Early childhood teachers' misconceptions about mathematics education for
young children in the United States (free full-text available) Print <#>
*Joon Sun Lee*
/Hunter College, The City University of New York/
*Herbert P. Ginsburg*
/Teachers College, Columbia University/
/ In this article we discuss nine common misconceptions about learning
and teaching mathematics for young children that are widespread among
prospective and practicing early childhood teachers in the United
States. These misconceptions include: 1. Young children are not ready
for mathematics education; 2. Mathematics is for some bright kids with
mathematics genes; 3. Simple numbers and shapes are enough; 4. Language
and literacy are more important than mathematics; 5. Teachers should
provide an enriched physical environment, step back, and let the
children play; 6. Mathematics should not be taught as a stand?alone
subject matter; 7. Assessment in mathematics is irrelevant when it comes
to young children; 8. Children learn mathematics only by interacting
with concrete objects; 9. Computers are inappropriate for the teaching
and learning of mathematics. These misconceptions often interfere with
understanding and interpreting the new recommendations of early
childhood mathematics education (NAEYC & NCTM, 2002), and become subtle
(and sometimes overt) obstacles to implementing the new practices in the
classrooms. We hope this article provides an opportunity for
practitioners to examine and reflect on their own beliefs in order to
become more effective and proactive early childhood mathematics teachers. /
New vision for early childhood mathematics education in the United States
Mathematics education for young children is not new. Mathematics has
been a key part of early childhood education around the world at various
times during the past 200 years. For example, in the 1850s, Friedrich
Fröbel in Germany introduced a system of guided instruction centred on
various 'gifts', including blocks that have been widely used to help
young children learn basic mathematics, especially geometry, ever since
(Brosterman, 1997). In the early 1900s in Italy, Maria Montessori
(1964), working in the slums of Rome, developed a structured series of
mathematics activities to promote young children's mathematics learning.
In the United States, however, as the early childhood education field
has maintained its timehonoured tradition of emphasising social,
emotional and physical development, historically not much attention has
been paid to teaching academics, especially mathematics, to young
children (Balfanz, 1999). Although there had been attempts from time to
time to make early childhood programs more academically rigorous, the
focus was primarily on language and literacy development (National
Research Council, 2009). In the turn of the 21st century, the early
childhood education field in the United States has begun to take a big
step forward in promoting early childhood mathematics education. In
2002, the National Association for the Education of Young Children
(NAEYC), jointly with the National Council of Teachers of Mathematics
(NCTM), issued a position statement that advocates 'high quality,
challenging, and accessible mathematics education for three- to six-year
old children' (p. 1), and provided research based essential
recommendations to guide classroom practices. Since then, many national,
state and local organisations have embraced this new vision (Clements &
Sarama, 2004; NAEYC, 2003; NAEYC & NCTM, 2002; NCTM, 2000, 2006). As a
result, early childhood teachers across the United States are now faced
with a mandate to teach mathematics to young children.
The authors, as early childhood teacher educators and researchers, have
attempted to assist prospective and practising teachers to realise the
new vision of early childhood mathematics education. Our experiences
tell us that many teachers, despite their good faith efforts to provide
best practices to young children, are still confused and anxious about
the teaching and learning of mathematics, and hesitant to change (Lee &
Ginsburg, 2007a, 2007b). This hesitancy is perfectly understandable
given that, until recently, instruction in mathematics was not expected
in early childhood classrooms in the US (Balfanz, 1999). Rather,
teachers were cautioned that purposefully teaching mathematics was
unnecessary, inappropriate, or even harmful to young children (e.g.
Elkind, 1981, 1998). In the absence of sound preparation for early
mathematics education, many early childhood practitioners continue to
hold opinions or beliefs that are not consistent with nor based on
up-to-date research evidence.
In this article, we discuss nine common misconceptions about learning
and teaching mathematics for young children that are widespread among
prospective and practicing early childhood teachers in the United
States. These misconceptions were identified based on our in-depth
interviews with early childhood teachers about the key issues in early
mathematics education (Lee & Ginsburg, 2007a, 2007b) as well as our
experiences in teaching early childhood students, conducting workshops
with early childhood teachers (Ginsburg, Jang, Preston, VanEsselstyn &
Appel, 2004; Ginsburg et al., 2006), working with them in early
childhood classrooms, and engaging in informal conversations with them.
