Below are the first 10 and last 10 pages of uncorrected machine-read text (when available) of this chapter, followed by the top 30 algorithmically extracted key phrases from the chapter as a whole.

Intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text on the opening pages of each chapter.
Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

Do not use for reproduction, copying, pasting, or reading; exclusively for search engines.

OCR for page 225

7
Standards, Curriculum,
Instruction, and Assessment
In this chapter, we address the topic of effective mathematics curricu-
lum and teaching—what is known about how teachers can effectively sup-
port children’s learning of important foundational mathematics content. We
begin the chapter with a description and analysis of current state standards
for early learning. Standards are intended to influence the development of
curriculum and assessment tools, and therefore they have the potential to
serve as a bridge between what research says about children’s learning and
the kinds of teaching and learning that actually occur.
Next, the chapter provides an overview about the state of mathematics
teaching and learning experiences in early childhood settings and reviews
the literature on effective practices for teaching young children mathemat-
ics. Following this is a discussion of formative assessment, an essential and
often overlooked element of effective instruction. The chapter concludes
with a discussion of research on effective curricula.
DEFINITIONS
To enhance understanding of the content of this chapter, we first define
some of the most frequently used early childhood education terminology.
Teacher-Initiated and Child-Initiated Experiences
Early childhood practices are often described as either teacher-initiated
or child-initiated. Teacher-initiated or teacher-guided means that teachers
plan and implement experiences in which they provide explicit information,
225

OCR for page 225

226 MATHEMATICS LEARNING IN EARLY CHILDHOOD
model or demonstrate skills, and use other teaching strategies in which they
take the lead. Teacher-initiated learning experiences are determined by the
teacher’s goals and direction, but they should also reflect children’s active
engagement (Epstein, 2007). Ideally, teacher-initiated instruction actively
involves children. Indeed, when appropriately supportive and focused,
teacher-initiated instruction can lead to significant learning gains (French
and Song, 1998; Howes et al., 2008). In practice, however, most teacher-
initiated instruction is associated with the passive engagement of children
(Pianta et al., 2005).
By contrast, child-initiated or child-guided means that children acquire
knowledge and skills through their own exploration and through interac-
tions with objects and with peers (Epstein, 2007, p. 2). Child-initiated expe-
rience emanates primarily from children’s interests and actions with support
from teachers. For child-initiated learning to occur, teachers organize the
environment and materials and provide the learning opportunities from
which children make choices (Epstein, 2007). Teachers thoughtfully observe
children during child-initiated activity, gauging their interactions and the
provision of new materials, as well as reorganization of the environment,
to support their continued learning and development.
During optimal child-initiated experience, teachers are not passive, nor
are children entirely in control—although this ideal is not always realized
in practice. For example, classroom observational research reveals that
teachers tend to spend little time with children during free play (Seo and
Ginsburg, 2004), or they focus their interactions on behavior management
rather than on helping children learn (Dickinson and Tabors, 2001; Kontos,
1999).
Instruction and Intentional Teaching
In early childhood education, the term instruction is most often used to
mean “direct instruction,” implying that teachers are entirely in control and
children are passive recipients of information. The term is also used pejo-
ratively to refer to drill and practice on isolated skills. Direct instruction is
more accurately defined as situations in which teachers give information or
present mathematics content directly to children. The National Mathemat-
ics Advisory Panel (2008) uses the term explicit instruction to refer to the
many ways that teachers can intentionally structure children’s experiences
so that they support learning in mathematics.
Throughout the day and across various contexts—whole group, small
group, centers, play, and routines—teachers need to be active and draw on
a repertoire of effective teaching strategies. This skill in adapting teaching
to the content, type of learning experience, and individual child with a
clear learning target as a goal is called intentional teaching (Epstein, 2007;

OCR for page 225

STANDARDS, CURRICULUM, INSTRUCTION, AND ASSESSMENT 227
National Association for the Education of Young Children, 1997). To be
effective, intentional teaching requires that teachers use formative assess-
ment to determine where children are in relation to the learning goal and
to provide the right kind and amount of support for them to continue to
make progress. Intentional teaching is useful to get beyond the dichoto-
mies that arise when teaching is characterized as either teacher-directed or
child-initiated.
Integrated and Focused Curriculum
Early childhood curriculum is often integrated across content domains
or subject matter disciplines. Integration is the blending together of two
or more content areas in one activity or learning experience (Schickedanz,
2008). The purpose of an integrated curriculum is to make content mean-
ingful and accessible to young children. Integration also enables more
content to be covered during the limited school day.
Integration typically occurs in two ways. One approach is to add a
mathematics content goal to a storybook reading. In this situation, lan-
guage and literacy goals related to storybook reading are primary, and
mathematics learning is secondary. Another way of integrating curriculum
is to use a broad topic of study, a theme (such as animals or plants), or a
project of interest to children through which mathematics content goals
are addressed. Projects are extended investigations into a topic that intel-
lectually engages and interests children, such as how to create a garden
or build a house (Katz and Chard, 1989). In both of these approaches to
integration, mathematics learning is a secondary objective, rather than the
primary focus of attention. In this report, we use both integrated learning
experience and secondary focus on mathematics (which some studies have
referred to as embedded mathematics) to reflect the teaching/exposure to
mathematics content as an ancillary activity.
By contrast, focused curriculum or primary focus on mathematics
refers to experiences in which mathematics is the major learning goal. A
focused mathematics curriculum should also be meaningful and connect to
children’s interests and prior knowledge. In this report, we use the terms,
“primary focus on mathematics” and “focused mathematics time” to refer
to dedicated time for a learning experience with mathematics as the primary
goal.
STANDARDS FOR CHILDREN’S MATHEMATICS LEARNING
State standards for students’ learning have had an increasingly impor-
tant role in education over at least the past decade, particularly in K-12
education. More recently, standards have begun to play a role in early

OCR for page 225

228 MATHEMATICS LEARNING IN EARLY CHILDHOOD
childhood education as well. Standards have great potential for shaping
instruction, curricula, and assessment; however, the impact of standards
on learning depends heavily on the content and specific learning goals laid
out in them.
The number of states with published early learning standards has
grown over the past eight years from 27 in 2002 to 49 as of 2008. To
inform their early learning standards in mathematics, states have used a va-
riety of National Council of Teachers of Mathematics (NCTM) resources,
including Principles and Standards for School Mathematics (2000) (14
states) and Early Childhood Mathematics: Promoting Good Beginnings,
issued by NCTM and National Association for the Education of Young
Children (NAEYC). Engaging Young Children in Mathematics (2004) is
also a widely recognized guide for state early learning standards.
Curriculum Focal Points (National Council of Teachers of Mathemat-
ics, 2006), the most recent set of guidelines provided by NCTM, was
developed after most states had already established their standards. The
Curriculum Focal Points provides guidance about the most significant math-
ematical concepts and skills (i.e., number and operations, geometry and
measurement) that should be addressed during children’s early education.
Curriculum Focal Points also has a clear emphasis on the PSSM process
standards, which are essential for meaningful and substantive mathematics
learning. The process strands of communication, reasoning, representation,
connections, and particularly problem solving allow children to understand
their mathematics learning as a coherent and connected body of knowledge
(National Council of Teachers of Mathematics, 2006). Curriculum Focal
Points does not, however, provide the kind of in-depth coverage of what
children should know and can do that this report does.
In order to gain a more systematic understanding of the content of
states’ mathematics standards, the committee commissioned two content
analyses of current standards for young children: one at the prekindergarten
level (here termed “early learning standards”) and one at the kindergarten
level (Reys, Chval, and Switzer, 2008; Scott-Little, 2008).
Early Learning Standards
Many states developed early learning standards to improve classroom
instruction and professional development; they also serve as a component
of accountability systems. The age levels addressed in the standards docu-
ments vary across states. In 17 states the standards targeted children ages 3
to 5, 12 states targeted 3- and 4-year-olds, and 11 states targeted children
finishing prekindergarten or starting kindergarten.
State-funded prekindergarten programs are the most common target
audience for the early learning standards (42 states), which are usually
required to implement the standards (39 states) (Scott-Little et al., 2007).

