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The DREME Network: Research and Interventions in Early Childhood Mathematics

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The DREME Network was created to advance the field of early mathematics research and improves the opportunities to develop math competencies offered to children birth through age 8 years, with an emphasis on the preschool years. All four main Network projects will have implications for interventions. Section 1 introduces the Network and its four projects. The remainder of the chapter focuses on one of these four projects, Making More of Math (MMM), in depth. MMM is directly developing an intervention for children, based on selecting high-quality instructional activities culled from the burgeoning curriculum resources. We first report a review of 457 activities from 6 research-based curricula, which describes the number of activities by content focus, type (nature), and setting of each activity. Given the interest in higher-order thinking skills and self-regulation, we then identified activities that had the potential to, develop both mathematics and executive function (EF) proficiencies. We rated these, selecting the top 10 for extensive coding by mathematics content and EF processes addressed. We find a wide divergence across curricula in all these categories and provide comprehensive reports for those interested in selecting, using, or developing early mathematics curricula.
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CHAPTER ONE
The DREME Network: Research
and Interventions in Early
Childhood Mathematics
Crystal Day-Hess
1
, Douglas H. Clements
University of Denver, Denver, CO, United States
1
Corresponding author: e-mail address: crystal.day-hess@du.edu
Contents
1. The DREME Network 2
1.1 A Need for More Opportunity and Access 2
1.2 New Evidence on the Importance of Early Math 2
1.3 Increasing Acceptance of Academic Instruction in Preschool 3
1.4 DREMEs Central Goals 4
2. MMM Instruction: An In-Depth Look at a DREME Network Project 8
2.1 Early Math, EF, and Curricula 8
2.2 EF and Mathematics 13
2.3 Preliminary EF Study Work 14
3. Conclusion 35
Acknowledgments 35
References 35
Abstract
The DREME Network was created to advance the field of early mathematics research
and improves the opportunities to develop math competencies offered to children
birth through age 8 years, with an emphasis on the preschool years. All four main Net-
work projects will have implications for interventions. Section 1 introduces the Network
and its four projects. The remainder of the chapter focuses on one of these four projects,
Making More of Math (MMM), in depth. MMM is directly developing an intervention for
children, based on selecting high-quality instructional activities culled from the
burgeoning curriculum resources. We first report a review of 457 activities from 6
research-based curricula, which describes the number of activities by content focus,
type (nature), and setting of each activity. Given the interest in higher-order thinking
skills and self-regulation, we then identified activities that had the potential to, develop
both mathematics and executive function (EF) proficiencies. We rated these, selecting
the top 10 for extensive coding by mathematics content and EF processes addressed.
We find a wide divergence across curricula in all these categories and provide compre-
hensive reports for those interested in selecting, using, or developing early mathematics
curricula.
Advances in Child Development and Behavior, Volume 53 #2017 Elsevier Inc.
ISSN 0065-2407 All rights reserved.
http://dx.doi.org/10.1016/bs.acdb.2017.03.002
1
Responding to increased interest in early mathematics education, the
DREME Network was created to advance the field through research and
development. All four main Network projects will have implications for
interventions. This chapter introduces the Network and its projects and
describes one project in detail: Making More of Math (MMM), which is
directly developing an intervention for children.
1. THE DREME NETWORK
The Development and Research in Early Mathematics Education
(DREME) Network was created to advance the field of early mathematics
research and improve young children’s opportunities to develop math
skills—providing important information and resources to inform
mathematics-focused interventions at multiple levels. The Network focuses
on math from birth through age 8 years, with an emphasis on the preschool
years. Network members and colleagues collaborate to conduct basic and
applied research and develop innovative tools that address high-priority
early math topics and inform and motivate other researchers, educators,
policymakers, and the public (https://dreme.stanford.edu/).
1.1 A Need for More Opportunity and Access
There is a critical need for new knowledge and resources to guide and facil-
itate effort to promote young children’s math learning and increase equity
and excellence in math achievement (National Research Council, 2009).
Although important research has been conducted in recent years, it does
not adequately address the need for effective math instruction as an interven-
tion, especially for preschool-aged children. It also does not speak to the
organizational conditions that enable teachers to deliver this kind of instruc-
tion and intervention. Recent developments in the fields of education and
developmental science make this an opportune time to invest in building the
field of research and development on early math to support teaching and
learning interventions.
1.2 New Evidence on the Importance of Early Math
Several empirical studies have found that compared to literacy and social
emotional development at kindergarten entry, early math concepts were
the most powerful predictors of later learning (Duncan, Claessens, &
Engel, 2004; Duncan et al., 2007; Watts, Duncan, Siegler, & Davis-Kean,
2014), perhaps making them a prime candidate for interventions to support
2Crystal Day-Hess and Douglas H. Clements
multiple areas of learning and growth. Across the nation, most children who
have low math scores in their kindergarten year continue to lag behind their
better-prepared peers throughout their school years (Clements & Sarama,
2014; National Research Council, 2009). The least prepared and the lowest
performing are disproportionately children from low-income families, who
are disproportionately children of color (Clements & Sarama, 2009, 2014;
Denton & West, 2002; National Research Council, 2009). Additionally,
children with developmental delays and disabilities often struggle in math
throughout their school years due to the lack of appropriate resources
(e.g., Geary, 2013; Kovas, Haworth, Dale, & Plomin, 2007; Olkun,
Altun, Goc¸er S¸ahin, & Akkurt Denizli, 2015). Clearly, any serious interven-
tion effort to close the achievement gap needs to include children before
school entry and in the early elementary grades.
1.3 Increasing Acceptance of Academic Instruction in
Preschool
In the past, there has been resistance to discipline-based instruction in pre-
school, in favor of learning through play and a focus on socialemotional
development. A review of the National Association for the Education of
Young Children (NAEYC) Guidelines over the last few decades, however,
reveals a shift toward productively integrating academic instruction with
playful learning and efforts to develop social skills (Clements, Fuson, &
Sarama, 2017; Fuson, Clements, & Sarama, 2015; Sarama & Clements,
2009a). This shift toward embracing academic instruction is clearly evident
in reading, less so in math. But the general acceptance that young children
can and should learn basic academic skills provides fertile ground for pro-
moting effective and developmentally appropriate strategies for teaching
math to preschool-aged children. This is consistent with research showing
that, given opportunities to learn, young children can develop an informal
knowledge of mathematics that is surprisingly broad, complex, and sophis-
ticated (National Research Council, 2009; Sarama & Clements, 2009b;
Thomson, Rowe, Underwood, & Peck, 2005). Young children are also
interested in mathematics; for example, preschoolers engage it in spontane-
ously in their free play (Seo & Ginsburg, 2004). However, high-quality,
playful mathematics instruction, rather than free-play time, promotes chil-
dren’s learning (Geary & Liu, 1996; Klein, Starkey, Clements, Sarama, &
Iyer, 2008). Such instruction is effective (Case, Griffin, & Kelly, 1999;
Clements & Sarama, 2007, 2011; Klein et al., 2008; Lewis Presser,
Clements, Ginsburg, & Ertle, 2015), scalable (Clements, Sarama, Spitler,
Lange, & Wolfe, 2011), and capable of addressing the severe equity problem
3The DREME Network: Research and Interventions in Early Childhood Mathematics
in US early mathematics education (Morgan, Farkas, Hillemeier, &
Maczuga, 2014; National Research Council, 2009; Rouse, Brooks-
Gunn, & McLanahan, 2005). Thus, enhancing learning is not an
“imposition” on children nor a “schoolification” of preschool, but a positive
contribution, especially for those children with the fewest opportunities to
learn outside of school.
1.4 DREMEs Central Goals
With these current developments in mind, one of the main goals of the
DREME Network is to convene a national network of scholars and
researchers to conduct rigorous basic and applied research and development
projects that address high-priority early math topics needed to inform and
motivate other researchers, educators, policymakers, and the public. The
DREME Network consists of four projects with the potential to inform
mathematics intervention at multiple levels—child, parent, teacher, school,
and district.
1.4.1 Increasing Capacity: Creating Resources for Early Childhood
Teacher Educators
Improving early math learning requires teachers to know the content,
understand children’s thinking, engage in pedagogical practices that support
learning, and see themselves as capable math teachers. Currently, most pres-
ervice teachers do not have access to robust course offerings in early child-
hood math and there are few faculty members at the college level who have
sufficient expertise in early math teaching and learning to teach the needed
courses (ATME, 2017; Sarama & DiBiase, 2004). In-service professional
development opportunities are also few and far between in part because
not enough experts in early math teaching are available to provide them.
To support the training of prospective and practicing early childhood
teachers, the Network is creating a system of resources that will be available
on the web. The resources are organized into flexible professional develop-
ment modules that can be used in a variety of settings (e.g., live or online
college courses, continuing education institutes, and ongoing in-service
workshops). Each module will offer a variety of materials designed to help
students (prospective or practicing preschool teachers) understand a specific
mathematical topic. Ultimately, there will be six modules on the website:
Overview, Counting, Spatial Relations, Operations, Patterns/Algebra,
and Measurement/Data. The website will include be a variety of materials
which provide activities, worksheets, handouts, and other resources (both
video and published) developed for the Teacher Educator to use. The
4Crystal Day-Hess and Douglas H. Clements
resources are designed to help Teacher Educators support prospective and
practicing teachers of young children develop learning opportunities that
are intentional, appropriate, engaging, and playful.
