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Do young children naturally develop the foundations of science, technology, engineering, and math (STEM)? And if so, should we build on these foundations by using STEM curricula in preschools? In this article, Douglas Clements and Julie Sarama argue that the answer to both these questions is yes. First, the authors show that young children possess a sophisticated informal knowledge of math, and that they frequently ask scientific questions, such as why questions. Preschoolers’ free play involves substantial amounts of foundational math as they explore patterns, shapes, and spatial relations; compare magnitudes; and count objects. Moreover, preschool and kindergarten children’s knowledge of and interest in math and science predicts later success in STEM. And not only in STEM: the authors show that early math knowledge also predicts later reading achievement—even better than early literacy skills do. Thus mathematical thinking, Clements and Sarama say, may be cognitively foundational. That is, the thinking and reasoning inherent in math may contribute broadly to cognitive development. Is teaching STEM subjects to preschool children effective? The authors review several successful programs. They emphasize that STEM learning for young children must encompass more than facts or simple skills; rather, the classroom should be infused with interesting, appropriate opportunities to engage in math and science. And instruction should follow research-based learning trajectories that include three components: a goal, a developmental progression, and instructional activities. Clements and Sarama also discuss barriers to STEM teaching in preschool, such as the cultural belief in the United States that math achievement largely depends on native aptitude or ability, and inadequate professional development for teachers. © 2016, Center for the Future of Children. All rights reserved.
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Math, Science, and Technology in the Early Grades
VOL. 26 / NO. 2 / FALL 2016 75
Math, Science, and Technology
in the Early Grades
Douglas H. Clements and Julie Sarama
Summary
Do young children naturally develop the foundations of science, technology, engineering,
and math (STEM)? And if so, should we build on these foundations by using STEM curricula
in preschools? In this article, Douglas Clements and Julie Sarama argue that the answer to
both these questions is yes.
First, the authors show that young children possess a sophisticated informal knowledge of
math, and that they frequently ask scientific questions, such as why questions. Preschoolers’
free play involves substantial amounts of foundational math as they explore patterns, shapes,
and spatial relations; compare magnitudes; and count objects.
Moreover, preschool and kindergarten children’s knowledge of and interest in math and
science predicts later success in STEM. And not only in STEM: the authors show that
early math knowledge also predicts later reading achievement—even better than early
literacy skills do. Thus mathematical thinking, Clements and Sarama say, may be cognitively
foundational. That is, the thinking and reasoning inherent in math may contribute broadly to
cognitive development.
Is teaching STEM subjects to preschool children effective? The authors review several
successful programs. They emphasize that STEM learning for young children must
encompass more than facts or simple skills; rather, the classroom should be infused with
interesting, appropriate opportunities to engage in math and science. And instruction
should follow research-based learning trajectories that include three components: a goal, a
developmental progression, and instructional activities.
Clements and Sarama also discuss barriers to STEM teaching in preschool, such as the
cultural belief in the United States that math achievement largely depends on native aptitude
or ability, and inadequate professional development for teachers.
www.futureofchildren.org
Douglas H. Clements is the Kennedy Endowed Chair in Early Childhood Learning, a professor, and the execuve director of the Marsico
Instute at the University of Denver’s Morgridge College of Educaon. Julie Sarama is the Kennedy Endowed Chair in Innovave
Learning Technologies, a professor, and the co-execuve director of the Marsico Instute at the University of Denver’s Morgridge
College of Educaon.
The authors wish to express their appreciaon to the issue editors and all the contributors to this issue of Future of Children for their
suggesons for improving this arcle, and to Camille Driver for her proofreading. The research reported here was supported in part by
the Instute of Educaon Sciences, US Department of Educaon, through Grant R305A080200 and also R305K05157 and R305A110188
to the Marsico Instute for Early Learning and Literacy, University of Denver. The opinions expressed are those of the authors and don’t
represent the views of the US Department of Educaon.
Elida Laski of Boston College reviewed and criqued a dra of this arcle.
Douglas H. Clements and Julie Sarama
76 THE FUTURE OF CHILDREN
Other articles in this issue
make a strong case that
early education is important.
The issue we address here
is whether early education
should include substantial science,
technology, engineering, and mathematics
(STEM) content—which some educators
view, often from ideological perspectives,
as appropriate only for older students. To
examine this question, we review research
on the appropriateness, benefits, and
effectiveness of various programs. Our
findings are often surprising.
Many adults, including some researchers,
believe that “open-ended free play” is good
for preschoolers and kindergartners, but
“lessons” are not. They don’t believe that
the youngest children should be taught
specific subjects, especially math, science,
and technology. They may grudgingly
accept math in the primary grades, but
they believe that literacy is more important,
more motivating, and more appropriate for
children. In this article we show that research
doesn’t support such thinking.
We begin by asking whether young children
naturally develop the foundations of
STEM. If so, should adults build on these
foundations intentionally, for example
by using STEM curricula in preschools?
Will children enjoy such interactions and
learning? Do curricula and intentional
teaching produce substantial gains in STEM
competencies? What teaching approaches are
most effective through the primary grades?
Does teaching STEM have other positive
effects, such as supporting high-quality
play and building executive function and
language? If so, what kind of professional
development will help teachers engage
children in STEM from preschool through
third grade? (Note that because more
research has focused on mathematics than on
the other STEM subjects, our examples tend
to favor math.)
Young Children’s Surprising
Competence in STEM
Especially when they’re given opportunities
to learn, young children possess a surprisingly
broad, complex, and sophisticated informal
knowledge of math.1 For example, they can
invent solutions to arithmetic problems by
using a variety of strategies. When asked
what 75 added to 25 would be, a first-grader
told us, “That’s like three quarters and one
more quarter—so four quarters, a dollar…
100!” Young children also are remarkably
successful with geometry tasks that go
beyond what older students are usually asked
to complete. A kindergartner in one of our
studies was making rectangles by inputting a
length and a width into a computer program
called Logo. He entered 50 and 50, and said,
“It’s a square! Sure, all sides the same—it’s a
square rectangle.”
Young children possess
a broad, complex, and
sophisticated informal
knowledge of math.
Another surprise is how early these
competencies develop in all STEM subjects.
Even before they begin school, young
children possess foundational science and
engineering concepts, at least at an implicit
level.2 For example, they ask whether cow
babies come from eggs, they observe that
people’s eyes are different colors (and
generate explanations for that), and they
Math, Science, and Technology in the Early Grades
VOL. 26 / NO. 2 / FALL 2016 77
frequently ask questions that begin with
“why.” Entering kindergartners possess
knowledge of the natural world, including
some understanding of things like cause
and effect; the differences between animate
and inanimate objects; the ways that
people’s beliefs, goals, and desires affect
their behavior; and substances and their
properties. This knowledge includes concepts
related to physics, biology, psychology,
and chemistry—though admittedly, their
intuitions aren’t always based on scientific
theories, or on any theory at all.
Even infants show sensitivity to principles
that adults would classify as physics,
measurement, and other science topics. For
example, infants as young as three or four
months have an intuition that objects need
support to keep them from falling. In the first
year of life, infants understand that inanimate
objects can’t move themselves and need to
be propelled into action. In one experiment,
five- to seven-month-olds watched a film that
showed a hand approaching a doll, picking it
up, and moving away with it. After seeing this
repeatedly, the infants lost interest (called
habituation). They remained uninterested
even when the direction or pace of the
movement changed. But when the film
changed again to show both the hand and
doll moving simultaneously and separately,
without the hand touching the doll, the
infants showed renewed interest by staring
intently. Thus they’re sensitive to the fact that
the lack of contact between the hand and doll
violates the causal principles of physics.
Similarly, children show surprising
competencies in mathematics that either are
innate or develop in the first years of life.
Consider a study in which five-month-old
children were repeatedly shown four groups
of two dots on a computer screen. Once
they were habituated to seeing those groups,
they looked longer when shown two groups
of four dots—they perceived the difference
and were more interested. Other studies
have demonstrated that nine-month-olds can
distinguish sets of 10 from sets of 15, and
that toddlers can use geometric information
about the shape of their environment to find
objects. Toddlers also show early competence
in arithmetic, noticing when a small
collection of things increases or decreases by
one item. By 24 months, many children have
learned number words and begun to count.
