this position paper, we address issues regarding equity in
mathematics achievement and education, including students who live in poverty and who
are members of linguistic and ethnic minority groups (the next position paper will
address students who have mathematical disabilities or difficulties).
Poverty and Minority Status
The U.S. mathematics education system needs substantial improvement. The
mathematics achievement of American students compares unfavorably with the
achievement of students from many other nations, even as early as first grade and
kindergarten (6). Some cross-national differences in informal mathematics knowledge
appear as early as three to five years of age (7, 8). Children in East Asia and Europe learn
more advanced math than most children in the U. S. are taught (9).
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James C. Kennedy Institute for Educational Success Position Paper #2
Children from
some groups
come to school
with fewer
experiences in
mathematics
than others. Yet
they have full
potential to
learn.
Further, children from some groups come to school with fewer experiences in
mathematics than others. For too many, these differences do not disappear. In the U.S.,
they increase (10). That is, the "achievement gap" does not close; it widens (9). This gap
is most pronounced in the performance of U.S. children living in economically deprived
urban communities (11-15). There is no age so young that equity is not a concern. The
achievement gaps have origins in the earliest years, with low-income children possessing
less extensive math knowledge than middle-income children of pre-K and kindergarten
age (3, 14, 16-20). As one example, the ECLS-B found that the percentage of children
demonstrating proficiency in numbers and shapes was 87% in higher SES families but
only 40% among lower socioeconomic status (SES) families (21, but this involved simply
reading numerals and so the report does not provide useful details). These differences
start early and widen (22).
Equity demands that we establish guidelines for quality mathematics education
for all children.
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James C. Kennedy Institute for Educational Success Position Paper #2
What Accounts for These Differences?
It is is not parents’ IQ or children’s ability to learn (see our Position Paper #1.)
The key factors in one study were the educational level attained by the child's mother and
the level of poverty in the child's neighborhood (23). These are distinct factors, with
income having a direct effect on the child and also an effect that is mediated by the
parents’ interaction with children (e.g., higher, compared to lower, income parents
providing more support for problem solving, 24, 25). Similarly, an analysis of the ECLS
data shows that SES indicators and the number of books in the home both strongly
predict math (as well as reading) test scores (26, also controlling for these substantially
reduces ethnic differences). Low SES children score .55 standard deviations below
middle-SES children and 1.24 standard deviations below high-SES children.
Differences in parents’ beliefs may also play a role. Compared to middle-income parents,
lower-income parents believe that math education is the responsibility of the preschool
and that children cannot learn aspects of math that research indicates they can learn (7).
Also, low-income families more strongly endorsed a skills perspective than middleincome families, and the skills and entertainment perspectives were not predictive of later
school achievement. What was predictive was the “math in daily living” perspective
adopted by more middle-income parents (27). Such deleterious effects of living in lowresource communities are more prevalent and stronger in the U.S. than other countries
and stronger in early childhood that for other age ranges.
Equity Concerns Start Early
Consider these two children. Peter was at the highest levels of competence in
number. He could count beyond 120, state the number word before or after any given
number word, including those in the hundreds. He could also read those number words.
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James C. Kennedy Institute for Educational Success Position Paper #2
Finally, he could use counting strategies to solve a wide range of addition and subtraction
tasks. Tom could not count. The best he could do is say “two” for a pair of objects Asked
for the number after "six," said "horse." After one, he said, come "bike." He could not
read any numerals.
Both Peter and Tom were beginning their kindergarten year (28).
Some children have acquired
number knowledge before the
age of 4 that other children will
not acquire before the age of 7
(29).
A large-scale study of this gap, a survey of U.S. kindergartners found that 94% of
first-time kindergartners passed their Level I test (counting to 10 and recognizing
numerals and shapes) and 58% passed their Level 2 test (reading numerals, counting
beyond 10, sequencing patterns, and using nonstandard units of length to compare
objects). However, 79% of children whose mothers had a bachelor's degree passed the
Level 2 test, compared to 32% of those whose mothers had less than a high school
degree. Large differences were also found between ethnic groups on the more difficult
Level 2 test (30). Differences appear even in the preschool years.
Other analyses from the same large ECLS showed that children who begin with
the lowest achievement levels show the lowest growth in mathematics from Kindergarten
to the 3rd grade (31). The authors conclude that more time on mathematics for these
children in preschool is essential.
