Abstract

The development of early numeracy knowledge is influenced by a number of non-mathematical factors—particularly language skills. However, much of the focus on the relation between language and early numeracy has utilized general language measures and not domain-specific measures of mathematical language. The primary purpose of this study was to determine if the variance accounted for by general language skills in predicting numeracy performance was better accounted for by mathematical language. Further, age- and parental education-related differences in mathematical language performance were explored. Using a sample of 136 3- to 5-year-old preschool and kindergarten children (M = 4.28 years, SD = 0.67 years), a series of mixed-effect regressions were conducted. Results indicated that although general language performance was initially a significant predictor of numeracy performance, when both mathematical language and general language were included in the model, only mathematical language was a significant predictor of numeracy performance. Further, group-difference analyses revealed that children from families where both parents had less than a college education performed significantly lower on mathematical language than their peers; and even by 3-years-old, children have acquired a substantial body of mathematical language skills. Implications and future directions are discussed.

Abstract

Previously, researchers have relied on asking young children to plot a given number on a 0-to-10 number line to assess their mental representation of numbers 1 to 9. However, such a (“conventional”) number-to-position (N-P) task may underestimate the accuracy of young children’s magnitude estimates and misrepresent the nature of their number representation. The purpose of this study was to compare young children’s performance on the conventional N-P task and a “modified” N-P task that is more consistent with a discrete-quantity view of number and with measures of theoretically related mathematical competencies. Participants (n = 45), ranging in age from 4;0 to 6;0, were administered both versions of the N-P task twice during 4 sessions in 1 of 2 randomly assigned and counterbalanced orders. Between and within conditions, children were significantly more accurate on the modified version than on the conventional task. The results indicate that the conventional task, in particular, may be confusing and that several simple modifications can make it more understandable for young children. However, when performance on theoretically related number tasks is taken into account, both the conventional and the modified N-P tasks appeared to underestimate competence.

Abstract

A critical component in enhancing academic success is identifying children at risk of later academic difficulties. Although significant efforts have been devoted to design effective assessment processes in elementary school, fewer efforts (particularly for mathematics) have been made for preschool. The focus of this study was to design and evaluate a brief early numeracy skills screening tool. Measure development and validation occurred in a two-stage process with diverse and distinct samples. In the first stage, 393 preschool children were assessed on a battery of early numeracy tasks. By use of an item response theory framework, 24 items that spanned the ability continuum were selected for inclusion in the brief measure. In the second stage, 129 preschool children were assessed on the brief measure, the Test of Early Mathematics Ability-Third Edition, and two literacy measures. The data resulted in acceptable psychometric properties and strong diagnostic accuracy. Theoretical and practical implications are discussed.

Abstract

A 9-month training experiment was conducted to evaluate the efficacy of highly and minimally guided discovery interventions targeting the add-1 rule (the sum of a number and one is the next number on the mental number list) and doubles relations (e.g., an everyday example of the double 5 + 5 is five fingers on the left hand and five fingers on the right hand make 10 fingers in all) and to compare their impact with regular classroom instruction on adding 1 and the doubles. After pretest, 81 kindergarten to second-grade participants were randomly assigned to one of three training conditions: highly guided add-1 training, highly guided doubles training, or minimally guided add-1 and doubles practice. The highly guided add-1 training served as an active control for the highly guided doubles training and vice versa, and the minimally guided practice condition served to control for the impact of extra practice. ANCOVAs using pretest score and age as covariates indicated that both highly guided and minimally guided interventions were successful in promoting retention and transfer for the relatively salient add-1 rule, but only highly guided training produced transfer for the less-salient doubles relations. The findings indicate that the degree of guidance needed to achieve fluency with different addition reasoning strategies varies.

Abstract

The purpose of this study was to examine early mathematical skill differences among preschool children in US Head Start classrooms. Latent class analysis based on six early mathematical subtest scores (i.e. counting aloud, measurement, counting objects, numbers and shapes, pattern recognition, and grouping) from a sample of 279 Head Start children yielded evidence for a high-achieving class, a typical-achieving class, and a low-achieving class, relative to other children attending Head Start. Average skill profiles of the three latent classes were in general parallel to one another, reflecting that most of the differences across latent classes were in level rather than type of skills. Changes in subtest scores over a 3-month interval indicated that the skill levels of the low-achieving class at time 2 were still below those of the typically achieving class at time 1. These findings provide evidence for skill variability among children enrolled in Head Start and a group of children who appear unlikely to demonstrate the skill level of their peers without additional instruction or intervention.

Abstract

Currently, there are few strengths-based preschool rating scales that sample a wide array of behaviors believed to be essential for early academic success. The purpose of this study was to assess the factor structure of a new measure of early academic competence for at-risk preschool populations. The Teacher Rating Scales of Early Academic Competence (TRS-EAC) includes two broad scales (Early Academic Skills and Early Academic Enablers) and was completed by 60 teachers for 440 children enrolled in Head Start and public preschool classrooms. Evidence from two exploratory factor analyses supported a five-factor solution for the Early Academic Skills Scale (Creative Thinking, Critical Thinking Skills, Numeracy, Early Literacy, and Comprehension) and a five-factor solution for the Early Academic Enablers Scale (Approaches to Learning, Social and Emotional Competence, Fine Motor Skills, Gross Motor Skills, and Communication). TRS-EAC scores also demonstrated good to excellent reliability and were related to children’s performance on direct measures of early academic skills.