1.4.2 MMM Instruction: Using Math Activities to Support Math and
Executive Function Skills in Early Childhood
Empirical research has shown a link between mathematical thinking in
early childhood and executive function (EF) skills (Clements, Sarama, &
Germeroth, 2016). EF skills share a focus on deliberate and effortful cognitive
processes, including the ability to maintain attention during a task (sustained
attention), the ability to resist making an automatic or desired response (inhib-
itory control), the flexibility to consider multiple perspectives (cognitive
flexibility), and the ability to simultaneously think about and manipulate infor-
mation in our “mental workspace” (working memory) (Zelazo,Craik,&
Booth, 2004). In other words, EF skills enable children to pay attention, wait
their turn, consider different approaches to solving problems, and remember
and execute many steps when following directions. Thus, EF skills play a crit-
ical role in math as well as other domains. Moreover, both math and EF skills
are linked to a wide range of important long-term academic outcomes.
Preschool EF skills predict later math achievement, and students who
excel at math tend to also have strong EF skills (Clements et al., 2016). It is
clear that an association between math and EF exists, but it is not fully under-
stood. Do these skills need to be taught separately? Does one cause the other?
Are they mutually reinforcing? Does support for EF skills matter more for
children who are at risk for low math achievement? How can competencies
in math and EF be enhanced through high-quality early childhood education?
Based on what is known about EF and its development, the Network is
designing a variety of mathematical activities to test how these activities
shape children’s mathematical thinking and EF behaviors. Our goal is to
develop instructional materials that help teachers prioritize teaching prac-
tices that simultaneously promote the development of children’s mathemat-
ical thinking and EF. The knowledge gained from this work will also be
useful in guiding parents’ interactions with children. Section 2 reports on
one major accomplishment of this project.
1.4.3 Parentsand Early CaregiversEngagement in Math Activities
With Young Children
At home, children begin their initial explorations into everyday mathemat-
ics, progressively developing and refining their skills as well as their learning
expectations, motivation, and beliefs about math and their own math ability
5The DREME Network: Research and Interventions in Early Childhood Mathematics
(National Research Council, 2009). Yet, there is wide variation—linked in
part to socioeconomic status and culture—in the kinds of math learning
experiences children enjoy at home and the ways parents stimulate their
children’s development and academic learning (Clements & Sarama,
2014). Further, two-thirds of young children today spend significant time
in nonparental care, which includes family childcare as well as organized
preschool. Quantity and quality of math learning stimulation in these early
childhood care and education (ECCE) settings vary enormously and have
lasting consequences for achievement not only for math but also for reading.
Relative to the large body of research on language and literacy, less attention
has been given to young children’s learning at home and in ECCE settings.
The DREME Network seeks to address these limitations. The Net-
work’s goal is to advance knowledge on effective ways to increase the quan-
tity and quality of parents’ and caregivers’ engagement in their young
children’s math learning. Network collaborators are focusing specifically
on caregivers of children growing up in poverty, many of whom are not
native English speakers. The initial phases of this project blend research
and development as a first step toward the experimental testing of books,
games, and activities designed to maximize high-quality math interactions
with preschool children. Collaborators are conducting observations of par-
ent and informal childcare teachers engaging in math activities with young
children, using materials that are widely available at present or have been
developed by Network members. The goal is to determine which activities
hold the most promise for increasing children’s math learning. Additionally,
collaborators are piloting, and will ultimately test, teaching modules
designed to help parents and caregivers engage in productive “math talk”
with young children and to understand the development of children’s math-
ematical thinking.
Early work on this project has been focused on observing parents and
childcare teachers engaged in play and reading activities with children. In
doing so, we have observed caregiverchild interacting with a variety of
learning materials, storybooks (paperback and electronic), and counting
books. In addition, the team has been analyzing the mathematical affor-
dances of learning activities, storybooks, and counting books. From these
studies, it is evident that there is considerable variability across caregivers
in the amount of math talk and scaffolding of numerical and spatial skills that
they provide. Moreover, there is considerable variability in the quality of
learning affordances provided by toys and books that were, seemingly,
designed to support early numerical or spatial skill development. In the
6Crystal Day-Hess and Douglas H. Clements
illustrations of many storybooks that explicitly deal with counting, for exam-
ple, there are often mismatches between number words and numerical rep-
resentations of objects or highly cluttered scenes in which the number of
objects is difficult for even advanced learners to identify. While the study
is in its earliest stages, we are seeing that caregivers could often benefit from
increased knowledge and support, and perhaps reduced anxiety, when it
comes to engaging with their young children in ways that could promote
early math learning. In addition, we are finding considerable room for
improving the affordances of commonly available learning materials and
books, as well as a need to help caregivers select the highest quality learning
materials for early math learning.
1.4.4 PreschoolElementary Continuity and Coherence
Policy makers, educators, and researchers complained that math learning in
preschool is often disconnected from math learning in the early elementary
grades. This disconnect can lead to students experiencing uneven instruc-
tional practices which can compromise their learning. In response, some
state and district policy makers across the country are working toward
creating greater policy alignment in elements of policy affecting pre-K
and elementary schools. Others focus on creating greater curricular coher-
ence by coordinating learning goals and curriculum within and across gra-
des. But there is limited research on the impact of these policies and
practices on students’ experiences and learning outcomes as they move
from preschool through the early elementary grades (Perry,
MacDonald, & Gervasoni, 2015).
To address these limitations, the Network is investigating the relationship
between efforts to create policy alignment and curricular coherence on stu-
dents’ learning opportunities, experiences, and achievement in mathematics
from pre-K through grade 2. The Network is developing and piloting mea-
sures of children’s mathematical knowledge, experiences of mathematics
instruction, their opportunities to learn (curriculum and teachers’ instruc-
tional practices), and their understanding of the nature of math. Collaborators
have conducted cross-sectional analyses of children pre-K through grade 2 in
a district that is working toward policy alignment and curricular coherence.
In longitudinal studies of two districts endeavoring to improve coherence,
they are using our newly developed and refined measures to assess the degree
to which students in these districts have coherent learning opportunities and
experiences across grades in a given school. In particular, they are studying
7The DREME Network: Research and Interventions in Early Childhood Mathematics
how district-level policies are mediated by school-level policies and practices
to affect children’s math learning experiences and outcomes.
The four projects vary on a number of dimensions as well as in their
emphasis on research vs development. Perhaps most important, there is syn-
ergy among the projects; the work that is undertaken in one will be used to
inform others to, ultimately improve and support children’s mathematical
learning and knowledge.
2. MMM INSTRUCTION: AN IN-DEPTH LOOK AT A DREME
NETWORK PROJECT
This section provides a detailed look at one DREME Network pro-
ject, MMM Instruction: Using Math Activities to Support Math and EF Skills in
Early Childhood. We present an overview of the project and then describe
one core research activity that we have completed.
2.1 Early Math, EF, and Curricula
There is presently a burgeoning interest in early mathematics. However,
there is a wide divergence in both general perspectives toward children’s
development and learning of mathematical proficiencies and in the nature
and content of available mathematics curricula. As part of a larger study,
we analyzed and described the activities constituting six research-based pre-
school curricula. We then rated these for their potential to develop not only
mathematical concepts and procedures, but also EF processes, given the
comutual benefits documented between the development of mathematical
and EF proficiencies (and the importance of the latter for school success).
2.1.1 Early Mathematics Curricula
Although several new research-based preschool curricula have been devel-
oped and most evaluated (see Table 1), there are no analyses of the similar-
ities and differences among these efficacious programs and the instructional
activities of which they are constituted. Such analyses should include
the content focus (e.g., What topics and standards are addressed?), setting
(e.g., whole or small group, learning center, educational technology), and
type and nature (e.g., didactic, game, construction) of the instructional
activities. Before describing our approach to such analyses, we discuss a
unique focus of our approach, the interactions between early mathematics
and EF.
8Crystal Day-Hess and Douglas H. Clements
Table 1 Evaluations of Early Mathematics Programs
Program/
Curriculum
Content
Assessed
Age/
Grade SES
No. of
Children Design Results Comments References
Building
Blocks
Math PK Low (Head Start
and state funded)
68 No random assignment;
quasiexperimental
comparison
Moderate effect size
(ES ¼0.85) for
number, large (1.47)
for geometry
Caveats
regeneralizability: a
superrealization
(Cronbach et al.,
1980, p. 109); small
scale; teachers had
access to research
assistants
Clements and
Sarama (2007)
Building
Blocks
Math PK Low (Head Start
and state funded)
276 Random assignment to
group groups: Building
Blocks, comparison
(different curriculum
intervention with
professional
development), and
control
Large effect size
(1.07) compared to
business-as-usual
control and medium
effect size (0.47)
compared to the
different
mathematics
curriculum (pre-K
mathematics
curriculum)
Benefitted both low-
and middle-SES
children equally
Clements and
Sarama (2008)
TRIAD/
Building
Blocks
Math
Language
PK Low (two cities
in different
states, about 50%
African-
American, 25%
Latino)
1375 Random assignment of
schools to three
treatments, TRIAD
with Follow Through
(TRIAD-FT), TRIAD
with no follow through
(TRIAD-NFT), and
business-as-usual
control. At pre-K the
two TRIAD groups
were identical
Moderate effect
(0.72) on math, with
stronger positive
benefits African-
American children.
On language,
positive effects,
statistically
significant on four of
six subscores (0.16 to
0.36)
Research focused on
the TRIAD model of
scale-up rather than
the curriculum.
Classroom culture
specific to
mathematics and the
use of the Building
Blocks software were
mediators of the
effects
Clements et al.
