The concrete-representational-abstract (CRA) approach is an instructional framework for teaching math wherein students move from using concrete materials to solve problems to using visual representations of the materials, and finally abstract concepts. This study provides a literature synthesis and meta-analysis of the effectiveness of the CRA…

Visualisation has been a critical means of scientific reasoning, knowledge development, and communication. In science classrooms, visualisation plays significant roles for teaching and learning. To better understand the landscape of the existing research on visualisation for supporting student science learning in K to 12 classroom contexts, we…

With the increasing attention and surge of empirical research in providing academic instruction for students with autism spectrum disorder (ASD) comes the need to provide teachers with research-supported strategies. Using one evidence-based strategy for teaching mathematics to students with high incidence disabilities, and another for teaching…

Proposes a model of mathematics conceptual development consisting of two phases: abstraction and generalization. Illustrates model by references to the development of multiplication and angle concepts. (19 references) (MKR)

A Swedish interview study of how deaf pupils reason about phenomena in a science context revealed significant variation in the extent to which pupils used scientific principles for reasoning about science phenomena, which suggests that for some pupils, school science offers little as a framework for reasoning. (Contains references.) (DB)

Discusses Vygotsky's theories about concept formation, his distinctions between everyday and theoretical concepts, and how empirical generalizations can lead to misconceptions. Examines the implications of these theories for mathematics instruction and its relationship to the current mathematics reform. (34 references) (MDH)

The task consisted of categorizing a set of slides depicting concepts of freedom, nonfreedom, justice, and nonjustice. The results of the analysis indicated that abstract thinkers performed significantly better than did concrete thinkers and that performance increased as a function of grade level. (Author/BJG)

This is one of a series that is a collection of translations from the extensive Soviet literature of the past 25 years on research in the psychology of mathematics instruction. It also includes works on methods of teaching mathematics directly influenced by the psychological research. Selected papers and books considered to be of value to the…

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.…

In earlier research the writer was constrained by the variables which were continuously appearing in both experimental class teaching experiences and various psychological experiments to distinguish four levels of cognitive sophistication in so far as mathematical material was concerned between the ages of 7 years and 17 years. In current research…

A colliding spheres type of experiment is used with several hundred 4-12 grade students to test for knowledge of the concept of controlling variables. Results support the contention that the concept is developed gradually during the concept stage but not fully attained until around 14 years of age. (CP)

Although mathematics deals with generalizations relating abstract ideas, very little attention has been given in the mathematics education literature to the role of abstraction and generalization in the development of mathematical knowledge. In this paper, the meanings of "abstraction" and "generalization" are first explored by…

Holds that ethical inquiry, as a "craft," causes students in this area to be "apprentices," and the classroom a "community of inquiry" wherein the tools, methods, practices, and procedures of the craft are imparted. States that the generic procedures of reasoning, necessary for moral reasoning, should be taught within…

An extensive bibliography on teaching thinking skills is presented. This bibliography incorporates from an earlier one (1989) the available relevant references in the field of cognitive education as well as new references that have appeared since early 1989. This field of cognitive education is expanding at such a rapid rate that no bibliography…

It is becoming increasingly important to teach students higher-order thinking skills in addition to mere factual knowledge. Recent scientific and technological advances offer significant opportunities to implement more effective teaching of these skills. By investigating intellectual processes, cognitive science has led to a significantly better…