Our description of the myths is also based on available research
literature (Ginsburg, Lee & Boyd, 2008). The nine misconceptions are:
1. Young children are not ready for mathematics education.
2. Mathematics is for some bright kids with mathematics genes.
3. Simple numbers and shapes are enough.
4. Language and literacy are more important than mathematics.
5. Teachers should provide an enriched physical environment, step
back, and let the children play.
6. Mathematics should not be taught as stand-alone subject matter.
7. Assessment in mathematics is irrelevant when it comes to young
children.
8. Children learn mathematics only by interacting with concrete objects.
9. Computers are inappropriate for the teaching and learning of
mathematics.
These misconceptions often interfere with understanding and interpreting
the new recommendations on sound early childhood mathematics education,
and become subtle (and sometimes overt) obstacles to implementing the
new practices in the classrooms (Richardson, 1996).
These misconceptions often interfere with understanding and interpreting
the new recommendations on sound early childhood mathematics education,
and become subtle (and sometimes overt) obstacles to implementing the
new practices in the classrooms (Richardson, 1996).
1. Young children are not ready for mathematics education
When we begin to talk about teaching mathematics to young children,
there are always teachers who express their concerns, sometimes
fiercely, that 'Young children are just not ready to learn math yet!'
These teachers feel there is no need to hurry children or overwhelm them
with mathematics; it would do more harm than good to children who are
too young and thus not ready to understand.
Why do these teachers underestimate children's mathematical abilities in
the early years? We suspect it is their interpretation of Piaget's
theory, which they believe focuses on what children /cannot/ do,
suggesting that children so young are cognitively immature and therefore
not capable of understanding abstract concepts or the logical thinking
required in mathematics. So there is no point in attempting to teach or
push development in this area when children are not ready to construct
true understanding.
Yet, over the past 25 years or so, many researchers have focused on what
young children can do, and have accumulated a wealth of evidence that
young children are more competent in a wider range of mathematical
abilities than Piaget's theory might lead one to believe. While young
children display certain kinds of mathematical ineptitude, they also
show astonishing competence. As Vygotsky (1978) stated:
/Children's learning begins long before they enter school ? They
have had to deal with operations of division, addition, subtraction,
and the determination of size. Consequently, children have their own
preschool arithmetic, which only myopic psychologists could ignore
(p. 84)./
Young children can actively construct from their everyday experiences a
variety of fundamentally important informal mathematical concepts and
strategies, which are surprisingly broad, complex, and sometimes
sophisticated. They appear to be predisposed, perhaps innately, to
attend to mathematical situations and problems. (For more extensive
reviews, refer to Baroody, 2000; Clements & Sarama, 2007a.)
Teachers should not overlook these impressive informal mathematical
strengths of children in the early years. Given their interests and
capabilities, it does not make sense to avoid involving young children
in rich and meaningful mathematical experiences. Adults who fear
introducing mathematics to young children may be reacting more to their
own unfortunate encounters (and their low feelings of competence) with
mathematics than to any appreciation of young children's interests and
capabilities. Young children are ready and eager to learn stimulating
and challenging mathematics, and, as we shall see below, their
mathematical learning is not limited to the concrete; it is often abstract.
2. Mathematics is for some bright kids with mathematics genes
Many teachers believe, either explicitly or implicitly, that some
children may be born with mathematical aptitudes or mathematics genes,
and others are not. Some teachers even believe that children from
certain groups (such as gender, ethnicity and race) are blessed with
superior mathematical ability. Some teachers feel there is not much that
can be done to change or improve the innate ability of those unfortunate
children who are inherently not good at mathematics.
When looking at mathematics achievement, disparities among children from
different national, gender and income groups emerge as early as
preschool and kindergarten. American children are out?performed by their
counterparts from East Asia in mathematics achievement (Miller, Kelly &
Zhou, 2004). Within the US, children who live in poverty, a group
comprised of a disproportionate number of African?Americans and Latinos
(National Center for Children in Poverty, 2006), show significantly
lower average levels of achievement (Denton & West, 2002). Boys,
especially in the upper end of the percentile range, demonstrate higher
mathematics proficiency than girls do (McGraw, Lubienski & Strutchens,
2006; Robinson, Abbott, Berninger, Busse & Mukhopadhyay, 1997). Most of
all, females and minorities of African?American and Latino backgrounds
are under-represented in mathematically related areas (Jacobs, 2005).