OCR for page 225

STANDARDS, CURRICULUM, INSTRUCTION, AND ASSESSMENT 229
Currently, 17 states have developed monitoring systems to ensure that stan-
dards are being implemented, and 4 others are in the process of developing
such a system. States also report that they intend for the early learning
standards to be used in child care (39 states), Head Start (38 states), the
Individuals with Disabilities Education Act (26 states), and Even Start (27
states) programs, although the use of the standards in these programs is
typically voluntary.
For the early learning standards it was possible to evaluate how much
emphasis each state has given to mathematics across all of the standards
as a whole. On average, states devoted 15 percent of the total number of
early learning standards to mathematics, although there was wide variation
across states (from a low in New Mexico of only 4 percent to a high in
Colorado of 54 percent).
In the content analysis of the mathematics early learning standards
(Scott-Little, 2008), each standard was first coded into 1 of the 10 math-
ematics content and process areas in the PSSM. These categories include the
three content areas emphasized in this report and in the Curriculum Focal
Points—number and operations and geometry and measurement. After
the mathematics standards items from a state’s document were coded, the
total number of items in each area was summed. Because the total number
of items varied from state to state, the total for each area was divided by
the total number of mathematics items to produce a percentage that was
comparable across documents. In effect, the percentage represents the rela-
tive emphasis given to each area of mathematics. Table 7-1 presents these
results.
TABLE 7-1 Percentages of States Early Learning Mathematics Standards
That Fall in Each of the PSSM Areas
PSSM Area Mean SD Min. Max.
Content
Numbers and operations 32.3 9.8 9 50
Algebra 19.0 8.8 0 50
Geometry 17.8 7.9 0 44
Measurement 15.8 8.7 0 50
Data analysis 5.3 5.8 0 17
Process
Problem solving 3.7 6.2 0 25
Communication 1.4 3.6 0 4
Reasoning 1.3 3.1 0 13
Representation 0.6 1.8 0 11
Connections 0.4 1.3 0 7
Other 2.5 3.4 0 15
NOTE: PSSM = Principles and Standards for School Mathematics, n = 49 states.
SOURCE: Scott-Little (2008).

OCR for page 225

230 MATHEMATICS LEARNING IN EARLY CHILDHOOD
These data show a focus on the area of number and operations; on av-
erage, states devoted 32 percent of their mathematics standards to this area,
and all states had at least some standards in this area. Geometry received
less emphasis than number in the early learning standards (18 percent), and
measurement accounted for 16 percent of standards in mathematics. In ad-
dition, there was much greater overall emphasis on the content standards
areas than on the process standards areas (see Table 7-1).
A more detailed analysis was conducted of all standards in each of the
three content areas that are the focus of this report (as well as the NCTM
Curriculum Focal Points): (1) number and operations, (2) geometry, and (3)
measurement. Table 7-2 provides the details of the results for each area.
In the area of number and operations, states have most often addressed
number sense (an average of 24 percent of the number/operations stan-
dards); however, there is considerable variation among states—from 11
states with no standards in this area, to 4 states for which number sense
accounted for 100 percent of their number and operations standards. Three
other core areas of number were relatively frequent—the number word list,
1-to-1 counting correspondences, and written number symbols—and each
is addressed by 11 to 14 percent of the standards. Cardinality and the three
basic kinds of addition/subtraction situations received minimal attention.
In the geometry early learning standards, there was an emphasis on
children’s knowledge of properties of shapes (40 percent) and spatial rea-
soning (25 percent) (e.g., knowledge related to spatial location and direc-
tion), although, again, there was considerable variability among states.
Some important aspects of geometry for young children receive little atten-
tion, including transformation and visualization of shapes.
In the measurement standards, areas most often emphasized are mea-
surement of objects (34 percent of the standards), comparing objects (27
percent), and understanding of concepts related to time (27 percent). Again
there was variability—for example, 2 states had no measurement standards
at all, and 15 states had no standard related to comparisons of objects and
the concept of time (see Table 7-2).
Kindergarten Standards
The committee also commissioned an analysis of the 10 states with the
largest student populations that publish kindergarten-specific mathematics
standards: California, Florida, Georgia, Michigan, New Jersey, New York,
North Carolina, Ohio, Texas, and Virginia (Reys, Chval, and Switzer,
2008). These states were selected for analysis because they represent ap-
proximately 50 percent of the U.S. school population and therefore influ-
ence the intended curriculum for a substantial population of students. Given
their size, these 10 states are also likely to influence textbook development
and materials that are produced by commercial curriculum publishers.

OCR for page 225

STANDARDS, CURRICULUM, INSTRUCTION, AND ASSESSMENT 231
TABLE 7-2 Classification of State Mathematics Early Learning Standards
by Content Area and Focal Area
Content/Focal Area Mean% SD Minimum% Maximum%
Number and Operations
Number sense 24.1 26.6 0 100
1-to-1 correspondence 13.8 10.3 0 43
Number word list 13.1 10.2 0 50
Written number symbols 11.4 11.6 0 40
Perceptional comparisons 9.6 10.3 0 50
Combining/taking apart 7.3 9.6 0 33
Cardinality 5.4 7.2 0 25
Estimation 4.7 8.4 0 33
Change 3.9 7.9 0 33
Ordinal numbers 3.8 6.6 0 25
Counting comparisons 2.2 9.0 0 60
Additive comparisons 0.6 2.1 0 11
Place value 0.2 1.6 0 11
Geometry
Properties of shapes 39.6 17.9 0 100
Spatial reasoning 25.3 23.2 0 100
Analyzing and comparing shapes 13.3 15.8 0 67
Location and directionality 12.2 15.5 0 50
Composing/decomposing shapes 6.6 10.7 0 40
Symmetry 1.6 5.3 0 25
Transformation of shapes 1.5 6.0 0 33
Visualization of shapes 0.0 0.0 0 0
Measurement
Measurement of objects 33.9 25.3 0 100
Comparing objects 27.1 26.0 0 100
Time 26.9 23.3 0 100
Measurable attributes 12.7 16.0 0 50
Composing objects 0.0 0.0 0 0
NOTE: For number and operations n = 49 states; for geometry n = 48 as one state had no
geometry standards; for measurement n = 47 as two states had no measurement standards.
Percentages represent the number of a state’s standards in a focal area divided by the total
number of standards in the content area (content areas are number and operation, geometry,
and measurement).
SOURCE: Scott-Little (2008).
The kindergarten learning standards for each state were coded into the
five PSSM mathematical content areas or strands: (1) number and opera
tion, (2) geometry, (3) measurement, (4) algebra, and (5) data analysis/
probability (Clements, 2004; National Council of Teachers of Mathematics,
2000). Results allow an examination of which of these mathematical strands
are emphasized across and within states. Relative emphasis devoted to each
strand was calculated as a percentage of standards in that strand within the
total number of mathematics standards.

OCR for page 225

232 MATHEMATICS LEARNING IN EARLY CHILDHOOD
There was considerable variability across the 10 states studied. The
total number of mathematics standards varied widely, from 11 in Florida
to 74 in Virginia (average number of standards was 29). Of the “total set”
of 103 specific standards identified in the analysis, only 1 standard was
common to all 10 states (extending a pattern) and another 3 standards were
common to 9 states. Only 20 percent of the 103 standards were common
to 6 or more states.
In kindergarten (as with the early learning standards), the greatest
emphasis across all the mathematics standards is placed on number and
operations—40 percent of a state’s mathematics standards on average (with
a range from a low of 27 percent to a high of 56 percent among states).
Geometry and measurement each receive less emphasis than number (19
and 21 percent, respectively), although, again, variability is high (from 9
to 45 percent across states for geometry and from 11 to 28 percent for
measurement).
In the number strand, the heaviest emphasis is placed on counting.
Areas of emphasis (meaning at least 6 of the 10 states had standards in this
focal area) include counting objects, reading and writing numerals, identify-
ing ordinal numbers, comparing the relative size of groups of objects, and
modeling and solving problems using addition and subtraction. Consistent
with the theme of state variability, however, no single number/operations
standard appeared in all 10 state documents.
In both geometry and measurement, few learning standards were com-
mon across the states; only 6 topics (of 43 total across geometry and
measurement) appeared in the documents of 6 or more states. In geometry,
these topics were identifying and naming two-dimensional (2-D) shapes and
knowing the relative position of objects. In measurement, the most common
topics were comparing the weight of objects; sort, compare, and/or order
objects; compare length of objects; and know days of the week.
Taken together, the three focal areas emphasized by the committee
(number, geometry, and measurement) account for 80 percent of the content
of the kindergarten standards across the 10 states. However, many states
also include some specific standards that would not be considered core or
primary mathematics by the committee—such as knowing the names of
the months, parts of the day, seasons, ordering events by time, comparing
time, understanding the concept of time, identifying the time of everyday
events to the nearest hour, and measurement of weight, capacity, and
temperature.
Process strands were addressed quite differently by different states,
so no systematic analyses could be done. Specifically, three states make
no mention of process standards at the kindergarten level (Florida, North
Carolina, and Virginia), and three other states include identification of