(2011) and Sarama,
Lange, Clements,
and Wolfe (2012)
Continued
Table 1 Evaluations of Early Mathematics Programscontd
Program/
Curriculum
Content
Assessed
Age/
Grade SES
No. of
Children Design Results Comments References
Follow
Through
(to Building
Blocks)
Math K As above 1305 As above Both TRIAD
groups higher than
control (ES ¼0.38
TRIAD-FT and
0.30 TRIAD-NFT)
As predicted, effect
sizes decreased after
pre-K, but less so in
the TRIAD-FT than
the TRIAD-NFT
group. However,
TRIAD-FT was not
statistically different
from TRIAD-NFT
(ES ¼0.14). The FT
treatment may have
been too little and
teachers may have
resisted changing
their just-adopted
(undemanding)
K math curriculum
Sarama, Clements,
Wolfe, and Spitler
(2012)
TRIAD
Follow
Through
(to Building
Blocks)
Math 1 As above 1305 As above Both TRIAD
groups higher than
control (ES ¼0.51
TRIAD-FT and
0.28 TRIAD-NFT)
and FT higher than
NFT (ES ¼0.24)
The effects of
TRIAD-FT
increased in first
grade (compared to
Kindergarten),
possibly because the
early conceptual
work formed a
foundation for new
mathematical topics
(e.g., arithmetic)
Clements, Sarama,
Wolfe, and Spitler
(2013)
Building
Blocks
+ OWL
Math
Literacy
Executive
Function
Emotions
PK Low 2018 Comparison of children
who “just made” and
“just missed” the age
cutoff
(quasiexperimental
regression-discontinuity
design)
Medium-to-
moderate impacts on
children’s language,
literacy, numeracy
and mathematics
skills, and small
impacts on children’s
executive
functioning and a
measure of emotion
recognition
Cannot attribute
results to any single
aspect of the
program, including a
coaching system and
consistent literacy
(OWL), language,
and mathematics
(Building Blocks)
curricula
Weiland and
Yoshikawa (2013)
Big Math for
Little Kids
(BMLK)
Math
Language
PK
and K
Low 762 Randomly assigned
childcare centers to
BMLK or control
Medium effect size
(0.32) on math;
informal language
evidence was
positive
Two years of the
curriculum
throughout pre-K
and kindergarten
Lewis Presser et al.
(2015)
Rightstart Math K-1 Low, mixed
language
100 in all
Rightstart
groups;
100
comparison
in some
studies
No random assignment;
matched controls in
some studies
In separate studies,
higher number of
children passed a
number knowledge
test than in
comparison groups.
In one, Rightstart
children surpassed
both a second low-
SES group and a
mixed-SES group
Caveats regarding
generalizability: a
superrealization;
most teachers were
research assistants;
teachers received
substantial help from
the program
developers; small
scale; and expert
teachers certain
components of the
curriculum are
difficult to
implement (Gersten
et al., 2008)
Griffin and Case
(1997) and Griffin,
Case, and Siegler
(1994)
Continued
Table 1 Evaluations of Early Mathematics Programscontd
Program/
Curriculum
Content
Assessed
Age/
Grade SES
No. of
Children Design Results Comments References
Pre-K
Mathematics
Curriculum
+ Building
Blocks
(software)
Math PK Low 276 Classrooms randomly
assigned to intervention
or control
Math intervention
higher than control
with moderate effect
(0.55)
First year of
implementation.
Caveats: teachers
were volunteers,
they received
substantial support,
and this was not
taken to scale.
Differences were not
detectable a year
later
Klein et al. (2008)
and Preschool
Curriculum
Evaluation
Research
Consortium
(2008)
Pre-K
Mathematics
Curriculum
Math PK Low and middle No random assignment Math intervention
higher than control
with moderate
effects
Affected both low-
and middle-SES
children. Caveats:
Unknown internal
validity, as
comparison group
was from a different
year and was never
pretested.
Lower effects than
Building Blocks in a
comparison
(Clements, 2008)
Starkey, Klein, and
Wakeley (2004)
2.2 EF and Mathematics
Although there has been much recent attention to young children’s develop-
ment of EF and early mathematics, few studies have integrated the two.
We first briefly describe EF, then its relationship to mathematics learning
in the early years. Researchers and other educators have used the term EF
to refer to the processes involved in intentionally controlling ones’ impulses,
attention, thinking, and behavior. Although the field lacks a common set
of processes and definitions, the broad concept of EF can be viewed as a
unit functionally, but has also been analyzed into several processes (e.g.,
Best, Miller, & Naglieri, 2011; Huizinga, Dolan, & van der Molen, 2006;
Lehto, Juujarvi, Kooistra, & Pulkkinen, 2003; Miyake, Friedman, Emerson,
Witzki,&Howerter,2000;Raver,2013;Schoemaker,Bunte,Espy,
Dekovic, & Matthys, 2014). Three processes are frequently distinguished:
(a) attention shifting and cognitive flexibility, or switching a “mental set” from
one aspect of a situation to another as the situation requires; (b) inhibitory con-
trol, involving suppressing unproductive responses or strategies, such as con-
trolling a proponent response to think about better strategies or ideas; and
(c) working memory, a system that is responsible for the short-term holding
and processing of information. Several studies have shown positive correla-
tions between EF and achievement in young children (e.g., Alloway &
Alloway, 2010; Alloway, Alloway, & Wootan, 2014; Bierman, Nix,
Greenberg, Blair, & Domitrovich, 2008; Blair, Protzko, & Ursache, 2011;
Blair & Razza, 2007; Bull, Espy, Wiebe, Sheffield, & Nelson, 2011; Bull,
Johnston, & Roy, 1999; Cameron et al., 2012; Cerda, Im, & Hughes,
2014; Cortina et al., 2013; Gathercole & Pickering, 2000; Gawrilow et al.,
2014; McClelland et al., 2014; Ng, Tamis-LeMonda, Yoshikawa, &
Sze, 2014; Roebers, Cimeli, Rothlisberger, & Neuenschwander, 2012;
Welsh, Nix, Blair, Bierman, & Nelson, 2010), although there are exceptions
(e.g., Edens & Potter, 2013). This has led some to posit that EF is foundational
to learning and must be developed before academic instruction (Best et al.,
2011;e.g.,Clark, Pritchard, & Woodward, 2010; for a review, see
Clements et al., 2016; LeFevre et al., 2013). For this to be practical, of course,
EF must be malleable.
EF seems to be amenable to learning through instruction, such as with
computer games (Otero, Barker, & Naglieri, 2014; Razza & Raymond,
2015; Rueda, Rothbart, McCandliss, Saccomanno, & Posner, 2008), direct
training of specific EF tasks (Dowsett & Livesey, 2000; Espinet, Anderson, &
Zelazo, 2012; Rothlisberger, Neuenschwander, Cimelia, Michel, &
13The DREME Network: Research and Interventions in Early Childhood Mathematics
Roebers, 2012), or particular curricula (e.g., Bierman, Domitrovich, et al.,
2008; Bierman, Nix, et al., 2008; Diamond, Barnett, Thomas, & Munro,
2007; Diamond & Lee, 2011; Klingberg, 2009; Lillard & Else-Quest,
2007; Lyons & Zelazo, 2011; Otero et al., 2014; Perels, Merget-
Kullmann, Wende, Schmitz, & Buchbinder, 2009; Raver et al., 2011;
Riggs, Greenberg, Kusche, & Pentz, 2006; Weiland, Ulvestad, Sachs, &
Yoshikawa, 2013; Weiland & Yoshikawa, 2013). However, effects and
any transfer to other tasks are often small and sometimes nonexistent even
when the curriculum is implemented with good fidelity (Clements,
Sarama, Layzer, Unlu, & Germeroth, 2012; Farran, Lipsey, & Wilson,
2011; Lonigan & Phillips, 2012; Morris et al., 2014). Thus, there appears
to be some successful strategies for developing EF in young children,
although the training and the results may need to be narrowly focused
and persistence of these effects has not been evaluated (Clements et al.,
2016). There is also surprisingly little evidence for a causal relationship from
EF to achievement (Clements et al., 2016; Jacob & Parkinson, 2015).
Further, although gains on EF may be important outcomes per se, both
EF processes and subject-matter proficiencies are required to support con-
tinued learning and problem solving. Thus, it is an open question whether it
would be more effective to teach EF first and then content such as mathe-
matics, or to develop both simultaneously. A small set of studies, however,
suggests that teaching mathematics may develop both mathematics and EF
proficiencies (Clements et al., 2017; Farran et al., 2011; Weiland &
Yoshikawa, 2013).
In conclusion, developing both EF processes and mathematical profi-
ciencies appear to be essential for young children’s development and there
is a suggestion in the research corpus that high-quality mathematics educa-
tion may have the dual benefit of teaching this important content area and
developing EF processes. This open question led to the wider DREME pro-
ject of which this study is a part.
2.3 Preliminary EF Study Work
Given the possibility that mathematics instruction may have the additional
benefit of increasing children’s EF proficiencies, but little rigorous evalua-
tions of that possibility, we, along with other DREME colleagues, decided
to conduct a series of studies to test the causal connection. We began by
acquiring and describing all the activities in six research-based preschool
mathematics curricula. We then evaluated each of these in an interesting
14 Crystal Day-Hess and Douglas H. Clements
process to identify, and then analyze, a subset that had the potential to
develop both substantial mathematics and EF proficiencies. We planned
to conduct our research and development activities in four phases.
In phase 1, we described and coded all activities in research-based pre-
school mathematics curricula. In phase 2, we evaluated all activities coded in
phase 1 to reduce these to a small proper subset that had the potential to
develop both substantial mathematics and EF proficiencies. We then
intensely coded and analyzed these so others could benefit from our descrip-
tions and to identify commonalities among this select subset. In phase 3, we
developed and piloted newly developed archetype activities. Phase 4, which
is currently underway, involves conducting microgenetic studies to further
evaluate and refine the activities.
