Book Review
National
Research Council. (2009). Mathematics Learning in Early Childhood:
Paths
Toward Excellence and Equity. Committee on Early Childhood Mathematics,
Christopher T. Cross, Taniesha A. Woods, and Heidi Schweingruber, Editors. Center for Education, Division of
Behavioral and Social Sciences
and Education. Washington, DC: The National Academies Press.
Many people admit that they
have a weakness in the subject area of Mathematics. Working with numbers can be so threatening to
them that it has the power to determine the courses they take in college or the
career they choose. Some people even avoid careers that directly deal with Math
like Engineering, Accounting, Architecture, and the like. Such fear of numbers may be based on poor
mathematical foundations that were expected to have been solidified in
childhood. The book to be reviewed,
“Mathematical Learning in Early Childhood:
Paths Toward Excellence and Equity” is one to illuminate several
misunderstandings over Mathematics learning and finally bring justice to early
learning of the subject.
A
special committee was formed to evaluate how the subject of Math has been dealt
with by schools and teachers and how children and their parents have accepted
and understood it over the years. The
main conclusion that the committee came up with was that most young children have
the ability to learn and be really competent in Math, but there are many
constraints that deter them from being so.
One is parental attitudes that influence how they regard Math. Another is also the way teachers of early
childhood education do not prioritize Math as much as literacy learning. Children are very impressionable and have
strong tendencies to just imbibe adult influences on them. If not curbed appropriately, children who are
exposed to negative views of Math at such an early age, are most likely to
develop the same negative attitudes towards a subject area that will prove to
be very significant in their lives. The
book hopes to prevent such unfortunate development by disseminating relevant
information on math based on thorough research.
The
No Child Left Behind (NCLB) act prompted schools to focus more on academic
competencies of students in the early elementary grades. Although testing requirements for NCLB does
not commence until third grade, the move is for earlier grades and even from
the preschool level, the children should be adequately prepared. From way back, early childhood education has
emphasized young children’s social-emotional development, leaving academics as
second priority. Now, the NCLB encourages that both academic development and
social-emotional development are given equal emphasis in the early childhood
program.
The
book is overwhelmingly thorough in presenting facts from research. It is written in a very confident tone that
bespeaks of the credibility of the writers.
As a joint project of the Committee on Early Childhood Mathematics, book
editors Christopher Cross, Taniesha Woods and Heidi Schweingruber, the Center
for Education, Division of Behavioral and Social Sciences and Education, and
supervised overall by the National Rsearch Council, the reader would expect
only the highest quality of knowledge dissemination from the book.
The
main points of the book are discussed in the following portions. These include the committees evaluations of
the current state of math learning in schools, the important mathematical
concepts and skills that young children need to learn, explanations of the
significance of these concepts and skills and how best to teach them as well as
recommendations as to the strategies in engaging children’s learning of
math. The external influences and future
directions of math learning have also been taken up in quite a reflective
manner.
Lack of Opportunities To Learn
Math
Children who lack opportunities to learn math
both in early childhood settings and from their daily experiences in their
homes and communities have been found to also lack competence in math. Mostly,
they are children coming from economically disadvantaged families who are left
behind in the development of their mathematical skills and if not provided with
high quality early mathematics instruction, will remain delayed in their
mathematical development. It is
important that before children enter the elementary grades, they have already
acquired the concepts and skills necessary to support more complex mathematical
understanding later in their academic lives.
Early Childhood Settings
Upon
investigation of the state of early childhood education today in terms of its
current standards, curricula and instruction, it has been found that early
childhood settings do not provide enough quality experiences in Math as much as
in Language Arts. This reflects the fact
that literacy development precedes numeracy development in terms of priority
throughout the childhood education system.
It implies the lack of attention given to upgrading standards,
curriculum, instruction and the preparation and training of teachers in
mathematics.
The issue of the “subjugation” of mathematics to
other curricular areas in the increasingly popular trend of integrating all
subjects in the curriculum is becoming an issue to math educators. The book laments that education and training
for most early childhood educators place heavy emphasis on the development of
children’s socio-emotional aspects and literacy skills, leaving less attention
to mathematics. The committee members
feel that mathematics can be a context where in socio-emotional development and
literacy development can* flourish. In
this reviewer’s perspective, this point in the book seems as if the committee
desires children’s development of Math skills to be prioritized over other
developmental areas. However, in early
childhood, children do not learn in segregated ways. They learn holistically and do not give much
importance to the delineations of subject or developmental areas as long as the
lesson captivates their attention and motivates them in learning the concepts
and skills more.