OCR for page 225

STANDARDS, CURRICULUM, INSTRUCTION, AND ASSESSMENT 233
specific standards by process strand (Georgia, New York, and Texas). No-
tably, although these strands are specified for kindergarten, these process
standards are very similar, if not identical, at each grade, K-8. Two states
(Arizona and Massachusetts) provide a general description of process stan-
dards in the introductory material of their K-6 or K-8 document. These
descriptions emphasize the importance of the process strands outlined
in the PSSM (National Council of Teachers of Mathematics, 2000). The
California and Ohio documents include process standards organized within
one strand (“Mathematical Reasoning” in the California document and
“Mathematical Process Standard” in the Ohio document) for each grade.
The California document lists process standards that are common across
kindergarten and Grade 1. Likewise, the Ohio document includes a list of
process standards that are common to Grades K-2.
Summary
A total of 49 states have early learning standards in mathematics; on
average, states devote the greatest emphasis to the area of number (32
percent of the standards on average). Specific emphasis within the areas
of number, geometry, and measurement showed considerable state-to-state
variation. According to our analysis for the 10 largest states, the greatest
emphasis in kindergarten is also placed on number (40 percent of the stan-
dards on average). However, there is also considerable variation in content
of the specific standards across all of the areas. In fact, of the 103 total stan-
dards across the 10 states, 47 are unique to just 1 or 2 state documents.
A pattern of wide variation across states in emphasis given to math-
ematics as a whole and relative emphasis given to various topics in math-
ematics emerges from these analyses of standards. Thus, while some
common topics could be identified, when taken as a whole, the state stan-
dards do not communicate a clear consensus about the most important
mathematical ideas for young children to learn.
THE CLASSROOM CONTEXT
We begin with a description of the classroom context in which math-
ematics instruction takes place. We then focus specifically on what is known
about mathematics teaching and learning practices in preschool and kinder-
garten classrooms—when it occurs, how often, and in what contexts.
Results from several large studies of prekindergarten (pre-K) and kin-
dergarten classrooms paint a detailed picture of how young children spend
their time in these settings and the quality of their learning experiences.
We draw particularly on two studies conducted by the National Center for

OCR for page 225

234 MATHEMATICS LEARNING IN EARLY CHILDHOOD
Early Development and Learning (NCEDL) and on the Early Childhood
Longitudinal Study-Kindergarten (ECLS-K).
The NCEDL conducted two major studies of state-funded pre-K and
kindergarten classrooms: the six-state Multi-State Study of Preschool (MS)
and the five-state State-wide Early Education Programs (SWEEP) Study
(Early et al., 2005). While neither of these studies included a nationally
representative sample, as of 2001-2002, almost 80 percent of all children
in the United States who were participating in state-funded prekindergarten
were in one of these 11 states (Early et al., 2005). When combined, these
two studies provide observational data on over 700 preschool and 800 kin-
dergarten classrooms across the United States and offer a unique window
on children’s classroom experiences.
It is important to note that classrooms were included in these studies
only if they received state pre-K funding, so the results are not representa-
tive of the larger segment of schooling opportunities for 4-year-olds. State-
funded pre-K classrooms are a small subset of early childhood classrooms,
generally with greater funding and tighter regulation and monitoring, than
the larger set of early childhood classrooms. The studies must be interpreted
in this context.
In both studies, classrooms were observed using a variety of measures
to capture the content and quality of learning opportunities and materials
afforded to children, including the Early Childhood Environment Rating
Scale (ECERS-R; Harms, Clifford, and Cryer, 1998), Classroom Assessment
Scoring System (CLASS; Pianta, La Paro, and Hamre, 2008), and Emerging
Academics’ Snapshot (Ritchie et al., 2001).
How Children Spend Their Time in Prekindergarten and Kindergarten
Results from both of the NCEDL studies (the MS and the SWEEP) in-
dicate that children in state pre-K programs spend a great deal of time not
engaged in any type of instructional activity. Using the Emerging Academics
Snapshot, both NCEDL studies recorded the proportion of time spent in all
major areas of curriculum, assessing the amount of time students spent in
Material in this section is based on a paper prepared for the committee by Hamre et al.
(2008), which included a review of the published literature related to these studies as well as
some reanalysis of the data conducted for this report.
During pre-K, observation days lasted from the beginning of class until the end of class in
part-day rooms and until nap in full-day rooms. In pre-K, observers stayed with the children
all day, including lunch, outside time, and special activities. In kindergarten, the observations
were slightly different because the days were generally longer. Snapshot and CLASS observa-
tions lasted the entire day, but no observations were made during lunch, recess, or nap. For this
reason, pre-K and kindergarten Snapshot percentages of time spent are discussed separately.
More information about these studies can be found on the NCEDL website (http://www.fpg.
unc.edu/~ncedl/) and in several published articles (Clifford et al., 2005; Howes et al., 2008;
Pianta et al., 2005).

OCR for page 225

STANDARDS, CURRICULUM, INSTRUCTION, AND ASSESSMENT 235
reading, oral language and phonemic awareness activities, writing, math-
ematics, science, social studies, aesthetics, and fine and gross motor activi-
ties. Each area was broadly defined so that time spent in dramatic play,
block areas, coloring with markers, talking with teachers about things out-
side school, and singing songs were included in one of these areas. During
the preschool day, the average student spent 44 percent of the time engaged
in none of these curriculum activities. Data from kindergarten classrooms
revealed that the average student was not engaged in any instructional ac-
tivity in 39 percent of the observed intervals.
What were children doing during this noninstructional time? In pre-
school classrooms, much of the time (22 percent) was spent engaged in
routine activities, such as transitioning, waiting in line, or washing hands.
Some time (11 percent) was also spent in meals and snacks (Early et al.,
2005). Importantly, routine, meal, and snack times could be included as
instructional time if, for example, teachers and children engaged in a con-
versation, sang a song, or played a number game during a transition. But
few preschool or kindergarten teachers appeared to take advantage of the
learning opportunities that arose during transitional periods or employed
strategies for getting the most out of this time in the classroom.
Which types of instructional opportunities are young children exposed
to most often? Of all content areas, young children spent more time in lan-
guage and literacy activities than any other—14 percent of the observed day
in preschool and 28 percent of the observed day in kindergarten (La Paro
et al., 2008). None of the other major areas occurred much more than 10
percent, on average, in any given day. Pre-K children in the NCEDL studies
were exposed to mathematics content in only 6 percent of the observations,
and kindergarten children were exposed to mathematics an average of 11
percent of the day.
Another relevant question concerns the use of various instructional
contexts, such as free choice/center time or whole-group instruction. Data
from the NCEDL studies suggest there is a major shift in the preferred in-
structional context from preschool to kindergarten. Children in preschool
classrooms spent an average of 33 percent of the school day in free choice
or center time, compared with only 6 percent of the day in kindergarten
classrooms. Once in kindergarten, both whole-group instruction and indi-
vidual time, in which children work independently at desks, becomes much
more frequent. Across kindergarten and preschool, teachers rarely made use
of small-group instruction.
Quality of Teacher-Child Interactions in Preschool and Kindergarten
The NCEDL data also provide a window into the quality of teacher-
child interactions and instruction to which young children are exposed,
using the CLASS Framework for Children’s Learning Opportunities in