Abstract

Achieving fluency with basic subtraction and add-with-8 or -9 combinations is difficult for primary grade children. A 9-month training experiment entailed evaluating the efficacy of software designed to promote such fluency via guided learning of reasoning strategies. Seventy-five eligible first graders were randomly assigned to one of three conditions: guided subtraction (e.g., If 5 + 3 = 8, then 8 – 3 is 5), guided use-a-10 (e.g., If 10 + 7 = 17, then 9 + 7 is 16), or an unguided-practice condition for 30-minute sessions twice a week for 12 weeks. An ANCOVA revealed that at the delayed posttest, the guided-subtraction group outperformed both comparison groups on unpracticed subtraction combinations. Analyses of gains in slow but appropriate use of reasoning and decreases in inefficient strategy use indicated that both types of guided training promoted the learning of a targeted reasoning strategy.

Abstract

We explore the power of allowing students to construct their own conceptual understanding as they “read an object” in a series of guided inquiry steps, developing their own questions about the object. Their ownership of questions increases the learner’s engagement and results in more efficacious learning and meets the standards of quality intellectual work and meaningful lifelong learning, as opposed to school-based “mastery learning” for the test.

Abstract

In a 9-month training experiment, 64 first graders with a risk factor were randomly assigned to computer-assisted structured discovery of the add-1 rule (e.g., the sum of 7 + 1 is the number after “seven

Abstract

This study examines the construct validity of a new teacher interview designed to assess teachers’ pedagogical content knowledge (PCK) for preschool mathematics. PCK describes the subject matter knowledge a teacher needs for effective teaching. Data from 22 teachers and 113 Head Start children in a large midwestern city in the United States were used to test predictive relationships between the PCK interview and two dependent variables: good preschool math teaching practices and improved child learning outcomes. Using a method from previous published work, frequency of math-related language is assessed as a proxy for good preschool math teaching. Changes in children’s mathematical achievement were measured from fall to spring within a single school year using the Test of Early Mathematics Ability (3rd ed.). Analysis by hierarchical linear modeling found significant positive relationships between scores on the new measure and both variables, suggesting that the PCK interview adequately represents the knowledge needed for effective teaching of preschool mathematics. A theoretical framework for the interview’s construction is provided.

Abstract

Abstract

Clements and Sarama’s informative review centers on three key questions for improving mathematics education: How do students learn mathematics? What pedagogical strategies are supported by research? What approaches to professional development are supported by research? Their review of the

Abstract

A 9-month training experiment evaluated whether computer-assisted discovery learning of arithmetic regularities can facilitate kindergartners’ fluency with the easiest sums. After a pretest, kindergartners with at least one risk factor (n = 28) were randomly assigned to either a structured add-0/1 training condition, which focused on recognizing the n + 0/0 + n = n and the n + 1/1 + n = the number-after-n rules, or an active control group. Using pretest fluency as the covariate, ANCOVAs revealed that the structured add-0/1 group significantly outperformed the control group on both practiced and unpracticed (transfer) n + 0/0 + n and n + 1/1 + n items at the delayed posttest and had significantly larger gains in mathematics achievement. Key instructional implications include: Early intervention that targets discovering rules for adding with 0 and 1 and “family-specific” developmental prerequisites is feasible and more effective than typical classroom instruction in promoting fluency with such basic sums. Such rules may be a critically important bridge between informal and formal mathematics. (Contains 8 footnotes, 5 tables, and 4 figures.)

Abstract

In this essay, we describe a conceptual framework designed specially to guide early childhood teacher professional development. Called development of the whole teacher, the framework emphasizes promoting all aspects of teacher’s growth, including attitudes, knowledge, and practice. To exemplify the framework, we describe an Early Mathematics Education Project that is guided by the whole teacher approach for setting program goals, selecting instructional strategies, and evaluating outcomes. The utility power of the whole teacher approach to teacher professional development is discussed in terms of four interrelated characteristics, namely, multidimensional, integrated, developmental, and contextualized.

Abstract

This study examined longitudinal predictive relationships between young children’s classroom behaviors and their growth in mathematics skills during the primary grades. Using the Early Childhood Longitudinal Study–Kindergarten cohort, the authors tested a longitudinal model featuring positive (interpersonal skills and approaches to learning) and negative (internalizing and externalizing) behaviors at kindergarten entry as predictors of growth in mathematics achievement through 3rd grade. Results indicated that negative behaviors demonstrate negligible relationships with early development of mathematics skills. Interpersonal skills demonstrated a small negative relationship with mathematics growth when other positive behaviors were included as predictors in the model. In contrast, approaches to learning (goal-directed behavior, persistence, organization) demonstrated small positive relationships with growth in mathematical skills and may represent a skill domain for educators to consider in designing their instructional practices.

Abstract

The contribution of early education to children’s well-being and school success is widely recognized. Effective teachers are the most critical factor in the quality of a child’s education. The key to sustaining teacher effectiveness and supporting continuous growth is high-quality professional development. Despite its critical importance, professional development for early childhood teachers is inconsistent and fragmented. The field of early education lacks a common conceptual framework to organize and integrate teacher development experiences. In this paper, the whole teacher development approach is proposed as an organizing framework. The approach is distinguished by its simultaneous focus on teacher attitudes, skills and knowledge, and practices. Also distinctive is its application of an integrated developmental framework that promotes teacher proficiency in a wide range of specific domains. To test the approach, a study of teachers’ technology proficiency was carried out. The study analyzed relationships among teacher attitudes, skills, and practices, using data collected from teachers in the process of developing computer proficiency. Among teachers who participated in a technology program based on the whole teacher development approach, significant degrees of association among attitudes, skills, and practices were found. Further, program participants reported significantly higher levels of technology skill and classroom practice than nonparticipants. Distinctive features of the approach are compared to other professional development practices in early childhood education. Implications for conceptualizing and designing effective professional development programs for early childhood teachers are discussed.