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Math in the Early Years
A Strong Predictor for Later School Success
Education Reform
Vol. 14, No. 5
The earliest years of a child’s education—from birth through 3rd grade—set the
foundation upon which future learning is built. In recent years, state policymakers have
emphasized the need to improve children’s reading skills early on because a lack in this
essential skill is a strong predictor of low student performance and increased high school
dropout rates. By 2012, a total of 32 states plus the District of Columbia had policies in
statute aimed at improving 3rd-grade literacy, with 14 of those states requiring retention
of students on the basis of reading proficiency. While the emphasis on reading proficiency
is critical, research shows that the development of mathematics skills early on may be an
even greater predictor of later school success. Early knowledge of math not only predicts
later success in math, but also predicts later reading achievement even better than early
reading skills.
Young children have a surprising capacity to learn substantial mathematics, but most
children in the U.S. have a discouraging lack of opportunities to do so. Too many
children not only start behind, but they also begin a negative and immutable trajectory in
mathematics, with insidious long-term effects. These negative effects are in one of the most
important subjects of academic life and also affect children’s overall life course.
The good news is that programs and curricula
designed to facilitate mathematical learning from
the earlier years, continued through elementary
school, have a strong positive effect on these
children’s lives for many years thereafter.
Starting early—in preschool—with high-quality
mathematics education, creates an opportunity
for substantial mathematical learning in the
primary years that builds on these foundational
This issue of The Progress of Education Reform
reveals five surprising findings about the
importance of early math learning, and provides
implications and recommendations for state policy.
What’s Inside
Surprise 1: Math’s predictive power
Surprise 2: Children’s math potential
Surprise 3: Educators underestimate
children’s potential
Surprise 4: Math intervention for all
Surprise 5: How children think about
and learn math
Written for ECS by Drs. Douglas H. Clements and Julie Sarama (
Surprising Research Findings
Surprise 1: There is predictive power in early mathematics
Mathematical thinking is cognitively foundational1, and
children’s early knowledge of math strongly predicts their
later success in math.2 More surprising is that preschool
mathematics knowledge predicts achievement even into high
school.3 Most surprising is that it also predicts later reading
achievement even better than early reading skills.4 In fact,
research shows that doing more mathematics increases oral
language abilities, even when measured during the following
school year. These include vocabulary, inference, independence,
and grammatical complexity.5 Given the importance of
mathematics to academic success in all subjects6, all children
need a robust knowledge of mathematics in their earliest years.
Surprise 2: Given opportunities to learn, young children possess an informal knowledge of mathematics that is amazingly broad,
complex, and sophisticated7
When children ‘play,’ they are often doing much more than that. Preschoolers can learn to invent solutions to solve
simple arithmetic problems, and almost all of them engage in substantial amounts of pre-mathematical activity
in their free play.8 In fact, early childhood programs that include more mathematics have increased higher-level
free play, all of which promotes self-regulation and executive function. Through higher-level play, children explore
patterns, shapes, and spatial relations; compare magnitudes; and count objects. Importantly, this is shown to be true
regardless of the children’s income level or gender.9 These explorations through play are pre-mathimatical. It is high-
quality education that can help all children utilize their inherent skills in order to truly mathematize.10 However, if
high-quality mathematics education does not start in preschool and continue through the early years, most children
are trapped in a trajectory of failure.11
Surprise 3: Teachers vastly underestimate what their children know and can learn12
In numerous countries, professionals in multiple educational roles vastly
underestimate beginning students' abilities.13 One study showed that groups
of teachers, teacher trainers, and counselors who worked with preschoolers
underestimated the mathematical competencies of these very same students
when they entered kindergarten.14 For example, more than 80% of the
students could count out nine marbles, but the adults’ estimates were from
20% to 50%. More than 40% of the students could subtract 10 – 8 without
objects, but all adults estimated less than 10%. If teachers and those who
work with teachers underestimate what students already know and can learn,
they will not present appropriate, challenging mathematics activities.
Surprise 4: All students need a math intervention
Most children benefit from a math intervention.15 As W. Steven Barnett and
others’ research has shown, it is not just the poorest children who need
interventions.16 When they enter kindergarten, most children are behind
their peers from the best-funded communities. That is, there is a significant
gap between every “quintile” and the highest 20% (see Figure 1 on following
page). Still, those in poverty need mathematics interventions the most.17
There is a three-year difference in mathematics developmental level for
students from low-resource versus high-resource communities.18
What do parents and children say about math?
Math is very important
Schools need to help the
brightest learn math (parents)
Children who like math before
middle school
Math is very important
I am good at math
Source: Harrison Group, PROMISE research, Phase 2, June 2010, Michigan
State University.