OCR for page 225

278 MATHEMATICS LEARNING IN EARLY CHILDHOOD
Clements, D.H., and Battista, M.T. (1994). Computer environments for learning geometry.
Journal of Educational Computing Research, 10(2), 173-197.
Clements, P., and Lewis, A.E. (2009). The Effectiveness of the Big Math for Little Kids
Curriculum: Does It Make a Difference? Paper presented at the American Educational
Research Association Annual Meeting, April, San Diego, CA.
Clements, D.H., and McMillen, S. (1996). Rethinking “concrete” manipulatives. Teaching
Children Mathematics, 2(5), 270-279.
Clements, D.H., and Sarama, J. (2003). Young children and technology: What does the re-
search say? Young Children, 58(6), 34-40.
Clements, D.H., and Sarama, J. (2004). Building blocks for early childhood mathematics.
Early Childhood Research Quarterly, 19, 181-189. Available: http://www.gse.buffalo.
edu/RP/PDFs/BB_ECRQ.pdf [accessed July 2008].
Clements, D.H., and Sarama, J. (2005). Young children and technology: What’s appropriate?
In W. Masalski and P.C. Elliott (Eds.), Technology-supported Mathematics Learning
Environments: 67th Yearbook (pp. 51-73). Reston, VA: National Council of Teachers
of Mathematics.
Clements, D.H., and Sarama, J. (2007a). Early childhood mathematics learning. In F.K. Lester,
Jr. (Ed.), Second Handbook of Research on Mathematics Teaching and Learning (pp.
461-555). New York: Information Age.
Clements, D.H., and Sarama, J. (2007b). Effects of a preschool mathematics curriculum:
Summative research on the Building Blocks project. Journal of Research in Mathematics
Education, 38(2), 136-163.
Clements, D.H., and Sarama, J. (2008a). Experimental evaluation of the effects of a research-
based preschool mathematics curriculum. American Educational Research Journal, 45,
443‑494.
Clements, D.H., and Sarama, J. (2008b). Mathematics and technology: Supporting learning
for students and teachers. In O.N. Saracho and B. Spodek (Eds.), Contemporary Perspec-
tives on Science and Technology in Early Childhood Education (pp. 127-147). Charlotte,
NC: Information Age.
Clifford, R.M., Barbarin, O., Chang, F., Early, D., Bryant, D., Howes, C., Burchinal, M. and
Pianta, R. (2005). What is prekindergarten? Characteristics of public prekindergarten
programs. Applied Developmental Science, 9(3), 126-143.
Cobb, P., Wood, T., Yackel, E., Nicholls, J., Wheatley, G., Trigatti, B., and Perlwitz, M.
(1991). Assessment of a problem-centered second grade mathematics project. Journal
for Research in Mathematics, 22, 3-29.
Cohen, D.H., Stern, V., and Balaban, N. (1997). Observing and Recording the Behavior of
Young Children (4th ed.). New York: Teachers College Press.
Connor, C.M., Son, S., and Hindman, A.H. (2005). Teacher qualifications, classroom prac-
tices, family characteristics, and preschool experience: Complex effects on first graders’
vocabulary and early reading outcomes. Journal of School Psychology, 43(4), 343-375.
Copley, J.V., Jones, C., and Dighe, J. (2007). Math: The Creative Curriculum® Approach.
Washington, DC: Teaching Strategies.
Copple, C., and Bredekamp, S. (2006). Basics of Developmentally Appropriate Practice: An
Introduction for Teachers of Children 3 to 6. Washington, DC: National Association for
the Education of Young Children.
Copple, C., and Bredekamp, S. (2009). Developmentally Appropriate Practice in Early Child-
hood Programs Serving Children from Birth Through Age 8. Washington, DC: National
Association for the Education of Young Children.
Davis, E.A., and Miyake, N. (2004). Explorations of scaffolding in complex classroom sys-
tems. Journal of the Learning Sciences, 13(3), 265-272.

OCR for page 225

STANDARDS, CURRICULUM, INSTRUCTION, AND ASSESSMENT 279
Denham, S.A., and Weissberg, R.P. (2004). Social-emotional learning in early childhood: What
we know and where to go from here. In E. Chesebrough, P. King, T.P. Gullotta, and M.
Bloom (Eds.), A Blueprint for the Promotion of Prosocial Behavior in Early Childhood
(pp. 13-50). New York: Kluwer Academic.
Diamond, A., Barnett, S., Thomas, J., and Munro, S. (2007). Preschool program improves
cognitive control. Science, 318, 1387-1388.
Dickinson, D., and Smith, M.W. (1993). Long-term effects of preschool teachers’ book read-
ings on low-income children’s vocabulary and story comprehension. Reading Research
Quarterly, 29(2), 104-122.
Dickinson, D., and Tabors, P. (2001). Beginning Literacy with Language: Young Children
Learning at Home and School. Baltimore, MD: Paul H. Brookes.
diSessa, A.A. (2007). An interactional analysis of clinical interviewing. Cognition and Instruc-
tion, 25(4), 523-565.
Dodge, D.T., Colker, L., and Heroman, C. (2002). The Creative Curriculum® for Preschool
(4th ed.). Washington, DC: Teaching Strategies.
Early, D.M., Barbarin, O., Bryant, D., Burchinal, M., Chang, F., Clifford, R., et al. (2005). Pre-
kindergarten in Eleven States: NCEDL’s Multi-state Study of Pre-Kindergarten and Study
of State-wide Early Education Programs (SWEEP). Chapel Hill: University of North
Carolina. Available: http://www.fpg.unc.edu/NCEDL/pdfs/SWEEP_MS_summary_final.
pdf [accessed August 2008].
Edwards, C., Gandini, L., and Forman, G. (Eds.) (1998). The Hundred Languages of Children:
The Reggio Emilia Approach—Advanced Reflections (2nd ed.) Greenwich, CT: Ablex.
Emmer, E.T., and Stough, L. (2001). Classroom management: A critical part of educational
psychology, with implications for teacher education. Educational Psychologist, 36(2),
103-112.
Epstein, A.S. (2007). The Intentional Teacher: Choosing the Best Strategies for Young Chil-
dren’s Learning. Washington, DC: National Association for the Education of Young
Children.
Epstein, A.S., Schweinhart, L.J., and McAdoo, L. (1996). Models of Early Childhood Educa-
tion. Ypsilanti, MI: High/Scope Educational Research Foundation.
Farran, D.C., Lipsey, M., Watson, B., and Hurley, S. (2007). Balance of Content Emphasis
and Child Content Engagement in an Early Reading First Program. Paper presented at
the American Educational Research Association.
Fennema, E., Carpenter, T., Franke, M., Levi, L., Jacobs, V., and Empson, S. (1996). A longi-
tudinal study of learning to use children’s thinking in mathematics instruction. Journal
for Research in Mathematics Learning, 27(4), 403-434.
Fisch, S.M. (2008). The Role of Educational Media in Preschool Mathematics Education.
Paper commissioned by the Committee for Early Childhood Mathematics, Mathematics
Science Education Board, Center for Education, Division of Behavioral and Sciences and
Education, National Research Council, Washington, DC.
Flavell, J.H., Green, F.L., and Flavell, E.R. (1995). Young children’s knowledge about think-
ing. Monographs of the Society for Research in Child Development, 60(Serial No. 243,
No. 1).
Foegen, A., Jiban, C., and Deno, S. (2007). Progress monitoring measures in mathematics: A
review of the literature. Journal of Special Education, 41(2), 121-139.
Forman, G.E. (1982). A search for the origins of equivalence concepts through a microanaly-
sis of block play. In G.E. Forman (Ed.), Action and Thought (pp. 97‑135). New York:
Academic Press.
Frede, E., Jung, K., Barnett, W.S., Lamy, C.E., and Figueras, A. (2007). The Abbott Preschool
Program Longitudinal Effects Study (APPLES). Rutgers, NJ: National Institute for Early
Education Research.
French, L., and Song, M. (1998). Developmentally appropriate teacher-directed approaches:
Images from Korean kindergartens. Journal of Curriculum Studies, 39, 409-430.