If young children naturally think and learn
about STEM content, then enhancing that
learning clearly isn’t an imposition.
Young Children’s Interest in STEM
In a similar vein, the scientific questions
children ask, such as why questions, show
that science is natural and motivating for
young children, as are engineering and
technology. Perhaps more surprisingly,
this is also true for mathematics, regarding
both what children can accomplish and
what they’re interested in. For instance,
preschoolers’ free play involves substantial
amounts of foundational math. Regardless of
their income level and gender, preschoolers
explore patterns, shapes, and spatial relations;
compare magnitudes; and count objects.
As an example, Kyoung-Hye Seo and Herb
Ginsburg of Columbia University watched
a child putting away blocks by placing each
one in a box that contained only other blocks
of the same size and shape.3 They saw three
girls draw pictures of their families and
discuss the number and ages of their siblings.
It’s not surprising, then, that high-quality
education can help children build on these
nascent tendencies. Unfortunately, when
such education doesn’t begin in preschool
and continue through the early years, this
Douglas H. Clements and Julie Sarama
78 THE FUTURE OF CHILDREN
potential may be unrealized, leaving children
trapped in a trajectory of failure.
The Value of Early Math and
Science
Preschool and kindergarten children’s
knowledge of and interest in math and
science predicts later success in STEM.4
For example, early math knowledge strongly
predicts later math achievement, even after
controlling for differences in other academic
skills, attention, and personal and family
characteristics.5 This surprising result comes
not from a single study, but from a meta-
analysis that combined six studies, each
involving large databases that had followed
the same children over time. Essentially,
math seems to be a fundamental component
of thinking.
Measuring Early Competency in
Math and Science
Our methods for measuring early math and
science knowledge are important, not only
for researchers but also for teachers who wish
to discover what their children know and how
they can teach them better.6 Whether we
use quick screeners or long diagnostic tests,
most assessments should cover skills, facts,
concepts, and problem-solving strategies. In
math, verbal (rote) counting is a simple skill,
whereas problem-solving might be tested by
showing children two groups of chips and
asking them to count to determine which
group has more chips. Posing an arithmetic
word problem is another approach.
Assessments should also be age appropriate.
Multiple-choice group tests may not be
adequate. For teachers, a positive approach
to assessing children’s strengths and needs
should include curriculum-embedded
assessment (observing and taking notes
during small group instruction), documenting
children’s talk, and individual interviews.
These strategies are more likely to illuminate
children’s background knowledge and
emerging ideas, giving teachers the insight
they need. The richer the instructional
environment, the broader the range of
evidence for assessing learning. Careful
assessment is especially important for
children with special needs or disabilities.
Teaching Math and Science in the
Early Grades
Based on children’s foundational
competencies and natural interest, learning
math and science should be viewed as an
appropriate and important educational goal.
Teachers need to understand that these
subjects encompass more than facts or simple
skills.7 Unfortunately, young children aren’t
given enough math and science experiences.
Teachers spend less time in science learning
centers (tables or areas stocked with books
and other materials that promote exploration)
than in other learning centers, and they
rarely offer science-related activities in any
context, either planned or spontaneous. Even
well-regarded programs for young children
tend to have a strong focus on language and
social development but a weaker focus on
math, and little or no focus on developing
children’s potential for scientific thinking.
Teachers rarely offer science-
related activities in any
context, either planned or
spontaneous.
What’s more, the small amount of science
that children are taught isn’t of high quality.
Math, Science, and Technology in the Early Grades
VOL. 26 / NO. 2 / FALL 2016 79
For example, Head Start children arrive at
kindergarten with lower scores in science
readiness than in any other area. Many
teachers still retain a bias against computer
technology, considering it inappropriate
in classrooms for young children. With
little appreciation for science, math, and
technology (not just computer technology,
but also the technology and engineering of
everyday objects), most teachers are poorly
prepared to help young children realize their
potential for learning STEM content.
Similarly, most three- and four-year-olds
have few or no experiences in mathematics.
Teachers often believe they are “doing math”
through puzzles, blocks, and songs. But even
when such activities do include mathematics,
it’s not the main focus; instead, the math is
embedded in reading or a fine-motor activity.
Evidence suggests that such an approach is
ineffective.8
Too many primary-grade classrooms teach
children simple facts and skills that they
either already know or can learn relatively
quickly, instead of more advanced math
concepts. Learning such processes as
arithmetic problem-solving and reasoning
is arguably more important to their
development over time.9 Even later reading
success requires such conceptually oriented
science and math instruction.
Certain experiences can ameliorate such
problems, however, especially for low-income
children and those from minority racial
and ethnic groups. But several traditional
approaches, such as developmentally
appropriate practice, haven’t been
consistently successful. According to the
National Association for the Education
of Young Children, developmentally
appropriate practice involves “meeting
young children where they are” and helping
them reach goals that are both challenging
and achievable. Unfortunately, it hasn’t
been shown to increase children’s learning,
perhaps because it’s too often restricted to
the use of free play only.10 To combat this
lack of learning, we need to infuse the young
child’s day with interesting, appropriate
opportunities to engage in math and science,
from preschool through the primary grades.
Learning Better Mathematics
Recently, research-based standards have
been developed to describe what should
be taught and emphasized when it comes
to math. For example, the Common Core
State Standards—Mathematics followed
research on how children learn as well as the
structure of math. Just as important, all math
curricula and standards should identify and
support a few core ideas rather than many
disconnected topics. The best way to achieve
academic gains and understanding is to focus
on these core concepts coherently, within and
across age levels, rather than trying to teach a
little of everything at every age.
Moreover, as President Bush’s National
Mathematics Advisory Panel stated in a
comprehensive research review published in
2008, “The curriculum must simultaneously
develop conceptual understanding,
computational fluency, and problem-solving
skills.”11 A study of second-graders shows
the benefits of this approach.12 One group
was taught skills along with conceptual
understanding, as well as how to flexibly
apply multiple strategies. These students
scored higher on math tests than did students
in a traditional textbook program that focused
only on mastering skills. The first group
more often selected strategies related to the
number properties of the problems, and
Douglas H. Clements and Julie Sarama
80 THE FUTURE OF CHILDREN
used strategies more adaptively. Even after
months of instruction, the skills-only group
didn’t apply their skills flexibly. Students who
have fluent and adaptive competencies can
propose problems, make connections, and
then work out solutions in ways that make the
connections visible.
Rich learning in mathematics can support
existing approaches to early education. For
example, children given specific learning
activities tend to engage in higher-quality
social-dramatic play. That is, children in
classrooms that strongly emphasize either
literacy or math are more likely to display
higher-quality social-dramatic play, while
those in classrooms that emphasize both have
the highest-quality play.13 By contrast, the
lowest gains in learning come from free-play-
only classrooms, and even using so-called
teachable moments during play is ineffective
in these circumstances.14
Children also benefit from a related type
of play, playing with mathematical ideas.
Many researchers consider this the “child as
scientist” approach: Children are motivated to
explore science concepts while they interact
with their environment.15 As a mathematical
example, just after her third birthday, our
daughter Abby was playing with three of five
identical toy train engines. Passing by, her
mother asked, “Where are the other trains?”
After her mother was out of sight, Abby was
heard speaking to herself. “Oh, I have five.
Ummm … [pointing to each engine] you are
one, two, three. I’m missing four and five—
two are missing! [She played with the trains a
few more seconds.] No, I changed my mind
… I have one, three, and five. I’m missing two
and four. I gotta find them two.”
When Abby first figured out how many she
was missing, she was using mathematics in her
play. But when she decided that she would
call the three engines she had one, three,
and five, and call the missing engines two
and four, she was playing with the notion that
assigning numbers to a collection of objects
is arbitrary. She was also counting not just
objects but words. She counted the words
“four and five” to see that two were missing,
and then she figured out that counting the
renumbered counting words “two” and “four”
also yielded the result of “two.” She was
playing with the idea that counting words
themselves can be counted.