The committee’s main
contention is the need for provision of high quality early mathematics instruction
to young children in the fervent belief that such will provide a strong
foundation for later learning of more complex mathematical concepts and closing
of the long-term achievement gap between children provided with a variety of
quality in math learning modules. The
preschool level was selected as the committee’s focus because they believe that
it is the perfect time when cognitive and social development opportunities
should be provided so that the children are made more ready when they get into
formal schooling in the elementary grades.
This level is characterized by young children’s excitement and zest for
learning new skills and testing out their potentials and they enjoy activities
that develop their competencies, including those involving Math (Gelman, 1980,
Ginsburg et al., 2006, National Research Council, 2001; Saxe et al.,
1987). This critical period must be
exploited to maintain and enhance the high motivation to learn especially for
children with disadvantaged backgrounds.
Early learning experiences can help them achieve a more equal footing
with their more advantaged counterparts.
With this book, the
committee was successful in assembling pertinent research from various
disciplines that focus on the teaching-learning of early mathematics. It analyzed the available literature to be
able to develop the appropriate mathematics learning goals for children in the
preschool level. Their commentaries were
not only based on their professional opinions, but their insights were culled
from critical evidence-based research. The
committee does not stop at evaluation of the current state of mathematics
teaching and learning. It goes on to recommend some actions to be undertaken by
stakeholders in the education of America’s future citizens. The overarching
recommendation is:
Recommendation
1: A coordinated national early childhood mathematics
initiative
should be put in place to improve mathematics teaching
and
learning for all children ages 3 to 6 (National Research Council, 2009, p. 3).
This
is a tall order and would necessitate a huge network of cooperative educators,
policy-makers, parents, educational associations and everyone concerned in the
education of young children to come into agreement of the need to improve
mathematical learning in early childhood education. From this main recommendation branches out several other
recommendations, as follows:
Recommendation
2: Mathematics experiences in early childhood settings
should
concentrate on (1) number (which includes whole number,
operations,
and relations) and (2) geometry, spatial relations, and
measurement,
with more mathematics learning time devoted to number
than
to other topics. The mathematical process goals should be integrated
in
these content areas. Children should understand the concepts
and
learn the skills exemplified in the teaching-learning paths described
in
this report (p. 3)
These
are the two main concepts and skills that young children should first be adept
in, as these may be directly applicable to the children’s daily experiences. Number is all around them…their age, their
address, their telephone number. They need to find meaning and connections
between numbers, as if trying to understand another language. In a sense, Math
is another language in another form that children need to decipher. At a very early age, children can already
learn the concepts of numerical operations such as addition, subtraction,
multiplication and division, but of course, presented in a developmentally-appropriate
manner. Understanding such operations
the way the book explained it seemed to be much easier to comprehend, but when
teachers apply such understanding to very young preschoolers, they may seem
amazed that such children are capable of complicated concepts because they have
been used to presenting it in a very easy and shallow context. With geometry, young children and even
infants and toddlers are exposed to shapes and perceptually try to understand
its relationship to space. Going beyond
the surface is what the committee aims for early childhood education to do
because they believe that it is the deeper meaning of geometrical concepts that
need to be implanted in young minds.
Measurement is another concept that has been largely ignored because
teachers reserve it till the preschoolers are old enough. Early exposure to measurement is using
nonstandard units such as popsicle sticks, strings of similar length, etc. The
book gives more ways to teach children about measurement. It suggests that measurement should not be
taught as a simple skill because it involves complex combinations of concepts
and skills which develop over the years.
Teachers adept in the teaching of measurement know how to interpret
children’s understanding of measurement and how to ask the appropriate questions
that would spark children’s further understanding of the concept.
Recommendation
3: All early childhood programs should provide high-quality mathematics curricula and instruction as
described in this report (p.3).
Providing
clear explanations of mathematical concepts and skills that young children need
to learn, this book expects nothing less from educators when they advocate for
such a recommendation. High quality
should not remain on print but should be manifested in the actual curricula
designed by well-meaning educators.