Yet the existence of these differences, especially the differences young
children bring to school, cannot be attributed to a certain group having
a genetically endowed advantage in mathematics. Rather, it is the result
of a complex set of factors such as family, linguistic and cultural
experiences.
For example, while American parents tend to believe that innate ability
influences their children's mathematical achievement, Asian parents tend
to emphasise effort (Uttal, 1997), and tend to encourage their young
children to spend more time on mathematics related activities (Song &
Ginsburg, 1987). As well, mothers in the US are more likely to purchase
mathematics and science items for their sons than for their daughters
(Jacobs & Bleeker, 2004). Regular number-naming systems in Asian
languages such as Korean (the Korean word for 'eleven' is ship ill, or
'ten one'), compared to irregular English names, make it easier for
Korean children to learn certain number concepts (Miura, 2001). Also,
although poor children exhibit difficulty with verbal addition and
subtraction problems, they perform as well as their more privileged
peers on non-verbal forms of these tasks. It seems that weak language
proficiency interferes with the comprehension of problems and the
demands of a task (Jordan, Huttenlocher & Levine, 1994).
The mathematical interests and knowledge young children bring to school
may indeed differ, but the causes are more likely to be their varying
experiences, rather than their biological endowment. While teachers
should be aware of and sensitive to these differences, they should never
lose sight of the fact that all children, regardless of their
backgrounds and prior experiences, have the potential to learn
mathematics. In fact, the gaps in early mathematics knowledge can be
narrowed or even closed by good mathematics curricula and teaching
(Clements & Sarama, 2007b; Griffin, 2007a; Klein & Starkey, 2002;
Sophian, 2004). Teachers should strive to hold high expectations and
support for all children, without any ungrounded biases. When a teacher
expects a child to succeed (or fail), the child tends to live up to that
expectation.
3. Simple numbers and shapes are enough
Many teachers typically have a very narrow concept of the mathematical
content that young children should learn. Teachers often limit their
focus to one-to-one correspondence, simple counting and numbers, and
perhaps naming and sorting simple shapes, even when children are capable
of learning far more complex content. It is unfortunate that mathematics
is often equated to arithmetic or numeracy (perhaps because it rhymes
with and seems at the same level as literacy).
Early childhood mathematics education is both deep and broad. It should
cover the big ideas of mathematics in many areas?including number and
operations, geometry (shape and space), measurement, algebra
(particularly pattern), and data analysis?within learning contexts that
promote problem-solving, analysis and communication (NCTM, 2000, 2006).
In turn, each of these big ideas comprises several interesting
subtopics. Consider the domain of geometry, for example. The topic of
shape includes not only simple plane figures (e.g. circle, triangle) but
also hexagons and octagons (if young children can say and understand
'brontosaurus', they can do the same for 'octagon'), solids (e.g. cubes,
cylinders), and symmetries in two and three dimensions. Spatial
relations include ideas such as position (e.g. in front of, behind),
navigation (e.g. first go three steps to the left), and mapping (e.g.
creating a schematic representing the location of objects in the
classroom). Children can enjoy and learn the full spectrum of all of
these topics in geometry.
In order for mathematics education to include more than a superficial
focus on simple numbers and shapes, teachers need to expand their
concept of mathematical content for young children, and develop a deep
appreciation and understanding of the fundamental mathematical ideas
that young children should learn.
4. Language and literacy are more important than mathematics
Many teachers claim that language and literacy are by far the most
important topics to be taught in early childhood, and that a focus on
these subjects leaves little time for mathematics. While teachers speak
passionately and confidently about language and literacy, the silence
can be deafening regarding the teaching of mathematics.