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James C. Kennedy Institute for Educational Success Position Paper #2
These studies have a clear message. If high-quality mathematics education does
not start in preschool and continue through the early years, children are trapped in a
trajectory of failure (32).Another study combined the two types of comparisons. Results
showed that mathematical knowledge is greater in 3- and 4-year-old Chinese children
than in American middle-class children and greater in American middle-class children
than in 3- and 4-year-olds from low-income families (7).
Young children from low-income families show specific difficulties in
mathematics. Too often, they do not understand the relative magnitudes of numbers and
how they relate to the counting sequence (12). They have more difficulty solving addition
and subtraction problems. Working-class children in the U.K. are a year behind in simple
addition and subtraction as early as 3 years of age (33). Similarly, U.S. low-income
children begin kindergarten behind middle-income children and, although they
progressed at the same rate on most tasks, they ended behind and made no progress in
some tasks. For example, although they performed adequate on nonverbal arithmetic
tasks, they made no progress over the entire kindergarten year on arithmetic story
problems (34). Further, lower-class children were more likely to show a “flat” growth
curve for the year.
A recent survey of preschoolers’ competencies (35) revealed that children from
preschools serving middle-SES populations outperformed those serving low-SES
populations on the total number score and most individual subtests. The particular
subtests that showed significant differences were, with few exceptions, those that measure
more sophisticated mathematical concepts and skills. In number, there we no significant
differences for simple verbal counting or recognition of small numbers (36, 37). There
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James C. Kennedy Institute for Educational Success Position Paper #2
were significant differences on object counting and especially more sophisticated
counting strategies, comparing numbers and sequencing, number composition, arithmetic,
and matching numerals to dot cards. In geometry, there were no significant differences on
the simple tasks involving shape and comparison of shapes. There were significant
differences on representing shapes, composing shapes, and patterning.
Other research from across the world confirms the finding that there is greater
variation in number knowledge among young children of lower SES background (29) and
that there is a definite trend for students from lower SES backgrounds to perform at a
lower level, and this was more apparent for the difficult items (38, see also 39). This was
especially so for beginning kindergartners in the verbal counting and numeral
recognition. On the other hand, the most advanced children were the least well served.
They were learning nothing throughout the entire kindergarten year. They did not
advance in reading multi-digit numerals throughout their first grade year.
Similarly, lower-income preschoolers lag behind higher-income peers in the
earliest form of subitizing, spontaneous recognition of numerosity (40). They often lack
foundational abilities to classify and seriate (41). Older children entering first grade
showed a smaller effect of familial factors on computation than on mathematics concepts
and reasoning. Majority-minority contrasts were small, but parents’ economic and
psychological (e.g., high school graduation) resources were strong influences (42).
Early research indicated that such problems have existed for decades, with serious
negative effects (22). The first year of school has a substantial influence on the
trajectories of young children’s knowledge of number. Black children gained less than
white children in this study, and the gap widened over a two-year period. Transitions to
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James C. Kennedy Institute for Educational Success Position Paper #2
school, and recovering from initial gaps in learning, may be more problematic for black
children than white children.
Into kindergarten and the primary grades, lower-income children use less-adaptive
and maladaptive strategies more than middle-class children, probably revealing a deficit
in intuitive knowledge of numbers and different strategies (12, 15). Most 5- and 6-yearold low-income children are unable to answer the simplest arithmetic problems, where
most middle-income kindergartners could do so (12). In one study, 75% of children in an
upper middle class kindergarten were capable of judging the relative magnitude of two
different numbers and performing simple mental additions, compared to only 7% of
lower-income children from the same community (12, 43). As another example, about
72% of high, 69% of middle and 14% of low-SES groups can answer an orally-presented
problem, “If you had 4 chocolate candies and someone gave you 3 more, how many
chocolates would you have altogether?” Low-income children often guess or use other
maladaptive strategies such as simple counting (e.g., 3 + 4 = 5). They often do this
because they lack knowledge of strategies and understandings of why they work and
what goal they achieve (15) However, given more experience, lower-income children use
multiple strategies, with the same accuracy, speed, and adaptive reasoning as middleincome children.