2.3.1 Phase 1: Description of Activities
Level 0. Six research-based preschool mathematics curricula were identi-
fied from the literature as having a strong theoretical and empirical base;
from these, 457 activities were identified (Level 0 Coding, Table 2, note that
Everyday Math was including because of the strong bases, http://
everydaymath.uchicago.edu/research,although we know of no study foc-
used only on pre-K). Note that the number of activities is a rudimentary
measure, as some activities are simple and short, while others have multiple
parts and are conducted over multiple days. We then coded the activities
according to their topic content (i.e., adding/subtracting, comparing/
ordering, counting, data/graphing, geometry/spatial, measurement, num-
ber, numeral, pattern, sorting, subitizing, and other), type of activity (i.e.,
charts/visuals, game, kinesthetic, math construction, musical, problem solv-
ing, read aloud, using tools/manipulatives, etc.), and setting (i.e., individual,
pairs, small group, whole group, or some combination). The authors taught
two graduate research assistants (GRAs, doctoral candidates), to perform this
coding, and then checked the codes for the first 20 activities; thereafter, any
questions the GRA coders had were directed to the authors, and were
checked via double coding, with consensus reached for final coding.
Table 3 presents the findings by topic, type of activity, and setting. Across
all curricula activities, counting was the most frequently represented content
area (40%), followed by geometry/spatial (19%) and measurement (13%).
The least frequently represented content areas were numeral recognition
(4%), subitizing (4%), number (3%), and “other” topics (1%; e.g., division,
numeral writing). When coded for type, over one-third of all activities
reviewed were categorized as using tools/manipulatives (34%). Games
15The DREME Network: Research and Interventions in Early Childhood Mathematics
Table 2 Early Math Curricula Included for Study
Program/
Curriculum
Number of Activities
Initially Reviewed:
Level 0
Number of
Activities:
Level 1
Number of
Activities:
Level 2
Number of
Activities:
Levels 34
Number of
Activities:
Level 5 References
Big Math for Little
Kids (BMLK)
52 5 5 1 1 Ginsburg, Greenes, and
Balfanz (2003)
Building Blocks
(BB)
94 36 23 9 6 Clements and Sarama (2013)
Developing Math
Concepts (DMC)
71 11 5 1 0 Richardson (2008)
Everyday Math
(EM)
117 25 9 0 0 Leslie, Audrain, Bell, Bell,
and O’Nan Brownell (2012)
Pre-K
Mathematics
Curriculum
(PMC)
32 11 5 3 2 Klein, Starkey, and Ramirez
(2002)
Rightstart/
Number Worlds
(R/NW)
91 14 11 1 1 Griffin, Clements, and
Sarama (2007) and Griffin
et al. (1994)
Total activities 457 102 58 15 10
Table 3 Description of All Activities Across All Curricula (Level 0, 457 Activities)
BMLK BB DMC EM PMC R/NW Total
Content
a
Adding/Subtracting 6 10 0 0 4 1 21
Comparing/Ordering 4 12 3 5 3 19 46
Counting 9 41 27 45 7 53 182
Data/Graphing 1 0 2 10 1 3 17
Geometry/Spatial 15 29 15 18 6 6 89
Measurement 9 5 10 16 4 17 61
Number 0 2 2 8 0 0 12
Numeral 3 2 0 6 1 4 16
Pattern 5 8 7 10 4 3 37
Sorting 0 0 5 10 2 0 17
Subitizing 1 10 0 3 0 2 16
Other 1 0 2 1 1 0 5
Type
Art 2 0 0 5 0 1 8
Charts/Visuals 3 0 5 12 3 9 32
Discussion of Theme 0 0 0 3 0 0 3
Drawing 1 1 0 0 0 0 2
Game 3 10 4 20 7 22 66
Kinesthetic 7 8 3 8 0 4 30
Language/Vocab 1 1 1 0 1 0 4
Math Construction 0 2 2 5 1 0 10
Model-then-Guide 3 9 1 2 1 4 20
Musical 1 14 3 6 0 4 28
Practice Skills 2 6 12 12 1 23 56
Problem Solving 8 6 1 6 0 2 23
Read Aloud 5 7 0 4 0 0 16
Continued
17The DREME Network: Research and Interventions in Early Childhood Mathematics
(14%) and activities that focused on practice skills (12%) were also frequently
represented, though to a lesser extent. The majority of activities reviewed
was identified by curriculum materials as whole group (45%) or small group
(28%) activities.
2.3.2 Phase 2: Selecting Fecund Activities
The goal of phase 2 was to rate activities as to their potential to develop both
math and EF proficiencies and ultimately to cull, from all activities identified
and coded, 10 archetypical instructional activities that were evaluated as hav-
ing the greatest potential.
Level 1. To ensure the inclusion of activities that included the potential
for high-quality mathematics learning and instruction, we first conducted a
high-level review of all 457 activities. Three coders, including one of the
authors, participated in the Level 1 coding and rated the activities according
to a 3-point scale of “yes,” “maybe,” or “no” for further inclusion and con-
sideration based on the level and content of mathematics learning involved.
The same coders trained for Level 0 were trained to perform coding for
Level 1. Codes for the first 10 activities were checked; thereafter, any ques-
tions the GRAs had were directed to the authors, and were checked via dou-
ble coding, with consensus reached for final coding.
At this initial level, we used the criteria that the topic had to be cen-
tral to mathematics learning (counting, subitizing, ordering, comparing,
Table 3 Description of All Activities Across All Curricula (Level 0, 457 Activities)contd
BMLK BB DMC EM PMC R/NW Total
Role Play 0 1 0 0 0 0 1
Using Tools/Manipulatives 16 28 39 33 18 22 156
Other 0 1 0 1 0 0 2
Setting
Individual 1 2 22 0 0 2 27
Pairs 3 3 2 4 8 2 22
Small Group 9 18 26 42 24 9 128
Small Group or Pairs 1 0 0 18 0 0 19
Small Group or Whole Group 2 11 0 42 0 0 55
Whole Group 36 60 21 11 0 78 206
a
Some activities represented more than one content category.
18 Crystal Day-Hess and Douglas H. Clements
addition/subtraction, geometry, spatial, pattern, or measurement). A sample
“yes” activity is Mr. Mixup from the Building Blocks curriculum. In this
activity, children are introduced to a puppet, Mr. Mixup, that often makes
mistakes when practicing various math concepts related to shapes, counting,
and measuring. Children help Mr. Mixup count, for example. If he makes a
mistake, they need to stop him right away and correct the error. A sample
“no” activity is Number Jump from the Building Blocks curriculum. In this
activity, the teacher holds up a numeral card, children say the numeral, then
jump that many times. The activity is repeated with different numerals and
other movements.
When the full list of 457 activities was coded for content of math learning
at Level 1, a total of 102 “yes” activities (22%) remained for further consid-
eration (Table 4). Owing to the large number of “yes” activities that
remained after Level 1 coding, all “maybe” activities were removed from
further consideration. Of the remaining 102 activities at this coding level,
counting (38%), geometry/spatial (28%), and comparing/ordering (20%)
were the most often represented content areas; other areas were much less
frequently represented. Activities using tools/manipulatives (36%) and in
the form of games (31%) were most common. Most remaining activities
were small group activities (39%), with whole group activities (26%) the
next most common.
Level 2. To further narrow the field, we conducted a Level 2 triage of the
remaining activities. For the mathematics activity per se, we again used the
criteria that the topic had to be central to mathematics learning and also
added the criteria that the activity support child engagement and learning.
More specifically, this meant that preschool-aged children should be able to
(a) easily comprehend the task (perceive and interpret the materials and ver-
bal interactions of the task and interpret the mathematical requirements, at
least intuitively); (b) act on the task in a way that involves engagement with
and action upon the ideas/requirements comprehended; and (c) make a
response that is then received by others (including acting on materials), often
starting a cycle of interaction. The previously established codes of content
area, activity type, and setting were considered secondarily to ensure an ade-
quate distribution of activities across these categories the next step. The same
coders trained for Levels 0 and 1 were trained to perform coding for Level 2.
Similar to previous coding rounds, codes for the first 10 activities were
checked; thereafter, any questions the GRAs had were directed to the
authors, and were checked via double coding, with consensus reached for
final coding.
19The DREME Network: Research and Interventions in Early Childhood Mathematics
Table 4 Description of Level 1 Activities Across All Curricula (102 Activities)
BMLK BB DMC EM PMC R/NW Total
Content
a
Adding/Subtracting 6 6 0 0 2 1 15
Comparing/Ordering 3 9 1 2 1 4 20
Counting 1 12 5 11 2 8 39
Data/Graphing 1 0 0 0 1 0 2
Geometry/Spatial 0 16 3 6 3 1 29
Measurement 0 2 1 3 0 2 8
Number 0 1 0 3 0 0 4
Numeral 1 0 0 0 0 0 1
Pattern 0 2 0 2 1 0 5
Sorting 0 0 1 2 0 0 3
Subitizing 0 3 0 3 0 1 7
Other 1 0 0 0 0 0 1
Type
Art 0 0 0 0 0 0 0
Charts/Visuals 0 0 0 0 1 1 2
Discussion of Theme 0 0 0 0 0 0 0
Drawing 0 1 0 0 0 0 1
Game 0 9 2 7 4 10 32
Kinesthetic 0 0 0 1 0 0 1
Language/Vocab 0 1 0 0 0 0 1
Math Construction 0 1 1 1 0 0 3
Model-then-Guide 0 3 0 2 0 0 5
Musical 0 0 0 0 0 0 0
Practice Skills 0 3 1 1 0 0 5
Problem Solving 3 3 1 6 0 0 13
Read Aloud 1 0 0 0 0 0 1
Role Play 0 1 0 0 0 0 1
20 Crystal Day-Hess and Douglas H. Clements
Level 2 resulted in 58 activities for further consideration (Table 5). At this
level of coding, the most frequent content area was counting (47%),
followed by geometry/spatial (31%); comparing/ordering (24%) and
adding/subtracting (14%) were next, with the other topics much less fre-
quent. The game (36%) and using tools/manipulatives (33%) were the most
frequent type, with problem solving (12%) the next most frequent. Similar
to previous levels, small group (43%) and whole group (34%) were the most
common activity settings.