Mathematics is at least as important as language and literacy, if not
more. Mathematics ability upon entry to kindergarten is a strong
predictor of later academic success, and is in fact an even better
predictor of later success than early reading ability. While reading
predicts only later reading ability, mathematics performance predicts
not only later mathematics but also later reading ability (Duncan et
al., 2007). Mathematics is indeed a core component of education from
very early ages to the higher grades.
Mathematics education is, in part, education in language and literacy.
Children learn to speak, read and write the language of mathematics in
order to communicate mathematical ideas. From the age of about two
years, children learn the language and grammar of counting. They
memorise the first 10 or so counting words (which are essentially
nonsense syllables with no underlying structure or meaning) and then
learn a set of rules to generate the higher numbers. For example, once
you figure out that 40 comes after 30, just as four comes after three,
it is easy to append to the 40 the numbers one through nine, and then go
on to the next logical ten number, 50, which comes after 40, just as
five comes after four.
Young children also learn other kinds of mathematical language, like the
names of shapes ('square') and words for quantity ('bigger', 'less').
Indeed, some of these words (such as 'more') are among the first words
spoken by many babies (Bloom, 1970). As children grow, they expand their
vocabulary and mathematical concepts embedded in it. That is, they learn
that terms and expressions such as 'altogether', 'put together', and 'in
all' are often used to indicate addition; that 'how many are left?',
'take away', and 'the difference between' are often used to indicate
subtraction; and that 'equal shares' and 'share equally' are often used
to indicate division (Moseley, 2005). Mathematical words are so
pervasive in everyday life and so deep in the core of human cognition
that they are not usually thought of as belonging to mathematics.
The most important kind of language children can learn in a stimulating
mathematics program is the language of thinking, justification and
proof. Children learn to talk about their own thinking ('I added by
counting them all up on my fingers'). They learn to justify their
answers ('I knew it was a triangle because I saw that it had three
sides'). They may even learn to propose proofs ('This can?t be a circle.
It only has straight lines'). This kind of communication is a key part
of mathematics, certainly more important than remembering that five and
four is nine.
In addition, children struggle with a very narrow form of mathematical
language, namely formal symbolism. Children begin to use the
mathematical symbols, such as addition (+), subtraction (?), and equals
(=). The special written symbolism of mathematics is the hardest form of
language for children to learn. For example, when asked to represent a
quantity such as five blocks, young children exhibit idiosyncratic (e.g.
scribbling) and pictographic (e.g. drawing blocks) responses, and only
much later can they employ iconic (e.g. tallies) and symbolic (e.g.
numerals such as '5' responses (Hughes, 1986).
The importance of mathematical language is underscored by the fact that
the amount of teachers' mathematics-related talk is significantly
related to the growth of preschoolers' mathematical knowledge over the
school year (Klibanoff, Levine, Huttenlocher, Vasilyeva & Hedges, 2006).
Also, promoting children's mathematics through books and literature is
an effective teaching practice (Hong, 1999). Language and literacy are
clearly deeply embedded in mathematics learning and teaching.
5. Teachers should provide an enriched physical environment, step back,
and let the children play
Another common misconception is that the teacher's role is to set up a
physical environment with a rich variety of mathematical objects and
materials, and that mathematical learning occurs incidentally, through
exploration during free play, with little teacher participation.
Teachers need to play an active role in teaching early mathematics to
young children. A rich physical environment, while an important
indicator of quality, is not enough by itself. The crucial factor is not
what the environment makes possible, but what children actually do in
it. The environment may provide 'the food for mathematical thought', but
the existence of mathematical food for thought in a classroom does not
guarantee that children will ingest it, let alone digest it.
Children do indeed learn some mathematics on their own from free play.
However, it does not afford the extensive and explicit examination of
mathematical ideas that can be provided only with adult guidance. As we
have discussed, early mathematics is broad in scope and there is no
guarantee that much of it will emerge in free play. In addition, free
play does not usually help children to mathematise ? to interpret their
experiences in explicitly mathematical forms and understand the
relations between the two. For example, children need to understand that
combining one bear with two others can be meaningfully interpreted in
terms of the mathematical principles of addition and the symbolism 1 + 2.