Learning Mathematics Better
If developmentally appropriate practice
classrooms don’t support math learning, how
do we ensure that a new approach remains
appropriate to children’s development?16 The
answer lies in seeing that learning progresses
along research-based trajectories. A learning
trajectory has three components: a goal, a
developmental progression, and instructional
activities.17 To attain a certain competence
in a given math topic (the goal), students
progress through several levels of thinking
(the developmental progression), aided by
tasks and experiences (instructional activities)
designed to build the mental actions-on-
objects that enable thinking at each level.
For example, we might set a goal for young
children to become competent counters.
The developmental progression describes a
typical path that children follow to achieve
this. A child might start by learning simple
verbal counting, then learn one-to-one
correspondence between counting words
and objects. The next step is understanding
that the final counting word tells how many;
after that, connecting the final number
of the counting process to the cardinal
quantity (how many) of a set. Finally, the
Math, Science, and Technology in the Early Grades
VOL. 26 / NO. 2 / FALL 2016 81
child acquires counting strategies for solving
arithmetic problems (up to multidigit
problems, for example, 36 + 12: “I counted
36 . . . 46 . . . then 47, 48!”). Although
learning trajectories share characteristics
with other ways to sequence teaching,
they’re based on a core of subject-specific
knowledge, on cognitive science, and on
educational research into how children learn
that subject.18 Most curricula, assessments,
and professional development omit critical
levels in the learning trajectory for counting
and don’t recognize these research-based
levels in such topics as measurement and
geometry.
Teachers who know how to
use and connect the three
components of a learning
trajectory—content, levels
of thinking, and activities
that are fine-tuned for
their children’s level of
thinking—are more effective
professionals.
Teachers who know how to use and
connect the three components of a learning
trajectory—content, levels of thinking,
and activities that are fine-tuned for their
children’s level of thinking—are more
effective professionals.19 Without such
knowledge, teachers often give young
children tasks that are either too easy or
too hard, and they don’t recognize the
mismatch.20 When teachers understand
how levels of thinking progress along
these paths, and are able to sequence and
individualize activities that are based on
these levels, they can build effective math-
learning environments. In this way, learning
trajectories make it easier to provide
appropriate and effective teaching for all
children. Substantial work on standards,
curricula, and professional development
has been based on the concept of learning
trajectories in one form or another.21
Developing Mathematically Rich
Curricula
Through our own program, Building Blocks,
we illustrate how a curriculum can be based
entirely on learning trajectories and use the
kinds of assessment we discussed earlier.
From 1998 to the present, we developed
and evaluated Building Blocks according to
a comprehensive research framework. Our
basic approach was to find the mathematics
in children’s everyday activities and develop
math from there. Building Blocks helps
children bring math into activities ranging
from art and stories to puzzles and games.
We connected every aspect—including text,
software, and professional development—to
an explicit core of learning trajectories for
each math topic. Multiple evaluations have
documented that our approach has strong
positive effects on children’s achievement,
even when the curriculum was implemented
at a large scale. (One study covered an entire
school district, using a scale-up model called
TRIAD—short for technology-enhanced,
research-based instruction, assessment, and
professional development.)22
Most groups of children who experienced
this curriculum (for example, girls and
boys, or children of different income levels)
demonstrated equal learning gains, with
one notable exception. Although African
American children in the control group
showed smaller gains than their peers in the
Douglas H. Clements and Julie Sarama
82 THE FUTURE OF CHILDREN
same group, African American children in
the treatment group showed larger gains
than their peers, thus narrowing the initial
achievement gap. By providing learning
trajectories that help teachers see what
children can achieve and how they can be
assisted to progress to higher levels, the
TRIAD/Building Blocks intervention may
be particularly effective in overcoming the
negative effects that result from the low
expectations some educators hold for African
American children when it comes to math
learning.23
An evaluation of Boston’s prekindergarten
program offers more evidence of Building
Blocks’ effectiveness.24 This study used a
different design and evaluated a literacy
curriculum combined with Building Blocks.
Children in the program scored higher
on math, literacy, and language skills than
other children, raising a child at the 50th
percentile to the 69th to 73rd percentile.
Furthermore, the children in the program
scored significantly higher in multiple
executive-function skills, such as attention-
shifting, working memory, inhibitory control,
and emotion recognition. (See the article in
this issue by Cybele Raver and Clancy Blair
for an examination of executive function in
young children.) The program narrowed the
school readiness gap in early math between
poor and non-poor children and eliminated
the gap between Latino and white children.
Changing teachers’ perceptions of all
children’s abilities to be strong learners
and thinkers about math topics may have
substantial benefits. But the above results
should be tempered by initial findings from
a large evaluation of Building Blocks in New
York City. In that study, gains seen at the
beginning of prekindergarten were no longer
statistically significant when prekindergarten
ended. Researchers are still analyzing several
other anomalies, including the large amount
of math taught in the control classrooms, the
lack of high-quality instructional strategies
(such as promoting dialogue and formative
assessment) in intervention classrooms,
and the finding that effects appeared
to be greater for children who entered
prekindergarten with strong receptive
language skills. The evaluation is continuing
into the children’s kindergarten year.
Other preschool math curricula have shown
positive results in high-quality evaluations,
including Big Math for Little Kids and the
Pre-K Mathematics Curriculum. Table 1
summarizes the main studies. We know
of only one direct comparison of Building
Blocks with another math curriculum. In
that case, Building Blocks outperformed the
other curriculum, Pre-K Mathematics, when
all other factors were kept the same—that is,
the amount of coverage, new materials, and
professional development. Beyond this, there
is little to tell us which curriculum would be
a better choice for any particular context. All
successful interventions appear to depend
on raising the quality and quantity of specific
mathematics teaching strategies. This has
implications for policy and practice, as it
suggests that although adopting a curriculum
is an important step, other factors, such as
professional development and coaching, are
also critical.
Do positive effects last? Three types of long-
term impact are important: sustainability,
persistence, and diffusion. Sustainability
is the continued and accurate use of an
innovation such as a curriculum. Persistence
means that the effects of an intervention on
individual children’s learning trajectories
continue to be felt. Diffusion is the process
by which an innovation spreads among the
Math, Science, and Technology in the Early Grades
VOL. 26 / NO. 2 / FALL 2016 83
Table 1: Evaluaons of Early Mathemacs Programs
Program/ Age/ No. of
Curriculum Content Grade Children Design Results
Building Math Pre-K 276 Random assignment Building Blocks: large
Blocks to one of three groups: eect compared to
Building Blocks, control; medium eec t
Pre-K Mathemacs compared to Pre-K
Curriculum, or control Mathemacs Curriculum
TRIAD/ Math, Pre-K 1,305 Random assignment of Large eect on math;
Building Language schools to one of three small to medium eect
Blocks groups: TRIAD with on four of six language
follow-through subtests
(TRIAD–FT), TRIAD
with no follow-through
(TRIAD –NFT), and
control
TRIAD Math K 1,218 Random assignment to Both TRIAD groups
follow-through same three groups as had a medium eect
(to Building in TRIAD/Building compared to control
Blocks) Blocks evaluaon and were similar to
each other.
TRIAD Math 1 1,079 Random assignment to TRIAD– FT had a
follow-through same three groups as medium eect and
(to Building in TRIAD/Building TRIAD–NFT a small
Blocks) Blocks evaluaon eec t compared to
control; FT had a small
eect compared to NFT.
Building Math Pre-K 2,018 Comparison of Medium eect on
Blocks + Liter ac y, children just above and language, literacy,
OWL Execuve just below the age numeracy, and
Funcon, cuto mathemacs skills;
Emoons small eect on
execuve funcon and
measure of emoon
recognion
Big Math for Math Pre-K 762 Randomly assigned Medium eect
Lile Kids and K child-care centers
(BMLK)
Pre-K Math Pre-K 276 Classrooms randomly Moderate eec t
Mathemacs assigned to
Curriculum + intervenon or control
Building
Blocks
(soware)
Note: Many of these studies included control groups that used a variety of early childhood curricula, most oen Creave
Curriculum, but also Opening the World of Living, Where Bright Futures Begin, and curricula developed by districts and
teachers. Thus we may be condent that business-as-usual curricula don’t eecvely develop children’s potenal for
learning math.