In summary, the SES gap is broad and encompasses several aspects of
mathematical knowledge: numerical, arithmetic, spatial/geometric, patterning, and
measurement knowledge (35, 44). The reason for this gap appears to be that children
from low-income families receive less support for math development in their home and
school environments (7, 14, 45, 46). Public pre-K programs serving low-income,
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James C. Kennedy Institute for Educational Success Position Paper #2
compared to those serving higher-income, families provide fewer learning opportunities
and supports for mathematical development, including a narrower range of mathematical
concepts (47, 48). Lack of resources is the main problem, but research indicates it is not
the only explanation. There are also differences in attitudes, motivations, and beliefs that
need to be addressed (10). For example, "stereotype threat" —the imposition of societal
biases such as the lower ability mathematics of Blacks or woman to learn mathematics—
can have a negative influence on the performance of the threatened groups (10). We need
research on whether this affects young children and how this and other problems can be
avoided.
Further, quality is lower in classrooms with more than 60% of the children from
homes below the poverty line, when teachers lacked formal training (or a degree) in early
childhood education, and held less child-centered beliefs (49). An analysis of the large
ECLS data set found that black children had made real gains in mathematics knowledge
upon entering kindergarten—but that over the first two years of school, they lost
substantial ground relative to other races (26). These differences are on arithmetic—
addition, subtraction, and even multiplication and division—rather than lower-order
skills. There are insufficient resources in these settings to address the needs of the
children.
Conclusions and Implications
Thus, there is an early developmental basis for later achievement differences in
mathematics: Children from different sociocultural backgrounds are provided different
foundational experiences (7). Programs need to recognize sociocultural and individual
differences in what children know and in what they bring to the educational situation.
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James C. Kennedy Institute for Educational Success Position Paper #2
Knowledge of what children bring should inform planning for programs and instruction.
Extra support should be provided those from low-resource communities. We must meet
the special needs of all children, especially groups disproportionately under-represented
in mathematics, such as children of color and children whose home language is different
that that of school. All these children also bring diverse experiences on which to build
meaningful mathematical learning (50). The younger the child, the more their learning is
enhanced by contexts that they find relevant and meaningful. There is no evidence that
such children cannot learn the mathematics that other children learn. Too often, children
are not provided with equivalent resources and support (13). They have different and
inequitable access to foundational experiences, mathematically-structured materials such
as unit blocks, technology, and so forth. The settings in which children from different
sociocultural backgrounds are served too often have fewer resources and lower levels of
high-quality interaction. They also have less to support their physical and mental health
(51). The needs of children with physical difficulties (e.g., hearing impaired) and learning
difficulties (e.g., the mentally retarded) must also be considered. There is a critical need
for everyone involved with education to address this problem, so that children at risk
receive equitable resources and additional time and support for learning mathematics.
This does not mean we should treat children as if they were the same; it means equivalent
resources should be available to meet the needs of children who differ in myriad ways,
including socio-culturally and individually (e.g., developmentally delayed and gifted
children). This is important, as knowledge of mathematics in preschool predicts later
school success (52-54). Specific quantitative and numerical knowledge is more predictive
of later achievement than are tests of intelligence or memory abilities (55). Those with
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James C. Kennedy Institute for Educational Success low mathematics in the earliest years
fall farther behind each year (16, 56,
Position Paper #2
More children are in deep poverty
in the U.S. than other countries.
The effects are devastating (24).
57).
Students in Linguistic and Ethnic Minority Groups
Children who are members of linguistic minority groups also deserve special
attention (58). Although teaching specific vocabulary terms ahead of time, emphasizing
cognates, is a useful approach, vocabulary alone is insufficient. Teachers need to help
students see multiple meanings of terms in both languages (and conflicts between the two
languages), and address the language of mathematics, not just the "terms" of
mathematics. Building on the resources that bilingual children bring to mathematics is
also essential. For example, all cultures have "funds of knowledge" that can be used to
develop mathematical contexts and understandings (50). Further, bilingual children can
often see general mathematical idea more clearly than monolingual children, because,
after expressing it in two languages, they understand that the abstract mathematical idea
is not "tied" to given terms (see 5). In general, then, "talking math" is far more than just
using math vocabulary.
Final Words
Children who live in poverty and who are members of linguistic and ethnic
minority groups need more math and better math programs (32). They need programs that
emphasize the higher-order concepts and skills at each level, as well as base knowledge
and skills (26, 35). What programs address these problems? We will describe several
research-based programs in a future position paper (for the early years, see 59).
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James C. Kennedy Institute for Educational Success Position Paper #2
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