Before her 4th birthday, Abby was given five train
engines. She walked in one day with three of them. Her
father said, “Where’s the other ones?” “I lost them,” she
admitted. “How many are missing?” he asked. “I have
one, two, three. So [pointing in the air] foooour, fiiiive ...
two are missing, four and five. [pause] No! I want these
to be [pointing at the three engines] one, three, and five.
So, two and four are missing. Still two missing, but they’re
numbers two and four.”Abby thought about counting and
numbers—at least small numbers—abstractly. She could
assign one, two, and three to the three engines, or one,
three, and five! Moreover, she could count the numbers.
That is, she applied counting ... to counting numbers!
Surprise 5: We know a lot
A lot is known about how children
think about and learn math, and
teachers can use learning trajectories
to synthesize this knowledge into
effective interventions for children.
There are books and research
available to districts that detail the
learning trajectories that can help
underlie scientific approaches to
standards, assessment, curricula,
and professional development and
provide teachers with curricula that
show effect sizes that are large and
significant.19 Two such models are
the Building Blocks curriculum and
TRIAD scale-up model (see figures
2 and 3). High-quality instruction
has meaningful effects on children’s
mathematics knowledge.20
40 Lowest
20% Second Lowest
20% Second Highest
20% Highest
Source: Analysis of data from the
Early Childhood Longitudinal Study, Kindergarten Class of 1998-99
(See by W. Steven Barnett and Milagros Nores for
the National Institute for Early Childhood Education Research.
General Knowledge
When they enter kindergarten, children from lower- and middle-income families are, on average, far behind their wealthier peers in reading,
mathematics, and general knowledge. High-quality preschool could help close this gap in school readiness.
Figure 1: Closing the school-readiness gap
Average Academic Ability Scores
Family Outcome by Quintile
PreK Pre PreK Post Kindergarten Post 1st Grade Post
TRIAD Follow Through
TRIAD > Control, ES = .28
TRIAD FT > Control, ES = .51
Source: D.H. Clements, J. Sarama, C.B. Wolfe, and M.E. Spitler, "Longitudinal Evaluation of a Scale-up Model for Teaching
Mathematics with Trajectories and Technologies: Persistence of Effects in the Third Year,"
American Educational Research Journal
50(4), (2013): 812-850, doi: 10.3102/0002831212469270.
Figure 2: Mathematics achievement scores for
children using Triad Scale-up Model
Policy Implications and Recommendations
The Importance of High-Quality Curriculum and Instruction
The quality of mathematics education varies across settings but is
generally disappointing, especially in the earliest years. For example,
60% of 3-year-olds had no mathematical experience of any kind across
180 observations.21 Even if a program adapts an ostensibly “complete”
curriculum, mathematics is often inadequate, with the most commonly
used engendering no more math instruction than a control group.22
It is little surprise, then, that evaluations show little or no learning of
mathematics in these schools.23 As an example, observations of Opening
the World of Learning (OWL), which includes mathematics in its
curriculum, found that out of a 360-minute school day, only 58 seconds
were devoted to mathematics. Most children made no gains in math
skills, and some lost mathematics competence over the school year.24 Teachers often believe that they are “doing
mathematics” when they provide puzzles, blocks, and songs. Even when they teach mathematics, that content is
usually not the main focus, but is “embedded” in a fine-motor or reading activity.25 Unfortunately, evidence suggests
such an approach is ineffective.26 To ensure a program is truly effective, policymakers and school leaders must
prioritize investing in high-quality math curricula and instruction that meet the needs of all students.
Qualified Instructors
Teacher certification for pre-K through 3rd-grade teachers should emphasize both knowledge of the subject
(specifically, a profound knowledge of the math taught in early and elementary years) and strengths in pedagogy. It is
only recently that some states are requiring teachers to be evaluated on fluency in literacy instruction. What we now
know is that math instruction is far more effective coming from a specialist who understands both the subject matter
and the most effective ways in which young children learn math. A successful program will be one that ensures that
early math instructors specialize in these areas. One solution may be for a school to designate a teacher in each grade
who is responsible for teaching only math to all students.
Percent of adults who cannot
compute a 10% tip
Percent who cannot compute
the interest paid on a loan
Percent who cannont calculate
miles per gallon on a trip
Source: G.W. Phillips,
Chance Favors the Prepared Mind: Mathematics and Science
Indicators for Comparing States and Nations
(Washington, DC: American Institutes
for Research, 2007).
Control Building Blocks
Source: J. Sarama, A. Lange, D.H. Clements, and C.B. Wolfe, "The Impacts of an Early Mathematics Curriculum on Emerging Literacy and Language,"
Early Childhood Research Quarterly
, 27, (2012): 489-
502, doi: 10.1016/j.ecresq.2011.12.002.