Level 3. To select activities that had potential to be fecund in simulta-
neously developing substantial mathematics and EF proficiencies, Level 3
coding was performed. The goal of this level was to narrow the activities
to a subset, targeted a priori as a maximum of 15 activities. This followed
the same holistic procedures as the previous level with two alterations. First,
of course, there was a recalibration of the level of acceptance, as these activ-
ities survived the first screening. A “high” rating now required providing
substantial opportunity for an activity’s EF demands to be able to be adapted,
via altering EF demands or providing scaffolding of an activity for children
without significantly changing the math content inherent in the activity.
Only activities rated as “high” were included for further review and consid-
eration. A sample “high” EF adaptability activity is Shape Touch from the Big
Math for Little Kids curriculum (also related to the “Feely Box” activity
from Building Blocks). In this activity, children are shown a picture of a
shape, and they have to find the same shape in a bag of shapes without
Table 4 Description of Level 1 Activities Across All Curricula (102 Activities)contd
BMLK BB DMC EM PMC R/NW Total
Using Tools/Manipulatives 1 14 6 7 6 3 37
Other 0 0 0 0 0 0 0
Setting
Individual 0 2 1 0 0 0 3
Pairs 0 2 1 1 3 1 8
Small Group 0 13 7 8 8 4 40
Small Group or Pairs 0 0 0 10 0 0 10
Small Group or Whole Group 1 8 0 5 0 0 14
Whole Group 4 1 2 1 0 9 27
a
Some activities represented more than one content category.
21The DREME Network: Research and Interventions in Early Childhood Mathematics
Table 5 Description of Level 2 Activities Across All Curricula (58 Activities)
BMLK BB DMC EM PMC R/NW Total
Content
a
Adding/Subtracting 0 5 0 0 2 1 8
Comparing/Ordering 1 8 0 2 0 3 14
Counting 1 9 4 4 1 8 27
Data/Graphing 0 0 0 0 0 0 0
Geometry/Spatial 2 9 1 4 2 0 18
Measurement 0 1 0 1 0 1 3
Number 0 0 0 0 0 0 0
Numeral 0 0 0 0 0 0 0
Pattern 1 1 0 0 0 0 2
Sorting 0 0 0 0 0 0 0
Subitizing 0 0 0 0 0 2 2
Other 0 0 0 0 0 0 0
Type
Art 0 0 0 0 0 0 0
Charts/Visuals 0 0 0 0 0 0 0
Discussion of Theme 0 0 0 0 0 0 0
Drawing 0 0 0 0 0 0 0
Game 0 6 2 3 1 9 21
Kinesthetic 0 0 0 0 0 0 0
Language/Vocab 0 1 0 0 0 0 1
Math Construction 0 1 0 1 0 0 2
Model-then-Guide 0 1 0 2 0 0 3
Musical 0 0 0 0 0 0 0
Practice Skills 0 3 0 0 0 0 3
Problem Solving 3 3 1 0 0 0 7
Read Aloud 1 0 0 0 0 0 1
Role Play 0 1 0 0 0 0 1
22 Crystal Day-Hess and Douglas H. Clements
looking. A sample “low” EF adaptability activity is the previously described
Mr. Mixup; this activity was rated as high in math content at Level 2, but was
removed for further consideration in Level 3 because it did not include sub-
stantial EF adaptability opportunities.
Second, when two or more activities were identified as similar in content
and nature, we synthesized them into an archetype no longer taken exclusively
from one curriculum (rather, combiningthe advantages gleaned from each) and
we conducted all furthercoding on that archetype. For example, two “high”EF
adaptability activities, “Shape Touch” (from the Big Math for Little Kids
curriculum) and the related activity, “Feely Box” (from the Building Blocks
curriculum), were combined. Both activities have children match shapes,
identify and name shapes by touch, and identify and count vertices and sides.
One to two GRAs at each of three project sites were trained on math
content/quality and EF adaptability coding. All activities from two math
curricula (Big Math for Little Kids and Building Blocks) were coded by GRAs
from two project sites. Similar to previous procedures, for the remaining
curricula, coders were trained and the first 10 activities were coded and
checked for 100% agreement in coding; thereafter, any questions the GRAs
had were directed to the authors, and were checked via double coding, with
consensus reached for final coding.
Of the 15 activities remaining after Level 3 coding, geometry/spatial
content-focused activities were most frequently represented (40%), followed
Table 5 Description of Level 2 Activities Across All Curricula (58 Activities)contd
BMLK BB DMC EM PMC R/NW Total
Using Tools/Manipulatives 1 7 2 3 4 2 19
Other 0 0 0 0 0 0 0
Setting
Individual 0 1 0 0 0 0 1
Pairs 0 2 0 1 0 1 4
Small Group 0 7 4 6 5 3 25
Small Group or Pairs 0 0 0 1 0 0 1
Small Group or Whole Group 1 6 0 0 0 0 7
Whole Group 4 7 1 1 0 7 20
a
Some activities represented more than one content category.
23The DREME Network: Research and Interventions in Early Childhood Mathematics
by adding/subtracting (33%), counting (20%), comparing/ordering (13%),
measurement (7%), and subitizing (7%); other content areas were not rep-
resented at this level (Table 6). Activities types at this level included those
using tools/manipulatives (40%), games (40%), problem solving (13%),
and practice skills (7%). A variety of settings were represented at this level:
small group (40%), small group or whole group (33%), whole group (13%),
and pairs (13%).
Level 4. Level 4 began with two preparatory activities. First, EF bench-
marks were created based on work on a previous intervention (see Table 7)
(SECURe Intervention—Jones, Bouffard, Bailey, & Jacob, 2011; Philips,
2016). The following EF dimensions and higher-order cognitive skills were
coded: working memory, inhibitory control, cognitive flexibility, attention
control/focus, planning skills, and self-reflection/error monitoring. Second,
to prepare the 15 activities for extensive coding, each was separated into
sematic units (e.g., teacher makes a statement or demonstrates a procedure,
teacher asks a question, children response) to facilitate the application of the
EF benchmarks coding of each significant step. Those accomplished, we
completed the EF coding of the 15 archetype activities using this bench-
mark. For all EF benchmark coding activity, consensus was reached for
all activity codes.
Level 4 EF coding was then completed on the remaining 15 activities
(Table 8) using the same procedures. All areas of EF and selected higher-
order cognitive skills coded were represented to various extents across the
15 activities. Working memory, inhibitory control, and cognitive flexibility
were the most frequently coded categories. Perhaps not surprising, all of the
activities required children to use their working memory skills, at least to
some extent, to successfully complete the activity. When considering the
EF coding, it is important to keep in mind that coding at this level only
involved coding the scripts for the activities; EF skills actually utilized by
children to complete the activity (i.e., behavioral coding of EF) was not
completed at this level of coding.
Level 5. At Level 5, all previous codes were used to narrow the field to a
total of 10 archetypical activities. The first authors reviewed the remaining
15 activities and 4 members of the team each ranked them after reviewing all
associated coding data, including both math and EF codes from various
levels. These ratings were then aggregated and consensus reached to deter-
mine the final 10 activities to inform new archetype activity development.
The specific criteria were as follows:
24 Crystal Day-Hess and Douglas H. Clements
Table 6 Description of Levels 3 and 4 Activities Across All Curricula (15 Activities)
BMLK BB DMC EM PMC R/NW Total
Content
a
Adding/Subtracting 0 3 0 0 1 1 5
Comparing/Ordering 0 2 0 0 0 0 2
Counting 0 2 1 0 0 0 3
Data/Graphing 0 0 0 0 0 0 0
Geometry/Spatial 1 3 0 0 2 0 6
Measurement 0 1 0 0 0 0 1
Number 0 0 0 0 0 0 0
Numeral 0 0 0 0 0 0 0
Pattern 0 0 0 0 0 0 0
Sorting 0 0 0 0 0 0 0
Subitizing 0 1 0 0 0 0 1
Other 0 0 0 0 0 0 0
Type
Art 0 0 0 0 0 0 0
Charts/Visuals 0 0 0 0 0 0 0
Discussion of Theme 0 0 0 0 0 0 0
Drawing 0 0 0 0 0 0 0
Game 0 3 1 0 1 1 6
Kinesthetic 0 0 0 0 0 0 0
Language/Vocab 0 0 0 0 0 0 0
Math Construction 0 0 0 0 0 0 0
Model-then-Guide 0 0 0 0 0 0 0
Musical 0 0 0 0 0 0 0
Practice Skills 0 1 0 0 0 0 1
Problem Solving 0 2 0 0 0 0 2
Read Aloud 0 0 0 0 0 0 0
Role Play 0 0 0 0 0 0 0
Using Tools/Manipulatives 1 3 0 0 2 0 6
Other 0 0 0 0 0 0 0
Continued
25The DREME Network: Research and Interventions in Early Childhood Mathematics
Table 6 Description of Levels 3 and 4 Activities Across All Curricula (15 Activities)
contd
BMLK BB DMC EM PMC R/NW Total
Setting
Individual 0 0 0 0 0 0 0
Pairs 0 2 0 0 0 0 2
Small Group 0 2 1 0 3 0 6
Small Group or Pairs 0 0 0 0 0 0 0
Small Group or Whole Group 1 4 0 0 0 0 5
Whole Group 0 1 0 0 0 1 2
a
Some activities represented more than one content category.