Recommendation
4: States should develop or revise their early childhood
learning
standards or guidelines to reflect the teaching-learning paths described in
this report.(p.3)
After a thorough evaluation of early
mathematical learning and the presentation of research facts on the value of a
more knowledgeable approach to the teaching-learning paths, the committee is
justified enough to advocate to the whole nation an upgrade in early childhood
standards. It uses itself as a guide to
light the path of others in fulfillment of higher quality in education for all.
Recommendation
5: Curriculum developers and publishers should base
their materials
on the principles and teaching-learning paths described
in this report
(p.3).
Again, this confidence in the material the
committee has come up with is strengthened by its credibility. The book is recommendable to be used as a
basis for curriculum development as it fully explains how concepts should be
learned in a sequential order.
Recommendation
6: An essential component of a coordinated national
early childhood
mathematics initiative is the provision of professional
development to
early childhood in-service teachers that helps them (a) to understand the
necessary mathematics, the crucial teaching-learning
paths, and the
principles of intentional teaching and curriculum and
(b) to learn
how to implement a curriculum.(pp.3-4)
Continuing
professional development for faculty and staff should be a priority of schools. However, in most cases, the basic knowledge
of teachers may point to a poor foundation in their education way back from
undergraduate studies. Colleges and
universities produce teachers who are not truly knowledgeable in what young
children are capable of learning and the developmentally-appropriate practices
to help them learn what they should know.
The professional training must begin from the time teachers are students
themselves. For practicing teachers,
regular in-service training by experts in the field must be invested on, along
with attendance in offered seminars and workshops on the teaching-learning
paths.
Recommendation
7: Coursework and practicum requirements for early
childhood
educators should be changed to reflect an increased emphasis
on children’s
mathematics as described in the report. These changes
should also be
made and enforced by early childhood organizations
that oversee
credentialing, accreditation, and recognition of teacher
professional
development programs (p. 4)
If we are to make
reforms in the curriculum of children, we also need to reform the curriculum of
teacher education to gear it towards higher standards in all curricular areas,
including Mathematics. This is also in
recognition of children’s growing capabilities and the value of developing
higher thinking skills. Reconciling this
with developmentally-appropriate practices will make it more acceptable to
parents and their children in the knowledge that the more challenging concepts
need not pressure children to learn lessons that may be considered agonizingly
difficult for them. Math, in this case,
should be put in a better light that it may be learned as easy as Language Arts
using more innovative teacher strategies.
Recommendation
8: Early childhood education partnerships should be formed between family and
community programs so that they are equipped to work together in promoting
children’s mathematics (p.4).
Families and
communities are useful resources early childhood programs can maximize in the
implementation of a viable curriculum that promotes mathematics learning. Establishing healthy links with them in terms
of the provision of materials, venues, activities and even resource persons to
help teachers demonstrate certain mathematical concepts better is
recommended. An example is seeking the
cooperation and support of a local grocery for a field trip that children can
do to learn about basic economic trade of goods for cash and that each item has
a price to be paid for with money.
Recommendation
9: There is a need for increased informal programming,
curricular
resources, software, and other media that can be used to support young
children’s mathematics learning in such settings as homes, community centers,
libraries, and museums (p.4).
This recommendation
aims to give children maximum exposure to a mathematical learning environment
to equip them with more skills and understanding and ultimately, applicable
mathematical knowledge.
For regular preschool teachers who have not
been privileged to learn a more complete curriculum in teaching-learning paths
to math learning, the text in the book may initially seem to be too technical
because they have been trained in more general terms. Reading it may seem to be
directed to more specialized teachers.
However, with further reading, the clarity of the language of the
writers brings about much understanding to the readers and a wealth of ideas to
preschool teachers.