Figure 3: Expressive oral language scores at the beginning of kindergarten for
children who used the Building Block curriculum in preschool.
Seamless Learning Trajectories
The most common argument offered for limiting investments in preschool is that the gains made are soon lost as
a child matriculates through the early primary grades. The losses primarily signify a siloed approach to education,
where each grade level and teacher holds different expectations for students, creating a learning trajectory that is not
seamless. Therefore, in order for students to benefit from math instruction in the early years, primary grade teachers
must build on early math interventions and engage students in more interesting, challenging, and substantial math
lessons as students progress through competency levels. If there are follow-through interventions in kindergarten and
the primary grades, students maintain their preschool advantages.27 This effect is highlighted in Figure 2 (page 3),
which presents a significant, positive effect on student math scores when the Triad Model is used on an ongoing basis.
Professional Development
Early math is not often emphasized in teacher preparation programs. As a result, pre-service and in-service teachers
alike lack content knowledge, such as understanding of mathematical concepts and procedures. More importantly,
they lack mathematics knowledge for teaching—how mathematical knowledge is interconnected and connected to
the real world, how a student’s thinking about mathematical content develops, and how mathematical content can be
taught in a meaningful manner.28 They suffer from negative effects, including math anxiety and a lack of confidence
in their own mathematical ability and ability to teach mathematics—beliefs that lead to undervaluing the teaching
of mathematics or prevent effective teaching.29 Therefore, professional development for early childhood mathematics
needs to address content (mathematical) knowledge, particularly mathematics knowledge for teaching, as well as
pedagogical knowledge, and affective issues.30
It is time to begin shifting the mindset of teachers, district leaders, and policymakers from a ‘reading only’ early
intervention strategy to one that incorporates and even emphasizes mathematical thinking and reasoning. To do
so, stakeholders should take a deep look into the current state of early math instruction beginning in preschool and
creating a seamless trajectory for math learning through the early grades. Education leaders should find ways to
maximize children’s abilities to learn by evaluating the current state of mathematics instruction within schools, based
not only on the current curricula, but also the time committed to instruction, as well as who is doing that instructing.
Most children can master the required skills early if given the chance.
Dr. Clements engages in math activites with two kindergarteners in order to help them understand
the core unit of patterns.
1 D.H. Clements and J. Sarama, Learning and Teaching Early Math: The Learning Trajectories Approach (New York, NY: Routledge, 2009);
D.H. Clements and J. Sarama, Early Childhood Mathematics Education Research: Learning Trajectories for Young Children (New York, NY:
Routledge, 2009).
2 K. Denton and J. West, Children's Reading and Mathematics Achievement in Kindergarten and First Grade (Washington, D.C., vol. 2002,
3 National Mathematics Advisory Panel, Foundations for Success: The Final Report of the National Mathematics Advisory Panel (Washington
D.C.: National Research Council, 2008); Mathematics in Early Childhood: Learning Paths Toward Excellence and Equity (Washington, D.C.:
National Academy Press, 2009); H.W. Stevenson and R.S. Newman, “Long-term Prediction of Achievement and Attitudes in Mathematics and
Reading,” Child Development, 57, 646-659, 1986.
4 G.J. Duncan, C.J. Dowsett, A. Claessens, K. Magnuson, A.C. Huston, P. Klebanov, and C. Japel, “School Readiness and Later Achievement,”
Developmental Psychology, 43(6), 1428–1446, 2007; D.C. Farran, C. Aydogan, S.J. Kang, M. Lipsey, Preschool Classroom Environments and
the Quantity and Quality of Children's Literacy and Language Behaviors, 2005; M.K. Lerkkanen, H. Rasku-Puttonen, K. Aunola, and J.E.
Nurmi, “Mathematical Performance Predicts Progress in Reading Comprehension Among 7-year-olds,” European Journal of Psychology of
Education, 20(2), 121-137, 2005.
5 J. Sarama, A. Lange, D.H. Clements, and C.B. Wolfe, “The Impacts of an Early Mathematics Curriculum on Emerging Literacy and
Language,” Early Childhood Research Quarterly, 27, 489-502, 2012, doi: 10.1016/j.ecresq.2011.12.002.
6 P.M. Sadler and R.H. Tai, “The Two High-School Pillars Supporting College Science,” Science, 317, 457-458, 2007.
7 A.J. Baroody, The Developmental Bases for Early Childhood Number and Operations Standards, 2004; B.A. Clarke, D.M. Clarke, and J.