Table 7 Executive Function Benchmark Categories and Operational Definitions
EF Category Operational Definition
Attention
Control/Focus
Maintaining focus while selecting and attending to relevant
information and sustaining progress toward a goal (presumably to
solve a math problem). This includes actively attending to
instructions, the activity itself, feedback on the activity, or to
peers’ math problem-solving behavior in a group work context.
“Actively attending” does not require action on the child’s part,
because it might be indicated by the child watching or listening
Planning Skills Identifying and organizing the steps or sequence of events needed
to complete an activity and achieve a desired goal
Working
Memory
Maintaining information in memory during the activity
(monitoring working memory) or manipulating/revising
information in working memory during the activity (updating
working memory)
Inhibitory
Control
The ability to suppress or modify a (distracting) behavioral
response in the service of engaging behaviors required to attain a
longer-term goal (i.e., inhibiting automatic reactions: 4 +5 ¼6as
in counting), while initiating more “effortful” yet appropriate
responses (i.e., 4 + 5 ¼9)
Cognitive
Flexibility
The mental ability to switch between thinking about two different
concepts and to think about multiple concepts simultaneously.
Additionally, the ability to redirect or shift one’s focus of attention
away from one salient object, instruction, or strategy to another
Self-
Reflection/
Error
Monitoring
The ability to review work either independently or with the help
of peers or teachers for accuracy. The ability to rehearse the steps
taken or answers given/chosen and/or evaluate them
26 Crystal Day-Hess and Douglas H. Clements
Table 8 Executive Function Benchmark Categorizations (Levels 45 and Phase 4 Archetype Activities)
EF Dimensions & Higher-Order Cognitive Skills
Activity Curriculum
Attention
Control/Focus
Planning
Skills
Working
Memory
Inhibitory
Control
Cognitive
Flexibility
Self-Reflection/Error
Monitoring
Continued
Table 8 Executive Function Benchmark Categorizations (Levels 45 and Phase 4 Archetype Activities)contd
EF Dimensions & Higher-Order Cognitive Skills
Activity Curriculum
Attention
Control/Focus
Planning
Skills
Working
Memory
Inhibitory
Control
Cognitive
Flexibility
Self-Reflection/Error
Monitoring
a
Represents activities that were selected to move forward for Level 5 archetype activity development and coding.
Most frequently represented EF/Higher-Order Cognitive Skills Category based on activity script coding.
Indicates EF/Higher-Order Cognitive Skills Category was represented based on activity script coding.
1. Math content and activity structure
a. Representation of four primary activity types identified in Levels 03
activity selection (game, problem solving, practice skills, using tools/
manipulatives).
b. Representation of five primary content focus areas identified in
Levels 03 activity selection (addition/subtraction, comparing/
ordering, counting, geometry/spatial, measurement).
c. Representation of activities that can be introduced and conducted in
small group or pairs setting.
2. EF demands
a. Representation of main components of EF identified in the litera-
ture, as informed by EF benchmark coding (Level 4).
3. Applicability for future microgenetic study
a. Representation of activities that are amenable to small group
instruction.
b. Representation of activities that are amenable to eventual indepen-
dent use by children in centers.
The Level 5 ten finalist activities are described in Tables 8 and 9. The topics of
geometry/spatial (50%) and arithmetic (30%) dominated the selected activ-
ities, with counting (20%), subitizing, (10%), and comparing/ordering (10%)
also represented. Half used tools or manipulatives, 30% were games, 10%
were involved problem solving, and 10% were practice skills. Half of the
activities were coded as small or whole group, 20% as whole group (but were
modified to also work as small group), 20% as small group, and 10% as pairs.
2.3.3 Phase 3: Developing Archetype Activities
Initial activity development. The 10 activities remaining after coding served as
the basis for creating the same number of archetype activities (Table 10),
which were defined as activities that are representative of a particular activity
type/setting/content-focus that include high-quality math content and EF
demands. Following the lead of the Big Math for Little Kids and the Building
Blocks curricula, activities were also developed so that they included mul-
tiple subactivities and phases that built upon one another in terms of content
and complexity. This design will allow for opportunities to support children
at various levels and across time as they learn math skills and practice EF skills
(while also keeping the activities fresh and exciting). Each activity was
designed and written such that activities could be scaffolded up or down
to make content more or less challenging for children depending on their
individual needs; two sets of scaffolds were developed for every phase of each
29The DREME Network: Research and Interventions in Early Childhood Mathematics
Table 9 Description of Level 5 Activities Across All Curricula (10 Activities)
BMLK BB DMC EM PMC R/NW Total
Content
a
Adding/Subtracting 0 1 0 0 1 1 3
Comparing/Ordering 0 1 0 0 0 0 1
Counting 0 2 0 0 0 0 2
Data/Graphing 0 0 0 0 0 0 0
Geometry/Spatial 1 3 0 0 1 0 5
Measurement 0 0 0 0 0 0 0
Number 0 0 0 0 0 0 0
Numeral 0 0 0 0 0 0 0
Pattern 0 0 0 0 0 0 0
Sorting 0 0 0 0 0 0 0
Subitizing 0 1 0 0 0 0 1
Other 0 0 0 0 0 0 0
Type
Art 0 0 0 0 0 0 0
Charts/Visuals 0 0 0 0 0 0 0
Discussion of Theme 0 0 0 0 0 0 0
Drawing 0 0 0 0 0 0 0
Game 0 1 0 0 1 1 3
Kinesthetic 0 0 0 0 0 0 0
Language/Vocab 0 0 0 0 0 0 0
Math Construction 0 0 0 0 0 0 0
Model-then-Guide 0 0 0 0 0 0 0
Musical 0 0 0 0 0 0 0
Practice Skills 0 1 0 0 0 0 1
Problem Solving 0 1 0 0 0 0 1
Read Aloud 0 0 0 0 0 0 0
Role Play 0 0 0 0 0 0 0
30 Crystal Day-Hess and Douglas H. Clements
activity—one for mathematics and one for EF. The activities were then sup-
plemented by relevant handouts for teachers with additional information to
assist with content presentation (for example, a handout was created that
provided guidance on shape descriptions to use with children).
Prepilot of activities. After developing these new activities, we conducted
pilot evaluations of the resulting 10 activities across multiple sites, with each
team providing qualitative feedback to the development team. As a conve-
nience sample for the prepilot, sites implemented the activities with
preschool-aged children attending schools affiliated with their respective
universities. More diverse samples are currently being included in the full
pilot phase. The questions the pilots were designed to answer the following
questions: Does the implementation reflect adequate and similar fidelity
across sites and teachers? Are the materials and structure of the text adequate?
Do children appear to be learning the math concepts/skills as postulated? Is
EF use observed and is it supported by the activities as postulated? What
improvements can be made? We also asked several master teachers for their
reactions to the archetypes as written.
The sites involved in prepiloting activities remained in contact during
implementation to address any questions or concerns related to the activities.
Each site also completed a form that included specific questions related to
the activities to inform ongoing and future activity development and
refinement. Videos and feedback were provided on a daily basis from
the teacherresearchers, and changes were made in tight revision cycles
Table 9 Description of Level 5 Activities Across All Curricula (10 Activities)contd
BMLK BB DMC EM PMC R/NW Total
Using Tools/Manipulatives 1 3 0 0 1 0 5
Other 0 0 0 0 0 0 0
Setting
Individual 0 0 0 0 0 0 0
Pairs 0 1 0 0 0 0 1
Small Group 0 0 0 0 2 0 2
Small Group or Pairs 0 0 0 0 0 0 0
Small Group or Whole Group 1 4 0 0 0 0 5
Whole Group 0 1 0 0 0 1 2
a
Some activities represented more than one content category.
31The DREME Network: Research and Interventions in Early Childhood Mathematics
Table 10 Final Archetype Activities Developed for Further Study (Phase 3)
Archetype
Name
Original
Curriculum
(Activity) Related Activities
Content
Focus
Activity
Type Brief Descriptions
Count to
Add and
Subtract
Pre-K Math
(Bears in the
Cave)
How Many Now (Building
Blocks), Mouse in the Cookie Jar
(Number Worlds)
Counting,
Adding/
Subtracting
Game Relating counting (the successor
principle) to arithmetic. Addition and
subtraction using hidden objects
Change
Game
Number Worlds
(PlusMinus
Game)
Number Line Team Game, Race
to Ten, Race to Zero, Ice be Nice
to my Skating Party (all Number
Worlds), Adding: Board Game
(Building Blocks)
Adding/
Subtracting
Game Students roll dot cube, count, and
request that many counters, which are
put on the game board. +/cards are
drawn to determine movement of
counters
Cookie
Game
Building Blocks
(Pizza Game
12)
Counting,
Subitizing
Game Using cookie activity sheets, players
roll number cube and put that many
counters on their sheet, asking the
other player if they are correct or not.
Other player must agree. Continues
until a player has all spaces covered
Big Fish
Story
Building Blocks
(Gone Fishing 2)
Adding/
Subtracting
Using
Tools/
Manips
Children are given fish crackers and
are told to add/subtract various
amounts of fish to their lake, and asked
how many after adding and
subtracting.
Magician’s
Tricks
Building Blocks
(X-Ray Vision)
Ordering/
Comparing,
Counting
Practice
Skills
Counting cards 110 (or 120) placed
in numerical order. Children point to
any card, and other child uses their
“magician’s tricks” (counting) to tell
which card it is without looking
True or
False?