OCR for page 225

280 MATHEMATICS LEARNING IN EARLY CHILDHOOD
Fuchs, L.S., Fuchs, D., Karns, K., Hamlett, C.L., and Katzaroff, M. (1999). Mathematics per-
formance assessment in the classroom: Effects on teacher planning and student problem
solving. American Educational Research Journal, 36(3), 609‑646.
Fujiki, M., Brinton, B., and Clarke, D. (2002). Emotion regulation in children with specific lan-
guage impairment. Language, Speech, and Hearing Services in Schools, 33, 102-111.
Fuson, K.C. (1988). Children’s Counting and Concept of Number. New York: Springer-
Verlag.
Fuson, K.C., and Murata. A. (2007). Integrating NRC principles and the NCTM process stan-
dards to form a class learning path model that individualizes within whole-class activities.
National Journal of Math Education Leadership, 19(1), 72-91.
Fuson, K.C., Smith, S.T., and Lo Cicero, A. (1997). Supporting Latino first graders’ ten-
structured thinking in urban classrooms. Journal for Research in Mathematics Education,
28, 738-760.
Fuson, K., Carroll, W.M., and Drueck, J.V. (2000). Achievement results for second and third
graders using the standards-based curriculum, everyday mathematics. Journal for Re-
search in Mathematics Education, 31(3), 277-295.
Gamel-McCormick, M., and Amsden, D. (2002). Investing in Better Outcomes: The Delaware
Early Childhood Longitudinal Study. Dover: Delaware Interagency Resource Manage-
ment Committee and the Department of Education.
Gerhardt, C. (1973). Hypersurfaces of Prescribed Mean Curvature over Obstacles, Math.
Available: http://www.math.uni-heidelberg.de/studinfo/gerhardt/dissertation-MZ133.pdf
[accessed August 2008].
Gersten, R., Chard, D., Jayanthi, M., Baker, S., Morpy, S.K., and Flojo, J.R. (in press). Teach-
ing Mathematics to Students with Learning Disabilities: A Meta-analysis of the Interven-
tion Research. Portsmouth, NH: RMC Research Corporation, Center on Instruction.
Ginsburg, H.P. (1997). Entering the Child’s Mind: The Clinical Interview in Psychological
Research and Practice. New York: Cambridge University Press.
Ginsburg, H.P. (2006). Mathematical play and playful mathematics: A guide for early educa-
tion. In D. Singer, R.M. Golinkoff, and K. Hirsh-Pasek (Eds.), Play = Learning: How
Play Motivates and Enhances Children’s Cognitive and Social-Emotional Growth (pp.
145-165). New York: Oxford University Press.
Ginsburg, H.P., and Amit, M. (2008). What is teaching mathematics to young children? A
theoretical perspective and case study. Journal of Applied Developmental Psychology,
29(4), 274-285.
Ginsburg, H.P., and Baroody, A.J. (2003). The Test of Early Mathematics Ability (3rd ed.).
Austin, TX: Pro Ed.
Ginsburg, H.P., and Russell, R.L. (1981). Social class and racial influences on early math-
ematical thinking. Monographs of the Society for Research in Child Development, 46(6,
Serial No. 193).
Ginsburg, H.P., Greenes, C., and Balfanz, R. (2003). Big Math for Little Kids. Parsippany,
NJ: Dale Seymour.
Ginsburg, H.P., Lee, J., and Boyd, J.S. (2008). Mathematics education for young children:
What it is and how to promote it. Social Policy Report Giving Child and Youth Devel-
opment Knowledge Away, 22(1). Available: http://www.srcd.org/index.php?option=com_
contentandtask=viewandid=232andItemid=1 [accessed August 2008].
Greabell, L.C. (1978). The effect of stimuli input on the acquisition of introductory geom-
etry concepts by elementary school children. School Science and Mathematics, 78(4),
320-326.
Greenberg, M.T., Weissberg, R.P., and O’Brien, M.U. (2003). Enhancing school-based pre-
vention and youth development through coordinated social, emotional, and academic
learning. American Psychologist, 58(6-7), 466-474.

OCR for page 225

STANDARDS, CURRICULUM, INSTRUCTION, AND ASSESSMENT 281
Gregory, K.M., Kim, A.S., and Whiren, A. (2003). The effect of verbal scaffolding on the
complexity of preschool children’s block constructions. In D.E. Lytle (Ed.), Play and
Educational Theory and Practice: Play and Culture Studies (pp. 117-134). Westport,
CT: Praeger.
Griffin, S. (2004). Number worlds: A research-based mathematics program for young chil-
dren. In D.H. Clements, J. Sarama, and A.-M. DiBiase (Eds.), Engaging Young Children
in Mathematics: Standards for Early Childhood Mathematics Education (pp. 325-342).
Mahwah, NJ: Erlbaum.
Griffin, S. (2007). SRA Number Worlds: A Prevention/Intervention Math Program. Assess-
ment Level A. Columbus, OH: SRA/McGraw-Hill.
Griffin, S., Case, R. and Siegler, R.S. (1994). Rightstart: Providing the central conceptual
prerequisites for first formal learning of arithmetic to students at risk for school failure.
In K. McGilly (Ed.), Classroom Lessons: Integrating Cognitive Theory and Classroom
Practice (pp. 25-40). Cambridge, MA: MIT Press.
Griffin, S., Case, R., and Capodilupo, A. (1995). Teaching for understanding: The importance
of the central conceptual structures in the elementary mathematics curriculum. In A.
McKeough, J. Lupart, and A. Marini (Eds.), Teaching for Transfer: Fostering Generaliza-
tion in Learning (pp. 121-151). Mahwah, NJ: Erlbaum.
Grupe, L.A., and Bray, N.W. (1999). What Role Do Manipulatives Play in Kindergartners’
Accuracy and Strategy Use When Solving Simple Addition Problems? Albuquerque, NM:
Society for Research in Child Development.
Guarino, C.M., Hamilton, L.S., Lockwood, J.R., and Rathbun, A.H. (2006). Teacher Qualifi-
cations, Instructional Practices, and Reading and Mathematics Gains of Kindergartners.
NCES# 2006-031. Washington, DC: National Center for Education Statistics, U.S.
Department of Education.
Hamre, B.K., and Pianta, R.C. (2001). Early teacher-child relationships and the trajectory of
children’s school outcomes through eighth grade. Child Development, 72(2), 625-638.
Hamre, B.K., and Pianta, R.C. (2005). Can instructional and emotional support in the first
grade classroom make a difference for children at risk of school failure? Child Develop-
ment, 76(5), 949-967.
Hamre, B.K., and Pianta, R.C. (2007). Learning opportunities in preschool and early elemen-
tary classrooms. In R.C. Pianta, M.J. Cox, and K. Snow (Eds.), School Readiness and the
Transition to School (pp. 49-84). Baltimore, MD: Paul H. Brookes.
Hamre, B.K., Downer, J.T., Kilday, C.R., and McGuire, P. (2008a). Effective Teaching Prac-
tices for Early Childhood Mathematics. Paper commissioned by the Committee for Early
Childhood Mathematics, Mathematics Science Education Board, Center for Education,
Division of Behavioral and Sciences and Education, National Research Council, Wash-
ington, DC.
Hamre, B.K., Mashburn, A.J., Pianta, R.C., and Downer, J. (2008b). Validation of a 3-Factor
Model for Classroom Quality Across Preschool to Fifth Grade. Manuscript submitted
for publication.
Hannula, M.M. (2005). Spontaneous Focusing on Numerosity in the Development of Early
Mathematical Skills. Turku, Finland: University of Turku.
Harms, T., Clifford, R.M., and Cryer, C. (1998) Early Childhood Environment Rating Scale-
Revised. New York: Teachers College Press.
Hart, B., and Risley, T.R. (1995). Meaningful Differences in the Everyday Experience of Young
American Children. Baltimore, MD: Paul H. Brookes.
Hart, B., and Risley, T.R. (1999). The Social World of Children: Learning to Talk. Baltimore,
MD: Paul H. Brookes.
Head Start Bureau. (1998). Head Start Program Performance Standards. Washington, DC:
Administration for Children and Families.

OCR for page 225

282 MATHEMATICS LEARNING IN EARLY CHILDHOOD
Helm, J.H., and Katz, L. (2000). Young Investigators: The Project Approach in the Early
Years. New York: Teachers College Press.
Heritage, M., Kim, J., and Vendlinski, T. (2008). From Evidence to Action: A Seamless
Process in Formative Assessment? Presentation at the American Educational Research
Association Annual Meeting, March 24-28, New York. Available: http://www.cse.ucla.
edu/products/overheads/AERA2008/heritage_assessment.ppt [accessed July 2008].
Hirsch, E.S. (1996). The Block Book (3rd ed.). Washington, DC: National Association for the
Education of Young Children.
Hohmann, M., and Weikart, D. (2002). Educating Young Children: Active Learning Practices
for Preschool and Child Care Programs. Ypsilanti, MI: High/Scope Press.
Holton, D., Ahmed, A., Williams, H., and Hill, C. (2001). On the importance of mathemati-
cal play. International Journal of Mathematical Education in Science and Technology,
32, 401-415.
Hong, H. (1996). Effects of mathematics learning through children’s literature on math
achievement and dispositional outcomes. Early Childhood Research Quarterly, 11,
477-494.
Howes, C., Burchinal, M., Pianta, R., Bryant, D., Early, D., Clifford, R., and Barbarin, O.
(2008). Ready to learn? Children’s pre-academic achievement in pre-kindergarten pro-
grams. Early Childhood Research Quarterly, 23(1), 27-50.
Hughes, M. (1981). Can preschool children add and subtract? Educational Psychology, 1,
207-219.
Hyson, M. (2008). Preparing Teachers to Promote Young Children’s Mathematical Com-
petence. Paper commissioned by the Committee for Early Childhood Mathematics,
Mathematics Science Education Board, Center for Education, Division of Behavioral and
Sciences and Education, National Research Council, Washington, DC.
Johnson-Gentile, K., Clements, D.H., and Battista, M.T. (1994). The effects of computer and
noncomputer environments on students’ conceptualizations of geometric motions. Jour-
nal of Educational Computing Research, 11(2), 121-140.
Jones, E., and Nimmo, J. (1994). Emergent Curriculum. Washington, DC: National Associa-
tion for the Education of Young Children.
Jordan, N.C., Huttenlocher, J., and Levine, S.C. (1992). Differential calculation abilities in
young children from middle- and low-income families. Developmental Psychology, 28,
644-653.
Jordan, N.C., Hanich, L.B., and Uberti, H.Z. (2003). Mathematical thinking and learning
difficulties. In A.J. Baroody and A. Dowker (Eds.), The Development of Arithmetic
Concepts and Skills: Constructing Adaptive Expertise (pp. 359-383). Mahwah, NJ:
Erlbaum.
Kamii, C., Miyakawa, Y., and Kato, Y. (2004). The development of logico-mathematical
knowledge in a block-building activity at ages 1-4. Journal of Research in Childhood
Education, 19, 13-26.
Karweit, N. and Wasik, B. (1996). The effects of story reading programs on literacy and
language development of disadvantaged preschoolers. Journal of Education for Students
Placed At-Risk, 4, 319-348.
Katz, L.G., and Chard, S.C. (1989). Engaging Children’s Minds: The Project Approach.
Norwood, NJ: Ablex.
Kersh, J., Casey, B., and Young, J.M. (2008). Research on spatial skills and block building in
girls and boys: The relationship to later mathematics learning. In B. Spodek and O.N.
Saracho (Eds.), Mathematics, Science, and Technology in Early Childhood Education
(pp. 233-252). Charlotte, NC: Information Age.
Klein, A., and Starkey, P. (2004). Fostering preschool children’s mathematical knowledge:
Findings from the Berkeley math readiness project. In D.H. Clements, J. Sarama, and
A.-M. DiBiase (Eds.), Engaging Young Children in Mathematics: Standards for Early
Childhood Mathematics Education (pp. 343-360). Mahwah, NJ: Erlbaum.