Cheeseman, “The Mathematical Knowledge and Understanding Young Children Bring to School,” Media Education Research Journal, 18(1),
81-107, 2006; D.H. Clements, S. Swaminathan, M.A.Z. Hannibal, and J. Sarama, “Young Children’s Concepts of Shape,” Journal for Research
in Mathematics Education, 30, 192-212, 1999.
8 J. Sarama and D.H. Clements, Early Childhood Mathematics Education Research: Learning Trajectories for Young Children (New York, NY:
Routledge, 2009); H.P. Ginsburg, N. Inoue, and K.H. Seo, “Young Children Doing Mathematics: Observations of Everyday Activities,” in J.V.
Copley (Ed.), Mathematics in the Early Years (Reston, VA: National Council of Teachers of Mathematics, 1999, 88-89).
9 K.H Seo and H.P. Ginsburg, “What is Developmentally Appropriate in Early Childhood Mathematics Education?” in D.H. Clements, J.
Sarama, and A.M. DiBiase (Eds.), Engaging Young Children in Mathematics: Standards for Early Childhood Mathematics Education
(Mahwah, NJ: Erlbaum, 2004, 91-104).
10 B. Doig, B. McCrae, and K. Rowe, A Good Start to Numeracy: Effective Numeracy Strategies from Research and Practice in Early Childhood
(Canberra ACT, Australia, 2003); S. Thomson, K. Rowe, C. Underwood, and R. Peck, Numeracy in the Early Years: Project Good Start
(Camberwell, Victoria, Australia: Australian Council for Educational Research, 2005).
11 C. Rouse, J. Brooks-Gunn, and S. McLanahan, “Introducing the Issue,” The Future of Children, 15, 2005, 5-14.
12 D.H. Clements and J. Sarama, Learning and Teaching Early Math: The Learning Trajectories Approach (New York, NY: Routledge, 2009).
13 C. Aubrey, “Children’s Early Learning of Number in School and Out,” in I. Thompson (Ed.) Teaching and Learning Early Number (Philadel-
phia, PA: Open University Press, 1997, 20-29).
14 M. Van den Heuvel-Panhuizen, “Realistic Arithmetic/Mathematics Instruction and Tests,” in K.P.E. Gravemeijer, M. Van den Heuvel-
Panhuizen & L. Streefland (Eds.), Contexts Free Productions Tests and Geometry in Realistic Mathematics Education (Utrecht, The
Netherlands: OW&OC, 1990, 53-78).
15 D.H. Clements and J. Sarama, “Early Childhood Mathematics Intervention,” Science, 333(6045), 2011, 968-970, doi: 10.1126/
science.1204537; D.H. Clements, J. Sarama, M.E. Spitler, A.A. Lange, C.B. Wolfe, “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(2), 2011, 127-166.
16 R.C. Pianta, W.S. Barnett, M.R. Burchinal, and K.R. Thornburg, “The Effects of Preschool Education: What We Know, How Public Policy Is
or Is Not Aligned with the Evidence Base, and What We Need to Know,” Psychological Science in the Public Interest, 10(2), 2009, 49-88, doi:
17 J. Sarama and D.H. Clements, Early Childhood Mathematics Education Research: Learning Trajectories for Young Children (New York,
NY: Routledge, 2009); D.H. Clements and J. Sarama, “Early Childhood Mathematics Intervention,” Science, 333(6045), 2011, 968-970, doi:
18 B. Wright, “What Number Knowledge Is Possessed by Children Beginning the Kindergarten Year of School?” Mathematics Education
Research Journal, 3(1), 1991, 1-16.
19 D.H. Clements, & J. Sarama, Learning and Teaching Early Math: The Learning Trajectories Approach (New York, NY: Routledge, 2009); J.
Sarama, and D.H. Clements, Early Childhood Mathematics Education Research: Learning Trajectories for Young Children (New York, NY:
Routledge, 2009).
20 D.H. Clements and J. Sarama, “Early Childhood Mathematics Intervention,” Science, 333(6045), 2011, 968-970; D.H. Clements and J.