Sources: Douglas H. Clements and Julie Sarama, “Experimental Evaluaon of the Eects of a Research- Based Preschool
Mathemacs Curriculum,” American Educaonal Research Journal 45 (2008): 443–94; Douglas H. Clements et al.,
“Mathemac s Learned by Young Children in an Inter venon Based on Learning Trajectories: A Large-S cale Cluster Randomized
Tri al ,” Journal for Research in Mathemacs Educaon 42 (2011): 127–66; Julie Sarama et al., “ The Impac ts of an Early
Mathemacs Curriculum on Emerging Literacy and Language,” Early Childhood Research Quarterly 27 (2012): 489–502; Julie
Sarama et al., “Longitudinal Evaluaon of a Scale-up Model for Teaching Mathemacs with Trajectories and Technologies,”
Journal of Research on Educaonal Eec veness 5 (2012): 105–35; Chrisna Weiland and Hirokazu Yoshikawa, “Impacts of
a Prekindergarten Program on Children’s Mathemacs, Language, Literacy, Execuve Funcon, and Emoonal Skills,” Child
Development 84 (2013): 2112–30; Ashley Lewis Presser et al., “Big Math for Lile Kids: The Eec veness of a Preschool and
Kindergarten Mathemacs Curriculum,” Early Educaon and Development 26 (2015): 399–426; Alice Klein et al., “Eec ts of a
Pre-Kindergarten Mathemacs Intervenon: A Randomized Experiment,” Journal of Research on Educaonal Eecveness 1
(2008): 155–78; Preschool Curriculum Evaluaon Research Consorum, Eects of Preschool Curriculum Programs on School
Readiness (Washington, DC: Government Prinng Oce, 2008).
Douglas H. Clements and Julie Sarama
84 THE FUTURE OF CHILDREN
members of a social system—for example,
wider dissemination of a curriculum.
Sustainability of implementation is especially
important, given the importance of high-
quality teaching for any curriculum and
the short life of many reforms. Logically,
we might expect to see decreasing fidelity
after the external support and professional
development provided by the intervention
teachers have ceased. In the TRIAD/
Building Blocks study, however, we saw the
opposite: Teachers demonstrated increasing
levels of fidelity years after support ended.
It would appear that when teachers saw
children gaining competence in math, they
increased their efforts to carry out all of the
intervention’s components.
Persistence of effects may be a more
important and complex issue than
sustainability. Gains made in high-quality
prekindergarten interventions often fade
in the following few years. Policy makers
have tried to promote persistence through
alignment (for example, making connections
between curricula and assessments within
each grade) and continuity (making similar
connections across grade levels). We have
hints but little empirical evidence that lack of
alignment and continuity is at least partially
responsible for the fadeout of early gains.
We also see some evidence that professional
development can support curricular
continuity that produces better induction
experiences for new teachers, shared goals
and instructional strategies, and increased
student performance.
The TRIAD project promoted continuity
between prekindergarten and the primary
grades, testing the hypothesis that gains
would appear to fade without follow-
through in the primary school years. That
is, if children transition into a kindergarten
curriculum that assumes little or no
competence in math and thus emphasizes
low-level skills, children who had a strong
prekindergarten math experience would
not continue their learning, whereas others
might catch up. In the TRIAD evaluation,
the effects from prekindergarten persisted
when follow-through interventions took
place in kindergarten and first grade; without
follow-through, the effects were significantly
smaller.
Interventions such as TRIAD are exceptions
in US schools. Because the new trajectories
are exceptions, many things may weaken
their positive effects, such as programs that
assume low levels of math knowledge and
focus on lower-level skills, or a culture of
low expectations for certain groups. Without
continued support, children’s nascent
learning trajectories revert to their original,
limited course. On the other hand, perhaps
stronger prekindergarten interventions are
necessary to counteract early disadvantage
in children’s school-readiness skills. But that
approach may be unrealistic when children
attend poor-quality schools, as African-
American students are more likely to do.
Just as experiencing consecutive years of
high-quality teaching can have a cumulative
positive effect, the opposite is also true.
Diffusion of the innovation is difficult to
assess. However, reports have documented
diffusion of the TRIAD/Building Blocks
intervention in Boston. And New York City
schools are adopting the curriculum and
the TRIAD model for all prekindergarten
classrooms.
Several successful interventions in the
primary grades also apply some version of
the learning trajectories idea. First-grade
Math, Science, and Technology in the Early Grades
VOL. 26 / NO. 2 / FALL 2016 85
teachers in Japan commonly move along
multiple learning trajectories, culminating
at the point when children develop an
effective base-10 strategy to solve addition
problems. For example, children solve 8 +
6 by thinking, “I take 2 from the 6 to make
the 8 into 10, then have 4 left, so 10 + 4 =
14.” Such interventions explicitly promote
conceptual understanding by discussing and
developing connections among concepts,
facts, procedures, and processes. The
interventions don’t practice basic facts
for mastery until the children develop
conceptual foundations and meaningful
strategies. They challenge students to solve
demanding math problems, helping them
learn to think mathematically. Interventions
like these may offer effective follow-through
after prekindergarten programs, thus
minimizing the fadeout effect. And they
may be particularly successful if they use
formative assessment—that is, continuous
monitoring of student learning to guide
instruction that’s based on the idea of
learning trajectories.25
Three curricula implemented in first
and second grade are among the other
approaches to primary-grade math that
have also been evaluated. One of these is
consistent with the learning trajectories
approach (Math Expressions), one is a
more conventional textbook series, and the
third emphasized procedural skills but did
make some connections to concepts. All
three outperformed a curriculum that was
less structured and put more demands on
teachers mathematically and pedagogically.26
Learning Better Science and
Learning Science Better
Like early math education, early science
education should be more than a surface
treatment of traditional topics—describing
the weather, for instance. Research has
identified learning trajectories for key
topics in science and engineering, such as
physics and biology, and evidence shows that
following these pathways is educationally
effective. Admittedly, efforts to identify
learning progressions and core concepts in
science are not as far along as they are in
math. We still need to identify a few core
ideas and to plan standards, curricula, and
teaching around those ideas.27 But we do
have a foundation on which to build.
Developing Scientifically Rich
Curricula
As with mathematics, high-quality science
education that emphasizes richer and
deeper content appears to be effective,
although experimental and long-term
studies have yet to be conducted for
most curricula. Early results suggest that
consistent science experiences can increase
children’s vocabulary. They also promote
the use of more complex grammatical
structures, such as causal connectives: “It’s
green because I mixed yellow and blue
paint.” Such experiences may also close
a science gender gap in motivation and
interest.
Several science curricula encourage children
as young as preschoolers to think about and
work with science concepts (for example,
the change in a plant’s height) for many
weeks or months. Primary grade teachers
also need access to all three components of
learning trajectories, especially instructional
activities that work when connected to
their understanding of students’ scientific
thinking and learning.28 And our early
elementary educators sorely need more
professional development in science. Ideally,
Douglas H. Clements and Julie Sarama
86 THE FUTURE OF CHILDREN
that would involve multi-year efforts to
focus on both subject-matter content and
pedagogy.29
Effects on Competencies beyond
Math and Science
The time spent by primary-grade teachers
on science and social studies instruction has
decreased in the past 15 to 20 years, and the
long-term negative effects on achievement
may be substantial.30 Math and science
vocabulary and concepts are essential for
reading comprehension, because early math
and science instruction develops language
within those subjects.31 And the benefits
may run deeper. In one study, children who
experienced the Building Blocks curriculum
in prekindergarten outperformed children
in a control group on four oral language
competencies when they were asked to
retell a story: ability to recall key words,
use of grammatically complex utterances,
willingness to reproduce narratives
independently, and inferential reasoning.
This revealed transfer both in content and in
time. That is, the children learned language
skills that had not been directly taught in the
math curriculum, and they maintained these
skills into their kindergarten year.