OCR for page 225

STANDARDS, CURRICULUM, INSTRUCTION, AND ASSESSMENT 283
Klein, A., Starkey, P., and Wakeley, A. (1999). Enhancing Pre-Kindergarten Children’s Readi-
ness for School Mathematics. Paper presented at the American Educational Research
Association. Montreal, Canada.
Klein, A., Starkey, P., and Ramirez, A.B. (2002). Pre-K Mathematics Curriculum. Glenview,
IL: Scott Foresman.
Klibanoff, R.S., Levine, S.C., Huttenlocher, J., Vasilyeva, M., and Hedges, L.V. (2006). Pre-
school children’s mathematical knowledge: The effect of teacher ‘math talk’. Develop-
mental Psychology, 42(1), 59-69.
Kontos, S. (1999). Preschool teachers’ talk, roles, and activity settings during free play. Early
Childhood Research Quarterly, 14(3), 363-382.
Kuhn, D. (2000). Metacognitive development. Current Directions in Psychological Science,
9(5), 178-181.
Kuhn, D. (2005). Education for Thinking. Cambridge, MA: Harvard University Press.
Kühne, C., van den Heuvel-Panhulzen, M., and Ensor, P. (2005). Learning and teaching early
number: Teachers’ perceptions. In H.L. Chick and J.L. Vincent (Eds.), Proceedings of the
29th Conference of the International Group for the Psychology of Mathematics Educa-
tion (vol. 3, pp. 217-224). Melbourne: PME. Available: http://www.emis.de/proceedings/
PME29/PME29RRPapers/PME29Vol3KuhneEtAl.pdf [accessed July 2008].
La Paro, K.M., Hamre, B.K., LoCasale, J., Pianta, R.C., et al. (2008). Pre-K and Kindergar-
ten Classrooms: Observational Evidence for the Need to Increase Quality of Children’s
Learning Opportunities in Early Education Classrooms. Manuscript submitted for
publication.
Lee, J.S., and Ginsburg, H.P. (2007). Preschool teachers’ beliefs about appropriate early
literacy and mathematics education for low- and middle-socioeconomic status children.
Early Education and Development, 18(1), 111-143.
Limon, M. (2001). On the cognitive conﬂict as an instructional strategy for conceptual change:
A critical appraisal. Learning and Instruction, 11(4-5), 357-380.
Lonigan, C.J., and Whitehurst, G.J. (1998). Relative efficacy of parent and teacher involve-
ment in a shared-reading intervention for preschool children from low-income back-
grounds. Early Childhood Research Quarterly, 13(2), 263-290.
MacDonald, M. (2007). Toward formative assessment: The use of pedagogical documentation
in early elementary classrooms. Early Childhood Research Quarterly, 22, 232-242.
Magnuson, K.A., Meyers, M.K., Rathbun, A., and West, J. (2004). Inequality in preschool
education and school readiness. American Educational Research Journal, 41, 115-157.
Martin, T., Lukong, A., and Reaves, R. (2007). The role of manipulatives in arithmetic and
geometry tasks. Journal of Education and Human Development, 1, 1. Available: http://
www.scientificjournals.org/journals2007/articles/1073.htm [accessed August 2008].
Mashburn, A.J., Pianta, R., Hamre, B.K., Downer, J.T., Barbarin, O., Bryant, D., Burchinal,
M., Clifford, R., Early, D., and Howes, C. (2008). Measures of classroom quality in pre-
kindergarten and children’s development of academic, language, and social skills. Child
Development, 79(3), 732-749.
Mayer, R.E. (2002). Rote versus meaningful learning. Theory into Practice, 41, 226-233.
Morrow, L.M. (1988). Young children’s responses to one-to-one reading in school settings.
Reading Research Quarterly, 23, 89-107.
National Association for the Education of Young Children. (1997). Developmentally Appro-
priate Practice in Early Childhood Programs. S. Bredekamp and C. Copple (Eds.). Wash-
ington, DC: Author. Available: http://www.naeyc.org/about/positions/pdf/PSDAP98.pdf
[accessed August 2008].
National Association for the Education of Young Children. (2007). Developmentally Ap-
propriate Practice in Early Childhood Programs Serving Children from Birth Through
Age 8. Draft position statement. Available: http://www.naeyc.org/about/positions/pdf/
draftdap0208.pdf [accessed August 2008].

OCR for page 225

284 MATHEMATICS LEARNING IN EARLY CHILDHOOD
National Association for the Education of Young Children and National Council of Teachers
of Mathematics. (2002). Early Childhood Mathematics: Promoting Good Beginnings. A
joint position statement of the National Association for the Education of Young Children
and the National Council of Teachers of Mathematics. Available: http://www.naeyc.
org/about/positions/pdf/psmath.pdf [accessed August 2008].
National Center for Early Development and Learning Pre-Kindergarten Study. (2005). Early
Developments, 9(1), spring issue. Available: http://www.fpg.unc.edu/~ncedl/PDFs/ED9_
1.pdf [accessed August 2008].
National Council of Teachers of Mathematics. (2000). Principles and Standards for School
Mathematics. Reston, VA: Author.
National Council of Teachers of Mathematics. (2006). Curriculum Focal Points. Reston, VA:
Author.
National Early Childhood Accountability Task Force. (2007). Taking Stock: Assessing and
Improving Early Childhood Learning and Program Quality. Washington, DC: Pew
Charitable Trusts. Available: http://www.policyforchildren.org/pdf/Task_Force_Report.
pdf [accessed August 2008].
National Mathematics Advisory Panel. (2008). Foundations for Success: The Final Report of
the National Mathematics Advisory Panel. Washington, DC: U. S. Department of Educa-
tion. Available: http://www.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf
[accessed August 2008].
National Research Council. (1999). How People Learn: Brain, Mind, Experience, and School.
Committee on Developments in the Science of Learning. J.D. Bransford, A.L. Brown,
and R.R. Cocking (Eds.). Commission on Behavioral and Social Sciences and Education.
Washington, DC: National Academy Press.
National Research Council. (2001a). Adding It Up: Helping Children Learn Mathematics.
Mathematics Learning Study Committee. J. Kilpatrick, J. Swafford, and B. Findell (Eds.).
Center for Education, Division of Behavioral and Social Sciences and Education. Wash-
ington, DC: National Academy Press.
National Research Council. (2001b). Eager to Learn: Educating Our Preschoolers. Com-
mittee on Early Childhood Pedagogy. B.T. Bowman, M.S. Donovan, and M.S. Burns
(Eds.). Commission on Behavioral and Social Sciences and Education. Washington, DC:
National Academy Press.
National Research Council. (2008). Assessing Accomplished Teaching: Advanced-Level Cer-
tification Programs. Committee on Evaluation of Teacher Certification by the National
Board for Professional Teaching Standards. M.D. Hakel, J.A. Koenig, and S.W. Elliott
(Eds.). Board on Testing and Assessment, Center for Education. Division of Behavioral
and Social Sciences and Education. Washington, DC: The National Academies Press.
Palincsar, A.S., and Brown, A.L. (1984). Reciprocal teaching of comprehension-fostering and
comprehension-monitoring activities. Cognition Instruct., 1, 117-175.
Peterson, P.L., Carpenter, T.P., and Fennema, E. (1989). Teachers’ knowledge of students’
knowledge in mathematics problem solving: Correlational and case analyses. Journal of
Educational Psychology, 81(4), 558-569.
Piaget, J. (1955). The Language and Thought of the Child. Cleveland, OH: World.
Piaget, J. (1976a). The Child’s Conception of the World. (J. Tomlinson and A. Tomlinson,
Trans.). Totowa, NJ: Littlefield, Adams.
Piaget, J. (1976b). The Grasp of Consciousness: Action and Concept in the Young Child. (S.
Wedgwood, Trans.). Cambridge, MA: Harvard University Press.
Piaget, J. (1985). The Equilibration of Cognitive Structures. (T. Brown and K J. Thampy,
Trans.). Chicago, IL: The University of Chicago Press.
Piaget, J., and Inhelder, B. (1967). The Child’s Conception of Space. (F.J. Langdon and J.L.
Lunzer, Trans.). New York: W.W. Norton.
Piaget, J., and Inhelder, B. (1969). The Psychology of the Child. (H. Weaver, Trans.). New
York: Basic Books.