Sarama, “Rethinking Early Mathematics: What Is Research-based Curriculum for Young Children?” in L.D. English & J.T. Mulligan
(Eds.), Reconceptualizing Early Mathematics Learning, 2013, 121-147; D.H. Clements, J. Sarama, M.E. Spitler, A.A. Lange, "Longitudinal
Evaluation of a Scale-up Model for Teaching Mathematics with Trajectories and Technologies: Persistence of Effects in the Third Year,”
American Education Research Journal, August 2013, vol. 50 no. 4, 812-850; J. Sarama and D.H. Clements, “Lessons Learned in the
Implementation of the TRIAD Scale-up Model: Teaching Early Mathematics with Trajectories and Technologies,” in T.G. Halle, A.J. Metz and
I. Martinez-Beck (Eds.), Applying Implementation Science in Early Childhood Programs and Systems, (Baltimore, MD: Brookes, 2013, 173-
191); J. Sarama, D.H. Clements, C.B. Wolfe, and M.E. Spitler, “Longitudinal Evaluation of a Scale-up Model for Teaching Mathematics with
Trajectories and Technologies,” Journal of Research on Educational Effectiveness, 5(2), 2012, 105-135; J. Sarama, A. Lange, D.H. Clements,
and C.B. Wolfe, “The Impacts of an Early Mathematics Curriculum on Emerging Literacy and Language,” Early Childhood Research
Quarterly, 27, 2012, 489-502, doi: 10.1016/j.ecresq.2011.12.002.
© 2013 by the Education Commission
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To reprint or excerpt some of
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The Education Commission of the
States is a nationwide nonprofit
organization formed in 1965 to
help governors, state legislators,
state education officials, and others
to develop policies to improve the
quality of education. ECS is the only
nationwide, nonpartisan interstate
compact devoted to education at
all levels.
Past issues of
The Progress of
Education Reform
are available
on our website at:
Education Leaders,
Advancing Ideas
This issue of
The Progress of Education Reform
was made possible by a
grant from the GE Foundation. This issue was written by Doug Clements,
Kennedy Endowed Chair in Early Childhood Learning and Professor at
the University of Denver, and Julie Sarama, Kennedy Endowed Chair in
Innovative Learning Technologies and Professor at the University of Denver
For more information on this topic, contact Emily Workman, Policy Analyst,
Education Commission of the States at
ECS Resources
Recent State Policies/Activities: Preschool Policies
Summaries and links to newly enrolled or enacted legislation and recently approved state board rules from
across the states. Updated weekly.
Third Grade Reading Policies
This paper outlines state policies relating to 3rd-grade reading proficiency, including identification of,
intervention for, and retention of struggling readers in the P-3 grades. The paper provides a state-by-state
policy summary, sample statutory language, and highlights from bills enacted this year.
ECS Research Studies Database:
Find research studies that provide features that define high-quality learning environments for PreK-3 students:
or on what mathematics practices impact student achievement:
21 J.R.H. Tudge and F. Doucet, “Early Mathematical Experiences: Observing Young Black and White
Children’s Everyday Activities,” Early Childhood Research Quarterly, 19, 2004, 21-39.
22 C. Aydogan, C.Plummer, S.J. Kang, C. Bilbrey, D.C. Farran, and M.W. Lipsey, An Investigation of
Prekindergarten Curricula: Influences on Classroom Characteristics and Child Engagement, 2005;
Preschool Curriculum Evaluation Research Consortium, Effects of Preschool Curriculum Programs on
School Readiness (NCER 2008-09, 2008).
23 D.H. Clements and J. Sarama, "Effects of a Preschool Mathematics Curriculum: Summative Research on
the Building Blocks Project," Journal for Research in Mathematics Education, 38, 2007, 136-163; Head
Start Impact Study: First Year Findings (Washington, D.C.: Department of Health and Human Services,
24 D.C. Farran, M.W. Lipsey, B. Watson, and S. Hurley, Balance of Content Emphasis and Child Content
Engagement in an Early Reading First Program, 2007; K.C. Fuson, “Pre-K to Grade 2 Goals and
Standards: Achieving 21st Century Mastery for All,” in D.H. Clements, J. Sarama, and A.M. DiBiase
(Eds.), Engaging Young Children in Mathematics: Standards for Early Childhood Mathematics
Education, 2004.
25 D.H. Clements and J. Sarama, Learning and Teaching Early Math: The Learning Trajectories Approach
(New York, NY: Routledge, 2009); National Research Council, Mathematics in Early Childhood: Learn-
ing Paths Toward Excellence and Equity (Washington, D.C.: National Academy Press, 2009).
26 National Research Council, Mathematics in Early Childhood: Learning Paths toward Excellence and
Equity (Washington, DC: National Academy Press, 2009).
27 D.H. Clements, J. Sarama, C.B.Wolfe, and M.E. Spitler, “Longitudinal Evaluation of a Scale-up Model
for Teaching Mathematics with Trajectories and Technologies: Persistence of Effects in the Third Year,”
American Educational Research Journal, 50(4), 2013, 812-850, doi: 10.3102/0002831212469270.
28 D.H. Clements and J. Sarama, Learning and Teaching Early Math: The Learning Trajectories Approach
(New York, NY: Routledge, 2009).