Free play can provide a useful foundation for learning, but a foundation
is only an opportunity for building a structure. Adult guidance is
necessary to build a structure on the foundation of children's informal
mathematics (Hildebrandt & Zan, 2002). Teachers should actively assist
children to advance beyond their informal, intuitive mathematics to the
formal concepts, procedures and symbolism of mathematics.
6. Mathematics should not be taught as stand-alone subject matter
Many teachers said they did not and should not teach mathematics as a
single subject. They strongly believed that mathematics should be
discussed only when children show interest or when it is integrated or
disguised within other activities (so that children do not know they are
learning mathematics).
All of this is not surprising, since the field's endorsement of an
integrated curriculum approach sometimes also seemed to mean a rejection
of a subject-matter curriculum. This is reflected in statements such as
'because a subject-matter approach to the curriculum is expert-based,
much of the content is difficult for children to understand' (Jalongo &
Isenberg, 2000, p. 205); and an example of inappropriate practice is
'times are set aside to teach each subject without integration'
(Bredekamp & Copple, 1997, p. 130). Yet, as Wheatley (2003) writes,
'inappropriate curriculum is not necessarily a result of an emphasis on
subject matter' (p. 98). In fact, particularly in mathematics, it is
recommended that 'teachers must set aside time specifically for the
study of mathematics and be purposeful in planning experiences that help
children develop specific mathematical understandings' (Richardson &
Salkeld, 1995, p. 42). Mathematics can be an interesting and exciting
subject of study in its own right. Children are fascinated with numbers
and shapes for their own sakes. Mathematics does not always need to be
integrated within other activities, or sugarcoated to appeal to young
children.
The integrated approach to teaching mathematics has its own merits. It
allows children to engage in, explore, and elaborate on mathematics as
it arises in the course of their in-depth investigation of a central
theme or topic. Thus, it situates the mathematics learning in a highly
motivating investigation of reallife problems, and also takes advantage
of the natural relationships between subjects such as literacy (Whitin &
Piwko, 2008) and music (Geist & Geist, 2008). However, 'the curriculum
should not become, in the name of integration, a grab bag of any
mathematics-related experiences that seem to relate to a theme or
project' (NAEYC & NCTM, 2002, p. 8). In addition, an integrated
curriculum too often results in an overemphasis on content areas that
teachers feel most comfortable with, and a neglect of mathematics, often
one of teachers? least favourite subjects (Copley & Padron, 1998).
In addition to integrating mathematics into classroom routines and
learning experiences across subject matters, 'an effective early math
program also provides carefully planned experiences that focus
children's attention on a particular mathematical idea or set of related
ideas', (NAEYC & NCTM, 2002, pp. 11-12). The organised mathematics
curriculum is an essential part of high-quality early childhood
mathematics education. It can serve as a blueprint and guide focus on
mathematics for thematic units in an integrated curriculum. Fortunately,
there are research-based mathematics curricula available. Some examples
in the United States are:
* /Big math for little kids/ (Balfanz, Ginsburg, & Greenes, 2003;
Ginsburg, Balfanz, & Greenes, 2003)
* /Building blocks/ (Clements, 2007; Clements & Sarama, 2007b)
* /Measurement-based/ (Sophian, 2004)
* /Number worlds/ (Griffin, 2007a, 2007b)
* /Pre-K mathematics curriculum/ (Klein & Starkey, 2002)
* /Storytelling sagas/ (Casey, 2004; Casey, Erkut, Ceder & Young, 2008)
* /Numbers plus in the High/Scope curriculum/ (Hohmann & Weikart, 2002)
7. Assessment in mathematics is irrelevant when it comes to young children
In the discussion of mathematics, very few teachers spontaneously
mentioned assessment. Some reported that they used observation to find
out whether children are interested in mathematics or not, but not so
much to gather information about what children know and are able to do
in mathematics. When we brought up the topic, the responses often
included, 'I don't test or quiz my kids, especially in math!' These
teachers appeared to have a narrow image of mathematics assessment as a
paper-and-pencil test. This may not come as a surprise considering that,
just as mathematics has been neglected for many years in early childhood
education, so have the methods needed to assess and evaluate it.
