Prentice Starkey

Numerical abstraction by human infants

Across several experiments, 6- to 8-month-old human infants were found to detect numerical correspondences between sets of entities presented in different sensory modalities and bearing no natural relation to one another. At the basis of this ability, we argue, is a sensitivity to numerosity, an abstract property of collections of objects and events. Our findings provide evidence that the emergence of the earliest numerical abilities does not depend upon the development of language or complex actions, or upon cultural experience with number.

The early development of numerical reasoning.

Children of age 1-4 years were found capable of engaging in numerical reasoning. Children were presented with a task in which they placed a set of objects one by one into an opaque container. An experimenter then visibly performed either an addition, a subtraction, or no transformation on the screened set. Children were then instructed to remove all objects from the container. Across two experiments, children searched for and removed the correct number of objects when set numerosity was small. Knowledge of numerical identity and knowledge of the effects of addition and subtraction transformations on numerosity were present even in children who had not yet begun to count verbally. These findings provide evidence that the emergence of numerical reasoning does not depend upon the prior development of a verbal counting ability or upon cultural experience with numbers.

Effects of a Pre-Kindergarten Mathematics Intervention: A Randomized Experiment.

Abstract Research indicates that a socioeconomic status-related gap in mathematical knowledge appears early and widens during early childhood. Young children from economically disadvantaged families receive less support for mathematical development both at home and in preschool. Consequently, children from different socioeconomic backgrounds enter elementary school at different levels of readiness to learn a standards-based mathematics curriculum. One approach to closing this gap is the development and implementation of effective mathematics curricula for public preschool programs enrolling economically disadvantaged children. A randomized controlled trial was conducted in 40 Head Start and state preschool classrooms, with 278 children, to determine whether a pre-kindergarten mathematics intervention was effective. Intervention teachers received training that enabled them to implement with fidelity, and a large majority of parents regularly used math activities teachers sent home. Intervention and control groups did not differ on math assessments at pretest; however, gain scores of intervention children were significantly greater than those of control children at posttest. Thus, the intervention reduced the gap in childrens early mathematical knowledge.

Scaling Up the Implementation of a Pre-Kindergarten Mathematics Curriculum: Teaching for Understanding With Trajectories and Technologies

Abstract This study used a randomized field trial design to evaluate the efficacy of a research-based model for scaling up an intervention focused on preschool mathematics. Although the successes of research-based educational practices have been documented, equally well known is the paucity of successful efforts to bring these practices to scale. The same research corpus provides guidelines to scale up successful interventions. We designed an intervention model based on that research, including mathematics curricula with an emphasis on teaching for understanding following developmental guidelines, or learning trajectories, and using technology at multiple levels. We then implemented that model and evaluated the implementation with a limited scale up study. Within a design involving 25 classrooms serving children at risk for later school failure, we examined the impact of the model, using measures of fidelity of implementation, classroom observations of mathematics environment and teaching, and child outcomes. High levels of fidelity of implementation resulted in consistently higher scores in the intervention, compared to control, classes on the observation instrument and significantly and substantially greater gains in childrens mathematics achievement in the intervention, compared to the control, children (effect size = .62).

Pretend Play by African American Children in Head Start.

Abstract Play behaviors of African American 4-year-olds from impoverished families were observed naturalistically. Childrens free play was videotaped in Head Start classrooms over several weeks in the playhouse, block corner, and outside play yard. Play was categorized into cognitive play types—functional, constructive, and pretend play. Children most frequently engaged in functional play. Contrary to Smilanskys findings, impoverished children also engaged in pretend play. This play type was high in quality (object use, number of participants, and subtypes of pretense exhibited) but low in quantity (number and duration of play episodes) compared to other types of play. These findings are discussed in the context of theories of pretend play.

Impacts of a Comprehensive School Readiness Curriculum for Preschool Children at Risk for Educational Difficulties.