29 J. Sarama and D.H. Clements, Early Childhood Mathematics Education Research: Learning Trajectories
for Young Children (New York, NY: Routledge, 2009).
30 D.L. Ball and H. Bass, “Interweaving Content and Pedagogy in Teaching and Learning to Teach: Know-
ing and Using Mathematics,” in J. Boaler (Ed.), Multiple Perspectives on the Teaching and Learning
of Mathematics (Westport, CT: Ablex., 2000, 83-104); A.J. Baroody, Fostering Children’s Mathematical
Power: An Investigative Approach to K-8 Mathematics Instruction (Mahwah, NJ: Erlbaum, 1998).
... Masih berkaitan dengan perkembangan kogni f anak, salah satu kemampuan yang menjadi perha an orang tua dan pendidik di banyak satuan PAUD adalah kemampuan matema ka. Berdasarkan peneli an yang dilakukan oleh Clements & Sarama (2013), kemampuan dasar matema ka anak dapat berkembang pesat mulai dari lahir sampai usia lima tahun. Menariknya, perkembangan kogni f juga mencakup perkembangan kemampuan memecahkan masalah dan berpikir logis yang sebenarnya dapat di ngkatkan melalui pembelajaran matema ka. ...
... Pembelajaran matema ka perlu diberikan sejak usia dini. Hal ini didukung oleh pendapat Clements & Sarama (2013) yang mengungkapkan bahwa kemampuan matema ka seorang anak pada usia dini dapat dijadikan tolok ukur kesuksesan seorang anak dalam belajar matema ka tahap selanjutnya. Bahkan, Cannon & Ginsburg (2008) menilai bahwa kemampuan matema ka pada anak usia dini lebih pen ng daripada kemampuan membaca dan berbahasa. ...
Publikasi ini merupakan bentuk kerja sama antara Direktorat Pendidikan Anak Usia Dini (PAUD),Direktorat Jenderal Pendidikan Anak Usia Dini, Pendidikan Dasar dan Pendidikan Menengah, Kementerian Pendidikan dan Kebudayaan (Kemendikbud) dan para alumni penerima beasiswa Lembaga Pengelola Dana Pendidikan (LPDP), baik dari dalam maupun luar negeri. Para kontributor yang terpilih dalam buku ini telah menyelesaikan studi di bidang pendidikan dengan fokus disiplin yang beragam (interdisipliner), dan lulus dengan predikat cumlaude atau distinction pada bidang masing-masing, baik pada jenjang sarjana maupun magister.
... Young children have a surprising capacity to learn substantial mathematics. Mathematical thinking is cognitively foundational, and children's early knowledge of math strongly predicts their later success in math (Clements, et al., 2013). Understanding probability is important for living in our society full of uncertainty and randomness and there is no better way to understand probability then to do simple experiments. ...
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Students in Serbia meet the notion of probability for the first time in high school, while the countries with high developed school systems introduce probability much earlier. In this paper we emphasize the need for introduction of probability in early education and briefly check whether the primary school students in our neighborhood are capable to catch on basic notions on probability. We give a short review of theoretical background and previous research, and present results obtained within original research. Previous researches indicate that students in primary school could understand probability intuitively as a possibility of something to happen. Our research clearly shows that students in lower grades of primary school are able to understand basic notions such as possibilities and chances intuitively and very fast. Our convenience sample consists of 122 students attending lower grades of primary school and indicates that it makes sense to introduce basics of probability even to preschool children.
This paper aims to explore the challenges that pre-service early childhood teachers (PECTs) face in the processes of planning and implementing STEM education–based activities and their solutions about these challenges. A total of 39 third-year pre-service teachers in İstanbul, Turkey, participated in the study, which lasted 14 weeks. The data were collected through an open-ended questionnaire and focus group interviews. The data were analyzed via qualitative approaches and codes and themes were determined. As a result of the analysis, five themes related to the planning of STEM education–based activities emerged: identifying the problem, group works conducted by the pre-service teachers, children’s development level, material selection, and STEM integration. Regarding the challenges the PECTs faced during the implementation process of STEM education–based activities, six themes emerged: expressing the problem, group works conducted by the pre-service teachers, targeted instruction and implementations, children’s development level, time management, and classroom management. The analysis revealed 8 themes regarding the pre-service teachers’ solutions about successful planning and implementation of STEM education–based activities: materials to be used, group works conducted by the pre-service teachers, classroom arrangement and management, time management, appropriateness to children’s level, identifying and expressing the problem, activity planning and implementation, and implementing STEM education. This study is important because it will contribute to the implementation of STEM-based activities more in early childhood classes, as it identifies the challenges faced in the process of designing and implementing STEM-based activities as well as providing suggestions for the solution of these problems.
