Teachers' knowledge of students' mathematical thinking is a growing area of research in mathematics education. The literature has reported plentiful evidence of the interplays between teachers' mathematical knowledge and their knowledge of students' mathematical thinking. The present study builds on this body of work to explain how such interplays…

The neural bases of cognition may be greatly informed by relating temporally defined developmental changes in behavior with concurrent alterations in neural function. A robust improvement in performance in spatial learning and memory tasks occurs at 3 wk of age in rodents. We reported that the developmental increase of spontaneous alternation in a…

In this paper, a learning progression for geometric transformations is developed based on research that demonstrates the importance of viewing transformations as functions of the plane. The 5 levels of the progression reflect a student's evolving understanding of transformations as functions and their evolving understanding of the domain of these…

This study focuses on relations between 7- and 9-year-old children's and adults' metacognitive monitoring and control processes. In addition to explicit confidence judgments (CJ), data for participants' control behavior during learning and recall as well as implicit CJs were collected with an eye-tracking device (Tobii 1750).…

Bhatt and Quinn (2011) present a compelling case that human learning is "early" in two very different, but interacting, senses. Learning is "developmentally" early in that even infants show strikingly robust adaptation to the structures present in their world. Learning is also early in an information processing sense because infants adapt their…

Executive function (EF) skills are the attention-regulation skills that make it possible to sustain attention, keep goals and information in mind, refrain from responding immediately, resist distraction, tolerate frustration, consider the consequences of different behaviors, reflect on past experiences, and plan for the future. As EF research…

Piaget proposed that understanding permanency, understanding occlusion events, and forming mental representations were synonymous; however, accumulating evidence indicates that those concepts are "not" unified in development. Infants reach for endarkened objects at younger ages than for occluded objects, and infants' looking patterns suggest that…

We explored whether a rising trend to blindly "overcopy" a model's causally irrelevant actions between 3 and 5 years of age, found in previous studies, predicts a more circumspect disposition in much younger children. Children between 23 and 30 months of age observed a model use a tool to retrieve a reward from either a transparent or opaque…

Children with reading comprehension difficulties display impaired performance on semantic processing tasks. These impairments are assumed to reflect weaker knowledge about abstract semantic associations between words in poor comprehenders [Nation, K., & Snowling, M. (1999). Developmental differences in sensitivity to semantic relations among good…

Elementary and secondary students identified as gifted produced representations of themselves as readers, writers, and mathematicians and were interviewed about what they chose to represent. Interviews indicated a developmental progression in the way academic learning is understood, a progression that also was evident in their representations.…

This paper presents the findings of a study exploring the self-regulated use of mathematical metalanguage in the early years. Young children were filmed on two occasions in the naturalistic context of their eight foundation stage settings, including both nursery and reception classes. The children were engaged in mathematical activities designed…

The National Council of Teachers of Mathematics (NCTM) poses constructivist ideas in its "Principles and Standards for School Mathematics" (2000). NCTM supports mathematics instruction that takes a developmental perspective; starts and builds on what children know; and leads children to construct relational understanding, problem-solving…

This article reviews the assessment data, literature and research on gender differences in mathematics. The question of whether boys are better at mathematics has been an issue in education for the past 5 years. The assumption is that there is a biological difference between boys and girls that make boys predisposed to do better in mathematics.…

Describes recent currents in psychological literature pertaining to the learning process, specifically the left and right hemispheres of the brain. Demonstrates how these psychological advances can help with economic analysis. (Author/KC)

An investigation of adult reasoning processes revealed that the more relevant the cognitive task was to the developmental task of the learner, the better the performance was likely to be. (JD)