This article reports findings from a cluster-randomized study of an integrated literacy- and math-focused preschool curriculum, comparing versions with and without an explicit socioemotional lesson component to a business-as-usual condition. Participants included 110 classroom teachers from randomized classrooms and approximately eight students from each classroom (N = 760) who averaged 4.48 (SD = 0.44) years of age at the start of the school year. There were positive impacts of the two versions of the curriculum on language, phonological awareness, math, and socioemotional outcomes, but there were no added benefits to academic or socioemotional outcomes for the children receiving explicit socioemotional instruction. Results are discussed with relevance to early childhood theory, policy, and goals of closing the school readiness gap.

Toward a comparative psychology of number

Garnham (1991) attributes to us three claims about the numerical ability of infants: it is species specific, it comprises a Fodorian module, and it is innate. He argues that these claims are insufficiently supported by available evidence. In contrast, we submit that human knowledge of number comprises a natural domain of cognition, centering on certain principles (notably. one-to-one correspondence) that are innate. We take no position on the species specificity of the set of mechanisms that subserve human knowledge of number early in ontogeny. We will address each claim in turn. We are puzzled as to why Garnham attributes to us the claim of species specificity. In fact, we and our collaborators have argued that mechanisms that subserve numerical ability are present in nonhuman species (Gallistel, 1990; Klein & Starkey, 1987). A wealth of evidence supports this position, although the nature of specific mechanisms remains in dispute (e.g.. Davis 24 Perusse, 1988; Gallistel, 1990; Klein & Starkey, 1987; Meek & Church, 1983; Rumbaugh, Savage-Rumbaugh, & Hegel, 1987). The claim that a single set of mechanisms underlies the numerical abilities of humans early in ontogeny and of other species is a hypothesis that existing research neither confirms nor refutes. A rigorous test of this hypothesis, however, would entail comparisons of numerical abilities and mechanisms of humans to those of another particular species rather than some superordinate grouping of species.

Effects of Tutorial Interventions in Mathematics and Attention for Low-Performing Preschool Children

ABSTRACT Two intervention approaches designed to address the multifaceted academic and cognitive difficulties of low-income children who enter pre-K with very low math knowledge were tested in a randomized experiment. Blocking on classroom, children who met screening criteria were assigned to a Math + Attention condition in which the Pre-Kindergarten Mathematics Tutorial (PKMT) intervention was implemented (4 days/week for 24 weeks) in addition to 16 adaptive attention training sessions, a Math-Only condition using the PKMT intervention, or a business-as-usual condition. Five hundred eighteen children were assessed at pretest and posttest. There was a significant effect of the PKMT intervention on a broad measure of informal mathematical knowledge and a small but significant effect on a measure of numerical knowledge. Attention training was associated with small effects on attention, but did not provide additional benefit for mathematics. A main effect of state on math outcomes was associated with a stronger, numeracy-focused Tier 1 mathematics curriculum in one state. Findings are discussed with respect to increasing intensity of math-specific and domain-general interventions for young children at risk for mathematical learning difficulties.

The Sequential Scale-Up of an Evidence-Based Intervention: A Case Study:

Policy makers face dilemmas when choosing a policy, program, or practice to implement. Researchers in education, public health, and other fields have proposed a sequential approach to identifying interventions worthy of broader adoption, involving pilot, efficacy, effectiveness, and scale-up studies. In this article, we examine a scale-up of an early math intervention to the state level, using a cluster randomized controlled trial. The intervention, Pre-K Mathematics, has produced robust positive effects on children’s math ability in prior pilot, efficacy, and effectiveness studies. In the current study, we ask if it remains effective at a larger scale in a heterogeneous collection of pre-K programs that plausibly represent all low-income families with a child of pre-K age who live in California. We find that Pre-K Mathematics remains effective at the state level, with positive and statistically significant effects (effect size on the Early Childhood Longitudinal Study, Birth Cohort Mathematics Assessment = .30, p < .01). In addition, we develop a framework of the dimensions of scale-up to explain why effect sizes might decrease as scale increases. Using this framework, we compare the causal estimates from the present study to those from earlier, smaller studies. Consistent with our framework, we find that effect sizes have decreased over time. We conclude with a discussion of the implications of our study for how we think about the external validity of causal relationships.