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8: Conditions of Learning in Mathematics: Sequence Theory Development
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The structure of an object is defined by specifying its elements and their interrelationships as mentioned in this paper, and an analysis of structure provides no information about the relations of the object under consideration to other objects.Abstract:
The structure of an object is defined by specifying its elements and their interrelationships. An analysis of structure provides no information about the relations of the object under consideration to other objects. Any description of structure is relative to certain elements (units) which are treated as devoid of structure on the particular occasion of description; on a different occasion and in a different context, the structure of those basic elements or units may be taken into account (Russell, 1962).read more
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A Categorization Scheme for Principles of Sequencing Content
TL;DR: The question of how content should be sequenced or ordered has been the subject of educational debates for at least the past 70 years (Dewey, 1902; Rugg, 1927; Tyler, 1950; Taba, 1962, Ausubel, 1964; Bruner, 1960; Suppes, 1966; Gagné, 1970, Popham & Baker, 1970; Posner, 1974) as mentioned in this paper.
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A Review of Strategies for Sequencing and Synthesizing Instruction
TL;DR: This paper reviewed instructional theory and research relating to three design criteria: (a) the order of presentation of instruction (sequencing), (b) the kinds of content relationships that should be taught, and (c) the way content relationships should be learnt (synthesis).
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1: Learning and Instructional Sequence:
TL;DR: The problem of arranging sequences of learning conditions, or, in other words, sequences of instruction, continues to be a topic of considerable importance for those who design and carry out instruction.
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Doing and Seeing Things Differently: A 25-Year Retrospective of Mathematics Education Research on Learning.
TL;DR: In this paper, a retrospective treatment of the general area of mathematics education research with a special emphasis on learning is presented, focusing on the evolution of the field in general, the movement from empirical to empirical, and the interaction between teachers, students, and mathematical content.
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3: Epistemological Perspectives on Conceptions of Curriculum Organization and Learning
TL;DR: In this article, the authors discuss the conceptual properties of the subject matter to be learned and how to best describe educational objectives, and what kinds of learning outcomes should be expected from teaching students the structure of knowledge.
References
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Book
Human knowledge: Its scope and limits
TL;DR: In this article, a rigorous examination of the problems of an empiricist epistemology is presented, where the relation between individual experience and the general body of scientific knowledge is examined.
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