Such transfer of learning may explain why
early math knowledge not only predicts later
mathematics achievement, but also predicts
later reading achievement—even better
than early literacy skills do. Mathematical
thinking may be cognitively foundational.32
That is, the thinking and reasoning inherent
in math may contribute broadly to cognitive
development. However, we still need to learn
more about how STEM education supports
later language and literacy learning. Would
having interesting, sustained conversations
on any topic be just as beneficial? We also
know little about how much time should be
focused on literacy and STEM topics.
Research also suggests that high-quality
implementation of math curricula in
preschool can develop self-regulation skills
(also called executive function skills).33
These are the cognitive skills that allow
people to control, supervise, or regulate
their own thinking and behavior, such as
the ability to shift attention or hold things
in working memory. In math, consider the
following problem: “There were six birds
in a tree. Three birds already flew away.
How many birds were there from the start?”
Children must use the executive function
of response inhibition to avoid the tempting
(but incorrect) procedure of subtraction,
engendered by the phrase “flew away.”
Instead, they must calculate the sum through
addition, counting on, or other strategies.
In some experiments, the effects of high-
quality math on executive function have been
found even when they weren’t planned. For
example, the combination of the Building
Blocks math curriculum and the Opening
the World of Learning literacy curriculum
produced unplanned but positive, albeit
small, statistically significant impacts on
executive function.
Another study hypothesized that combining
Building Blocks with Tools of the Mind, a
curriculum designed to develop executive
function through play, would produce better
results in executive function and in math than
a Building Blocks math curriculum alone
would. The study further hypothesized that
both the combined curriculum and Building
Blocks alone would outperform the control
group in math.34 The results were surprising.
The Building Blocks group had higher math
scores than either of the other groups. Even
more surprising was that the Building Blocks
Math, Science, and Technology in the Early Grades
VOL. 26 / NO. 2 / FALL 2016 87
group outperformed the others on two
measures of executive function, including
one that predicts later math achievement.
These and other studies suggest that high-
quality math education may have the dual
benefit of teaching an important content
area and developing at least some executive
function processes.35 They also suggest
that preschool curricula can successfully
combine social-emotional learning, literacy,
language, science, and math, all the while
enhancing rather than competing with play-
based approaches.36 We need research on
such efforts to see how they can benefit all
domains of development.
High-quality math education
may have the dual benefit
of teaching an important
content area and developing
at least some executive
function processes.
Barriers to Teaching Math and
Science
Widespread negative dispositions and beliefs
about learning and teaching mathematics and
about preservice training and professional
development in STEM constitute substantial
barriers to high-quality teaching.
Negative Dispositions and Beliefs
One deeply embedded cultural belief in
the United States is that math achievement
largely depends on native aptitude or ability.
In contrast, people in other countries, such
as Japan, believe that achievement comes
from effort. Research shows that the US
belief hurts teachers and students and,
furthermore, that it just isn’t true. Students
who believe—or are helped to understand—
that they can learn if they work diligently
will perform better throughout their school
careers than students who believe that a
person either gets it or doesn’t. That view
often leads to failure and what we call
“learned helplessness.” Similarly, students
who have mastery-oriented goals (that is,
students who try to learn and see that the
point of school is to develop knowledge and
skills) achieve more than students whose
goals are directed toward high grades or
outperforming others.
Early-childhood teachers often hold negative
dispositions and beliefs about math and
science, including dislike, trepidation, fear,
and a doubt in their own efficacy. In one
study, the strongest predictor of mathematics
learning among preschoolers was their
teachers’ belief that math education was
appropriate for that age group.
Children also need more positive beliefs
and attitudes about STEM. As early as the
primary grades, math anxiety hurts children’s
achievement in math. Primary-grade students
who score high on working memory but
also have math anxiety tend to perform
more poorly in math, because their working
memory capacity is co-opted by anxiety.
Primary graders who feel panicky about
math have increased activity in brain regions
associated with fear, and decreased activity in
brain regions involved in problem-solving. If
we can identify and treat math anxieties early,
we may be able to keep children with high
potential from avoiding math courses.
Fortunately, most very young students
have positive feelings about math; they’re
motivated to explore numbers and shapes.
Douglas H. Clements and Julie Sarama
88 THE FUTURE OF CHILDREN
But it takes just a couple of years in typical
schools before they begin to believe that only
some people have the ability to do math. We
believe that students who experience math as
a sense-making activity, rather than a series
of timed tests, will build positive feelings
about math throughout their school careers.
Similarly, we can change teachers’ negative
dispositions and beliefs through high-quality
preservice and professional development, a
subject to which we now turn.
Professional Development Is
Inadequate
Even though children are eager to learn,
many early childhood teachers aren’t eager
or prepared to engage children in rich
experiences in domains other than literacy.
Historically, teachers of young children
haven’t been prepared to teach subject-
specific knowledge to young children.
In-service professional development also
tends not to emphasize math and science,
despite learning standards and increased
curricular attention to these subjects. Of 50
state-funded preschool programs, 41 require
at least 15 hours of in-service training per
year. But content decisions are made locally,
and STEM is usually ignored. Professional
development must help teachers explore
content and pedagogy in depth. It must
also confront the distaste for math that
is widespread among teachers of young
children—and directly related to girls’
achievement in their classes.
Research on professional development for
math teachers offers some guidance. For
example, certification alone doesn’t reliably
predict high-quality teaching—probably
because certification programs vary widely
and too many are of low quality. On the other
hand, direct measures of teachers’ knowledge
of math and math pedagogy do predict the
quality of their teaching.37
In general, research suggests that effective
professional development in early STEM
is continuous, intentional, reflective, goal-
oriented, and focused on content knowledge
and children’s thinking; it’s grounded in
particular curriculum materials, and situated
in the classroom. But all training needn’t
occur in the classroom. While research-based
curricula can help teachers learn to teach
STEM, teachers need to understand all
three components of a learning trajectory—
goals (the STEM content), developmental
progressions, and instructional activities. This
requirement appears to place too heavy a
burden on curricula alone, even on curricula
designed to help teachers learn.
Teachers also need off-site, intensive training
that focuses on these three components and
the connections among them—though such
training must be connected to classroom
practice. Then they need time to try out the
new strategies in their classrooms, supported
by coaches who give them feedback. The
success of Building Blocks, TRIAD, and
other projects can largely be attributed to
such professional development organized
around learning trajectories. These projects
included far more extensive and intensive
professional development than the usual
one-shot workshop, ranging from five to 14
full days.
Technology and Engineering
Young children are motivated by such
simple engineering tasks as building with
blocks, and by interacting with technology.38
Unfortunately, few researchers have
examined engineering among young children.
Block-building has been widely studied, so
we know that preschoolers’ competence
Math, Science, and Technology in the Early Grades
VOL. 26 / NO. 2 / FALL 2016 89
at this activity predicts the number of
math courses they take and their grades in
high school. Furthermore, developmental
progressions for block-building are well
established.
Various computer technologies can improve
how and what children learn about STEM,
and about other subjects. However, the T in
STEM refers to learning about technology
rather than using technology, and learning
how to apply it to solve problems. Therefore,
we will only briefly describe computer-
assisted instruction, and then we’ll move on
to more active technologies.
Computer-Assisted Instruction (CAI)
CAI means structured software that instructs
students or lets them practice. Experiments
show that practice software can help young
students develop competence in such skills as
counting and sorting, and in addition facts.39
CAI can also teach at-risk first graders the
add-1 rule (adding 1 is the same as “counting
one more”) by way of pattern detection.40 The
software asks, “What number comes after
3 when we count?” and then immediately
follows by posing a related addition question,
“3 + 1 = ?”. The software also discourages
children from overgeneralizing by giving
counterexamples to the add-1 rule. Research
reviews of rigorous studies show that when
such applications are well designed and
implemented, they have a positive impact on
children’s math performance—raising a child
from the 50th to the 61st to 68th percentile
across different studies.41
Games may also be effective. Second-graders
who averaged one hour of interaction with
a technology game over a two-week period
responded correctly to twice as many items
on an addition facts speed test as students in
a control group.42
Computer Manipulatives
Other approaches that have also received
support address STEM more directly, as
they teach children to use tools for discovery
and for problem-solving. A recent review of
66 studies found that the use of computer
manipulatives raised a child from the 50th to
the 64th percentile.43 This positive effect may
come from the following seven advantages
of technology-based manipulatives and
activities: (1) They bring mathematical ideas
and processes to conscious awareness; (2)
they encourage and facilitate complete,
precise explanations; (3) they support mental
actions on objects; (4) they can change the
nature of the manipulative (for example,
computer shapes can be precisely cut apart
or scaled, unlike wooden or plastic shapes);
(5) they symbolize mathematical concepts;
(6) they link the concrete and the symbolic
with feedback; and (7) they record and replay
students’ actions.
