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…

Mathematics teaching and learning goes beyond computations and procedures; it rather includes complex problem-solving and critical thinking. Kilpatrick, Swafford, and Findell (2001) identify five mathematical competencies that are present in mathematics learning: conceptual understanding, procedural fluency, adaptive reasoning, strategic…

Many qualitative and quantitative studies performed on peer instruction based on interactive engagement method used in many different disciplines and courses were reviewed in the present study. The researchers examined the effects of peer instruction on students' cognitive skills (conceptual learning, problem solving, reasoning ability, etc.) and…

This paper considers mathematical abstraction as arising through a natural mechanism of the biological brain in which complicated phenomena are compressed into thinkable concepts. The neurons in the brain continually fire in parallel and the brain copes with the saturation of information by the simple expedient of suppressing irrelevant data and…

The concept model addressed in this paper is the set of assumptions, data, and inferences used in the instructional design of concept learning. A new way of looking at concepts is presented that takes into account the declarative and metacognitive components of concept learning and use. Implications for instruction are outlined. The paper is…

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)

Examines the differences between concrete and abstract concepts and their implications for instructional design and teaching. How specific concepts are stored in and retrieved from memory is described, analogies are discussed as an instructional tool in abstract concept learning, and a possible instructional strategy for teaching abstract concepts…

This paper examines the cognitive process of concept development in preschool children, based on recent psychological research. Rather than attempting an exhaustive review of the more than 7000 articles written on children's concepts of categories, the paper highlights and illustrates four key themes that emerge from recent research: first,…

Recent literature on the acquisition of "more" and "less" is reviewed with special emphasis on some key issues. The overriding goal of studies in this area has been the discovery of the developmental sequence that the child follows in acquiring "more" and "less," and, more generally, all comparative structures. The earliest empirical studies on…

This paper introduces successive and coordinate intellectual thinking skills, using concepts as a best case example. The attributes and optimal presentation requirements of successive and coordinate concepts are reviewed, and types of errors commonly associated with successive and coordinate skills are delineated. The effects of both of these…

From a review of the literature on modeling processes, observational learning, social learning theory, and vicarious concept learning by young children, the author draws guidelines for the teaching of abstractions to preschoolers. (SJL)

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…

An inquiry attempted to build an agenda for research that would result in a cognitive theory of instruction capable of informing educational practice and extending the limits of knowledge about how people learn and develop. What would such a theory look like, how close are we to having one, and what directions must be followed to further its…

Over the past several years, one study after another has uncovered a positive relationship between interpersonal interaction and individual achievement. According to a handful of these studies, interaction is more effective than are individually-based strategies for promoting reasoning. We give our attention here to the link that possibly exists…