OCR for page 225

STANDARDS, CURRICULUM, INSTRUCTION, AND ASSESSMENT 285
Pianta, R.C., Steinberg, M.S., and Rollins, K.B. (1995). The first two years of school: Teacher-
child relationships and deflections in children’s classroom adjustment. Development and
Psychopathology, 7, 295-312.
Pianta, R.C., Howes, C., Burchinal, M., Bryant, D., Clifford, R., Early, C., and Barbarin, O.
(2005). Features of pre-kindergarten programs, classrooms, and teachers: Do they pre-
dict observed classroom quality and child-teacher interactions? Applied Developmental
Science, 9(3), 144-159.
Pianta, R.C., La Paro, K., and Hamre, B.K. (2007). Classroom Assessment Scoring System™
(CLASS™). Baltimore, MD: Paul H. Brookes.
Pianta, R.C., Belsky, J., Houts, R., Morrison, F., and NICHD ECCRN. (2007). Opportunities
to learn in America’s elementary classrooms. Science, 315, 1795-1796. Available: http://
www.sciencemag.org/cgi/content/abstract/315/5820/1795?ijkey=09d80c0aad2b21db10
0d5ad6115fa1d36666bcdfandkeytype2=tf_ipsecsha [accessed August 2008].
Pianta, R.C., La Paro, K., and Hamre, B.K. (2008). Classroom Assessment Scoring System.
Baltimore, MD: Paul H. Brookes.
Poag, C.K., Cohen, R., and Weatherford, D.L. (1983). Spatial representations of young chil-
dren: The role of self-versus adult-directed movement and viewing. Journal of Experi-
mental Child Psychology, 35, 172-179.
Preschool Curriculum Evaluation Research Consortium. (2008). Effects of Preschool Cur-
riculum Programs on School Readiness. NCER 2008-2009. Washington, DC: National
Center for Education Research, Institute of Education Sciences, U.S. Department of
Education.
Prigge, G.R. (1978). The differential effects of the use of manipulative aids on the learn-
ing of geometric concepts by school children. School Science and Mathematics, 78(4),
320-326.
Ramey, C.T., and Ramey, S.L. (1998). Early intervention and early experience. American
Psychologist, 53, 109-120.
Raver, C.C. (2004). Placing emotional self-regulation in sociocultural and socioeconomic
contexts. Child Development, 75(2), 346-353.
Reggio Children. (1997). Shoe and Meter: Children and Measurement, First Approaches to the
Discovery, Function, and Use of Measurement. Reggio Emilia, Italy: Author.
Resnick, L.B. (1989). Developing mathematical knowledge. American Psychologist, 44,
162-169.
Resnick, L.B. (1992). From protoquantities to operators: Building mathematical competence
on a foundation of everyday knowledge. In G. Leinhardt, R. Putnam, and R.A. Hattrup
(Eds.), Analysis of Arithmetic for Mathematics Teaching (pp. 373-429). Hillsdale, NJ:
Erlbaum.
Reys, B.J., Chval, K.B., and Switzer, J. (2008). Mathematics Standards for Kindergarten:
Summary of State-Level Attention and Focus. Paper commissioned by the Committee for
Early Childhood Mathematics, Mathematics Science Education Board, Center for Edu-
cation, Division of Behavioral and Sciences and Education, National Research Council,
Washington, DC.
Rieser, J.J., Garing, A.E., and Young, M.F. (1994). Imagery, action, and young children’s
spatial orientation: It’s not being there that counts, It’s what one has in mind. Child
Development, 65, 1262-1278.
Rimm-Kaufman, S.E., Early, D.M., and Cox, M.J. (2002). Early behavioral attributes and
teachers’ sensitivity as predictors of competent behavior in the kindergarten classroom.
Journal of Applied Developmental Psychology, 23(4), 451-470.
Ritchie, S., Howes, C., Kraft-Sayre, M., and Weiser, B. (2001). Emerging Academics Snapshot.
Unpublished, University of California at Los Angeles.
Romberg, T.A., Carpenter, T.P., and Dremock, F. (2005). Understanding Mathematics and
Science Matters. Mahwah, NJ: Erlbaum.

OCR for page 225

286 MATHEMATICS LEARNING IN EARLY CHILDHOOD
Sarama, J. (2002). Listening to teachers: Planning for professional development. Teaching
Children Mathematics, 9, 36-39.
Sarama, J., and Clements, D.H. (2002a). Design of microworlds in mathematics and science
education. Journal of Educational Computing Research, 27(1 & 2), 1-6.
Sarama, J., and Clements, D.H. (2002b). Learning and teaching with computers in early child-
hood education. In O.N. Saracho and B. Spodek (Eds.), Contemporary Perspectives on
Science and Technology in Early Childhood Education (pp. 171-219). Greenwich, CT:
Information Age.
Sarama, J., and Clements, D.H. (2006). Mathematics, young students, and computers: Soft-
ware, teaching strategies and professional development. The Mathematics Educator,
9(2), 112-134.
Sarama, J., and Clements, D.H. (2009). Early Childhood Mathematics Education Research:
Learning Trajectories for Young Children. New York: Routledge.
Sarama, J., and DiBiase, A.-M. (2004). The professional developmental development challenge
in preschool mathematics. In D.H. Clements, J. Sarama, and A.-M. DiBiase (Eds.) Engag-
ing Children in Mathematics: Standards for Early Childhood Mathematics Education
(pp. 415-446). Mahwah, NJ: Erlbaum.
Sarama, J., Clements, D.H., and Vukelic, E.B. (1996). The role of a computer manipulative in
fostering specific psychological/mathematical processes. In E. Jakubowski, D. Watkins,
and H. Biske (Eds.), Proceedings of the 18th Annual Meeting of the North America
Chapter of the International Group for the Psychology of Mathematics Education.
Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental
Education.
Sarama, J., Clements, D.H., Starkey, P., Klein, A., and Wakeley, A. (2008). Scaling up the
implementation of a pre-kindergarten mathematics curriculum: Teaching for understand-
ing with trajectories and technologies. Journal of Research on Educational Effectiveness,
1, 89-119.
Schickedanz, J.A. (2008). Increasing the Power of Instruction: Integration of Language, Lit-
eracy, and Math Across the Preschool Day. Washington, DC: National Association for
the Education of Young Children.
Schweinhart, L. (2007, November). The High/Scope Model and Mathematics. PowerPoint
presentation at the 2nd Meeting of the Committee on Early Childhood Mathematics,
National Academies, Washington, DC. Available: http://www.nationalacademies.org/cfe/
Schweinhart%20Presentation.pdf [accessed August 2008].
Scott, L.F., and Neufeld, H. (1976). Concrete instruction in elementary school mathematics:
Pictorial vs. manipulative. School Science and Mathematics, 76, 68-72.
Scott-Little, C. (2008). Mathematics Content Addressed in State-Level Early Learning Stan-
dards. Paper commissioned by the Committee for Early Childhood Mathematics, Math-
ematics Science Education Board, Center for Education, Division of Behavioral and
Sciences and Education, National Research Council, Washington, DC.
Scott-Little, C., Lesko, J., Martella, J. and Milburn, P. (2007). Early learning standards:
Results from a national survey to document trends in state-level policies and practices.
Early Childhood Research in Practice, 9(1). Available: http://ecrp.uiuc.edu/v9n1/little.
html [accessed July 2008].
Seo, K.-H. (2003). What children’s play tells us about TEACHING mathematics. Young
Children, 58(1), 28-34.
Seo, K.-H., and Ginsburg, H.P. (2003). “You’ve got to carefully read the math sentence…”:
Classroom context and children’s interpretations of the equals sign. In A.J. Baroody and
A. Dowker (Eds.), The Development of Arithmetic Concepts and Skills: Recent Research
and Theory (pp. 161-187). Mahwah, NJ: Erlbaum.

