Representations of numerical value have been assessed by using bounded (e.g., 0-1,000) and unbounded (e.g., 0-?) number-line tasks, with considerable debate regarding whether 1 or both tasks elicit unique cognitive strategies (e.g., addition or subtraction) and require unique cognitive models. To test this, we examined how well a mixed log-linear…

In early childhood, humans learn culturally specific symbols for number that allow them entry into the world of complex numerical thinking. Yet little is known about how the brain supports the development of the uniquely human symbolic number system. Here, we use functional magnetic resonance imaging along with an effective connectivity analysis…

The integrated theory of numerical development posits that a central theme of numerical development from infancy to adulthood is progressive broadening of the types and ranges of numbers whose magnitudes are accurately represented. The process includes four overlapping trends: (1) representing increasingly precisely the magnitudes of non-symbolic…

The integrated theory of numerical development posits that a central theme of numerical development from infancy to adulthood is progressive broadening of the types and ranges of numbers whose magnitudes are accurately represented. The process includes four overlapping trends: 1) representing increasingly precisely the magnitudes of non-symbolic…

Young children have been taught simple sequences of alternating shapes and colors, referred to as "patterning", for the past half century in the hope that their understanding of pre-algebra and their mathematics achievement would be improved. The evidence that such patterning instruction actually improves children's academic achievement…

This research focuses on the associations between interactive processes of early childhood classrooms and gains in children's cognitive self-regulation (CSR) across the preschool year. Data from 803 children (45.8% female; "M" = 54 months; 39.1% Caucasian, 26.3% African American, 24.6% Hispanic, 9.9% Other) were collected at fall and…

Defining intelligence is a puzzle that has challenged educators and researchers for years. More recently, professionals are acknowledging that individuals possess many facets of intelligence and that learning is a complex combination of genetic factors, environmental influences, and life experiences that affect learning in unique ways (Salvia,…

Spina bifida (SB) is a neural tube defect diagnosed before or at birth that is associated with a high incidence of math disability often without co-occurring difficulties in reading. SB provides an interesting population within which to examine the development of mathematical abilities and disability across the lifespan and in relation to the…

This study reports the preliminary results from a field test of the College-readiness Performance Assessment System (C-PAS), a large-scale, 6th-12th grade criterion-referenced assessment system that utilizes classroom-embedded performance tasks to measure student progress toward the development of key cognitive skills associated with success in…

Metacognition is a multidimensional construct with two main dimensions: knowledge about cognition and regulation of cognition. The present study aimed to model the development of young pupils' metacognitive abilities in mathematics in relation to processing efficiency, working memory and mathematical performance. We developed instruments measuring…

This study describes the emerging mathematical understanding of one student enrolled in an elementary mathematics content course. Through the medium of her journal entries, a portrait of Elena's struggle to overcome her difficulty with mathematics and construct conceptual knowledge emerges. Though these struggles are not unique, Elena's story is…

Reviews research on the development of academic skills in arithmetic and early reading, emphasizing the individual cognitive processes occurring during learning. Offers implications for the development of new methods of assessment that stress processes, rather than just products. Suggests that researchers in cognitive development and assessment…

Examines one aspect of the cognitive development of preservice education students, the ability to utilize different modes of mental representation. Finds associations between the level of mathematics experience and both the ability to utilize three different modes of mental representation (enactive, visual, and verbal) and the overall use of…

Abstracts and comments are presented for 11 studies. There are two each on aspects of problem solving, mathematics achievement, and estimation. The remainder cover topics related to cognitive development, cognitive processes, evaluation, numeration, and student errors. Research as reported in RIE and CIJE between July and September 1982 is also…

This study investigated children's ability to interpret a natural social situation, depicted in a narrative story, and to use their understanding of that situation to generate and apply a mental model of debts and assets in solving problems including negative quantities. Fifty-one American students from a parochial school in a predominantly middle…