During language acquisition children generalise at multiple layers of granularity. Ambridge argues that abstraction-based accounts suffer from lumping (over-general abstractions) or splitting (over-precise abstractions). Ambridge argues that the only way to overcome this conundrum is in a purely exemplar/analogy-based system in which…

The syntactic behaviour of human beings cannot be explained by analogical generalization on the basis of concrete exemplars: analogies in surface form are insufficient to account for human grammatical knowledge, because they fail to hold in situations where they should, and fail to extend in situations where they need to. [For Ben Ambridge's…

Ambridge argues that the existence of exemplar models for individual phenomena (words, inflection rules, etc.) suggests the feasibility of a unified, exemplars-everywhere model that eschews abstraction. The argument would be strengthened by a description of such a model. However, none is provided. I show that any attempt to do so would immediately…

As a programmer when solving a problem, a number of conscious and unconscious cognitive operations are being performed. Problem-solving is a gradual and cyclic activity; as the mind is adjusting the problem to its schemas formed by its previous experiences, the programmer gets closer and closer to understanding and defining the problem. The…

This commentary critiques Ambridge's radical exemplar model of language acquisition using research from the Longitudinal Study of Early Language, which has tracked the language development of 30+ children with Autism Spectrum Disorders (ASD) since 2002. This research has demonstrated that the children's capacity for abstraction at the grammatical…

Ambridge argues that there is widespread agreement among child language researchers that learners store linguistic abstractions. In this commentary the authors first argue that this assumption is incorrect; anti-representationalist/exemplar views are pervasive in theories of child language. Next, the authors outline what has been learned from this…

Multilevel visual models can make teaching and learning theories more easily understood. The idea of graphic visualizationas developed in this model utilizes three stages of abstract concept formation dealing with concrete visualization, abstract visualization, and abstract generalization, which would provide the learner with an intuitive grasp of…

The term, "schema," used largely as a descriptive convenience rather than a theoretical guidepost in social psychology is examined through an analysis of its development, function, and structure. This paper articulates a model of schema development in adults by defining a schema as a representation of some stimulus domain and a set of…

Examples of high school case studies are used to illustrate prototypical mathematical images and the use of imagery in metaphoric and metonymic ways in mathematics. Discusses pattern imagery and other types of imagery as central components in a model of mathematical reasoning. (34 references) (MDH)

The Model of Conceptual Learning and Development (CLD) is an analytical, descriptive model. It defines four levels of concept attainment and the possible uses and extensions of attained concepts, specifies the cognitive operations involved in learning concepts at each of the four levels, and postulates internal and external conditions of learning…

The Model of Conceptual Learning and Development (CLD) is an analytical, descriptive model. It defines four levels of concept attainment and the possible uses and extensions of attained concepts, specifies the cognitive operations involved in learning concepts at each of the four levels, and postulates internal and external conditions of learning…

Imagery use in high school mathematics classrooms was studied. A visual image was defined as a mental scheme depicting visual or spatial information, but this definition was not spelled out to teachers or students, in order to learn what they meant by the concept. Subjects were 13 high school teachers and 54 of their students interviewed over 3…

The Model of Conceptual Learning and Development (CLD) is an analytical, descriptive model. It defines four levels of concept attainment and the possible uses and extensions of attained concepts, specifies the cognitive operations involved in learning concepts at each of the four levels, and postulates internal and external conditions of learning…

The Model of Conceptual Learning and Development (CLD) is an analytical, descriptive model. It defines four levels of concept attainment and the possible uses and extensions of attained concepts, specifies the cognitive operations involved in learning concepts at each of the four levels, and postulates internal and external conditions of learning…

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…