It is essential for teachers to 'support children's learning by
thoughtfully and continually assessing all children's mathematical
knowledge, skills, and strategies' (NAEYC & NCTM, 2002, p. 4). While
many educators are concerned (and complain) about teaching for testing,
assessment should drive instruction and curriculum. As mentioned
previously, young children come to school with intuitive ways of
thinking and reasoning regarding mathematics, although their ways may
not always be the same as those of adults. As children enter school,
their mathematical understanding and abilities continue to develop
quickly and broadly, in and out of school, with much individual
variation (Clements & Sarama, 2007a). Thus, 'well-conceived,
well-implemented, continuous assessment is an indispensable tool in
facilitating all children's engagement and success in mathematics'
(NAEYC & NCTM, 2002, p. 10).
In early childhood classrooms, observation is used most commonly for
understanding the children, as it is non-threatening and can be done
unobtrusively. In the case of mathematics, teachers often use checklists
to record their observations about whether a child has demonstrated
certain mathematics knowledge. Items in number and operation, for
example, include 'counts out loud in the correct order to 5, 10, 15 or
20', and 'counts or creates groups of objects and says how many
altogether'. A checklist like this is very broad and uncomfortably
vague. Knowledge of 'how many altogether', for example, is not at all
easy to assess, as cognitive research makes abundantly clear (Ginsburg,
1997). Obviously, observation is not enough.
For instance, a child says that 'three apples and two apples altogether,
are six apples'. This incorrect response is clearly important and needs
to be corrected. But it is even more important to understand the thought
process underlying the response in order to provide a sensitive guide to
instruction. The child may have got it through faulty memory ('I just
knew it'), faulty calculation (the child miscounts the objects in front
of him) or faulty reasoning ('I know that three and two is more than
four, and six is two more than four'). Depending on the reason, the
teaching solution may differ. To reach below the surface to learn about
children's conceptual understanding and the strategies behind their
answers, whether right or wrong, teachers need to engage children in a
dialogue, which we term 'flexible interviewing', asking the child to
elaborate on his or her ways of interpreting and approaching a problem
(Ginsburg, 1997).
No one method of assessment is perfect, always accurate, or completely
informative. Because of the natural fluctuation and rapid development of
children, a single assessment?whether done by observation or flexible
interview?may not provide accurate information. It is possible, and
sometimes desirable, to blend the methods. The teacher can observe in
the natural setting and at the same time give the children simple tasks
and interview them. It is necessary to assess young children frequently
and to base educational decisions on multiple sources of information.
8. Children learn mathematics only by interacting with concrete objects
Many teachers assume that young children learn mathematics by touching
and moving concrete objects. In much of the talk about improving
mathematics education, concrete objects, physical materials, or
manipulatives have been seen as essential for mathematics learning. For
example, Murray (2001) writes:
/ Concrete. Math is tangible. Children learn better when they're
using their senses; therefore, they should complete math tasks using
three?dimensional [sic] objects to represent the numbers under
examination (p. 28). /
It is a widespread belief that 'concrete is inherently good; abstract is
inherently not appropriate ? at least at the beginning, at least for
young learners' (Ball, 1992, p. 16).
But mathematics is not tangible; it is a set of ideas. Mathematics in
the early years does not need to be limited to the concrete or tangible.
While Piaget is widely cited regarding the concreteness of children's
thinking, what he meant by concrete was different from what people
usually mean by it. To Murray (2001), like many others, it means
something tangible that children can have their hands on. Piaget, on the
other hand (pun intended), showed that children were very abstract, and
in fact from the age of two onward sometimes over-generalise, employing
concepts that are overly inclusive, as when they refer to all men as
'daddy' (Ginsburg & Opper, 1988; Piaget & Inhelder, 1969). Their
thinking might be egocentric but is not concrete in the sense that some
writers believe.
These days there is a variety of mathematics manipulatives on the market
that are designed specifically to help children learn mathematics:
pattern blocks, counters, number sticks, base-10 blocks and Cuisenaire
rods, to name a few.
No matter how well-designed, these manipulatives, in and of themselves,
do not guarantee meaningful learning (Baroody, 1989). The use of
materials is effective only when they are used to encourage children to
think and make connections between the objects and the abstract
mathematical idea. It is not so much important that they simply have
their hands on, but rather that they have their minds on.