Syntheses of Approaches
Technologies that use a combination of
these teaching strategies and tools can
help children follow learning trajectories.
Manipulative-based, dynamic models
can help children develop foundational
understandings. Connecting multiple
representations (such as manipulatives,
spoken words, symbols, and actions) helps
to build understanding and to connect
children’s own concrete and symbolic mental
representations, all while they’re learning to
use the tools to solve problems. For example,
the Building Blocks software employs a series
of technological activities that incorporate
manipulatives and board games to
progressively develop children’s competence
in counting. This leads to counting-based
addition and subtraction strategies. If
Douglas H. Clements and Julie Sarama
90 THE FUTURE OF CHILDREN
children make several consecutive mistakes,
they receive brief hints and then tutorials.
A management system moves the children
along a research-based learning trajectory,
using formative assessment to ensure that
each child is learning new concepts and
skills through tasks that are challenging but
achievable. Building Blocks software was
one of the strongest mediators of children’s
learning, but it’s still unclear exactly how
the software contributed to learning.
Significantly, a separate study showed that
the Building Blocks software was effective
even when used alone, raising a child from
the 50th to the 67th percentile.44
Logo and Coding: Computer Science
and Engineering
Many types of software let children build
STEM objects virtually. The oldest and
most-studied software that teaches all
four STEM subjects for early childhood is
called Logo. In Logo’s computer coding,
children begin by directing an onscreen
robot or turtle to draw geometric shapes.
Many children can draw shapes with
pencil and paper, but drawing shapes using
Logo commands requires them to analyze
the visual aspects of the shape and the
movements needed to draw it. Writing a
sequence of Logo commands to draw a
shape encourages children to think precisely
about that process.
After working with the robot or turtle,
students show greater explicit awareness of
the properties of shapes and the meaning
of measurements. An evaluation of a
Logo-based geometry curriculum across
grades K–6 revealed that Logo students
scored statistically higher than control-
group students on a general geometry
achievement test, making about twice
the gains of children in comparison groups
(raising a child from the 50th to the 82nd
percentile).45
Finally, computer coding shouldn’t be
considered work on virtual worlds only. In
robotics environments, for example, children
are engineers. They create LEGO structures
that have lights, sensors, motors, gears, and
pulleys, and they control their structures
through computer code. The few studies
that have examined LEGO–Logo suggest
that such experiences can positively affect
children’s math and science achievement
as well as their higher-order thinking skills.
If they start as young as kindergarten,
both boys and girls benefit from work with
robots, and few differences appear between
them. Recently, researchers have described
how very young children at different
developmental levels approach programming
a robot, which suggests that this may be a
promising approach for future engineering
experiences.
Conclusions
Children from preschool through the primary
grades are interested in learning about
STEM and can think about these subjects in
ways that are surprisingly broad and deep.
Not only does math competency predict
later school success, but all areas of STEM
contribute to other developmental goals,
such as language and executive function.
Children whose teachers use research-
based approaches demonstrate higher
levels of STEM achievement and thinking.
Learning trajectories can support children’s
learning, and can also aid in assessment
and curriculum development. Children
whose teachers use research-based learning
trajectories demonstrate higher levels of
mathematical reasoning.
Math, Science, and Technology in the Early Grades
VOL. 26 / NO. 2 / FALL 2016 91
Current research in learning trajectories
points the way toward math learning that
is more effective and efficient—but also
creative and enjoyable—through culturally
relevant and developmentally appropriate
curricula and assessment. However, we
still have much to learn about teaching
certain topics in STEM and about the
characteristics of curriculum development
and professional development that will let
children realize their full potential in these
critical subjects.
Douglas H. Clements and Julie Sarama
92 THE FUTURE OF CHILDREN
ENDNOTES
1. National Research Council, Mathematics in Early Childhood: Learning Paths toward Excellence and
Equity (Washington, DC: National Academies Press, 2009); Sue Thomson et al., Numeracy in the Early
Years: Project Good Start (Camberwell, Victoria, Australia: Australian Council for Educational Research,
2005).
2. Institute of Medicine and National Research Council, Transforming the Workforce for Children Birth
through Age 8: A Unifying Foundation (Washington, DC: National Academies Press, 2015); National
Research Council, Taking Science to School: Learning and Teaching Sciences in Grades K–8 (Washington,
DC: National Academies Press, 2007).
3. Kyoung-Hye Seo and Herbert P. Ginsburg, “What Is Developmentally Appropriate in Early Childhood
Mathematics Education?” in Engaging Young Children in Mathematics: Standards for Early Childhood
Mathematics Education, ed. Douglas H. Clements, Julie Sarama, and Ann-Marie DiBiase (Mahwah, NJ:
Lawrence Erlbaum, 2004), 91–104.
4. National Research Council, Mathematics in Early Childhood; Institute of Medicine and National
Research Council, Transforming the Workforce; Kristin Denton and Jerry West, Children’s Reading
and Mathematics Achievement in Kindergarten and First Grade (Washington, DC: US Department of
Education, National Center for Education Statistics, 2002), http://nces.ed.gov/pubs2002/2002125.pdf.
(Washington, DC: US Department of Education, National Center for Education Statistics, 2002), http://
nces.ed.gov/pubs2002/2002125.pdf.
5. Greg J. Duncan et al., “School Readiness and Later Achievement,” Developmental Psychology 43 (2007):
1428–46, doi: 10.1037/0012-1649.43.6.1428.
6. Douglas H. Clements et al., “Assessment Using Technology—Formative Assessment with Young
Children,” in Contemporary Perspectives on Research in Assessment and Evaluation in Early Childhood
Education, ed. Olivia N. Saracho (Charlotte, NC: Information Age Publishing, 2015), 339–71.
7. National Research Council, Taking Science to School; Clements, Sarama, and DiBiase, Engaging Young
Children.
8. National Research Council, Mathematics in Early Childhood.
9. Douglas H. Clements and Julie Sarama, Learning and Teaching Early Math: The Learning Trajectories
Approach, 2nd ed. (New York: Routledge, 2014); Mimi Engel, Amy Claessens, and Maida A. Finch,
“Teaching Students What They Already Know? The (Mis)Alignment between Mathematics Instructional
Content and Student Knowledge in Kindergarten,” Educational Evaluation and Policy Analysis 35 (2013):
157–78, doi: 10.3102/0162373712461850.
10. M. Lee Van Horn et al., “Effects of Developmentally Appropriate Practices on Children’s Development:
A Review of Research and Discussion of Methodological and Analytic Issues,” Elementary School Journal
105 (2005): 325–51, doi: 10.1086/429946.
11. National Mathematics Advisory Panel, Foundations for Success: The Final Report of the National
Mathematics Advisory Panel (Washington DC: U.S. Department of Education, Office of Planning,
Evaluation and Policy Development, 2008), xix.
12. Anke W. Blöte, Eeke van der Burg, and Anton S. Klein, “Students’ Flexibility in Solving Two-Digit
Addition and Subtraction Problems: Instruction Effects,” Journal of Educational Psychology 93 (2001):
627–38.
13. Canan Aydogan et al., “An Investigation of Prekindergarten Curricula: Influences on Classroom
Characteristics and Child Engagement,” paper presented at the National Association for the Education of
Young Children annual conference, Washington, DC, December 7–10, 2005.
Math, Science, and Technology in the Early Grades
VOL. 26 / NO. 2 / FALL 2016 93
14. Van Horn et al., “Effects”; Seo and Ginsburg, “What Is Developmentally Appropriate?”; Deena Skolnick
Weisberg et al., “Making Play Work for Education,” Phi Delta Kappan 96, no. 8 (2015): 8–13.