OCR for page 225

STANDARDS, CURRICULUM, INSTRUCTION, AND ASSESSMENT 287
Seo, K.-H., and Ginsburg, H.P. (2004). What is developmentally appropriate in early child-
hood mathematics education? In D.H. Clements, J. Sarama, and A.M. DiBiase (Eds.),
Engaging Children in Mathematics: Standards for Early Childhood Mathematics Educa-
tion (pp. 91-104). Mahwah, NJ: Erlbaum.
Serbin, L.A., and Connor, J.M. (1979). Sex-typing of children’s play preferences and patterns
of cognitive performance. The Journal of Genetic Psychology, 134, 315-316.
Siegler, R.S., and Ramani, G.B. (in press). Playing board games promotes low-income chil-
dren’s numerical development. Developmental Science.
Silver, R.B., Measelle, J., Essex, M., and Armstrong, J.M. (2005). Trajectories of external-
izing behavior problems in the classroom: Contributions of child characteristics, family
characteristics, and the teacher-child relationship during the school transition. Journal
of School Psychology, 43, 39-60.
Simon, M. (1995). Reconstructing mathematics pedagogy from a constructivist perspective.
Journal for Research in Mathematics Education, 26, 114-145.
Skibbe, L., Behnke, M., and Justice, L.M. (2004). Parental scaffolding of children’s phonologi-
cal awareness skills: Interactions between mothers and their preschoolers with language
difficulties. Communication Disorders Quarterly, 25(4), 189-203.
Smith, C.L., Wiser, M., Anderson, C.W., and Krajcik, J., (2006). Implications of research on
children’s learning for standards and assessment: A proposed learning progression for
matter and the atomic molecular theory. Measurement: Interdisciplinary Research and
Perspectives, 4(1 & 2), 1-98.
Sophian, C. (2002). Learning about what fits: Preschool children’s reasoning about effects of
object size. Journal for Research in Mathematics Education, 33, 290-302.
Sophian, C. (2004). Mathematics for the future: Developing a Head Start curriculum to sup-
port mathematics learning. Early Childhood Research Quarterly, 19(1), 59-81.
Sowell, E. (1989). Effects of manipulative materials in mathematics instruction. Journal for
Research in Mathematics Education, 20, 498-505.
Sprafkin, C., Serbin, L.A., Denier, C., and Connor, J.M. (1983). Gender-differentiated play:
Cognitive consequences and early interventions. In M.B. Liss (Ed.), Social and Cognitive
Skills: Gender Roles and Children’s Play. New York: Academic Press.
Starkey, P., Klein, A., and Wakeley, P. (2004). Enhancing young children’s mathematical
knowledge through a pre-kindergarten mathematics intervention. Early Childhood Re-
search Quarterly, 19, 99-120.
Starkey, P., Klein, A., Sarama, J., and Clements, D.H. (2006). Preschool Curriculum Evalua-
tion Research. Paper presented at the American Educational Research Association.
Steffe, L.P., and Wiegel, H.G. (1994). Cognitive play and mathematical learning in computer
microworlds. Journal of Research in Childhood Education, 8(2), 117-131.
Stevenson, H.W., and McBee, G. (1958). The learning of object and pattern discriminations by
children. Journal of Comparative and Physiological Psychology, 51(6), 752-754.
Stiles, J., and Stern, C. (2001). Developmental change in spatial cognitive processing: Com-
plexity effects and block construction performance in preschool children. Journal of
Cognition and Development, 2, 157-187.
Taylor, B.M., Pearson, P.D., Peterson, D.S., and Rodriguez, M.C. (2003). Reading growth
in high-poverty classrooms: The influence of teacher practices that encourage cognitive
engagement in literacy learning. The Elementary School Journal, 104, 3-28.
Teaching Strategies, Inc. (2001). Creative Curriculum®. Available: http://www.creativecurriculum.
net/index.cfm [accessed February 2008].
Thomas, B. (1982). An Abstract of Kindergarten Teachers’ Elicitation and Utilization of
Children’s Prior Knowledge in the Teaching of Shape Concepts. Unpublished manuscript,
School of Education, Health, Nursing, and Arts Professions, New York University.
Thomas, G., and Ward, J. (2001). An Evaluation of the Count Me in Too Pilot Project. Wel-
lington, New Zealand: Ministry of Education.

OCR for page 225

288 MATHEMATICS LEARNING IN EARLY CHILDHOOD
Thomson, S., Rowe, K., Underwood, C., and Peck, R. (2005). Numeracy in the Early Years:
Project Good Start. Camberwell, Victoria, Australia: Australian Council for Educational
Research.
U.S. Department of Health and Human Services, Administration for Children and Families,
Office of Planning, Research, and Evaluation. (2005). Head Start Impact Study: First-
year Findings. Available: http://www.acf.hhs.gov/programs/opre/hs/faces/index.html [ac-
cessed August 2008].
U.S. Department of Health and Human Services, Administration for Children and Families,
Office of Planning, Research, and Evaluation. (2006). Head Start Family and Child
Experiences Survey (FACES 2000) Technical Report. Available: http://www.acf.hhs.
gov/programs/opre/hs/faces/index.html [accessed August 2008].
Veenman, M.V.J., Kok, R., and Blöte, A.W. (2005). The relation between intellectual and
metacognitive skills in early adolescence. Instructional Science, 33(3), 193-211.
Vygotsky, L.S. (1978). Mind in Society: The Development of Higher Psychological Processes.
Cambridge, MA: Harvard University Press.
Vygotsky, L.S. (1986). Thought and Language. (A. Kozulin, Trans.). Cambridge, MA: MIT
Press.
Vygotsky, L.S. (1991). Genesis of the higher mental functions. In P. Light, S. Sheldon,
and M. Woodhead (Eds.), Learning to Think (pp. 32-41). Florence, KY: Taylor and
Francis/Routledge.
Wharton-McDonald, R., Pressley, M., and Hampston, J.M. (1998). Literacy instruction in
nine first-grade classrooms: Teacher characteristics and student achievement. Elementary
School Journal, 99(2), 101-128.
Wiltz, N.W., and Klein, E.L. (2001). What do you do in child care? Children’s percep-
tions of high and low quality classrooms. Early Childhood Research Quarterly, 16(2),
209‑236.
Wolfgang, C.H., Stannard, L.L., and Jones, I. (2001). Block play performance among pre-
schoolers as a predictor of later school achievement in mathematics. Journal of Research
in Childhood Education, 15, 173-180.
Wood, K., and Frid, S. (2005). Early childhood numeracy in a multiage setting. Math-
ematics Education Research Journal, 16(3), 80-99. Available: http://www.merga.net.
au/documents/MERJ_16_3_Wood.pdf [accessed August 2008].
Wright, R.J. (1994). A study of the numerical development of 5-year-olds and 6-year-olds.
Educational Studies in Mathematics, 26, 25-44.
Wright, R.J. (2003). A mathematics recovery: Program of intervention in early number learn-
ing. Australian Journal of Learning Disabilities, 8(4), 6-11.
Wright, R.J., Martland, J., Stafford, A.K., and Stanger, G. (2002). Teaching Number: Advanc-
ing Children’s Skills and Strategies. London: Paul Chapman/Sage.
Young-Loveridge, J.M. (2004). Effects on early numeracy of a program using number books
and games. Early Childhood Research Quarterly, 19, 82-98.
Zins, J.E., Bloodworth, M.R., Weissberg, R.P., and Walberg, H. (2004). The scientific base
linking social and emotional learning to school success. In J.E. Zins, R.P. Weissberg, M.C.
Wang, and H.J. Walberg (Eds.), Building Academic Success on Social and Emotional
Learning: What Does the Research Say? New York: Teachers College Press.