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OKUL ÖNCESİ DÖNEMDE STEM YAKLAŞIMI Öz Okul öncesi dönemde kavramlar zihnin yapı yapıtaşlarıdır. Kavramların oluşumu, kullanılması ve kazanımı çocukların aktif katılımı ile gerçekleşir ve bu dönemde çocukların temel kavram gelişimlerinin yanı sıra fen, teknoloji, matematik, sanat gibi pek çok konuya ilişkin kavramlarında da hızlı bir gelişme gözlenmektedir. Ço-cuklara bu kavramlar kazandırılırken yeni edindikleri kavramları uygulamalarını, kendilerinde var olan kavramlarla birleştirerek genişletmelerini ve yeni kavramları kendilerinin yapılandırarak öğrenmelerini sağlayacak etkinliklere ve ortamlara ge-reksinim duyulur. Son yıllarda oldukça popüler olan STEM yaklaşımının erken ço-cukluk yılları itibariyle uygulanması önerilmektedir. Yani çocuklarımızın fizik, kimya, biyoloji ve matematik gibi temel bilimlerin ortaya koyduğu kuramsal bilgi-leri alıp teknoloji ve mühendisliği harmanlayarak yaşama değer katacak yenilikler yapması gerekmektedir. Bu nedenle STEM yaklaşımı alana yeterince açıklanmalı, tanıtılmalı ve bu yaklaşımı temel alan eğitim programları ve etkinlikler hazırlanma-lıdır. Bu çalışmada erken çocukluk döneminde STEM yaklaşımı açıklanmaya çalı-şılarak hem eğitimciler hem de aileler için önerilerde bulunulmuştur.
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This important new book synthesizes relevant research on the learning of mathematics from birth into the primary grades from the full range of these complementary perspectives. At the core of early math experts Julie Sarama and Douglas Clements's theoretical and empirical frameworks are learning trajectories-detailed descriptions of children's thinking as they learn to achieve specific goals in a mathematical domain, alongside a related set of instructional tasks designed to engender those mental processes and move children through a developmental progression of levels of thinking. Rooted in basic issues of thinking, learning, and teaching, this groundbreaking body of research illuminates foundational topics on the learning of mathematics with practical and theoretical implications for all ages. Those implications are especially important in addressing equity concerns, as understanding the level of thinking of the class and the individuals within it, is key in serving the needs of all children.
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This study employed a cluster randomized trial design to evaluate the effectiveness of a research-based intervention for improving the mathematics education of very young children. This intervention includes the Building Blocks mathematics curriculum, which is structured in research-based learning trajectories, and congruous professional development emphasizing teaching for understanding via learning trajectories and technology. A total of 42 schools serving low-resource communities were randomly selected and randomly assigned to 3 treatment groups using a randomized block design involving 1,375 preschoolers in 106 classrooms. Teachers implemented the intervention with adequate fidelity. Pre- to posttest scores revealed that the children in the Building Blocks group learned more mathematics than the children in the control group (effect size, g = 0.72). Specific components of a measure of the quantity and quality of classroom mathematics environments and teaching partially mediated the treatment effect.
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Descriptions of curricula as “research-based” have been overused and underdeveloped. Two major conceptual tools support efforts of researchers and practitioners to collaborate on producing, evaluating, and implementing truly research-based curricula for early mathematics. The first is a set of learning trajectories that describe how children learn major topics in mathematics and how teachers can support that learning. These learning trajectories constitute the core of the second conceptual tool, a framework for developing curricula and teaching strategies. The chapter describes a framework comprising criteria and procedures for creating scientifically-based curricula using learning trajectories.
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Competence in early mathematics is crucial for later school success. Although research indicates that early mathematics curricula improve children's mathematics skill, such curricula's impacts on oral language and early literacy skills are not known. This project is the first to investigate the effects of an intensive pre-kindergarten mathematics curriculum, Building Blocks, on the oral language and letter recognition of children participating in a large-scale cluster randomized trial project. Results showed no evidence that children who were taught mathematics using the curriculum performed differently than control children who received the typical district mathematics instruction on measures of letter recognition, and on two of the oral language (story retell) subtests, sentence length and inferential reasoning (emotive content). However, children in the Building Blocks group outperformed children in the control group on four oral language subtests: ability to recall key words, use of complex utterances, willingness to reproduce narratives independently, and inferential reasoning (practical content).
