Introducing new concepts to learners in an order of increasing complexity appears to be beneficial for learning, but typically introduction of concepts does not always adhere to this principle. We examined whether introducing new algebra concepts in a contrasted manner or in an order of increasing complexity instead of a different more typical…

The distinction between procedural and conceptual learning has long been a topic of discussion in mathematics education and the idea of compression into thinkable concepts that enable the individual make links between them (Tall, 2007). In addition to, the compression to thinkable concept was to be thinking mechanism arising naturally and…

This paper is a preliminary inquiry by a non-mathematician into graphic methods of sequential planning and ways in which hierarchical analysis and tree structures can be helpful in developing interest in the use of mathematical modeling in the search for creative solutions to real-life problems. Highlights include a discussion of hierarchical…

The purpose of this study was to investigate a proposed model for the acquisition of the concept of displacement volume and to compare two methods of conservation task presentation. A 12-stage hierarchical model for the acquisition of the concept was proposed, based on four primary assumptions: (1) concept attainment can be measured by…

SEQUENCE IN LEARNING IS USEFUL ONLY AS IT CONTRIBUTES TO THE CONTINUITY OF A CHILD'S OVERALL DEVELOPMENT. CHILDREN MAY NOT GO THROUGH THE SAME SEQUENCE TO ARRIVE AT A SIMILAR POINT OF UNDERSTANDING. EDUCATIONAL PROGRESS IS INDICATED BY A CHILD'S GROWTH IN THE DEVELOPMENT OF STRATEGIC CONCEPTS, IN WAYS OF PROCESSING INFORMATION, AND IN WAYS OF…

THREE- AND 4-YEAR-OLDS WERE GIVEN VERBAL LEARNING PRETRAINING TO DETERMINE ITS EFFECT UPON THE PERFORMANCE OF REVERSAL AND NONREVERSAL SHIFT DISCRIMINATION TASKS. THE EXPERIMENTAL TASK WAS THE CLASSICAL REVERSAL-NONREVERSAL SHIFT PARADIGM. THE 96 PRE-SCHOOLERS, PRIMARILY FROM THE PENNSYLVANIA STATE UNIVERSITY NURSERY SCHOOL, WERE DIVIDED INTO 4…

Sixty-four high school students, stratified by field-dependent or independent cognitive style, were randomly assigned to homogeneous or heterogeneous groups of four to attain concepts in the sequence of complex to simple or simple to complex, with either minimal or strategy instructions. Subsequently, each student individually attained four…

This material developed as a resource in Los Angeles, California, is designed to assist teachers in the planning of social studies programs for grades one, two, and three. The ideas and suggestions are related directly to the two State textbooks which were adopted in 1971--"The Social Sciences: Concepts and Values," and "Voices of Life." The…