Building Blocks
(Is It Or Not?)
Geometry/
Spatial
Using
Tools/
Manips
Review with children what makes a
triangle, for example, and then try to
fool them, asking why a shape or
drawing presented is or is not a triangle
What Shape
Am
I Touching?
Big Math for
Little Kids
(Shape Touch)
Feely Box (Building Blocks) Geometry/
Spatial
Using
Tools/
Manips
Children identify and name shapes by
touch, and match shapes to pictures.
Also identify and count corners and
straight sides
What Am
I Thinking?
Building Blocks
(Guess My
Rule)
Geometry/
Spatial
Problem
Solving
Sort shape sets into piles based on
something that makes them alike.
Children guess the rule, and explain
their answer
Shape
Puzzles
Pre-K Math
(Let’s Make
Tangram
Pictures)
Geometry/
Spatial
Using
Tools/
Manips
Children are given shapes to use to fill
in a picture puzzle
Don’t Burn
Your Feet!
Building Blocks
(Shape Step)
Geometry/
Spatial
Using
Tools/
Manips
Make large shapes on floor/ground.
Show several triangles, for example,
and tell children to step on triangles
only. Ask children how they know it is
a triangle
(e.g., daily edits). Regular meetings were also held to further discuss specific
activity reflections and observations from the multisite teams, as well as “big
picture” topics (e.g., format of activities, process of activity implementation,
etc.) to help inform steps moving forward with the full pilot and later micro-
genetic testing preparation. Initial reactions and observations included the
following: the activities were engaging and fun for children; the math con-
tent was either just right or too easy for the children (for the convenience
sample selected); the scaffolding sections in the activities were helpful in
adjusting the activities to meet children’s needs and levels; and that addi-
tional information or direction needs to be included in certain activities
around supporting EF or increasing EF demands.
Teacher feedback and activity refinement. The final act in the development
of the archetype activities was to share them with the entire research team
and a group of five teachers identified by each research group as excellent
teachers of preschool mathematics, with particular experience working with
children from low-SES backgrounds, with high needs, and/or dual language
learners. Comments were overwhelmingly positive in all areas of feedback
(e.g., appropriateness for age-group and special populations served, child
engagement, tactics and structures to support math and EF, etc.). Sugges-
tions included ways to make the activities more appropriate for different
cultures and for children with special needs, every one of which was
incorporated.
2.3.4 Phase 4: Microgenetic Testing of Select Archetype Activities
We are planning to use a subset of the archetype math activities selected during
phase 3 to conduct microgenetic studies, a methodological approach that
involves repeated observations over time to capture developmental change,
uncover the processes that may cause change, and conditions that facilitate
change or hinder it from happening. As part of the microgenetic studies, chil-
dren will receive pretests on math and EF, multiple math instructional sessions,
and posttests. Inclusion of multiple data collection sites will afford our use of
several math activities and ensure inclusion of diverse participant groups. Cod-
ing systems will be developed to measure relevant math and EF behaviors.
We will also conduct complementary experimental studies to further
understand how these activities support math and EF development and
learning. For example, one subset of studies will focus on select, isolated fea-
tures of math activities, including features that appear in some of the micro-
genetic study activities. These studies will test how specific features of
instructions or materials (e.g., variation in the size of shapes being compared
34 Crystal Day-Hess and Douglas H. Clements
in the shape identification task) influence children’s performance and learn-
ing, and if that influence depends on child factors such as EF level. Another
set of studies will examine activities that are designed to require low levels of
adult direction and, like the microgenetic study activities, manipulate EF
demands. Using these activities, we will study how children who vary in
their levels of EF benefit from these activities in terms of both math learning
and EF development. Once the manipulations involved in such experimen-
tal studies are optimized, we will take some of the activities that result into
classrooms to observe how children interact with the materials in authentic
learning environments.
3. CONCLUSION
Early childhood mathematics education has received increasing atten-
tion from researchers, practitioner, and policy makers. Over the next several
years, the DREME Network will conduct research and development activities
that will have implications for interventions, from the state and district levels,
to professional development, families, and teaching. As an immediate contri-
bution, we report on the initial work of one of the projects, a comprehensive
review of the instructional activities in six research-based curricula. These data
will provide researchers, curriculum developers and specialists, and other edu-
cators with new information and new perspectives when creating, evaluating,
and choosing curricula and instructional activities in early mathematics.
ACKNOWLEDGMENTS
This chapter and the research reported were supported in part by a grant from the Heising-
Simons Foundation, Grant #2015-156. The opinions expressed are those of the authors and
do not represent views of the Heising-Simons Foundation. We wish to thank Deborah
Stipek for her leadership on all aspects of the DREME Network and to the Network
members for their advice on this manuscript, especially Miche
`le Mazzocco, the lead on the
project described in more depth, and other members of her team, Dale Farran, Susan
Levine, Deborah Phillips, and Julie Sarama. It should be noted that several curricula
described in this article were published by one of the authors and/or members of the
DREME Network, who thus could have a vested interest in the results. However, an
external auditor oversaw the research design and coding, and five researchers independently
confirmed findings and procedures.
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41The DREME Network: Research and Interventions in Early Childhood Mathematics
... In addition, transfer from optimised high-quality preschool mathematics interventions to EF has been demonstrated (e.g. Clements et al., 2016Clements et al., , 2020Day-Hess & Clements, 2017;Scalise et al., 2020). While here we focus primarily on why combining EF and mathematics should improve transfer to mathematics (unlike EF-alone programmes), it has also been pointed out elsewhere that high quality mathematics interventions should and can transfer to EF improvements. ...
... For example, excellent examples integrating mathematics and EF are the DREME network projects (e.g. Day-Hess & Clements, 2017), and the EF + Math programme for older children . In combination with co-developing interventions with teachers and gathering more empirical evidence of efficacy, particularly in the early years, we urge cognitive and education scientists in this area to state as clearly as possible what theory of change underpins their EF interventions, be they isolated or integrated. ...
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A vast body of work highlights executive functions (EFs) as robust correlates of mathematics achievement over the primary and preschool years. Yet, despite such correlational evidence, there is limited evidence that EF interventions yield improvements in early years mathematics. As intervention studies are a powerful tool to move beyond correlation to causality, failures of transfer from executive functions interventions are, we argue, highly problematic for both applied and theoretical reasons. We review the existing correlational and intervention literature at complementary neuroscientific, cognitive, developmental and educational levels. We appraise distinct theories of change underpinning the correlations between EF and early mathematics, as well as explicit or implicit theories of change for different types of EF interventions. We find that isolated EF interventions are less likely to transfer to improvements in mathematics than integrated interventions. Via this conceptual piece, we highlight that the field of EF development is in need of (1) a clearer framework for the mechanisms underpinning the relationships between early EF and other developing domains, such as mathematical cognition; (2) clearer putative theories of change for how interventions of different kinds operate in the context of EF and such domains; (3) and greater clarity on the developmental and educational contexts that influence these causal associations. Our synthesis of the evidence emphasises the need to consider the dynamic development of EFs with co-developing cognitive functions, such as early math skills, when designing education environments. [234 words].
... The analytic sample was derived from a DREME Network study of the coherence of early mathematics education (e.g., Coburn et al., 2018;Day-Hess & Clements, 2017) conducted with two large public-school districts in the Western United States. We selected these two districts because (a) they were both making concerted efforts to create stronger connections between pre-K and elementary education in the district and (b) they were doing so using different strategies (Coburn et al., 2018, describes them in detail). ...
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Developing solution strategies, effortful procedures that students employ to solve a specific problem, is an important mathematical goal. Studies have documented intraindividual strategy variability and its significance for learning, but only some have addressed the interindividual strategic diversity across students within a classroom. This study analyzed classroom strategy diversity using assessments of 527 kindergartens to 2nd-grade students. Latent growth modeling analysis revealed that the best fit was a spline model featuring two phases of linear growth with different growth rates (i.e., one in Kindergarten, the other from Kindergarten spring to second grade). A growth mixture modeling analysis demonstrated that only one latent class existed within the data, which supports the homogeneity of the identified growth trajectory among students. We also analyzed the relations of their learning to the interindividual strategy diversity in their classrooms via a multilevel latent growth model. The results showed that early encouragement of student-generated strategies and later guidance toward research-based effective strategies most supported mathematical growth. This finding aligned with the previous work regarding classroom strategic diversity.
... Mathematics is one of the most important subjects in society [31,32]. It provides us with an understanding in various fields such as technology, engineering, and science. ...
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In this paper, we describe an investigation of brain activity while playing a serious game (SG). A SG is focused on improving logical thinking, specifically on cognitive training of students in the field of basic logic gates, and we summarize SG description, design, and development. A method based on various signal processing techniques for evaluating electroencephalographic (EEG) data was implemented in the MATLAB. This assessment was based on the analysis of the spectrogram of particular brain activity. Changes in brain activity power at a characteristic frequency band during the gameplay were calculated from the spectrogram. The EEG of 21 respondents was measured. Based on the results, the respondents can be divided into three groups according to specific EEG activity changes during the gameplay compared to a relaxed state. The beta/alpha ratio, an indicator of brain employment to a mental task, was increased during gameplay in 18 of the 21 subjects. Our results reflected the sex of respondents, time of the game and the indicator, and whether the game was successfully completed.
... Regressions indicated that EF significantly predicted math scores but the strength was greatest for children at the lowest level of math competencies. Interventions, whether directly addressing EF skills or using math activities fine-tuned to children's developmental level in both math using learning trajectories and EF Day-Hess & Clements, 2017) may be particularly useful for these children. Conversely, math predicted EF, similarly across levels in preK, but greater at the lower levels in kindergarten. ...