Mathematics ideas are not in the manipulatives; they are in the child's
mind. In this sense, the particular medium may be less important than
the fact that it could be used or manipulated to reflect and to
construct new meanings and ideas (Baroody, 1989). The medium could be
concrete objects, pictures of objects or mental images, as long as they
can be used or manipulated to think and reflect, and to construct
meanings and ideas (Baroody, 1989). Thus, as long as children can think
about what 'four' means in their minds, 'fourness is no more in four
blocks than it is in a picture of four blocks' (Clements, 1999a, p. 48)
or computer displays of pictured objects. Computers could indeed be an
effective learning tool, providing meaningful or concrete experiences to
young children.
9. Computers are inappropriate in teaching and learning of mathematics
Many teachers think computers are inappropriate learning tools for young
children, especially for mathematics, as they involve no thinking and
elicit mindless, random responses from children. Some even misunderstood
the concrete nature of computer experiences as hands-on keyboard and
mouse. In general, many teachers feel that computers isolate children
and prevent social interactions and communications, and so fear that
children will become antisocial.
Contrary to these beliefs, computers can be useful in teaching children
mathematics, if used appropriately. In fact, computers have some unique
advantages (Clements & Sarama, 2008). For example, computers increase
children's flexibility with manipulatives as they can move, cut, or even
resize onscreen objects; often it is more difficult, or even impossible,
to do these things with real objects. Onscreen objects do not pose the
awkwardness of handling that real ones might. Further, children can save
and retrieve their work on computers, and so can work on projects over a
long period. Computers can also provide immediate feedback. Capitalising
on these advantages, teachers can bring mathematics ideas to children's
explicit awareness.
Not all software designated for young children's mathematics education
is age?appropriate or high quality. The same can be said of almost any
educational material: manipulative, textbook, or television show.
Teachers need to select wisely. They should not let colourful graphics,
cute animation and music mislead them. Teachers need to critically
review content and underlying objectives to evaluate what kinds of
learning opportunities and experiences the software will provide for
their young students. Drill and practice software may lead to gains in
certain rote skills but not be as effective in improving children's
conceptual understanding of mathematical ideas. It can easily end up
being an electronic version of worksheets or flashcards. Discovery?based
software may be valuable when children are encouraged to think and to
apply mathematical ideas to solve problems.
In addition, effective use of computers can elicit, encourage and extend
children's communication and collaboration in learning. As Clements
(1999b) reports, computers serve as catalysts for social interaction.
Children working at the computer solve problems together, talk about
what they are doing, and help and teach friends. We do not mean to say
computers should replace concrete objects or other real-life experiences
or learning activities. Rather, computers can extend the range of tools
children use in their learning experiences. It makes as little sense to
say that computers are bad for children as it does to say that books or
manipulatives are good. It all depends on what kind of computer software
and books and manipulatives are used, and how they are used.
Conclusion
The concerns of many prospective and practising early childhood teachers
in the US, and their reluctance to teach mathematics to young children
are based on common misconceptions or misunderstandings as discussed
above. As the field has embraced the new vision of early childhood
mathematics education, teachers need to change their ideas about what
kinds of mathematics should be taught, and how they should be taught in
their classrooms. Further, as a result of fresh knowledge, teachers need
to change their classroom practices so they will support young
children's mathematical learning. There is a gap, a rather wide one,
between new recommendations and the current state of classroom practices
(Ginsburg et al., 2008).
The most pressing need in early mathematics education is to improve
early childhood teacher preparation and ongoing professional development
(Ginsburg et al., 2008). Currently, very few teacher preparation
programs in the United States offer courses devoted specifically to
mathematics education in early childhood. Most of them require their
students to take, at most, only one course in mathematics, compared to
several courses in language and literacy. For practising teachers,
in-service professional development needs to move beyond one-time
workshops or occasional readings of articles on the topic. As in other
areas, teachers need to keep up diligently with advances in research and
best practices, by reading professional journals or books, taking
courses, participating in conferences, and the like. In order for
teachers to implement effective early mathematics education, they need
to be supported by better teacher preparation and ongoing professional
development opportunities. The teacher is the key to effective,
high-quality mathematics education in early childhood classrooms.
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