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Direct linkOktaç, Asuman; Trigueros, María; Romo, Avenilde – For the Learning of Mathematics, 2019
Certain aspects of theoretical frameworks in mathematics education can remain unexplained in the literature, hence unnoticed by the readers. It is thus interesting to participate in a dialogue where they can be discussed and compared in terms of the aims, objects studied, results and their relation to teaching. This study is focused on how APOS…
Descriptors: Mathematics Instruction, Learning Theories, Knowledge Level, Constructivism (Learning)
Abrahamson, Dor – For the Learning of Mathematics, 2012
Motivated by the question, "What exactly about a mathematical concept should students discover, when they study it via discovery learning?", I present and demonstrate an interpretation of discovery pedagogy that attempts to address its criticism. My approach hinges on decoupling the solution process from its resultant product. Whereas theories of…
Descriptors: Learning Theories, Discovery Learning, Mathematical Concepts, Teaching Methods
Peer reviewedStanic, George A. – For the Learning of Mathematics, 1986
The role of mental discipline theory in the history of mathematics education is considered. The author argues that we now remember mental discipline theory only as a caricature of what it was; moreover, it persists among both teachers and researchers. (MNS)
Descriptors: Cognitive Processes, Educational Philosophy, Educational Theories, Learning Theories
Peer reviewedHawkins, David – For the Learning of Mathematics, 1980
An attempt is made to link the domain of mathematics and the natures and abilities of mathematicians to that which is perceptual, presentational, and implicit. (MP)
Descriptors: Cognitive Processes, Deduction, Learning Theories, Mathematical Concepts
Peer reviewedRadatz, Hendrik – For the Learning of Mathematics, 1980
A discussion of the history of error analysis in mathematics education research provides an overview of research published in German and Anglo-American publications since the early 1900s. (MP)
Descriptors: Cognitive Processes, Educational Research, Error Patterns, Evaluation Methods
Peer reviewedHarel, Guershon; Tall, David – For the Learning of Mathematics, 1991
The terms generalization and abstraction are used with various shades of meaning by mathematicians and mathematics educators. Introduced is the idea of "generic abstraction" that gives the student an operative sense of a mathematical concept and provides a passage point in the process toward formal abstraction. (MDH)
Descriptors: Cognitive Processes, Concept Formation, Generalization, Learning Theories
Peer reviewedLunkenbein, Dieter – For the Learning of Mathematics, 1981
The concepts of groupings, their characteristics, and possible developments in a context of concept formation processes are illustrated. (MP)
Descriptors: Cognitive Processes, Concept Formation, Educational Psychology, Elementary Secondary Education
Peer reviewedMason, John – For the Learning of Mathematics, 1980
The roles and uses of symbols in mathematical thinking are discussed. The thinking process is further subdivided into specialization, generalization, and reasoning. (MP)
Descriptors: Cognitive Processes, Discovery Learning, Inservice Teacher Education, Learning Theories
Peer reviewedBouvier, Alain – For the Learning of Mathematics, 1985
Principles on which the teaching of mathematics is based are discussed. Sections concern the skill principle, the curriculum principle, and learning strategy, with many classroom illustrations. (MNS)
Descriptors: Classroom Communication, Cognitive Processes, Elementary Secondary Education, Learning