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We used a cluster randomized trial to evaluate the effectiveness of a research-based model for scaling up educational interventions, focusing on the persistence of effects with and without a follow-through intervention. The instantiation of the Technology-enhanced, Research-based, Instruction, Assessment, and professional Development (TRIAD) model emphasized teaching early mathematics for understanding via learning trajectories and technology. The TRIAD implementation began in 42 schools in two city districts serving low-resource communities, randomly assigned to three conditions. In pre-kindergarten, the 2 experimental interventions were identical, but 1 included follow-through in the kindergarten year, including knowledge of the pre-K intervention and ways to build upon that knowledge using learning trajectories. Intent-to-treat analyses showed that students in both the follow-through condition (g = .33) and non-follow-through condition (g = .22) scored statistically significantly higher than children in the control condition. Both groups outperformed the control condition in treatment-on-the-treated analyses (g = .38, follow-through; g = .30 non-follow-through). Moderators and mediators were also analyzed. We conclude that the instantiation of the TRIAD model was successful and that follow through may contribute to the persistence of the effects of preschool interventions.
Future of Children 15.1 (2005) 5-14 Although racial and ethnic gaps in educational achievement have narrowed over the past thirty years, test score disparities among American students remain significant. In the 2002 National Assessment of Educational Progress, 16 percent of black and 22 percent of Hispanic twelfth-grade students displayed "solid academic performance" in reading, as against 42 percent of their white classmates. Similar gaps exist in mathematics, science, and writing. In response to such findings, policymakers have devised high-profile education initiatives to help schools address these disparities. The No Child Left Behind Act of 2002,for example, explicitly aims at closing achievement gaps. And such policies are important. As Christopher Jencks and Meredith Phillips, two highly regarded social scientists, conclude, "reducing the black-white test score gap would probably do more to promote [racial equality] than any other strategy that commands broad political support." To date, policymakers and practitioners have focused most attention on the gaps in achievement among school-aged children. And yet by many estimates sizable racial and ethnic gaps already exist by the time children enter kindergarten. Indeed, according to one report, about half of the test score gap between black and white high school students is evident when children start school. Why is so much attention focused on school-aged children? One reason is the lack of data on younger children. Many large and detailed surveys include only older children, and school-based administrative data necessarily exclude preschoolers. A second reason is that federal, state, and local policy focuses on public education, which has traditionally started with kindergarten. Finally, until recently the lives of preschool children were largely viewed as falling under the purview of the family and outside the scope of public policy. Nevertheless, research findings and common sense both suggest that what happens to children early in life has a profound impact on their later achievement. The behavioral and academic skills that children bring with them to school not only determine how schools must spend resources but also potentially affect disparities in outcomes. And some analysts argue that attending to disparities in the early years is likely to be cost effective. As Nobel laureate James Heckman notes, evaluations of social programs targeted at children from disadvantaged families suggest that it is easier to change cognition and behavior in early childhood than in adolescence. This issue of The Future of Children shines the spotlight on school readiness. In its broadest sense, school readiness includes the readiness of elementary school teachers and staff as well as of children and parents. Yet although schools must be ready for the children who arrive at their doors, in this volume we focus on the skills of the children themselves. Children who enter school not yet ready to learn, whether because of academic or social and emotional deficits, continue to have difficulties later in life. For example, children who score poorly on tests of cognitive skills during their preschool years are likely to do less well in elementary and high school than their higher-performing preschool peers and are more likely to become teen parents, engage in criminal activities, and suffer from depression. Ultimately, these children attain less education and are more likely to be unemployed in adulthood. Although most research focuses on academic skills, such as vocabulary size, complexity of spoken language, familiarity with the alphabet and books, basic counting, classification, and what is called "general knowledge," readiness for school also requires social and emotional skills. Children must be able to follow directions, work with a group, engage in classroom tasks, and exert some impulse control. In a 1997 report, the National Education Goals Panel emphasized that preparedness went beyond academics. And a poll of kindergarten teachers found that they rate knowledge of letters and numbers as less important readiness skills than being physically healthy, able to communicate verbally, curious and enthusiastic, and able to take turns and share. Like the child whose academic skills are weak, the child who cannot sit still (even for a few minutes), who interferes with his neighbors, who has temper tantrums, or who yells or hits...
Forty-five children, fifteen from each of two kindergarten year classes from different schools, and fifteen from a year one class from one of those schools, were interviewed to assess their knowledge of number word sequences and spatial patterns, and ability to recognise numerals and use counting to establish the numerosity of visible and screened collections. The schools were selected as typifying contrasting socio-economic levels. Five models, each of a different aspect of number development, and each containing up to five levels or stages, were used to generate for each child, a profile of numerical development. This led to consideration of the variations of children’s number knowledge, within and between year levels and schools. Findings included a wide variation in the number knowledge of children beginning the kindergarten year, greater variation in the lower socio-economic school, and evidence that the kindergarten year mathematics curriculum is most suited to the least advanced.