Teachers are tasked with supporting students' learning of abstract mathematical concepts. Students can represent their mathematical understanding in a variety of modes, for example: manipulatives, pictures, diagrams, spoken languages, and written symbols. Although most students easily pick up rudimentary knowledge through the use of concrete…

Two experiments were used to investigate the scope of imitation by testing whether 36-month-olds can learn to produce a categorization strategy through observation. After witnessing an adult sort a set of objects by a visible property (their color; Experiment 1) or a nonvisible property (the particular sounds produced when the objects were shaken;…

This research examined the effectiveness of Multipurpose Unit Early Classroom Intervention Program (MUECIP) prepared for 4-5-year-old (48-60 months) children whose development is at risk because of their families' socioeconomic conditions. The research adopted a preliminary test-final test control group trial model. The research participants were…

This study concentrated on the characteristics of Grade 2 students' writing in mathematics class who used the Project M[superscript 2] units to learn geometry and measurement. Included in the study were students with high and low levels of content knowledge. Archived data from the Project M[superscript 2] study were analyzed to determine the…

Learning must be constrained for it to lead to productive generalizations. Although biology is undoubtedly an important source of constraints, prior experience may be another, leading learners to represent input in ways that are more conducive to some generalizations than others, and/or to up- and down-weight features when entertaining…

Developmental predictors of children's fraction concepts and procedures at the end of fourth grade were investigated in a 2-year longitudinal study. Participants were 357 children who started the study in third grade. Attentive behavior, language, nonverbal reasoning, number line estimation, calculation fluency, and reading fluency each…

Given minimal evidence about novel objects, children might learn only relationships among the specific entities, or they might make a more abstract inference, positing classes of entities and the relations that hold among those classes. Here we show that preschoolers (mean: 57 months) can use sparse data about perceptually unique objects to infer…

This study explores young children's abstraction of the rules underlying a robot's emergent behavior. The study was conducted individually with six kindergarten children, along five sessions that included description and construction tasks, ordered by increasing difficulty. We developed and used a robotic control interface, structured as…

There now appears to be widespread agreement that early childhood mathematics education (ECME) should be implemented on a wide scale, particularly for disadvantaged children. Yet little is known about the teaching of early mathematics. The goal of this paper is to demystify the process. We analyze one early childhood teacher's work as she attempts…

Mental-content verbs such as "think," "believe," "imagine" and "hope" seem to pose special problems for the young language learner. One possible explanation for these difficulties is that the concepts that these verbs express are hard to grasp and therefore their acquisition must await relevant conceptual development. According to a different,…

In the current debate about the abstractness of children's early grammatical knowledge, Tomasello & Abbott-Smith (2002) have suggested that children might first develop "weak" or "partial" representations of abstract syntactic structures. This paper attempts to characterize these structures by comparing the development of constructions around…

Four experiments examined children's ability to reason about the causal significance of the order in which 2 events occurred (the pressing of buttons on a mechanically operated box). In Study 1, 4-year-olds were unable to make the relevant inferences, whereas 5-year-olds were successful on one version of the task. In Study 2, 3-year-olds were…

Two experiments explored the effect of linguistic input on 18-month-olds' ability to form an abstract categorical representation of support. Infants were habituated to 4 support events (i.e., one object placed on another) and were tested with a novel support and a novel containment event. Infants formed an abstract category of support (i.e.,…

Words are only one way of symbolizing ideas. Numbers, pictures, graphs, maps, diagrams, photographs, and other means are also used to convey information. Researchers refer to notational systems such as graphs, diagrams, and maps as "inscriptions." Inscriptions are tools that help people to perceive and to talk about spatial worlds. Spatial…

Most children who are congenitally deafblind are severely delayed in their communication development and many will not achieve symbolic understanding and expression. This article discusses developmental markers cited in the research literature as predictive of or facilitative of the development of symbolism. These markers include the growth toward…