Children's failure to reason often leads to their mathematical performance being shaped by spurious associations from problem input and overgeneralization of inapplicable procedures rather than by whether answers and procedures make sense. In particular, imbalanced distributions of problems, particularly in textbooks, lead children to create…

In recent years, linguists have increasingly turned to the cognitive sciences to broaden their investigation into the roots and development of language. With the advent of cognitive-linguistic, usage-based and complex-adaptive models of language, linguists today are utilizing approaches and insights from cognitive psychology, neuropsychology,…

Although discussions about inductive reasoning can be traced back thousands of years (Fitelson 2011), the implementation of the Standards for Mathematical Practice (SMP) within the Common Core State Standards (CCSSI 2010) is generating renewed attention to how students learn mathematics. The third SMP, "Construct viable arguments and critique…

The notions of "abstract" and "concrete" are central to the conceptualization of mathematical knowing and learning. Much of the literature takes a dualist approach, leading to the privileging of the former term at the expense of the latter. In this article, we provide a concrete analysis of a scientist interpreting an unfamiliar graph to show how…

Three task context factors that form obstacles to generalizing logical reasoning strategies for adolescents are discussed. The relationship between these obstacle factors and Piagetian theory is explored. Findings suggest that it is possible to make some predictions about how and when logical mechanisms will be generalized to new situations.…

The ADAPT program for freshmen emphasizes building an experiential base in introductory courses before moving to abstract formulations. The goal is to develop thinking processes that are integrated with the student's experiences. Students in the ADAPT program outperformed two comparison groups on a variety of thinking tasks. (Author)

The Philosophy for Children Program was introduced to a class of deaf fifth graders as an instructional approach for reasoning skills. The program is intended to develop analytic skills required for intellectual functioning (including concept development, generalization, inference making, question formulation, and analogies). The program's major…

This study investigated the effects of K. J. Klauer's (1989) inductive reasoning training program of teaching children. Effects of training and the range of transfer of the training were assessed. The subjects were 34 third-grade Dutch children of average ability, matched on age, sex, and IQ. Children from the training condition (N=17) received…

Preschoolers' ability to understand grammatical relations in passives and to generalize was studied using animate referents. Three- to five-year-old children were taught to produce passive sentence descriptions of events in which animacy of the actor and acted-on object were varied. After pretesting to determine passive sentence comprehension, the…

Piaget's model of children's conceptual learning and development was compared with Klausmeier's Conceptual Learning and Development (CLD) model in a longitudinal study. The CLD model suggests four successive levels of concept learning: (1) concrete--recognizing an object which has been encountered previously; (2) identity--recognizing a known…