15. Kimberly Brenneman, Judi Stevenson-Boyd, and Ellen C. Frede, “Early Math and Science in Preschool:
Policies and Practice,” National Institute for Early Education Research Preschool Policy Brief no. 19,
March 2009.
16. Van Horn et al., “Effects.”
17. Julie Sarama and Douglas H. Clements, Early Childhood Mathematics Education Research (New York:
Routledge, 2009); Douglas H. Clements and Julie Sarama, “Early Childhood Mathematics Learning,” in
Second Handbook of Research on Mathematics Teaching and Learning, ed. Frank K. Lester Jr. (New York:
Information Age Publishing, 2007), 461–555.
18. Douglas H. Clements and Julie Sarama, “Learning Trajectories: Foundations for Effective, Research-
Based Education,” in Learning over Time: Learning Trajectories in Mathematics Education, ed. Alan P.
Maloney, Jere Confrey, and Kenny H. Nguyen (New York, NY: Information Age Publishing, 2014), 1–30.
19. National Research Council, Mathematics in Early Childhood; Sarama and Clements, Early Childhood
Mathematics Education Research; National Research Council, A Framework for K–12 Science Education:
Practices, Crosscutting Concepts, and Core Ideas (Washington, DC: National Academies Press,
2012); Ken Appleton, “How Do Beginning Primary School Teachers Cope with Science? Toward an
Understanding of Science Teaching Practice,” International Journal of Science Education 33 (2003): 1–25,
doi: 10.1023/A:1023666618800.
20. Engel, Claessens, and Finch, “(Mis)Alignment.”
21. National Research Council, Mathematics in Early Childhood.
22. Douglas H. Clements et al., “Mathematics Learned by Young Children in an Intervention Based on
Learning Trajectories: A Large-Scale Cluster Randomized Trial,” Journal for Research in Mathematics
Education 42 (2011): 127–66.
23. National Mathematics Advisory Panel, Foundations.
24. Christina Weiland and Hirokazu Yoshikawa, “Impacts of a Prekindergarten Program on Children’s
Mathematics, Language, Literacy, Executive Function, and Emotional Skills,” Child Development 84
(2013): 2112–30, doi: 10.1111/cdev.12099.
25. National Mathematics Advisory Panel, Foundations.
26. Roberto Agodini et al., “After Two Years, Three Elementary Math Curricula Outperform a Fourth,”
NCEE Evaluation Brief, September 2013, http://ies.ed.gov/ncee/pubs/20134019/pdf/20134019.pdf.
27. National Research Council, Taking Science to School.
28. Douglas H. Clements et al., “Connect4Learning: Early Childhood Education in the Context of
Mathematics, Science, Literacyy, and Social-Emotional Development,” paper presented at the American
Educational Research Association annual meeting, Vancouver, Canada, April 13–17, 2012.
29. Lauren Scher and Fran O’Reilly, “Professional Development for K–12 Math and Science Teachers:
What Do We Really Know?” Journal of Research on Educational Effectiveness 2 (2009): 209–49, doi:
10.1080/19345740802641527.
30. Nell K. Duke and Meghan K. Block, “Improving Reading in the Primary Grades,” Future of Children 22,
no. 2 (2012): 55–72.
31. Ibid.; Catherine E. Snow and Timothy J. Matthews, “Reading and Language in the Early Grades,” Future
of Children 26, no. 2 (2016): 75–94.
Douglas H. Clements and Julie Sarama
94 THE FUTURE OF CHILDREN
32. Douglas H. Clements and Julie Sarama, “Early Childhood Mathematics Intervention,” Science 333, no.
6045 (2011): 968–70, doi: 10.1126/science.1204537.
33. Douglas H. Clements, Julie Sarama, and Carrie Germeroth, “Learning Executive Function and Early
Mathematics: Directions of Causal Relations,” Early Childhood Research Quarterly 36 (2016): 79–90, doi:
10.1016/j.ecresq.2015.12.009.
34. Douglas H. Clements et al., “Effects on Executive Function and Mathematics Learning of an Early
Mathematics Curriculum Synthesized with Scaffolded Play Designed to Promote Self-Regulation Versus
the Mathematics Curriculum Alone,” University of Denver, 2015.
35. Clements, Sarama, and Germeroth, “Directions of Causal Relations.”
36. For example, Julie Sarama et al., Connect4learning: The Pre-K Curriculum (Lewisville, NC:
Connect4Learning, 2016).
37. National Mathematics Advisory Panel, Foundations; Heather C. Hill, Brian Rowan, and Deborah
Loewenberg Ball, “Effects of Teachers’ Mathematical Knowledge for Teaching on Student Achievement,”
American Educational Research Journal 42 (2005): 371–406, doi: 10.3102/00028312042002371.
38. Clements and Sarama, Learning and Teaching Early Math; National Research Council, Taking Science
to School; National Research Council, Framework; Stuart Reifel, “Block Construction: Children’s
Developmental Landmarks in Representation of Space,” Young Children 40 (1984): 61–67; Julie Sarama
and Douglas H. Clements, “Promoting a Good Start: Technology in Early Childhood Mathematics,”
in Promising Models to Improve Primary Mathematics Learning in Latin America and the Caribbean
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This doctoral thesis is structured in a series of works, the main objective being the study of the impact on the attitude towards science and mathematics of a didactic proposal with a STEM orientation, in which the programming of robots and the work related to sustainability and environmental care are key elements of the design. This research has among its objectives to provide bibliometric information on the existing literature on STEM education and educational robotics as well as to perform a systematic review of this literature, together with the development of a study on school textbooks analyzing in the first instance the existence of STEM activities and subsequently investigating the level of integration of STEM presentations according to the models detailed. In turn, all of the above should contribute to the objective of designing, implementing and evaluating an interdisciplinary project, called CISOGRA (Ciudad Sostenible Granatensis-Granada), according to the STEM approach for Spanish students of third cycle of Primary Education in vulnerable contexts; This will be done through active methodologies, which allow to relate the contents of STEM areas with their environment, improving the attitude towards science and mathematics and enhancing key competences, especially mathematical competence and key competences in science and technology, thus improving learning in science and mathematics and identifying the perception that this work generates in the educational community, understanding as such the teachers of the courses to which the students belong. To achieve the bibliometric results, STEM scientific production is characterized according to various statistical indicators typical of bibliometrics (productivity, countries, etc.) in the Scopus database. Subsequently, the systematic review on the use of robotics and STEM education in Primary Education considers units of analysis or variables that are structured in three blocks: a) bibliometric indicators and typology of the analyzed documents, b) characterization of robotics and the educational improvements it promotes, and c) aspects on social context and gender. The sample for this study came from the databases Scopus (Elsevier), Educational Resource Information Center (ERIC) of the U.S. Department of Education, and Web of Science (WoS) of Clarivate Analytics. Subsequently, in the text analysis developed, we work under a qualitative and descriptive approach. Specifically, the content analysis method is used from a comparative perspective by focusing on textbooks from two Latin American countries, Chile and Spain, in which data collection is used based on numerical measurement and subsequent analysis of the results obtained. The sample consisted of 12 textbooks of Natural Sciences from Chile and Spain. Next, an analysis of the integration of STEM activities in Chilean and Spanish textbooks is carried out, showing results on the existence of activities that adjust to the development of a work proposal based on the STEM integration approach in a sample of 4 school textbooks. For the analysis of the work with students in the CISOGRA project, the research presents a quasiexperimental pre- and post-test design with a control group established by a matching process for the dependent variables attitude towards science, attitude towards mathematics and academic qualification. In relation to the teachers' view of the results of implementing the project, these are established within a qualitative perspective using the application of a semistructured interview that allows ordering, describing, analyzing and interpreting the data by means of concepts and reasoning. A script is used that includes a series of questions that have been used in a flexible way, together with a content analysis, using a system of categories built in a deductive and inductive way, generating several variables of analysis. Finally, the competency-based assessment research was carried out through an exploratorydescriptive and quasi-experimental methodological design with a single group. The instrument was created by compiling questions extracted from different external evaluations of scientifictechnological and mathematical competencies developed by different Autonomous Communities in Spain. Regarding the results of the bibliometric study, papers on STEM education between the years 2010 and 2018 show a gradual increase, with 2017 being the year of highest production (26.2%). The majority corresponds to sessional papers (52.3%). The author who stands out most in these papers is Justin L. Hess, researcher at the STEM Education Innovation and Research Institute (SEIRI) of Indiana University and Purdue University (Indianapolis, USA) who in the Scopus database presents 35 papers, with the year of highest production being 2016 with 10 publications. In relation to the keywords the most recurrent is "students", which appears in 19 documents (29.2%). On the other hand, 65.6% of the analyzed documents belong to the area of social sciences while the authors belong mostly to U.S. institutions, corresponding to 39 of the 65 documents. Considering the results of the systematic review, once again the United States (42.3%) leads productivity. In relation to the sex of the authors, there is a similarity of publication (13) for each gender and the STEM area or discipline most worked in the research corresponds to technology (38.1%). It is noteworthy that 88.5% of the documents present empirical results, with the