Likewise, teachers who
have believed that academic competence can be reserved for later learning may
find the content suggested for preschoolers in the book to be too advanced for
them. Nevertheless, the text offered
various ways teachers can approach math problems such as finding unknowns. In
most preschool math problems, it is the total sum or difference given focus and
not much on missing addends or subtrahends/minuends. Reversing actions will enhance understanding
of the mathematical operation and will engage children in higher order thinking
instead of relying on memorized facts. To illustrate, consider this “change unknown”
problem:
“Matt had 5 cards. After he got some more
cards, he had 8. How many cards did Matt get?” This problem can be formulated with
the addition equation 5 + ? = 8. Although young children will solve this
problem by adding on to 5 until they reach 8 (perhaps with actual cards or
other objects), older children and adults may solve the problem by subtracting,
8 − 5 = 3, which uses the opposite operation than the addition equation that
was used to formulate the problem. (p. 34)
It is higher thinking
skills such as the one involved in this problem that the committee wants young
children to develop more from a reformed early childhood education program
geared towards more academic learning. The
prescribed content areas of numbers, geometry and measurement lay the
foundations of understanding more potentially difficult math concepts. At the same time, children develop
proficiency in reasoning processes expected from engagement in math
problems. The National Association for
the Education of Young Children (NAEYC) and the National Council of Teachers of
Mathematics (NCTM) agree that “problem solving and reasoning are the heart of
mathematics” (2002, p. 6).
Many math skills
developed can be translated to non-mathematical cases. The skill of figuring out connections between
shapes or numbers may also be applied in making associations between words in order
to attain comprehension. For teachers
reading the text, it may help them understand the math concepts better, giving
them an “Oh I know this… so this is how it goes!” For some, the text gives them
the understanding of concepts that they never have had before. However, applying that knowledge to teaching
math to children is the challenge as they have to adjust to the level of the
child’s developmentally appropriate understanding. That is why it is important to come up with
interesting activities that children will enjoy and learn from either knowingly
or unknowingly. Among these are
child-initiated and teacher-initiated activities that were also discussed at
length in the text.
The committee, in
consultation with professional organizations such as NAEYC and NCTM uphold the
use of developmentally-appropriate activities in teaching mathematical
skills. Although the text of the book
may sound too directive due to all the technical language involved that
teachers may just prefer to direct the teaching themselves, it also values the
initiatives of children. Definitions of
teacher-initiated and child-initiated learning are given below:
Teacher-initiated or teacher-guided
means that teachers plan and implement experiences in which they provide
explicit information, model or demonstrate skills, and use other teaching
strategies in which they take the lead. Teacher-initiated learning experiences
are determined by the teacher’s goals and direction, but they should also
reflect children’s active engagement (Epstein, 2007 as cited in the National
Research Council, 2009, p. 225).
By contrast, child-initiated
or child-guided means that children acquire knowledge and skills
through their own exploration and through interactions with objects and with
peers (Epstein, 2007, p. 2 as cited in the National Research Council, 2009, p.
226).
In both, it is apparent that learning is very much an active process
instead of just passive receiving of instruction and imbibing of concepts and
skills. Considering both, the committee
reviews effective strategies in early childhood learning such as the use of
play activities incorporating math concepts and skills. Meaningful play activities that build math
competencies include block building, socio-dramatic play and games with mathematical
themes. Other
developmentally-appropriate methods in helping children learn math are grouping strategies for peer-teaching and
learning, use of concrete materials and manipulatives, computers, music and movement
activities with counting songs, and the like and book activities such as
storytelling based on math-related themes.
It is also exciting that media is exerting much effort in developing
children’s programs that enhance their learning. Computer software on math
activities and children’s shows such as Sesame Street are just a few
examples. These may be used in early
childhood education to supplement the curriculum since these are proven to hold
and stimulate young children’s attention and interest.
In the course of the
committee’s evaluation and review, they have come up with several conclusions
regarding children’s early math learning.
One of which is that young children are very much capable of learning
concepts and skills that are more complex that what they are usually provided
and given credit for. Beyond the
stereotype that children’s socio-emotional development should be the main
priority in early childhood programs, the current trend advocates for the
optimization of children’s competencies especially in the area of Math. This would greatly involve the cooperation
and support of families and communities.
It also has huge implications in the professional development of
educators of young children to reflect on their current practices and reform it
accordingly to suit the growing needs of young children today.
The book is a prime example of how people can join
efforts in upholding high standards of quality in education. The hard work meticulously done by the
committee members must now be considered as a challenge to all educators to
implement their recommendations based on the thorough research assembled and
evaluated. In doing so, they contribute
their share in helping raise competent students ready to embark on successful
careers which may involve mathematical expertise. At the very least, educators will be
responsible in helping children be ready for the challenges they will face in
the future by building their competencies in the present.
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