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Research on young children’s development of executive function (EF) and early mathematics has established relationships between the two, but studies have not investigated whether these relations differ for children with different outcomes in mathematics and EF, especially in the context of interventions. To examine the homogeneity of those relations and the intervention effects, we conducted quantile regression analyses on data from a large study of two prekindergarten interventions: the Building Blocks math curriculum alone (BB), or BB with scaffolding of play to promote executive function (BBSEF). Results revealed that EF competencies have a larger positive relationship to mathematics for children with low math competence compared to children with medium or high competence. The significant predictive relationship of mathematical competencies on EF did not vary for children with different levels of EF abilities at prekindergarten and varied only slightly at kindergarten. Also, interventions had similar immediate effects on math and EF for children with various abilities. The BB intervention had a larger positive delayed effect on math and EF competencies for children with low scores relative to children with high scores. The delayed effect of the BBSEF intervention was similar for children with different levels of EF and math competencies.
... This is not to say that there have been no viable attempts to build valid research-based curricula. There are many (for lists of examples, see Clements, 2008;Day-Hess & Clements, 2017). However, they remain relatively small in number and frequently do not explicate the methods and findings of the development process. ...
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Most developers and publishers claim that their curricula are based on research, but few explicate their claims. In this chapter, we briefly assess the state of affairs regarding “research-based curricula” and present a model to mitigate weaknesses in the field that is based on coordinated interdisciplinary research ranging from cognitive science to scale-up. We describe an example in early mathematics.
... This is not to say that there have been no viable attempts to build valid research-based curricula. There are many (for lists of examples, see Clements, 2008;Day-Hess & Clements, 2017). However, they remain relatively small in number and frequently do not explicate the methods and findings of the development process. ...
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The purpose of the study was to better understand the phenomenon of exploring early mathematics through book reading. The study centers on Head Start and lays on Bronfenbrenner’s bioecological framework). Two sub-questions guided the qualitative single case study of six Head Start adult participants (teachers, parents, administrators): (1) What are Head Start participants’ experiences in exploring early mathematics through picturebooks? and (2) What do Head Start participants say about exploring early mathematics through picturebooks? Findings showed that participants expressed interest toward exploring early mathematics through picturebooks. Picturebooks were commonly used in the classroom but also accessible for families. Participants provided evidence of mathematics practices and discussions around mathematics in the school and in the home. The participants’ sayings and experiences in exploring early mathematics through picturebooks aligned with child development and contexts of learning, two cornerstones of Developmentally Appropriate Practice (DAP), but potential obstacles emerged. Implications for researchers and practitioners are discussed.
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The purpose of this study is to investigate project-based and problem-based instruction STE(A)M activities for children aged 4-6 years old in STE(A)M Preschool Classroom Environments. A French film ("Le balloon rouge", 1956) was the occasion for the creation of an authentic communication framework that encouraged and supported the planning and the development of contextualized STE(A)M activities based on educational robotics and computational thinking. These were referred mainly to mathematical concepts through a problem-based solving process. Students using several materials and strategies tried and attempted to sculpt physical distances among nations and people using digital tools and in particular using the Bee-Bot Robot. The results showed that pre-schoolers enjoyed the use of digital tools and their possibilities corresponding to directional codes. They used mathematical concepts and many non-standard (arbitrary) or conventional measurement units as tools to solve the problem of sculpting the distances. Furthermore, under the appropriate guidance and into an educational robotic context, they managed to make the robot move in a correct and appropriate way after mane repetitions and utilizing the opportunity to construct and reflect on new learning trajectories.
Chapter
Math is fundamental to many situations in everyday life such as managing money, preparing food, or making music. Therefore education aims to learn children and adolescents number and math concepts, to enhance math fluency, and to obtain more advanced mathematics. However, a lot of learners have problems with reaching these goals, or even worse, they develop severe difficulties or disorders. This impacts their daily life as they are not able to transfer this knowledge to real-world problems, but it also impedes their future school career and chances on the labor market. Therefore it is crucial to pinpoint which interventions are effective in fostering learners’ number and math performance. For this purpose, we conducted a comprehensive overview of previous reviews and metaanalyses, i.e., a metareview, targeting early numeracy or more advanced mathematics, focusing on both typical and atypical (or at risk) achievers in preschool, primary, or secondary education. Forty-one reviews/metaanalyses were included in this metareview and were analyzed in order to find information that could help us provide an answer on one of the following questions: (1) are math interventions less/more effective in different age groups? (“when”); (2) are math interventions less/more effective for particular math content and does the duration of the intervention moderate effectivity? (“what and how long”); (3) are math interventions less/more effective when they make use of a specific instructional method? (“how”); (4) are math interventions less/more effective for specific samples? (“who”). In addition, all reviews and metaanalyses were also scanned for statements with respect to the quality of interventions. The metareview revealed evidence-based information about the effectiveness of particular interventions and reveals gaps in the literature that may provide challenges for future research.
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Several teaching moves have been suggested to support young children’s simple addition and subtraction performance, including use of a number path, directly modeling addition and subtraction, using mathematical symbols, and modifying problem difficulty. In the present study, teacher-researchers implemented an early arithmetic activity, Big Fish Story, with dyads of 3 to 4-year-old students. As part of the implementation, the teacher-researchers used these teaching moves to support young children’s in-the-moment answers to simple addition and subtraction problems. We use session-level data (n = 94 sessions) nested in dyads to examine and compare the frequency with which the use of these teaching moves are associated with two types of student responses, in order to preliminarily identify teaching moves that may support young children’s performance on simple arithmetic tasks. We conclude with implications for the field and early childhood practitioners.
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We address common criticisms of the Common Core State Standards—Mathematics, evaluating them based on comprehensive reviews of existing documentation and research to better ground future debates and to ameliorate negative effects of possible misconceptions or misinterpretations. The four main criticisms follow. (1) No one who helped develop the standards had any expertise in the education of young children. (2.) The CCSSM dictates scripted curricula and didactic instruction rigidly applied to all children at the same pace. (3.) The standards emphasize academic skills and leave no time for play, exploratory approaches, or social-emotional development. (4.) The standards are too early and therefore developmentally inappropriate for children in the early grades. We conclude that these criticisms are not valid, and that, given the importance of mathematics to academic success in all subjects, all children need and deserve to build a robust knowledge of mathematics in their earliest years and can do so if we use the research knowledge and research-based standards and programs presently available. We summarize and exemplify the research-based balanced approach to teaching based on learning trajectories that can provide guidance for engaging and developmentally appropriate mathematical experiences that have been demonstrated to help all children learn to high standards.
Book
As the pace of technological change accelerates, we are increasingly experiencing a state of information overload. Statistics show that we are interrupted every three minutes during the course of the work day. Multitasking between email, cell-phone, text messages, and four or five websites while listening to an iPod forces the brain to process more and more informaton at greater and greater speeds. And yet the human brain has hardly changed in the last 40,000 years. Are all these high-tech advances overtaxing our Stone Age brains or is the constant flood of information good for us, giving our brains the daily exercise they seem to crave? In The Overflowing Brain, cognitive scientist Torkel Klingberg takes us on a journey into the limits and possibilities of the brain. He suggests that we should acknowledge and embrace our desire for information and mental challenges, but try to find a balance between demand and capacity. Klingberg explores the cognitive demands, or “complexity,” of everyday life and how the brain tries to meet them. He identifies different types of attention, such as stimulus-driven and controlled attention, but focuses chiefly on “working memory,” our capacity to keep information in mind for short periods of time. Dr Klingberg asserts that working memory capacity, long thought to be static and hardwired in the brain, can be improved by training, and that the increasing demands on working memory may actually have a constructive effect: as demands on the human brain increase, so does its capacity. The book ends with a discussion of the future of brain development and how we can best handle information overload in our everyday lives. Klingberg suggests how we might find a balance between demand and capacity and move from feeling overwhelmed to deeply engaged.
Article
Research Findings: Big Math for Little Kids (BMLK) is a mathematics curriculum developed for use with 4- and 5-year-old children. To investigate the BMLK curriculum's effect on children's mathematics knowledge, this cluster-randomized controlled trial randomly assigned child care centers to provide mathematics instruction to children, using either the BMLK mathematics curriculum or the centers’ business-as-usual curriculum, over a 2-year period when children were in prekindergarten and kindergarten. Participants in the study were 762 children and their teachers at 16 publicly subsidized child care centers. The study assessed children's mathematics knowledge using the Early Childhood Longitudinal Study, Birth Cohort (ECLS-B), Direct Mathematics Assessment, a measure of young children's mathematics knowledge that is not aligned with the curriculum. The ECLS-B scores of children in the BMLK group increased significantly more than did those of children in the comparison group. The study also included exploratory analyses to examine whether children in the BMLK group demonstrated evidence of improved mathematical language. Practice or Policy: These results indicate that the BMLK curriculum, which is designed to help teachers use play-based, developmentally appropriate mathematics instruction, has a positive impact on young children's mathematics knowledge as measured by a general mathematics assessment that is not aligned with the curriculum.
Chapter
This edited book brings together for the first time an international collection of work built around two important components of any young child’s life—learning mathematics and starting (primary or elementary) school. The chapters take a variety of perspectives, and integrate these two components in sometimes explicit and sometimes more subtle ways. This chapter provides a theoretical framework for transition to school and investigates possible places for mathematics in that transition. It stresses the importance of considering the strengths of all involved in the transition to school and how these strengths can be used to assist children learn increasingly sophisticated mathematics. The chapter concludes with an analysis of each of the book chapters in terms of their links into the theoretical framework for transition to school and young children’s mathematics learning.