mixed type of research being the most frequent with 8 documents (30.7%). In relation to the analysis on the presence of activities with a STEM structure in textbooks according to the model of Toma and Greca (2017), the results evidence the presence of this type of activities in the books analyzed, although they are still scarce. In particular, there is a low presence of phases 4 (initial problem solving) and 5 (evaluation). These are the ones that require a higher degree of work, knowledge and development on the part of the students, so they should be more frequent with the passing of the courses. Likewise, the results allow observing coincidences in the indicators of: presence of STEM activities using devices for their development, the design of an experiment and its realization, which belong to the guided inquiry phase. In addition, there are activities where there is discussion of the results. On the other hand, the least frequent indicators are those related to the existence of a moment to propose new questions about the resolution of the problem (55.6% and 61.9%, in Chilean and Spanish texts, respectively), the generation of a solution to the problem (33.3% and 47.6%, in Chilean and Spanish texts, respectively) and the technological application of the discovery to the problem (11% and 0%, in Chilean and Spanish texts, respectively). The second text analysis, which seeks to identify the integration of STEM activities, was carried out by analyzing 12 school textbooks and identified 462 activities, of which 164 (less than 50%) worked in some STEM. These activities were classified according to the integrated curriculum analysis model, which proposes six ways of approaching the integration of an activity of this type, observing that the connected approach is more relevant in Spanish (50%) and Chilean (46%) textbooks. Subsequently, they were classified according to an adaptation of the Environmental Education perspectives approach. Within the 5 existing approaches, the experiential (60%) and the practical (50%) were the most present. The need to increase the number of STEM activities integrated into textbooks from the early grades should be emphasized. The CISOGRA project, which was designed and implemented according to the established objectives, involved 12 sessions with practical workshops outside school hours. Through the use of educational robotics, students were confronted with various programming problems, in which, prior to their resolution, they had to anticipateanswers by way of hypotheses, in a "sustainable city" environment. This city has several devices that model energy sources to support the power supply of buildings. In addition, sensors are used, such as a temperature, speed and distance meter, through which different physical magnitudes are recorded and presented, noting the variability of the measurements and the necessary mathematical treatment. The work with the students was carried out under a methodology of inquiry and problem solving. The evaluation of the program considered an experimental group with 15 students of 3rd cycle of Primary Education, forming the control group from a matching process with the rest of the students of the center. The results show that the implementation of the STEM program generates better results in the attitude towards science (p=.004 TE= 1.254), although not so much in the attitude towards mathematics where the differences are not statistically significant (p=.574 TE=.382). The technological tools used, the work time and the process of connection between disciplines in STEM reinforce the work done during the workshop. In the assessment of competencies, the scientist showed a positive difference of 0.35 points on average between the pretest and the posttest. In the case of mathematics, the difference in favor of the post-test is 0.18 points. In relation to the results of the general evaluation (16 questions), the difference between the pre-test and post-test is 0.26 positive points. Regarding the analysis of the interviews conducted with the teachers, we found the following categorizations: valuation of the project as a didactic proposal (42.39%), impact of the project on the attitude towards science and mathematics (30.43%), characterization of the students and family support (8.15%) and teacher characterization (19.02%). It is worth noting the teachers' assessment of the didactic intervention and that they valued that it facilitated the students' discovery and understanding of the reality that surrounds us and the technological change we face as a society.
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Chapter
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Early childhood mathematics is vitally important for young children's present and future educational success. Research demonstrates that virtually all young children have the capability to learn and become competent in mathematics. Furthermore, young children enjoy their early informal experiences with mathematics. Unfortunately, many children's potential in mathematics is not fully realized, especially those children who are economically disadvantaged. This is due, in part, to a lack of opportunities to learn mathematics in early childhood settings or through everyday experiences in the home and in their communities. Improvements in early childhood mathematics education can provide young children with the foundation for school success. Relying on a comprehensive review of the research, Mathematics Learning in Early Childhood lays out the critical areas that should be the focus of young children's early mathematics education, explores the extent to which they are currently being incorporated in early childhood settings, and identifies the changes needed to improve the quality of mathematics experiences for young children. This book serves as a call to action to improve the state of early childhood mathematics. It will be especially useful for policy makers and practitioners-those who work directly with children and their families in shaping the policies that affect the education of young children. © 2009 by the National Academy of Sciences. All rights reserved.
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How does literacy develop in children’s early years, and what programs or practices promote adequate literacy for all children? These are the questions Catherine Snow and Timothy Matthews tackle in this article. Fundamental literacy skills can be grouped into two categories, Snow and Matthews write. The first category is constrained skills, which are readily teachable because they’re finite: for example, the 26 letters of the alphabet, or a set of 20 to 30 common spelling rules. These skills have a ceiling; young children can and do achieve perfect performance. As they grow older, though, children need to understand words rarely encountered in spoken language and to integrate new information they encounter with relevant background information. Vocabulary and background knowledge are examples of unconstrained skills-large domains of knowledge acquired gradually through experience. Unconstrained skills are particularly important for children’s long-term literacy success (that is, success in outcomes measured after third grade). Compared to constrained skills, they’re also more strongly predicted by children’s social class or their parents’ education, and more difficult to teach in the classroom. And because of their open-ended nature, unconstrained skills are also much harder to test for. Snow and Matthews write that a drop in literacy scores we see as US children move from elementary to middle school suggests that our schools may be focusing too much on constrained skills—and too little on unconstrained ones-in the early grades. The authors review promising programs and practices for enhancing both constrained and unconstrained skills, ranging from comprehensive school-improvement programs to efforts to improve curricula and teachers’ professional development-although they note that vast differences in programs’ scope, cost, targets, and theories of change make comparing them difficult. Another challenge is that it’s hard to maintain quality and consistency when implementing complex programs over time. Snow and Matthews suggest that to improve young children’s success with literacy, it might be better to introduce and evaluate promising practices that can be mixed and matched, rather than complex programs that are implemented as a package. © 2016, Center for the Future of Children. All rights reserved.
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The use of formal observation in primary mathematics classrooms is supported in the literature as a viable method of determining effective teaching strategies and appropriate tasks for inclusion in the early years of mathematics learning. The twofold aim of this study was to (a) investigate predictive relationships between primary mathematics classroom observational data and student achievement data, and (b) to examine the impact of providing periodic classroom observational data feedback to teachers using a Relational-Feedback-Intervention (RFI) Database Model. This observational research effort focused on an empirical examination of student engagement levels in time spent on specific learning activities observed in primary mathematics classrooms as predictors of student competency outcomes in mathematics. Data were collected from more than 2,000 primary classroom observations in 17 primary schools during 2009-2011 and from standardised end-of-year tests for mathematics achievement. Results revealed predictive relationships among several types of teaching and learning tasks with student achievement. Specifically, the use of mathematics concepts, technology and hands-on materials in primary mathematics classrooms was found to produce substantive predictors of increased student mathematics achievement. Additional findings supported the use of periodic classroom observation data reporting as a positive influence on teachers' decisions in determining instructional tasks for inclusion in primary mathematics classrooms. Study results indicate classroom observational research involving a RFI Database Model is a productive tool for improving teaching and learning in primary mathematics classrooms.